diff --git a/doc/doxygen/thermoprops.dox b/doc/doxygen/thermoprops.dox
index de616722bd..d20cab627c 100644
--- a/doc/doxygen/thermoprops.dox
+++ b/doc/doxygen/thermoprops.dox
@@ -48,7 +48,7 @@
*
* The first type are those whose underlying species have a reference state associated
* with them. The reference state describes the thermodynamic functions for a
- * species at a single reference pressure, \f$p_0\f$. The thermodynamic functions
+ * species at a single reference pressure, @f$ p_0 @f$. The thermodynamic functions
* are specified via derived objects of the SpeciesThermoInterpType object class, and usually
* consist of polynomials in temperature such as the NASA polynomial or the SHOMATE
* polynomial. Calculators for these
@@ -68,7 +68,7 @@
* have any nontrivial examples of these types of phases.
* In general, the independent variables that completely describe the state of the
* system for this class are temperature, the
- * phase density, and \f$ N - 1 \f$ species mole or mass fractions.
+ * phase density, and @f$ N - 1 @f$ species mole or mass fractions.
* Additionally, if the
* phase involves charged species, the phase electric potential is an added independent variable.
* Examples of the first class of %ThermoPhase functions, which includes the
@@ -291,18 +291,18 @@
* Treatment of the %Phase Potential and the electrochemical potential of a species
*
*
- * The electrochemical potential of species k in a phase p, \f$ \zeta_k \f$,
+ * The electrochemical potential of species k in a phase p, @f$ \zeta_k @f$,
* is related to the chemical potential via
* the following equation,
*
- * \f[
+ * @f[
* \zeta_{k}(T,P) = \mu_{k}(T,P) + z_k \phi_p
- * \f]
+ * @f]
*
- * where \f$ \nu_k \f$ is the charge of species k, and \f$ \phi_p \f$ is
+ * where @f$ \nu_k @f$ is the charge of species k, and @f$ \phi_p @f$ is
* the electric potential of phase p.
*
- * The potential \f$ \phi_p \f$ is tracked and internally stored within
+ * The potential @f$ \phi_p @f$ is tracked and internally stored within
* the base %ThermoPhase object. It constitutes a specification of the
* internal state of the phase; it's the third state variable, the first
* two being temperature and density (or, pressure, for incompressible
@@ -314,9 +314,9 @@
* changed by the potential because many phases enforce charge
* neutrality:
*
- * \f[
+ * @f[
* 0 = \sum_k z_k X_k
- * \f]
+ * @f]
*
* Whether charge neutrality is necessary for a phase is also specified
* within the ThermoPhase object, by the function call
@@ -326,7 +326,7 @@
* Cantera::HMWSoln for the proper specification of the chemical potentials.
*
*
- * This equation, when applied to the \f$ \zeta_k \f$ equation described
+ * This equation, when applied to the @f$ \zeta_k @f$ equation described
* above, results in a zero net change in the effective Gibbs free
* energy of the phase. However, specific charged species in the phase
* may increase or decrease their electrochemical potentials, which will
@@ -346,14 +346,14 @@
*
*
*
- * The activity \f$a_k\f$ and activity coefficient \f$ \gamma_k \f$ of a
+ * The activity @f$ a_k @f$ and activity coefficient @f$ \gamma_k @f$ of a
* species in solution is related to the chemical potential by
*
- * \f[
+ * @f[
* \mu_k = \mu_k^0(T,P) + \hat R T \log a_k.= \mu_k^0(T,P) + \hat R T \log x_k \gamma_k
- * \f]
+ * @f]
*
- * The quantity \f$\mu_k^0(T,P)\f$ is
+ * The quantity @f$ \mu_k^0(T,P) @f$ is
* the standard chemical potential at unit activity,
* which depends on the temperature and pressure,
* but not on the composition. The
@@ -361,21 +361,21 @@
* molality convention, where solute species employ the molality-based
* activity coefficients:
*
- * \f[
+ * @f[
* \mu_k = \mu_k^\triangle(T,P) + R T ln(a_k^{\triangle}) =
* \mu_k^\triangle(T,P) + R T ln(\gamma_k^{\triangle} \frac{m_k}{m^\triangle})
- * \f]
+ * @f]
*
* And, the solvent employs the following convention
- * \f[
+ * @f[
* \mu_o = \mu^o_o(T,P) + RT ln(a_o)
- * \f]
+ * @f]
*
- * where \f$ a_o \f$ is often redefined in terms of the osmotic coefficient \f$ \phi \f$.
+ * where @f$ a_o @f$ is often redefined in terms of the osmotic coefficient @f$ \phi @f$.
*
- * \f[
+ * @f[
* \phi = \frac{- ln(a_o)}{\tilde{M}_o \sum_{i \ne o} m_i}
- * \f]
+ * @f]
*
* %ThermoPhase classes which employ the molality based convention are all derived
* from the MolalityVPSSTP class. See the class description for further information
@@ -418,37 +418,37 @@
* however, kinetics is usually expressed in terms of unitless activities,
* which most often equate to solid phase mole fractions. In order to
* accommodate variability here, %Cantera has come up with the idea
- * of activity concentrations, \f$ C^a_k \f$. Activity concentrations are the expressions
+ * of activity concentrations, @f$ C^a_k @f$. Activity concentrations are the expressions
* used directly in kinetics expressions.
* These activity (or generalized) concentrations are used
* by kinetics manager classes to compute the forward and
* reverse rates of elementary reactions. Note that they may
* or may not have units of concentration --- they might be
* partial pressures, mole fractions, or surface coverages,
- * The activity concentrations for species k, \f$ C^a_k \f$, are
- * related to the activity for species, k, \f$ a_k \f$,
+ * The activity concentrations for species k, @f$ C^a_k @f$, are
+ * related to the activity for species, k, @f$ a_k @f$,
* via the following expression:
*
- * \f[
+ * @f[
* a_k = C^a_k / C^0_k
- * \f]
+ * @f]
*
- * \f$ C^0_k \f$ are called standard concentrations. They serve as multiplicative factors
+ * @f$ C^0_k @f$ are called standard concentrations. They serve as multiplicative factors
* between the activities and the generalized concentrations. Standard concentrations
* may be different for each species. They may depend on both the temperature
* and the pressure. However, they may not depend
* on the composition of the phase. For example, for the IdealGasPhase object
* the standard concentration is defined as
*
- * \f[
+ * @f[
* C^0_k = P/ R T
- * \f]
+ * @f]
*
* In many solid phase kinetics problems,
*
- * \f[
+ * @f[
* C^0_k = 1.0 ,
- * \f]
+ * @f]
*
* is employed making the units for activity concentrations in solids unitless.
*
diff --git a/include/cantera/base/ct_defs.h b/include/cantera/base/ct_defs.h
index d042489170..e6eed62f7b 100644
--- a/include/cantera/base/ct_defs.h
+++ b/include/cantera/base/ct_defs.h
@@ -77,19 +77,19 @@ const double Sqrt2 = 1.41421356237309504880;
//! [NIST Reference on Constants, Units, and Uncertainty](https://physics.nist.gov/cuu/Constants/index.html).
//! @{
-//! Avogadro's Number \f$ N_{\mathrm{A}} \f$ [number/kmol]
+//! Avogadro's Number @f$ N_{\mathrm{A}} @f$ [number/kmol]
const double Avogadro = 6.02214076e26;
-//! Boltzmann constant \f$ k \f$ [J/K]
+//! Boltzmann constant @f$ k @f$ [J/K]
const double Boltzmann = 1.380649e-23;
-//! Planck constant \f$ h \f$ [J-s]
+//! Planck constant @f$ h @f$ [J-s]
const double Planck = 6.62607015e-34;
-//! Elementary charge \f$ e \f$ [C]
+//! Elementary charge @f$ e @f$ [C]
const double ElectronCharge = 1.602176634e-19;
-//! Speed of Light in a vacuum \f$ c \f$ [m/s]
+//! Speed of Light in a vacuum @f$ c @f$ [m/s]
const double lightSpeed = 299792458.0;
//! One atmosphere [Pa]
@@ -104,10 +104,10 @@ const double OneBar = 1.0E5;
//! These constants are measured and reported by CODATA
//! @{
-//! Fine structure constant \f$ \alpha \f$ []
+//! Fine structure constant @f$ \alpha @f$ []
const double fineStructureConstant = 7.2973525693e-3;
-//! Electron Mass \f$ m_e \f$ [kg]
+//! Electron Mass @f$ m_e @f$ [kg]
const double ElectronMass = 9.1093837015e-31;
//! @}
@@ -116,7 +116,7 @@ const double ElectronMass = 9.1093837015e-31;
//! These constants are found from the defined and measured constants
//! @{
-//! Universal Gas Constant \f$ R_u \f$ [J/kmol/K]
+//! Universal Gas Constant @f$ R_u @f$ [J/kmol/K]
const double GasConstant = Avogadro * Boltzmann;
const double logGasConstant = std::log(GasConstant);
@@ -124,16 +124,16 @@ const double logGasConstant = std::log(GasConstant);
//! Universal gas constant in cal/mol/K
const double GasConst_cal_mol_K = GasConstant / 4184.0;
-//! Stefan-Boltzmann constant \f$ \sigma \f$ [W/m2/K4]
+//! Stefan-Boltzmann constant @f$ \sigma @f$ [W/m2/K4]
const double StefanBoltz = 2.0 * std::pow(Pi, 5) * std::pow(Boltzmann, 4) / (15.0 * std::pow(Planck, 3) * lightSpeed * lightSpeed); // 5.670374419e-8
-//! Faraday constant \f$ F \f$ [C/kmol]
+//! Faraday constant @f$ F @f$ [C/kmol]
const double Faraday = ElectronCharge * Avogadro;
-//! Permeability of free space \f$ \mu_0 \f$ [N/A2]
+//! Permeability of free space @f$ \mu_0 @f$ [N/A2]
const double permeability_0 = 2 * fineStructureConstant * Planck / (ElectronCharge * ElectronCharge * lightSpeed);
-//! Permittivity of free space \f$ \varepsilon_0 \f$ [F/m]
+//! Permittivity of free space @f$ \varepsilon_0 @f$ [F/m]
const double epsilon_0 = 1.0 / (lightSpeed * lightSpeed * permeability_0);
//! @}
diff --git a/include/cantera/equil/ChemEquil.h b/include/cantera/equil/ChemEquil.h
index 4ec1889f8f..892e5c21ec 100644
--- a/include/cantera/equil/ChemEquil.h
+++ b/include/cantera/equil/ChemEquil.h
@@ -152,7 +152,7 @@ class ChemEquil
*
* @param s mixture to be updated
* @param x vector of non-dimensional element potentials
- * \f[ \lambda_m/RT \f].
+ * @f[ \lambda_m/RT @f].
* @param t temperature in K.
*/
void setToEquilState(ThermoPhase& s,
diff --git a/include/cantera/equil/MultiPhase.h b/include/cantera/equil/MultiPhase.h
index 8022bd1448..3617ed11c3 100644
--- a/include/cantera/equil/MultiPhase.h
+++ b/include/cantera/equil/MultiPhase.h
@@ -259,7 +259,7 @@ class MultiPhase
//! Charge (Coulombs) of phase with index \a p.
/*!
- * The net charge is computed as \f[ Q_p = N_p \sum_k F z_k X_k \f]
+ * The net charge is computed as @f[ Q_p = N_p \sum_k F z_k X_k @f]
* where the sum runs only over species in phase \a p.
* @param p index of the phase for which the charge is desired.
*/
@@ -276,9 +276,9 @@ class MultiPhase
* Write into array \a mu the chemical potentials of all species
* [J/kmol]. The chemical potentials are related to the activities by
*
- * \f$
+ * @f$
* \mu_k = \mu_k^0(T, P) + RT \ln a_k.
- * \f$.
+ * @f$.
*
* @param mu Chemical potential vector. Length = num global species. Units
* = J/kmol.
@@ -550,7 +550,7 @@ class MultiPhase
//! MultiPhaseEquil solver.
/*!
* @param XY Integer flag specifying properties to hold fixed.
- * @param err Error tolerance for \f$\Delta \mu/RT \f$ for all reactions.
+ * @param err Error tolerance for @f$ \Delta \mu/RT @f$ for all reactions.
* Also used as the relative error tolerance for the outer loop.
* @param maxsteps Maximum number of steps to take in solving the fixed TP
* problem.
diff --git a/include/cantera/equil/MultiPhaseEquil.h b/include/cantera/equil/MultiPhaseEquil.h
index 1474f0076e..171f584f64 100644
--- a/include/cantera/equil/MultiPhaseEquil.h
+++ b/include/cantera/equil/MultiPhaseEquil.h
@@ -109,7 +109,7 @@ class MultiPhaseEquil
//! Estimate the initial mole numbers. This is done by running each
//! reaction as far forward or backward as possible, subject to the
//! constraint that all mole numbers remain non-negative. Reactions for
- //! which \f$ \Delta \mu^0 \f$ are positive are run in reverse, and ones
+ //! which @f$ \Delta \mu^0 @f$ are positive are run in reverse, and ones
//! for which it is negative are run in the forward direction. The end
//! result is equivalent to solving the linear programming problem of
//! minimizing the linear Gibbs function subject to the element and non-
diff --git a/include/cantera/equil/vcs_solve.h b/include/cantera/equil/vcs_solve.h
index 93a81ff6f1..7f31cd9342 100644
--- a/include/cantera/equil/vcs_solve.h
+++ b/include/cantera/equil/vcs_solve.h
@@ -707,7 +707,7 @@ class VCS_SOLVE
/*!
* This is done by running each reaction as far forward or backward as
* possible, subject to the constraint that all mole numbers remain non-
- * negative. Reactions for which \f$ \Delta \mu^0 \f$ are positive are run
+ * negative. Reactions for which @f$ \Delta \mu^0 @f$ are positive are run
* in reverse, and ones for which it is negative are run in the forward
* direction. The end result is equivalent to solving the linear
* programming problem of minimizing the linear Gibbs function subject to
diff --git a/include/cantera/kinetics/Arrhenius.h b/include/cantera/kinetics/Arrhenius.h
index f7812a693d..71de76d728 100644
--- a/include/cantera/kinetics/Arrhenius.h
+++ b/include/cantera/kinetics/Arrhenius.h
@@ -161,9 +161,9 @@ class ArrheniusBase : public ReactionRate
/*!
* A reaction rate coefficient of the following form.
*
- * \f[
+ * @f[
* k_f = A T^b \exp (-Ea/RT)
- * \f]
+ * @f]
*
* @ingroup arrheniusGroup
*/
diff --git a/include/cantera/kinetics/BlowersMaselRate.h b/include/cantera/kinetics/BlowersMaselRate.h
index b359ead54e..3cbba5b4e8 100644
--- a/include/cantera/kinetics/BlowersMaselRate.h
+++ b/include/cantera/kinetics/BlowersMaselRate.h
@@ -50,19 +50,19 @@ struct BlowersMaselData : public ReactionData
* \Delta H)^2}{(V_P^2 - 4w^2 + (\Delta H)^2)}\; \text{Otherwise}
* \f}
* where
- * \f[
+ * @f[
* V_P = \frac{2w (w + E_0)}{w - E_0},
- * \f]
- * \f$ w \f$ is the average bond dissociation energy of the bond breaking
+ * @f]
+ * @f$ w @f$ is the average bond dissociation energy of the bond breaking
* and that being formed in the reaction. Since the expression is
- * very insensitive to \f$ w \f$ for \f$ w >= 2 E_0 \f$, \f$ w \f$
+ * very insensitive to @f$ w @f$ for @f$ w >= 2 E_0 @f$, @f$ w @f$
* can be approximated to an arbitrary high value like 1000 kJ/mol.
*
* After the activation energy is determined by Blowers-Masel approximation,
* it can be plugged into Arrhenius function to calculate the rate constant.
- * \f[
+ * @f[
* k_f = A T^b \exp (-E_a/RT)
- * \f]
+ * @f]
*
* @ingroup arrheniusGroup
*/
diff --git a/include/cantera/kinetics/ChebyshevRate.h b/include/cantera/kinetics/ChebyshevRate.h
index 2c12a49e7f..a2235e53df 100644
--- a/include/cantera/kinetics/ChebyshevRate.h
+++ b/include/cantera/kinetics/ChebyshevRate.h
@@ -61,27 +61,27 @@ struct ChebyshevData : public ReactionData
//! as a bivariate Chebyshev polynomial in temperature and pressure.
/*!
* The rate constant can be written as:
- * \f[
+ * @f[
* \log k(T,P) = \sum_{t=1}^{N_T} \sum_{p=1}^{N_P} \alpha_{tp}
* \phi_t(\tilde{T}) \phi_p(\tilde{P})
- * \f]
- * where \f$\alpha_{tp}\f$ are the constants defining the rate, \f$\phi_n(x)\f$
+ * @f]
+ * where @f$ \alpha_{tp} @f$ are the constants defining the rate, @f$ \phi_n(x) @f$
* is the Chebyshev polynomial of the first kind of degree *n* evaluated at
* *x*, and
- * \f[
+ * @f[
* \tilde{T} \equiv \frac{2T^{-1} - T_\mathrm{min}^{-1} - T_\mathrm{max}^{-1}}
* {T_\mathrm{max}^{-1} - T_\mathrm{min}^{-1}}
- * \f]
- * \f[
+ * @f]
+ * @f[
* \tilde{P} \equiv \frac{2 \log P - \log P_\mathrm{min} - \log P_\mathrm{max}}
* {\log P_\mathrm{max} - \log P_\mathrm{min}}
- * \f]
+ * @f]
* are reduced temperature and reduced pressures which map the ranges
- * \f$ (T_\mathrm{min}, T_\mathrm{max}) \f$ and
- * \f$ (P_\mathrm{min}, P_\mathrm{max}) \f$ to (-1, 1).
+ * @f$ (T_\mathrm{min}, T_\mathrm{max}) @f$ and
+ * @f$ (P_\mathrm{min}, P_\mathrm{max}) @f$ to (-1, 1).
*
* A ChebyshevRate rate expression is specified in terms of the coefficient matrix
- * \f$ \alpha \f$ and the temperature and pressure ranges. Note that the
+ * @f$ \alpha @f$ and the temperature and pressure ranges. Note that the
* Chebyshev polynomials are not defined outside the interval (-1,1), and
* therefore extrapolation of rates outside the range of temperatures and
* pressures for which they are defined is strongly discouraged.
diff --git a/include/cantera/kinetics/Falloff.h b/include/cantera/kinetics/Falloff.h
index f5b2b817fc..d4eed9511e 100644
--- a/include/cantera/kinetics/Falloff.h
+++ b/include/cantera/kinetics/Falloff.h
@@ -113,19 +113,19 @@ class FalloffRate : public ReactionRate
/**
* The falloff function. This is defined so that the rate coefficient is
*
- * \f[ k = F(Pr)\frac{Pr}{1 + Pr}. \f]
+ * @f[ k = F(Pr)\frac{Pr}{1 + Pr}. @f]
*
- * Here \f$ Pr \f$ is the reduced pressure, defined by
+ * Here @f$ Pr @f$ is the reduced pressure, defined by
*
- * \f[
+ * @f[
* Pr = \frac{k_0 [M]}{k_\infty}.
- * \f]
+ * @f]
*
* @param pr reduced pressure (dimensionless).
* @param work array of size workSize() containing cached
* temperature-dependent intermediate results from a prior call
* to updateTemp.
- * @returns the value of the falloff function \f$ F \f$ defined above
+ * @returns the value of the falloff function @f$ F @f$ defined above
*/
virtual double F(double pr, const double* work) const {
return 1.0;
@@ -288,29 +288,29 @@ class LindemannRate final : public FalloffRate
//! The 3- or 4-parameter Troe falloff parameterization.
/*!
- * The falloff function defines the value of \f$ F \f$ in the following
+ * The falloff function defines the value of @f$ F @f$ in the following
* rate expression
*
- * \f[ k = k_{\infty} \left( \frac{P_r}{1 + P_r} \right) F \f]
+ * @f[ k = k_{\infty} \left( \frac{P_r}{1 + P_r} \right) F @f]
* where
- * \f[ P_r = \frac{k_0 [M]}{k_{\infty}} \f]
+ * @f[ P_r = \frac{k_0 [M]}{k_{\infty}} @f]
*
* This parameterization is defined by
*
- * \f[ F = F_{cent}^{1/(1 + f_1^2)} \f]
+ * @f[ F = F_{cent}^{1/(1 + f_1^2)} @f]
* where
- * \f[ F_{cent} = (1 - A)\exp(-T/T_3) + A \exp(-T/T_1) + \exp(-T_2/T) \f]
+ * @f[ F_{cent} = (1 - A)\exp(-T/T_3) + A \exp(-T/T_1) + \exp(-T_2/T) @f]
*
- * \f[ f_1 = (\log_{10} P_r + C) /
- * \left(N - 0.14 (\log_{10} P_r + C)\right) \f]
+ * @f[ f_1 = (\log_{10} P_r + C) /
+ * \left(N - 0.14 (\log_{10} P_r + C)\right) @f]
*
- * \f[ C = -0.4 - 0.67 \log_{10} F_{cent} \f]
+ * @f[ C = -0.4 - 0.67 \log_{10} F_{cent} @f]
*
- * \f[ N = 0.75 - 1.27 \log_{10} F_{cent} \f]
+ * @f[ N = 0.75 - 1.27 \log_{10} F_{cent} @f]
*
- * - If \f$ T_3 \f$ is zero, then the corresponding term is set to zero.
- * - If \f$ T_1 \f$ is zero, then the corresponding term is set to zero.
- * - If \f$ T_2 \f$ is zero, then the corresponding term is set to zero.
+ * - If @f$ T_3 @f$ is zero, then the corresponding term is set to zero.
+ * - If @f$ T_1 @f$ is zero, then the corresponding term is set to zero.
+ * - If @f$ T_2 @f$ is zero, then the corresponding term is set to zero.
*
* @ingroup falloffGroup
*/
@@ -364,7 +364,7 @@ class TroeRate final : public FalloffRate
virtual void setParameters(
const AnyMap& node, const UnitStack& rate_units) override;
- //! Sets params to contain, in order, \f[ (A, T_3, T_1, T_2) \f]
+ //! Sets params to contain, in order, @f[ (A, T_3, T_1, T_2) @f]
/**
* @deprecated To be removed after %Cantera 3.0; superseded by getFalloffCoeffs()
*/
@@ -388,22 +388,22 @@ class TroeRate final : public FalloffRate
//! The SRI falloff function
/*!
- * The falloff function defines the value of \f$ F \f$ in the following
+ * The falloff function defines the value of @f$ F @f$ in the following
* rate expression
*
- * \f[ k = k_{\infty} \left( \frac{P_r}{1 + P_r} \right) F \f]
+ * @f[ k = k_{\infty} \left( \frac{P_r}{1 + P_r} \right) F @f]
* where
- * \f[ P_r = \frac{k_0 [M]}{k_{\infty}} \f]
+ * @f[ P_r = \frac{k_0 [M]}{k_{\infty}} @f]
*
- * \f[ F = {\left( a \; exp(\frac{-b}{T}) + exp(\frac{-T}{c})\right)}^n
- * \; d \; T^e \f]
+ * @f[ F = {\left( a \; exp(\frac{-b}{T}) + exp(\frac{-T}{c})\right)}^n
+ * \; d \; T^e @f]
* where
- * \f[ n = \frac{1.0}{1.0 + (\log_{10} P_r)^2} \f]
+ * @f[ n = \frac{1.0}{1.0 + (\log_{10} P_r)^2} @f]
*
- * \f$ c \f$ s required to greater than or equal to zero. If it is zero, then
+ * @f$ c @f$ s required to greater than or equal to zero. If it is zero, then
* the corresponding term is set to zero.
*
- * \f$ d \f$ is required to be greater than zero.
+ * @f$ d @f$ is required to be greater than zero.
*
* @ingroup falloffGroup
*/
@@ -464,7 +464,7 @@ class SriRate final : public FalloffRate
virtual void setParameters(
const AnyMap& node, const UnitStack& rate_units) override;
- //! Sets params to contain, in order, \f[ (a, b, c, d, e) \f]
+ //! Sets params to contain, in order, @f[ (a, b, c, d, e) @f]
/**
* @deprecated To be removed after %Cantera 3.0; superseded by getFalloffCoeffs()
*/
@@ -492,19 +492,19 @@ class SriRate final : public FalloffRate
//! The 1- or 2-parameter Tsang falloff parameterization.
/*!
* The Tsang falloff model is adapted from that of Troe.
- * It provides a constant or linear in temperature value for \f$ F_{cent} \f$:
- * \f[ F_{cent} = A + B*T \f]
+ * It provides a constant or linear in temperature value for @f$ F_{cent} @f$:
+ * @f[ F_{cent} = A + B*T @f]
*
- * The value of \f$ F_{cent} \f$ is then applied to Troe's model for the
- * determination of the value of \f$ F \f$:
- * \f[ F = F_{cent}^{1/(1 + f_1^2)} \f]
+ * The value of @f$ F_{cent} @f$ is then applied to Troe's model for the
+ * determination of the value of @f$ F @f$:
+ * @f[ F = F_{cent}^{1/(1 + f_1^2)} @f]
* where
- * \f[ f_1 = (\log_{10} P_r + C) /
- * \left(N - 0.14 (\log_{10} P_r + C)\right) \f]
+ * @f[ f_1 = (\log_{10} P_r + C) /
+ * \left(N - 0.14 (\log_{10} P_r + C)\right) @f]
*
- * \f[ C = -0.4 - 0.67 \log_{10} F_{cent} \f]
+ * @f[ C = -0.4 - 0.67 \log_{10} F_{cent} @f]
*
- * \f[ N = 0.75 - 1.27 \log_{10} F_{cent} \f]
+ * @f[ N = 0.75 - 1.27 \log_{10} F_{cent} @f]
*
* References:
* * Example of reaction database developed by Tsang utilizing this format
@@ -570,7 +570,7 @@ class TsangRate final : public FalloffRate
virtual void setParameters(
const AnyMap& node, const UnitStack& rate_units) override;
- //! Sets params to contain, in order, \f[ (A, B) \f]
+ //! Sets params to contain, in order, @f[ (A, B) @f]
/**
* @deprecated To be removed after %Cantera 3.0; superseded by getFalloffCoeffs()
*/
diff --git a/include/cantera/kinetics/ImplicitSurfChem.h b/include/cantera/kinetics/ImplicitSurfChem.h
index bc5d4fe3f6..e07ecd8a0e 100644
--- a/include/cantera/kinetics/ImplicitSurfChem.h
+++ b/include/cantera/kinetics/ImplicitSurfChem.h
@@ -27,31 +27,31 @@ namespace Cantera
* InterfaceKinetics object, in time. The following equation is used for each
* surface phase, *i*.
*
- * \f[
+ * @f[
* \dot \theta_k = \dot s_k (\sigma_k / s_0)
- * \f]
+ * @f]
*
* In this equation,
- * - \f$ \theta_k \f$ is the site coverage for the kth species.
- * - \f$ \dot s_k \f$ is the source term for the kth species
- * - \f$ \sigma_k \f$ is the number of surface sites covered by each species k.
- * - \f$ s_0 \f$ is the total site density of the interfacial phase.
+ * - @f$ \theta_k @f$ is the site coverage for the kth species.
+ * - @f$ \dot s_k @f$ is the source term for the kth species
+ * - @f$ \sigma_k @f$ is the number of surface sites covered by each species k.
+ * - @f$ s_0 @f$ is the total site density of the interfacial phase.
*
* Additionally, the 0'th equation in the set is discarded. Instead the
* alternate equation is solved for
*
- * \f[
+ * @f[
* \sum_{k=0}^{N-1} \dot \theta_k = 0
- * \f]
+ * @f]
*
- * This last equation serves to ensure that sum of the \f$ \theta_k \f$ values
+ * This last equation serves to ensure that sum of the @f$ \theta_k @f$ values
* stays constant.
*
* The object uses the CVODE software to advance the surface equations.
*
* The solution vector used by this object is as follows: For each surface
- * phase with \f$ N_s \f$ surface sites, it consists of the surface coverages
- * \f$ \theta_k \f$ for \f$ k = 0, N_s - 1 \f$
+ * phase with @f$ N_s @f$ surface sites, it consists of the surface coverages
+ * @f$ \theta_k @f$ for @f$ k = 0, N_s - 1 @f$
*
* @ingroup surfSolverGroup
*/
diff --git a/include/cantera/kinetics/InterfaceKinetics.h b/include/cantera/kinetics/InterfaceKinetics.h
index e0756a9b7f..ad9d6f900a 100644
--- a/include/cantera/kinetics/InterfaceKinetics.h
+++ b/include/cantera/kinetics/InterfaceKinetics.h
@@ -185,9 +185,9 @@ class InterfaceKinetics : public Kinetics
* This method carries out a time-accurate advancement of the
* surface coverages for a specified amount of time.
*
- * \f[
+ * @f[
* \dot {\theta}_k = \dot s_k (\sigma_k / s_0)
- * \f]
+ * @f]
*
* @param tstep Time value to advance the surface coverages
* @param rtol The relative tolerance for the integrator
@@ -364,8 +364,8 @@ class InterfaceKinetics : public Kinetics
//! Array of concentrations for each species in the kinetics mechanism
/*!
- * An array of generalized concentrations \f$ C_k \f$ that are defined
- * such that \f$ a_k = C_k / C^0_k, \f$ where \f$ C^0_k \f$ is a standard
+ * An array of generalized concentrations @f$ C_k @f$ that are defined
+ * such that @f$ a_k = C_k / C^0_k, @f$ where @f$ C^0_k @f$ is a standard
* concentration/ These generalized concentrations are used by this
* kinetics manager class to compute the forward and reverse rates of
* elementary reactions. The "units" for the concentrations of each phase
@@ -378,8 +378,8 @@ class InterfaceKinetics : public Kinetics
//! Array of activity concentrations for each species in the kinetics object
/*!
- * An array of activity concentrations \f$ Ca_k \f$ that are defined
- * such that \f$ a_k = Ca_k / C^0_k, \f$ where \f$ C^0_k \f$ is a standard
+ * An array of activity concentrations @f$ Ca_k @f$ that are defined
+ * such that @f$ a_k = Ca_k / C^0_k, @f$ where @f$ C^0_k @f$ is a standard
* concentration. These activity concentrations are used by this
* kinetics manager class to compute the forward and reverse rates of
* elementary reactions. The "units" for the concentrations of each phase
diff --git a/include/cantera/kinetics/InterfaceRate.h b/include/cantera/kinetics/InterfaceRate.h
index 24e8b6b721..eb25df2ad6 100644
--- a/include/cantera/kinetics/InterfaceRate.h
+++ b/include/cantera/kinetics/InterfaceRate.h
@@ -65,25 +65,25 @@ struct InterfaceData : public BlowersMaselData
* Rate expressions defined for interfaces may include coverage dependent terms,
* where an example is given by Kee, et al. @cite kee2003, Eq 11.113.
* Using %Cantera nomenclature, this expression can be rewritten as
- * \f[
+ * @f[
* k_f = A T^b \exp \left( - \frac{E_a}{RT} \right)
* \prod_k 10^{a_k \theta_k} \theta_k^{m_k}
* \exp \left( \frac{- E_k \theta_k}{RT} \right)
- * \f]
+ * @f]
* It is evident that this expression combines a regular modified Arrhenius rate
- * expression \f$ A T^b \exp \left( - \frac{E_a}{RT} \right) \f$ with coverage-related
- * terms, where the parameters \f$ (a_k, E_k, m_k) \f$ describe the dependency on the
- * surface coverage of species \f$ k, \theta_k \f$. In addition to the linear coverage
- * dependence on the activation energy modifier \f$ E_k \f$, polynomial coverage
- * dependence is also available. When the dependence parameter \f$ E_k \f$ is given as
+ * expression @f$ A T^b \exp \left( - \frac{E_a}{RT} \right) @f$ with coverage-related
+ * terms, where the parameters @f$ (a_k, E_k, m_k) @f$ describe the dependency on the
+ * surface coverage of species @f$ k, \theta_k @f$. In addition to the linear coverage
+ * dependence on the activation energy modifier @f$ E_k @f$, polynomial coverage
+ * dependence is also available. When the dependence parameter @f$ E_k @f$ is given as
* a scalar value, the linear dependency is applied whereas if a list of four values
- * are given as \f$ [E^{(1)}_k, ..., E^{(4)}_k] \f$, a polynomial dependency is applied as
- * \f[
+ * are given as @f$ [E^{(1)}_k, ..., E^{(4)}_k] @f$, a polynomial dependency is applied as
+ * @f[
* k_f = A T^b \exp \left( - \frac{E_a}{RT} \right)
* \prod_k 10^{a_k \theta_k} \theta_k^{m_k}
* \exp \left( \frac{- E^{(1)}_k \theta_k - E^{(2)}_k \theta_k^2
* - E^{(3)}_k \theta_k^3 - E^{(4)}_k \theta_k^4}{RT} \right)
- * \f]
+ * @f]
* The InterfaceRateBase class implements terms related to coverage only, which allows
* for combinations with arbitrary rate parameterizations (for example Arrhenius and
* BlowersMaselRate).
@@ -143,12 +143,12 @@ class InterfaceRateBase
* For reactions that transfer charge across a potential difference, the
* activation energies are modified by the potential difference. The correction
* factor is based on the net electric potential energy change
- * \f[
+ * @f[
* \Delta E_{p,j} = \sum_i E_{p,i} \nu_{i,j}
- * \f]
- * where potential energies are calculated as \f$ E_{p,i} = F \phi_i z_i \f$.
- * Here, \f$ F \f$ is Faraday's constant, \f$ \phi_i \f$ is the electric potential
- * of the species phase and \f$ z_i \f$ is the charge of the species.
+ * @f]
+ * where potential energies are calculated as @f$ E_{p,i} = F \phi_i z_i @f$.
+ * Here, @f$ F @f$ is Faraday's constant, @f$ \phi_i @f$ is the electric potential
+ * of the species phase and @f$ z_i @f$ is the charge of the species.
*
* When an electrode reaction rate is specified in terms of its exchange current
* density, the correction factor is adjusted to the standard reaction rate
@@ -186,9 +186,9 @@ class InterfaceRateBase
//! Boolean indicating whether rate uses electrochemistry
/*!
* If this is true, the Butler-Volmer correction
- * \f[
+ * @f[
* f_{BV} = \exp ( - \beta * Delta E_{p,j} / R T )
- * \f]
+ * @f]
* is applied to the forward reaction rate.
*
* @see voltageCorrection().
diff --git a/include/cantera/kinetics/Kinetics.h b/include/cantera/kinetics/Kinetics.h
index 3d2aa7ca65..75a05cfe34 100644
--- a/include/cantera/kinetics/Kinetics.h
+++ b/include/cantera/kinetics/Kinetics.h
@@ -59,8 +59,8 @@ class AnyMap;
//! that depend only on temperature, a manager class may choose to store these
//! quantities internally, and re-evaluate them only when the temperature has
//! actually changed. Or a manager designed for use with reaction mechanisms
-//! with a few repeated activation energies might precompute the terms \f$
-//! exp(-E/RT) \f$, instead of evaluating the exponential repeatedly for each
+//! with a few repeated activation energies might precompute the terms @f$
+//! exp(-E/RT) @f$, instead of evaluating the exponential repeatedly for each
//! reaction. There are many other possible 'management styles', each of which
//! might be better suited to some reaction mechanisms than others.
//!
@@ -400,9 +400,9 @@ class Kinetics
* units in array kc, which must be dimensioned at least as large as the
* total number of reactions.
*
- * \f[
+ * @f[
* Kc_i = exp [ \Delta G_{ss,i} ] prod(Cs_k) exp(\sum_k \nu_{k,i} F \phi_n) ]
- * \f]
+ * @f]
*
* @param kc Output vector containing the equilibrium constants.
* Length: nReactions().
@@ -413,10 +413,10 @@ class Kinetics
/**
* Change in species properties. Given an array of molar species property
- * values \f$ z_k, k = 1, \dots, K \f$, return the array of reaction values
- * \f[
+ * values @f$ z_k, k = 1, \dots, K @f$, return the array of reaction values
+ * @f[
* \Delta Z_i = \sum_k \nu_{k,i} z_k, i = 1, \dots, I.
- * \f]
+ * @f]
* For example, if this method is called with the array of standard-state
* molar Gibbs free energies for the species, then the values returned in
* array \c deltaProperty would be the standard-state Gibbs free energies of
@@ -733,8 +733,8 @@ class Kinetics
* mole fractions at constant temperature, pressure and molar concentration.
*
* The method returns a matrix with nReactions rows and nTotalSpecies columns.
- * For a derivative with respect to \f$X_i\f$, all other \f$X_j\f$ are held
- * constant, rather than enforcing \f$\sum X_j = 1\f$.
+ * For a derivative with respect to @f$ X_i @f$, all other @f$ X_j @f$ are held
+ * constant, rather than enforcing @f$ \sum X_j = 1 @f$.
*
* @warning This method is an experimental part of the %Cantera API and
* may be changed or removed without notice.
@@ -751,7 +751,7 @@ class Kinetics
* concentrations.
*
* The method returns a matrix with nReactions rows and nTotalSpecies columns.
- * For a derivative with respect to \f$c_i\f$, all other \f$c_j\f$ are held
+ * For a derivative with respect to @f$ c_i @f$, all other @f$ c_j @f$ are held
* constant.
*
* @warning This method is an experimental part of the %Cantera API and
@@ -806,8 +806,8 @@ class Kinetics
* mole fractions at constant temperature, pressure and molar concentration.
*
* The method returns a matrix with nReactions rows and nTotalSpecies columns.
- * For a derivative with respect to \f$X_i\f$, all other \f$X_j\f$ are held
- * constant, rather than enforcing \f$\sum X_j = 1\f$.
+ * For a derivative with respect to @f$ X_i @f$, all other @f$ X_j @f$ are held
+ * constant, rather than enforcing @f$ \sum X_j = 1 @f$.
*
* @warning This method is an experimental part of the %Cantera API and
* may be changed or removed without notice.
@@ -824,7 +824,7 @@ class Kinetics
* concentrations.
*
* The method returns a matrix with nReactions rows and nTotalSpecies columns.
- * For a derivative with respect to \f$c_i\f$, all other \f$c_j\f$ are held
+ * For a derivative with respect to @f$ c_i @f$, all other @f$ c_j @f$ are held
* constant.
*
* @warning This method is an experimental part of the %Cantera API and
@@ -879,8 +879,8 @@ class Kinetics
* mole fractions at constant temperature, pressure and molar concentration.
*
* The method returns a matrix with nReactions rows and nTotalSpecies columns.
- * For a derivative with respect to \f$X_i\f$, all other \f$X_j\f$ are held
- * constant, rather than enforcing \f$\sum X_j = 1\f$.
+ * For a derivative with respect to @f$ X_i @f$, all other @f$ X_j @f$ are held
+ * constant, rather than enforcing @f$ \sum X_j = 1 @f$.
*
* @warning This method is an experimental part of the %Cantera API and
* may be changed or removed without notice.
@@ -897,7 +897,7 @@ class Kinetics
* concentrations.
*
* The method returns a matrix with nReactions rows and nTotalSpecies columns.
- * For a derivative with respect to \f$c_i\f$, all other \f$c_j\f$ are held
+ * For a derivative with respect to @f$ c_i @f$, all other @f$ c_j @f$ are held
* constant.
*
* @warning This method is an experimental part of the %Cantera API and
@@ -940,8 +940,8 @@ class Kinetics
* mole fractions at constant temperature, pressure and molar concentration.
*
* The method returns a matrix with nTotalSpecies rows and nTotalSpecies columns.
- * For a derivative with respect to \f$X_i\f$, all other \f$X_j\f$ are held
- * constant, rather than enforcing \f$\sum X_j = 1\f$.
+ * For a derivative with respect to @f$ X_i @f$, all other @f$ X_j @f$ are held
+ * constant, rather than enforcing @f$ \sum X_j = 1 @f$.
*
* @warning This method is an experimental part of the %Cantera API and
* may be changed or removed without notice.
@@ -954,7 +954,7 @@ class Kinetics
* species.
*
* The method returns a matrix with nTotalSpecies rows and nTotalSpecies columns.
- * For a derivative with respect to \f$c_i\f$, all other \f$c_j\f$ are held
+ * For a derivative with respect to @f$ c_i @f$, all other @f$ c_j @f$ are held
* constant.
*
* @warning This method is an experimental part of the %Cantera API and
@@ -993,8 +993,8 @@ class Kinetics
* mole fractions at constant temperature, pressure and molar concentration.
*
* The method returns a matrix with nTotalSpecies rows and nTotalSpecies columns.
- * For a derivative with respect to \f$X_i\f$, all other \f$X_j\f$ are held
- * constant, rather than enforcing \f$\sum X_j = 1\f$.
+ * For a derivative with respect to @f$ X_i @f$, all other @f$ X_j @f$ are held
+ * constant, rather than enforcing @f$ \sum X_j = 1 @f$.
*
* @warning This method is an experimental part of the %Cantera API and
* may be changed or removed without notice.
@@ -1007,7 +1007,7 @@ class Kinetics
* species.
*
* The method returns a matrix with nTotalSpecies rows and nTotalSpecies columns.
- * For a derivative with respect to \f$c_i\f$, all other \f$c_j\f$ are held
+ * For a derivative with respect to @f$ c_i @f$, all other @f$ c_j @f$ are held
* constant.
*
* @warning This method is an experimental part of the %Cantera API and
@@ -1046,8 +1046,8 @@ class Kinetics
* mole fractions at constant temperature, pressure and molar concentration.
*
* The method returns a matrix with nTotalSpecies rows and nTotalSpecies columns.
- * For a derivative with respect to \f$X_i\f$, all other \f$X_j\f$ are held constant,
- * rather than enforcing \f$\sum X_j = 1\f$.
+ * For a derivative with respect to @f$ X_i @f$, all other @f$ X_j @f$ are held constant,
+ * rather than enforcing @f$ \sum X_j = 1 @f$.
*
* @warning This method is an experimental part of the %Cantera API and
* may be changed or removed without notice.
@@ -1060,7 +1060,7 @@ class Kinetics
* species.
*
* The method returns a matrix with nTotalSpecies rows and nTotalSpecies columns.
- * For a derivative with respect to \f$c_i\f$, all other \f$c_j\f$ are held
+ * For a derivative with respect to @f$ c_i @f$, all other @f$ c_j @f$ are held
* constant.
*
* @warning This method is an experimental part of the %Cantera API and
diff --git a/include/cantera/kinetics/PlogRate.h b/include/cantera/kinetics/PlogRate.h
index 3b333b4826..948ed8b5b8 100644
--- a/include/cantera/kinetics/PlogRate.h
+++ b/include/cantera/kinetics/PlogRate.h
@@ -59,14 +59,14 @@ struct PlogData : public ReactionData
/*!
* Given two rate expressions at two specific pressures:
*
- * * \f$ P_1: k_1(T) = A_1 T^{b_1} e^{-E_1 / RT} \f$
- * * \f$ P_2: k_2(T) = A_2 T^{b_2} e^{-E_2 / RT} \f$
+ * * @f$ P_1: k_1(T) = A_1 T^{b_1} e^{-E_1 / RT} @f$
+ * * @f$ P_2: k_2(T) = A_2 T^{b_2} e^{-E_2 / RT} @f$
*
- * The rate at an intermediate pressure \f$ P_1 < P < P_2 \f$ is computed as
- * \f[
+ * The rate at an intermediate pressure @f$ P_1 < P < P_2 @f$ is computed as
+ * @f[
* \log k(T,P) = \log k_1(T) + \bigl(\log k_2(T) - \log k_1(T)\bigr)
* \frac{\log P - \log P_1}{\log P_2 - \log P_1}
- * \f]
+ * @f]
* Multiple rate expressions may be given at the same pressure, in which case
* the rate used in the interpolation formula is the sum of all the rates given
* at that pressure. For pressures outside the given range, the rate expression
diff --git a/include/cantera/kinetics/StoichManager.h b/include/cantera/kinetics/StoichManager.h
index 63d3961626..7d88ea683a 100644
--- a/include/cantera/kinetics/StoichManager.h
+++ b/include/cantera/kinetics/StoichManager.h
@@ -32,14 +32,14 @@ namespace Cantera
* coefficient matrix and a vector of reaction rates. For example, the species
* creation rates are given by
*
- * \f[
+ * @f[
* \dot C_k = \sum_k \nu^{(p)}_{k,i} R_i
- * \f]
+ * @f]
*
- * where \f$ \nu^{(p)_{k,i}} \f$ is the product-side stoichiometric
+ * where @f$ \nu^{(p)_{k,i}} @f$ is the product-side stoichiometric
* coefficient of species \a k in reaction \a i. This could be done by
* straightforward matrix multiplication, but would be inefficient, since most
- * of the matrix elements of \f$ \nu^{(p)}_{k,i} \f$ are zero. We could do
+ * of the matrix elements of @f$ \nu^{(p)}_{k,i} @f$ are zero. We could do
* better by using sparse-matrix algorithms to compute this product.
*
* If the reactions are general ones, with non-integral stoichiometric
@@ -559,12 +559,12 @@ inline static void _scale(InputIter begin, InputIter end,
* products of irreversible reactions).
*
* This class is designed for use with elementary reactions, or at least ones
- * with integral stoichiometric coefficients. Let \f$ M(i) \f$ be the number of
+ * with integral stoichiometric coefficients. Let @f$ M(i) @f$ be the number of
* molecules on the product or reactant side of reaction number i.
- * \f[
+ * @f[
* r_i = \sum_m^{M_i} s_{k_{m,i}}
- * \f]
- * To understand the operations performed by this class, let \f$ N_{k,i}\f$
+ * @f]
+ * To understand the operations performed by this class, let @f$ N_{k,i} @f$
* denote the stoichiometric coefficient of species k on one side (reactant or
* product) in reaction i. Then \b N is a sparse K by I matrix of stoichiometric
* coefficients.
@@ -572,19 +572,19 @@ inline static void _scale(InputIter begin, InputIter end,
* The following matrix operations may be carried out with a vector S of length
* K, and a vector R of length I:
*
- * - \f$ S = S + N R\f$ (incrementSpecies)
- * - \f$ S = S - N R\f$ (decrementSpecies)
- * - \f$ R = R + N^T S \f$ (incrementReaction)
- * - \f$ R = R - N^T S \f$ (decrementReaction)
+ * - @f$ S = S + N R @f$ (incrementSpecies)
+ * - @f$ S = S - N R @f$ (decrementSpecies)
+ * - @f$ R = R + N^T S @f$ (incrementReaction)
+ * - @f$ R = R - N^T S @f$ (decrementReaction)
*
* The actual implementation, however, does not compute these quantities by
* matrix multiplication. A faster algorithm is used that makes use of the fact
* that the \b integer-valued N matrix is very sparse, and the non-zero terms
* are small positive integers.
- * \f[
+ * @f[
* S_k = R_{i1} + \dots + R_{iM}
- * \f]
- * where M is the number of molecules, and \f$ i(m) \f$ is the
+ * @f]
+ * where M is the number of molecules, and @f$ i(m) @f$ is the
* See @ref Stoichiometry
* @ingroup Stoichiometry
*/
diff --git a/include/cantera/kinetics/TwoTempPlasmaRate.h b/include/cantera/kinetics/TwoTempPlasmaRate.h
index f111531f5f..e7abe3d12b 100644
--- a/include/cantera/kinetics/TwoTempPlasmaRate.h
+++ b/include/cantera/kinetics/TwoTempPlasmaRate.h
@@ -47,12 +47,12 @@ struct TwoTempPlasmaData : public ReactionData
* the electron temperature instead. In addition, the exponential term with
* activation energy for electron is included.
*
- * \f[
+ * @f[
* k_f = A T_e^b \exp (-E_{a,g}/RT) \exp (E_{a,e} (T_e - T)/(R T T_e))
- * \f]
+ * @f]
*
- * where \f$ T_e \f$ is the electron temperature, \f$ E_{a,g} \f$ is the activation
- * energy for gas, and \f$ E_{a,e} \f$ is the activation energy for electron, see
+ * where @f$ T_e @f$ is the electron temperature, @f$ E_{a,g} @f$ is the activation
+ * energy for gas, and @f$ E_{a,e} @f$ is the activation energy for electron, see
* Kossyi, et al. @cite kossyi1992.
*
* @ingroup arrheniusGroup
diff --git a/include/cantera/numerics/DenseMatrix.h b/include/cantera/numerics/DenseMatrix.h
index 4654b0090f..b175df3b77 100644
--- a/include/cantera/numerics/DenseMatrix.h
+++ b/include/cantera/numerics/DenseMatrix.h
@@ -190,9 +190,9 @@ int solve(DenseMatrix& A, DenseMatrix& b);
//! Multiply \c A*b and return the result in \c prod. Uses BLAS routine DGEMV.
/*!
- * \f[
+ * @f[
* prod_i = sum^N_{j = 1}{A_{ij} b_j}
- * \f]
+ * @f]
*
* @param[in] A Dense Matrix A with M rows and N columns
* @param[in] b vector b with length N
@@ -202,9 +202,9 @@ void multiply(const DenseMatrix& A, const double* const b, double* const prod);
//! Multiply \c A*b and add it to the result in \c prod. Uses BLAS routine DGEMV.
/*!
- * \f[
+ * @f[
* prod_i += sum^N_{j = 1}{A_{ij} b_j}
- * \f]
+ * @f]
*
* @param[in] A Dense Matrix A with M rows and N columns
* @param[in] b vector b with length N
diff --git a/include/cantera/numerics/Func1.h b/include/cantera/numerics/Func1.h
index a817284622..56725772ad 100644
--- a/include/cantera/numerics/Func1.h
+++ b/include/cantera/numerics/Func1.h
@@ -40,7 +40,7 @@ const int TabulatedFuncType = 120;
class TimesConstant1;
//! @defgroup func1 Functor Objects
-//! Functors implement functions of a single variable \f$ f(x) \f$.
+//! Functors implement functions of a single variable @f$ f(x) @f$.
//! Functor objects can be combined to form compound expressions, which allows for
//! the implementation of generic mathematical expressions.
//! @ingroup numerics
@@ -266,9 +266,9 @@ shared_ptr newPlusConstFunction(shared_ptr f1, double c);
//! Implements the \c sin() function.
/*!
- * The functor class with type \c "sin" returns \f$ f(x) = \cos(\omega x) \f$,
- * where the argument \f$ x \f$ is in radians.
- * @param omega Frequency \f$ \omega \f$ (default=1.0)
+ * The functor class with type \c "sin" returns @f$ f(x) = \cos(\omega x) @f$,
+ * where the argument @f$ x @f$ is in radians.
+ * @param omega Frequency @f$ \omega @f$ (default=1.0)
* @ingroup func1simple
*/
class Sin1 : public Func1
@@ -315,9 +315,9 @@ class Sin1 : public Func1
//! Implements the \c cos() function.
/*!
- * The functor class with type \c "cos" returns \f$ f(x) = \cos(\omega x) \f$,
- * where the argument \f$ x \f$ is in radians.
- * @param omega Frequency \f$ \omega \f$ (default=1.0)
+ * The functor class with type \c "cos" returns @f$ f(x) = \cos(\omega x) @f$,
+ * where the argument @f$ x @f$ is in radians.
+ * @param omega Frequency @f$ \omega @f$ (default=1.0)
* @ingroup func1simple
*/
class Cos1 : public Func1
@@ -361,7 +361,7 @@ class Cos1 : public Func1
//! Implements the \c exp() (exponential) function.
/*!
- * The functor class with type \c "exp" returns \f$ f(x) = \exp(a x) \f$.
+ * The functor class with type \c "exp" returns @f$ f(x) = \exp(a x) @f$.
* @param a Factor (default=1.0)
* @ingroup func1simple
*/
@@ -405,7 +405,7 @@ class Exp1 : public Func1
//! Implements the \c log() (natural logarithm) function.
/*!
- * The functor class with type \c "log" returns \f$ f(x) = \log(a x) \f$.
+ * The functor class with type \c "log" returns @f$ f(x) = \log(a x) @f$.
* @param a Factor (default=1.0)
* @ingroup func1simple
* @since New in %Cantera 3.0
@@ -435,7 +435,7 @@ class Log1 : public Func1
//! Implements the \c pow() (power) function.
/*!
- * The functor class with type \c "pow" returns \f$ f(x) = x^n \f$.
+ * The functor class with type \c "pow" returns @f$ f(x) = x^n @f$.
* @param n Exponent
* @ingroup func1simple
*/
@@ -498,8 +498,8 @@ class Tabulated1 : public Func1
Tabulated1(size_t n, const double* tvals, const double* fvals,
const string& method="linear");
- //! Constructor uses \f$ 2 n\f$ parameters in the following order:
- //! \f$ [t_0, t_1, \dots, t_{n-1}, f_0, f_1, \dots, f_{n-1}] \f$
+ //! Constructor uses @f$ 2 n @f$ parameters in the following order:
+ //! @f$ [t_0, t_1, \dots, t_{n-1}, f_0, f_1, \dots, f_{n-1}] @f$
Tabulated1(const vector& params);
//! Set the interpolation method
@@ -533,7 +533,7 @@ class Tabulated1 : public Func1
//! Implements a constant.
/*!
- * The functor class with type \c "constant" returns \f$ f(x) = a \f$.
+ * The functor class with type \c "constant" returns @f$ f(x) = a @f$.
* @param a Constant
* @ingroup func1simple
*/
@@ -580,9 +580,9 @@ class Const1 : public Func1
/**
* Implements the sum of two functions.
- * The functor class with type \c "sum" returns \f$ f(x) = f_1(x) + f_2(x) \f$.
- * @param f1 Functor \f$ f_1(x) \f$
- * @param f2 Functor \f$ f_2(x) \f$
+ * The functor class with type \c "sum" returns @f$ f(x) = f_1(x) + f_2(x) @f$.
+ * @param f1 Functor @f$ f_1(x) @f$
+ * @param f2 Functor @f$ f_2(x) @f$
* @ingroup func1compound
*/
class Sum1 : public Func1
@@ -651,9 +651,9 @@ class Sum1 : public Func1
/**
* Implements the difference of two functions.
- * The functor class with type \c "diff" returns \f$ f(x) = f_1(x) - f_2(x) \f$.
- * @param f1 Functor \f$ f_1(x) \f$
- * @param f2 Functor \f$ f_2(x) \f$
+ * The functor class with type \c "diff" returns @f$ f(x) = f_1(x) - f_2(x) @f$.
+ * @param f1 Functor @f$ f_1(x) @f$
+ * @param f2 Functor @f$ f_2(x) @f$
* @ingroup func1compound
*/
class Diff1 : public Func1
@@ -724,9 +724,9 @@ class Diff1 : public Func1
/**
* Implements the product of two functions.
- * The functor class with type \c "product" returns \f$ f(x) = f_1(x) f_2(x) \f$.
- * @param f1 Functor \f$ f_1(x) \f$
- * @param f2 Functor \f$ f_2(x) \f$
+ * The functor class with type \c "product" returns @f$ f(x) = f_1(x) f_2(x) @f$.
+ * @param f1 Functor @f$ f_1(x) @f$
+ * @param f2 Functor @f$ f_2(x) @f$
* @ingroup func1compound
*/
class Product1 : public Func1
@@ -794,9 +794,9 @@ class Product1 : public Func1
/**
* Implements the product of a function and a constant.
- * The functor class with type \c "times-constant" returns \f$ f(x) = a f_1(x) \f$.
- * @param f1 Functor \f$ f_1(x) \f$
- * @param a Constant \f$ a \f$
+ * The functor class with type \c "times-constant" returns @f$ f(x) = a f_1(x) @f$.
+ * @param f1 Functor @f$ f_1(x) @f$
+ * @param a Constant @f$ a @f$
* @ingroup func1modified
*/
class TimesConstant1 : public Func1
@@ -874,9 +874,9 @@ class TimesConstant1 : public Func1
/**
* Implements the sum of a function and a constant.
- * The functor class with type \c "plus-constant" returns \f$ f(x) = f_1(x) + a \f$.
- * @param f1 Functor \f$ f_1(x) \f$
- * @param a Constant \f$ a \f$
+ * The functor class with type \c "plus-constant" returns @f$ f(x) = f_1(x) + a @f$.
+ * @param f1 Functor @f$ f_1(x) @f$
+ * @param a Constant @f$ a @f$
* @ingroup func1modified
*/
class PlusConstant1 : public Func1
@@ -940,9 +940,9 @@ class PlusConstant1 : public Func1
/**
* Implements the ratio of two functions.
- * The functor class with type \c "ratio" returns \f$ f(x) = f_1(x) / f_2(x) \f$.
- * @param f1 Functor \f$ f_1(x) \f$
- * @param f2 Functor \f$ f_2(x) \f$
+ * The functor class with type \c "ratio" returns @f$ f(x) = f_1(x) / f_2(x) @f$.
+ * @param f1 Functor @f$ f_1(x) @f$
+ * @param f2 Functor @f$ f_2(x) @f$
* @ingroup func1compound
*/
class Ratio1 : public Func1
@@ -1009,9 +1009,9 @@ class Ratio1 : public Func1
/**
* Implements a composite function.
- * The functor class with type \c "composite" returns \f$ f(x) = f_1\left(f_2(x)\right) \f$.
- * @param f1 Functor \f$ f_1(x) \f$
- * @param f2 Functor \f$ f_2(x) \f$
+ * The functor class with type \c "composite" returns @f$ f(x) = f_1\left(f_2(x)\right) @f$.
+ * @param f1 Functor @f$ f_1(x) @f$
+ * @param f2 Functor @f$ f_2(x) @f$
* @ingroup func1compound
*/
class Composite1 : public Func1
@@ -1082,10 +1082,10 @@ class Composite1 : public Func1
/**
* Implements a Gaussian function.
* The functor class with type \c "Gaussian" returns
- * \f[
+ * @f[
* f(t) = A e^{-[(t - t_0)/\tau]^2}
- * \f]
- * where \f$ \tau = \mathrm{fwhm} / (2 \sqrt{\ln 2}) \f$.
+ * @f]
+ * where @f$ \tau = \mathrm{fwhm} / (2 \sqrt{\ln 2}) @f$.
* @param A peak value
* @param t0 offset
* @param fwhm full width at half max
@@ -1102,7 +1102,7 @@ class Gaussian1 : public Func1
}
//! Constructor uses 3 parameters in the following order:
- //! \f$ [A, t_0, \mathrm{fwhm}] \f$
+ //! @f$ [A, t_0, \mathrm{fwhm}] @f$
Gaussian1(const vector& params);
Gaussian1(const Gaussian1& b) :
@@ -1138,10 +1138,10 @@ class Gaussian1 : public Func1
/**
* A Gaussian.
- * \f[
+ * @f[
* f(t) = A e^{-[(t - t_0)/\tau]^2}
- * \f]
- * where \f[ \tau = \frac{fwhm}{2\sqrt{\ln 2}} \f]
+ * @f]
+ * where @f[ \tau = \frac{fwhm}{2\sqrt{\ln 2}} @f]
* @param A peak value
* @param t0 offset
* @param fwhm full width at half max
@@ -1161,9 +1161,9 @@ class Gaussian : public Gaussian1
/**
* Implements a polynomial of degree \e n.
* The functor class with type \c "polynomial" returns
- * \f[
+ * @f[
* f(x) = a_n x^n + \dots + a_1 x + a_0
- * \f]
+ * @f]
* @ingroup func1advanced
*/
class Poly1 : public Func1
@@ -1174,8 +1174,8 @@ class Poly1 : public Func1
std::copy(c, c+m_cpoly.size(), m_cpoly.begin());
}
- //! Constructor uses \f$ n + 1 \f$ parameters in the following order:
- //! \f$ [a_n, \dots, a_1, a_0] \f$
+ //! Constructor uses @f$ n + 1 @f$ parameters in the following order:
+ //! @f$ [a_n, \dots, a_1, a_0] @f$
Poly1(const vector& params);
Poly1(const Poly1& b) :
@@ -1216,10 +1216,10 @@ class Poly1 : public Func1
/**
* Implements a Fourier cosine/sine series.
* The functor class with type \c "Fourier" returns
- * \f[
+ * @f[
* f(t) = \frac{A_0}{2} +
* \sum_{n=1}^N A_n \cos (n \omega t) + B_n \sin (n \omega t)
- * \f]
+ * @f]
* @ingroup func1advanced
*/
class Fourier1 : public Func1
@@ -1234,8 +1234,8 @@ class Fourier1 : public Func1
std::copy(b, b+n, m_csin.begin());
}
- //! Constructor uses \f$ 2 n + 2 \f$ parameters in the following order:
- //! \f$ [a_0, a_1, \dots, a_n, \omega, b_1, \dots, b_n] \f$
+ //! Constructor uses @f$ 2 n + 2 @f$ parameters in the following order:
+ //! @f$ [a_0, a_1, \dots, a_n, \omega, b_1, \dots, b_n] @f$
Fourier1(const vector& params);
Fourier1(const Fourier1& b) :
@@ -1282,9 +1282,9 @@ class Fourier1 : public Func1
/**
* Implements a sum of Arrhenius terms.
* The functor class with type \c "Arrhenius" returns
- * \f[
+ * @f[
* f(T) = \sum_{n=1}^N A_n T^b_n \exp(-E_n/T)
- * \f]
+ * @f]
* @ingroup func1advanced
*/
class Arrhenius1 : public Func1
@@ -1302,8 +1302,8 @@ class Arrhenius1 : public Func1
}
}
- //! Constructor uses \f$ 3 n\f$ parameters in the following order:
- //! \f$ [A_1, b_1, E_1, A_2, b_2, E_2, \dots, A_n, b_n, E_n] \f$
+ //! Constructor uses @f$ 3 n @f$ parameters in the following order:
+ //! @f$ [A_1, b_1, E_1, A_2, b_2, E_2, \dots, A_n, b_n, E_n] @f$
Arrhenius1(const vector& params);
Arrhenius1(const Arrhenius1& b) :
@@ -1343,7 +1343,7 @@ class Arrhenius1 : public Func1
/**
* Implements a periodic function.
- * Takes any function and makes it periodic with period \f$ T \f$.
+ * Takes any function and makes it periodic with period @f$ T @f$.
* @param f Functor to be made periodic
* @param T Period
* @ingroup func1modified
diff --git a/include/cantera/numerics/FuncEval.h b/include/cantera/numerics/FuncEval.h
index f29ddc99d1..84f50eca3c 100644
--- a/include/cantera/numerics/FuncEval.h
+++ b/include/cantera/numerics/FuncEval.h
@@ -22,10 +22,10 @@ namespace Cantera
/**
* Virtual base class for ODE/DAE right-hand-side function evaluators.
* Classes derived from FuncEval evaluate the right-hand-side function
- * \f$ \vec{F}(t,\vec{y})\f$ in
- * \f[
+ * @f$ \vec{F}(t,\vec{y}) @f$ in
+ * @f[
* \dot{\vec{y}} = \vec{F}(t,\vec{y}).
- * \f]
+ * @f]
* @ingroup odeGroup
*/
class FuncEval
diff --git a/include/cantera/numerics/IdasIntegrator.h b/include/cantera/numerics/IdasIntegrator.h
index 190343400b..7096d9274b 100644
--- a/include/cantera/numerics/IdasIntegrator.h
+++ b/include/cantera/numerics/IdasIntegrator.h
@@ -103,7 +103,7 @@ class IdasIntegrator : public Integrator
void* m_linsol_matrix = nullptr; //!< matrix used by Sundials
SundialsContext m_sundials_ctx; //!< SUNContext object for Sundials>=6.0
- //! Object implementing the DAE residual function \f$ f(t, y, \dot{y}) = 0\f$
+ //! Object implementing the DAE residual function @f$ f(t, y, \dot{y}) = 0 @f$
FuncEval* m_func = nullptr;
double m_t0 = 0.0; //!< The start time for the integrator
diff --git a/include/cantera/numerics/ResidEval.h b/include/cantera/numerics/ResidEval.h
index facf21e6c2..25eedda0ab 100644
--- a/include/cantera/numerics/ResidEval.h
+++ b/include/cantera/numerics/ResidEval.h
@@ -28,9 +28,9 @@ const int c_LT_ZERO = -2;
/**
* Virtual base class for DAE residual function evaluators.
* Classes derived from ResidEval evaluate the residual function
- * \f[
+ * @f[
* \vec{F}(t,\vec{y}, \vec{y^\prime})
- * \f]
+ * @f]
* The DAE solver attempts to find a solution y(t) such that F = 0.
* @deprecated Unused. To be removed after %Cantera 3.0.
* @ingroup DAE_Group
diff --git a/include/cantera/numerics/polyfit.h b/include/cantera/numerics/polyfit.h
index 5c40bc2992..3ad3572c17 100644
--- a/include/cantera/numerics/polyfit.h
+++ b/include/cantera/numerics/polyfit.h
@@ -17,7 +17,7 @@ namespace Cantera
* evaluated at those points, this function computes the weighted least-squares
* polynomial fit of degree *deg*:
*
- * \f[ f(x) = p[0] + p[1]*x + p[2]*x^2 + \cdots + p[deg]*x^deg \f]
+ * @f[ f(x) = p[0] + p[1] x + p[2] x^2 + \cdots + p[deg] x^deg @f]
*
* @param n The number of points at which the function is evaluated
* @param deg The degree of the polynomial fit to be computed. deg <= n - 1.
diff --git a/include/cantera/oneD/Sim1D.h b/include/cantera/oneD/Sim1D.h
index e9ef48aea0..dcd0af67e1 100644
--- a/include/cantera/oneD/Sim1D.h
+++ b/include/cantera/oneD/Sim1D.h
@@ -320,18 +320,18 @@ class Sim1D : public OneDim
void evalSSJacobian();
- //! Solve the equation \f$ J^T \lambda = b \f$.
+ //! Solve the equation @f$ J^T \lambda = b @f$.
/**
- * Here, \f$ J = \partial f/\partial x \f$ is the Jacobian matrix of the
- * system of equations \f$ f(x,p)=0 \f$. This can be used to efficiently
- * solve for the sensitivities of a scalar objective function \f$ g(x,p) \f$
- * to a vector of parameters \f$ p \f$ by solving:
- * \f[ J^T \lambda = \left( \frac{\partial g}{\partial x} \right)^T \f]
- * for \f$ \lambda \f$ and then computing:
- * \f[
+ * Here, @f$ J = \partial f/\partial x @f$ is the Jacobian matrix of the
+ * system of equations @f$ f(x,p)=0 @f$. This can be used to efficiently
+ * solve for the sensitivities of a scalar objective function @f$ g(x,p) @f$
+ * to a vector of parameters @f$ p @f$ by solving:
+ * @f[ J^T \lambda = \left( \frac{\partial g}{\partial x} \right)^T @f]
+ * for @f$ \lambda @f$ and then computing:
+ * @f[
* \left.\frac{dg}{dp}\right|_{f=0} = \frac{\partial g}{\partial p}
* - \lambda^T \frac{\partial f}{\partial p}
- * \f]
+ * @f]
*/
void solveAdjoint(const double* b, double* lambda);
diff --git a/include/cantera/thermo/BinarySolutionTabulatedThermo.h b/include/cantera/thermo/BinarySolutionTabulatedThermo.h
index 8f130ca334..0cd99dcfc8 100644
--- a/include/cantera/thermo/BinarySolutionTabulatedThermo.h
+++ b/include/cantera/thermo/BinarySolutionTabulatedThermo.h
@@ -31,25 +31,25 @@ namespace Cantera
*
* A good example of this type of phase is intercalation-based lithium storage
* materials used for lithium-ion battery electrodes. Measuring the open
- * circuit voltage \f$ E_eq \f$, relative to a reference electrode, as a
+ * circuit voltage @f$ E_eq @f$, relative to a reference electrode, as a
* function of lithium mole fraction and as a function of temperature, provides
* a means to evaluate the gibbs free energy of reaction:
*
- * \f[
+ * @f[
* \Delta g_{\rm rxn} = -\frac{E_eq}{nF}
- * \f]
+ * @f]
*
- * where \f$ n\f$ is the charge number transferred to the phase, via the
- * reaction, and \f$ F \f$ is Faraday's constant. The gibbs energy of
+ * where @f$ n @f$ is the charge number transferred to the phase, via the
+ * reaction, and @f$ F @f$ is Faraday's constant. The gibbs energy of
* reaction, in turn, can be separated into enthalpy and entropy of reaction
* components:
*
- * \f[
+ * @f[
* \Delta g_{\rm rxn} = \Delta h_{\rm rxn} - T\Delta s_{\rm rxn}
- * \f]
- * \f[
+ * @f]
+ * @f[
* \frac{d\Delta g_{\rm rxn}}{dT} = - \Delta s_{\rm rxn}
- * \f]
+ * @f]
*
* For the tabulated binary phase, the user identifies a 'tabulated' species,
* while the other is considered the 'reference' species. The standard state
@@ -57,15 +57,15 @@ namespace Cantera
* excess energy contributions, and are calculated according to the reaction
* energy terms:
*
- * \f[
+ * @f[
* \Delta h_{\rm rxn} = \sum_k \nu_k h^{\rm o}_k
- * \f]
- * \f[
+ * @f]
+ * @f[
* \Delta s_{\rm rxn} = \sum_k \nu_k s^{\rm o}_k + RT\ln\left(\prod_k\left(\frac{c_k}{c^{\rm o}_k} \right)^{\nu_k}\right)
- * \f]
+ * @f]
*
* Where the 'reference' species is automatically assigned standard state
- * thermo variables \f$ h^{\rm o} = 0\f$ and \f$ s^{\rm o} = 0\f$, and standard
+ * thermo variables @f$ h^{\rm o} = 0 @f$ and @f$ s^{\rm o} = 0 @f$, and standard
* state thermo variables for species in any other phases are calculated
* according to the rules specified in that phase definition.
*
@@ -73,7 +73,7 @@ namespace Cantera
* thermodynamics for binary solutions where the tabulated species is
* incorporated via an electrochemical reaction, such that the open circuit
* voltage can be measured, relative to a counter electrode species with
- * standard state thermo properties \f$ h^{\rm o} = 0\f$.
+ * standard state thermo properties @f$ h^{\rm o} = 0 @f$.
* It is possible that this can be generalized such that this assumption about
* the counter-electrode is not required. At present, this is left as future
* work.
@@ -81,35 +81,35 @@ namespace Cantera
* The user therefore provides a table of three equally-sized vectors of
* tabulated data:
*
- * - \f$ x_{\rm tab}\f$ = array of mole fractions for the tabulated species
+ * - @f$ x_{\rm tab} @f$ = array of mole fractions for the tabulated species
* at which measurements were conducted and thermo
* data are provided.
- * - \f$ h_{\rm tab}\f$ = \f$ F\left(-E_{\rm eq}\left(x,T^{\rm o} \right) + T^{\rm o} \frac{dE_{\rm eq}\left(x,T^{\rm o} \right)}{dT}\right) \f$
- * - \f$ s_{\rm tab}\f$ = \f$ F \left(\frac{dE_{\rm eq}\left(x,T^{\rm o} \right)}{dT} + s_{\rm counter}^{\rm o} \right) \f$
+ * - @f$ h_{\rm tab} @f$ = @f$ F\left(-E_{\rm eq}\left(x,T^{\rm o} \right) + T^{\rm o} \frac{dE_{\rm eq}\left(x,T^{\rm o} \right)}{dT}\right) @f$
+ * - @f$ s_{\rm tab} @f$ = @f$ F \left(\frac{dE_{\rm eq}\left(x,T^{\rm o} \right)}{dT} + s_{\rm counter}^{\rm o} \right) @f$
*
- * where \f$ E_{\rm eq}\left(x,T^{\rm o} \right) \f$ and \f$ \frac{dE_{\rm eq}\left(x,T^{\rm o} \right)}{dT} \f$
+ * where @f$ E_{\rm eq}\left(x,T^{\rm o} \right) @f$ and @f$ \frac{dE_{\rm eq}\left(x,T^{\rm o} \right)}{dT} @f$
* are the experimentally-measured open circuit voltage and derivative in
* open circuit voltage with respect to temperature, respectively, both
- * measured as a mole fraction of \f$ x \f$ for the tabulated species and at a
- * temperature of \f$ T^{\rm o} \f$. The arrays \f$ h_{\rm tab}\f$ and
- * \f$ s_{\rm tab}\f$ must be the same length as the \f$ x_{\rm tab}\f$ array.
+ * measured as a mole fraction of @f$ x @f$ for the tabulated species and at a
+ * temperature of @f$ T^{\rm o} @f$. The arrays @f$ h_{\rm tab} @f$ and
+ * @f$ s_{\rm tab} @f$ must be the same length as the @f$ x_{\rm tab} @f$ array.
*
* From these tabulated inputs, the standard state thermodynamic properties
- * for the tabulated species (subscript \f$ k\f$, tab) are calculated as:
+ * for the tabulated species (subscript @f$ k @f$, tab) are calculated as:
*
- * \f[
+ * @f[
* h^{\rm o}_{k,\,{\rm tab}} = h_{\rm tab}
- * \f]
- * \f[
+ * @f]
+ * @f[
* s^{\rm o}_{k,\,{\rm tab}} = s_{\rm tab} + R\ln\frac{x_{k,\,{\rm tab}}}{1-x_{k,\,{\rm tab}}} + \frac{R}{F} \ln\left(\frac{c^{\rm o}_{k,\,{\rm ref}}}{c^{\rm o}_{k,\,{\rm tab}}}\right)
- * \f]
+ * @f]
*
* Now, whenever the composition has changed, the lookup/interpolation of the
* tabulated thermo data is performed to update the standard state
* thermodynamic data for the tabulated species.
*
* Furthermore, there is an optional feature to include non-ideal effects regarding
- * partial molar volumes of the species, \f$ \bar V_k\f$. Being derived from
+ * partial molar volumes of the species, @f$ \bar V_k @f$. Being derived from
* IdealSolidSolnPhase, the default assumption in BinarySolutionTabulatedThermo
* is that the species comprising the binary solution have constant partial molar
* volumes equal to their pure species molar volumes. However, this assumption only
@@ -121,19 +121,19 @@ namespace Cantera
* (XRD) measurements of the unit cell volume. Therefore, the user can provide an optional fourth vector of
* tabulated molar volume data with the same size as the other tabulated data:
*
- * - \f$ V_{\mathrm{m,tab}}\f$ = array of the molar volume of the binary solution phase at
+ * - @f$ V_{\mathrm{m,tab}} @f$ = array of the molar volume of the binary solution phase at
* the tabulated mole fractions.
*
- * The partial molar volumes \f$ \bar V_1\f$ of the tabulated species and
- * \f$ \bar V_2\f$ of the 'reference' species, respectively, can then be derived from
+ * The partial molar volumes @f$ \bar V_1 @f$ of the tabulated species and
+ * @f$ \bar V_2 @f$ of the 'reference' species, respectively, can then be derived from
* the provided molar volume:
*
- * \f[
+ * @f[
* \bar V_1 = V_{\mathrm{m,tab}} + \left(1-x_{\mathrm {tab}}\right) \cdot
* \frac{\mathrm{d}V_{\mathrm{m,tab}}}{\mathrm{d}x_{\mathrm {tab}}} \\
* \bar V_2 = V_{\mathrm{m,tab}} - x_{\mathrm {tab}} \cdot
* \frac{\mathrm{d}V_{\mathrm{m,tab}}}{\mathrm{d}x_{\mathrm {tab}}}
- * \f]
+ * @f]
*
* The derivation is implemented using forward differences at the boundaries of the
* input vector and a central differencing scheme at interior points. As the
@@ -144,12 +144,12 @@ namespace Cantera
* The calculation of the mass density incorporates the non-ideal behavior by using
* the provided molar volume in the equation:
*
- * \f[
+ * @f[
* \rho = \frac{\sum_k{x_k W_k}}{V_\mathrm{m}}
- * \f]
+ * @f]
*
- * where \f$x_k\f$ are the mole fractions, \f$W_k\f$ are the molecular weights, and
- * \f$V_\mathrm{m}\f$ is the molar volume interpolated from \f$V_{\mathrm{m,tab}}\f$.
+ * where @f$ x_k @f$ are the mole fractions, @f$ W_k @f$ are the molecular weights, and
+ * @f$ V_\mathrm{m} @f$ is the molar volume interpolated from @f$ V_{\mathrm{m,tab}} @f$.
*
* If the optional fourth input vector is not specified, the molar volume is calculated
* by using the pure species molar volumes, as in IdealSolidSolnPhase. Regardless if the
@@ -199,12 +199,12 @@ class BinarySolutionTabulatedThermo : public IdealSolidSolnPhase
*
* The formula for this is
*
- * \f[
+ * @f[
* \rho = \frac{\sum_k{X_k W_k}}{V_\mathrm{m}}
- * \f]
+ * @f]
*
- * where \f$X_k\f$ are the mole fractions, \f$W_k\f$ are the molecular weights, and
- * \f$V_\mathrm{m}\f$ is the molar volume interpolated from \f$V_{\mathrm{m,tab}}\f$.
+ * where @f$ X_k @f$ are the mole fractions, @f$ W_k @f$ are the molecular weights, and
+ * @f$ V_\mathrm{m} @f$ is the molar volume interpolated from @f$ V_{\mathrm{m,tab}} @f$.
*/
virtual void calcDensity();
diff --git a/include/cantera/thermo/ConstCpPoly.h b/include/cantera/thermo/ConstCpPoly.h
index e4793b8c97..7c0459d236 100644
--- a/include/cantera/thermo/ConstCpPoly.h
+++ b/include/cantera/thermo/ConstCpPoly.h
@@ -23,21 +23,21 @@ namespace Cantera
* following relations are used to complete the specification of the
* thermodynamic functions for the species.
*
- * \f[
+ * @f[
* \frac{c_p(T)}{R} = Cp0\_R
- * \f]
- * \f[
+ * @f]
+ * @f[
* \frac{h^0(T)}{RT} = \frac{1}{T} * (h0\_R + (T - T_0) * Cp0\_R)
- * \f]
- * \f[
+ * @f]
+ * @f[
* \frac{s^0(T)}{R} = (s0\_R + (log(T) - log(T_0)) * Cp0\_R)
- * \f]
+ * @f]
*
* This parameterization takes 4 input values. These are:
- * - c[0] = \f$ T_0 \f$(Kelvin)
- * - c[1] = \f$ H_k^o(T_0, p_{ref}) \f$ (J/kmol)
- * - c[2] = \f$ S_k^o(T_0, p_{ref}) \f$ (J/kmol K)
- * - c[3] = \f$ {Cp}_k^o(T_0, p_{ref}) \f$ (J(kmol K)
+ * - c[0] = @f$ T_0 @f$ (Kelvin)
+ * - c[1] = @f$ H_k^o(T_0, p_{ref}) @f$ (J/kmol)
+ * - c[2] = @f$ S_k^o(T_0, p_{ref}) @f$ (J/kmol K)
+ * - c[3] = @f$ {Cp}_k^o(T_0, p_{ref}) @f$ (J(kmol K)
*
* @ingroup spthermo
*/
@@ -54,18 +54,18 @@ class ConstCpPoly: public SpeciesThermoInterpType
* @param coeffs Vector of coefficients used to set the parameters for
* the standard state for species n. There are 4
* coefficients for the ConstCpPoly parameterization.
- * - c[0] = \f$ T_0 \f$(Kelvin)
- * - c[1] = \f$ H_k^o(T_0, p_{ref}) \f$ (J/kmol)
- * - c[2] = \f$ S_k^o(T_0, p_{ref}) \f$ (J/kmol K)
- * - c[3] = \f$ {Cp}_k^o(T_0, p_{ref}) \f$ (J(kmol K)
+ * - c[0] = @f$ T_0 @f$ (Kelvin)
+ * - c[1] = @f$ H_k^o(T_0, p_{ref}) @f$ (J/kmol)
+ * - c[2] = @f$ S_k^o(T_0, p_{ref}) @f$ (J/kmol K)
+ * - c[3] = @f$ {Cp}_k^o(T_0, p_{ref}) @f$ (J(kmol K)
*/
ConstCpPoly(double tlow, double thigh, double pref, const double* coeffs);
/*!
- * @param t0 \f$ T_0 \f$ [K]
- * @param h0 \f$ h_k^o(T_0, p_{ref}) \f$ [J/kmol]
- * @param s0 \f$ s_k^o(T_0, p_{ref}) \f$ [J/kmol/K]
- * @param cp0 \f$ c_{p,k}^o(T_0, p_{ref}) \f$ [J/kmol/K]
+ * @param t0 @f$ T_0 @f$ [K]
+ * @param h0 @f$ h_k^o(T_0, p_{ref}) @f$ [J/kmol]
+ * @param s0 @f$ s_k^o(T_0, p_{ref}) @f$ [J/kmol/K]
+ * @param cp0 @f$ c_{p,k}^o(T_0, p_{ref}) @f$ [J/kmol/K]
*/
void setParameters(double t0, double h0, double s0, double cp0);
diff --git a/include/cantera/thermo/CoverageDependentSurfPhase.h b/include/cantera/thermo/CoverageDependentSurfPhase.h
index 5426dc9cd5..423c977259 100644
--- a/include/cantera/thermo/CoverageDependentSurfPhase.h
+++ b/include/cantera/thermo/CoverageDependentSurfPhase.h
@@ -35,32 +35,32 @@ namespace Cantera
* to cause lateral interaction. Therefore, it is logical to set ideal surface
* species properties as the low-coverage limit and add lateral interaction terms
* to them as excess properties. Accordingly, standard state coverage-dependent
- * enthalpy, entropy, and heat capacity of a surface species \f$ k \f$ can be
+ * enthalpy, entropy, and heat capacity of a surface species @f$ k @f$ can be
* formulated as follows.
*
- * \f[
+ * @f[
* h_k^o(T,\theta)
* = \underbrace{h_k^{o,ideal}(T)
* + \int_{298}^{T}c_{p,k}^{o,ideal}(T)dT}_{\text{low-coverage limit}}
* + \underbrace{h_k^{o,cov}(T,\theta)
* + \int_{298}^{T}c_{p,k}^{o,cov}(T,\theta)dT}_{\text{coverage dependence}}
*
- * \f]
+ * @f]
*
- * \f[
+ * @f[
* s_k^o(T,\theta)
* = \underbrace{s_k^{o,ideal}(T)
* + \int_{298}^{T}\frac{c_{p,k}^{o,ideal}(T)}{T}dT}_{\text{low-coverage limit}}
* + \underbrace{s_k^{o,cov}(T,\theta)
* + \int_{298}^{T}\frac{c_{p,k}^{o,cov}(T,\theta)}{T}dT}_{\text{coverage
* dependence}}
- * \f]
+ * @f]
*
- * \f[
+ * @f[
* c_{p,k}^o(T,\theta)
* = \underbrace{c_{p,k}^{o,ideal}(T)}_{\text{low-coverage limit}}
* + \underbrace{c_{p,k}^{o,cov}(T,\theta)}_{\text{coverage dependence}}
- * \f]
+ * @f]
*
* ## Mathematical Models for Coverage-dependent Correction Terms
*
@@ -68,27 +68,27 @@ namespace Cantera
* with one of the four algebraic models: linear dependecy model, polynomial
* dependency model, piecewise-linear, and interpolative dependency model.
* In the dependency model equations, a coverage-dependent correction term is denoted
- * by \f$ f^{cov} \f$ where \f$ f \f$ can be either enthalpy (\f$ h^{cov} \f$) or
- * entropy (\f$ s^{cov} \f$). Because lateral interaction can compose of both
- * self- and cross- interactions, the total correction term of species \f$ k \f$
- * is a sum of all interacting species \f$ j \f$ which can include itself.
- * Coefficients \f$ c^{(1)}_{k,j}-c^{(6)}_{k,j} \f$ are user-provided parameters
+ * by @f$ f^{cov} @f$ where @f$ f @f$ can be either enthalpy (@f$ h^{cov} @f$) or
+ * entropy (@f$ s^{cov} @f$). Because lateral interaction can compose of both
+ * self- and cross- interactions, the total correction term of species @f$ k @f$
+ * is a sum of all interacting species @f$ j @f$ which can include itself.
+ * Coefficients @f$ c^{(1)}_{k,j}-c^{(6)}_{k,j} @f$ are user-provided parameters
* that can be given in a input yaml.
*
* Linear dependency model:
- * \f[
+ * @f[
* f^{cov}_k(\theta) = \sum_j c^{(1)}_{k,j} \theta_j
- * \f]
+ * @f]
*
* Polynomial dependency model:
- * \f[
+ * @f[
* f^{cov}_k(\theta) =
* \sum_j \left[c^{(1)}_{k,j}\theta_j + c^{(2)}_{k,j}\theta_j^2
* + c^{(3)}_{k,j}\theta_j^3 + c^{(4)}_{k,j}\theta_j^4\right]
- * \f]
+ * @f]
*
* Piecewise-linear dependency model:
- * \f[
+ * @f[
* f^{cov}_k(\theta) = \sum_j \left\{
* \begin{array}{ll}
* c^{(5)}_{k,j}\theta_j & \text{, } \theta_j \leq \theta^\text{change}_{k,j} \\
@@ -97,31 +97,31 @@ namespace Cantera
* & \text{, } \theta_j > \theta^\text{change}_{k,j} \\
* \end{array}
* \right.
- * \f]
+ * @f]
*
* Interpolative dependency model:
- * \f[
+ * @f[
* f^{cov}_k(\theta) =
* \sum_j \left[\frac{f^{cov}_k(\theta^{higher}_j) - f^{cov}_k(\theta^{lower}_j)}
* {\theta^{higher}_j - \theta^{lower}_j}(\theta_j - \theta^{lower}_j)
* + f^{cov}_k (\theta^{lower}_j)\right] \\
* \text{where } \theta^{lower}_j \leq \theta_j < \theta^{higher}_j
- * \f]
+ * @f]
*
* Coverage-dependent heat capacity is calculated using an equation with a
* quadratic dependence on coverages and a logarithmic dependence on temperature.
* Temperature is nondimensionalized with a reference temperature of 1 K.
- * The coverage-dependent heat capacity of species \f$ k \f$ is a sum of
- * all quantities dependent on coverage of species \f$ j \f$. Coefficients
- * \f$ c^{(a)}_{k,j} \text{ and } c^{(b)}_{k,j} \f$ are user-provided parameters
+ * The coverage-dependent heat capacity of species @f$ k @f$ is a sum of
+ * all quantities dependent on coverage of species @f$ j @f$. Coefficients
+ * @f$ c^{(a)}_{k,j} \text{ and } c^{(b)}_{k,j} @f$ are user-provided parameters
* that can be given in an input yaml.
*
* Coverage-dependent heat capacity model:
- * \f[
+ * @f[
* c^{cov}_{p,k}(\theta) =
* \sum_j \left(c^{(a)}_{k,j} \ln\left(\frac{T}{1\text{ K}}\right)
* + c^{(b)}_{k,j}\right) \theta_j^2
- * \f]
+ * @f]
*/
class CoverageDependentSurfPhase : public SurfPhase
{
@@ -174,12 +174,12 @@ class CoverageDependentSurfPhase : public SurfPhase
size_t j;
//! array of polynomial coefficients describing coverage-dependent enthalpy
//! [J/kmol] in order of 1st-order, 2nd-order, 3rd-order, and 4th-order
- //! coefficients (\f$ c^{(1)}, c^{(2)}, c^{(3)}, \text{ and } c^{(4)} \f$
+ //! coefficients (@f$ c^{(1)}, c^{(2)}, c^{(3)}, \text{ and } c^{(4)} @f$
//! in the linear or the polynomial dependency model)
vector_fp enthalpy_coeffs;
//! array of polynomial coefficients describing coverage-dependent entropy
//! [J/kmol/K] in order of 1st-order, 2nd-order, 3rd-order, and 4th-order
- //! coefficients (\f$ c^{(1)}, c^{(2)}, c^{(3)}, \text{ and } c^{(4)} \f$
+ //! coefficients (@f$ c^{(1)}, c^{(2)}, c^{(3)}, \text{ and } c^{(4)} @f$
//! in the linear or the polynomial dependency model)
vector_fp entropy_coeffs;
//! boolean indicating whether the dependency is linear
@@ -293,10 +293,10 @@ class CoverageDependentSurfPhase : public SurfPhase
//! index of a species whose coverage affects heat capacity of
//! a target species
size_t j;
- //! coefficient \f$ c^{(a)} \f$ [J/kmol/K] in the coverage-dependent
+ //! coefficient @f$ c^{(a)} @f$ [J/kmol/K] in the coverage-dependent
//! heat capacity model
double coeff_a;
- //! coefficient \f$ c^{(b)} \f$ [J/kmol/K] in the coverage-dependent
+ //! coefficient @f$ c^{(b)} @f$ [J/kmol/K] in the coverage-dependent
//! heat capacity model
double coeff_b;
};
@@ -328,8 +328,8 @@ class CoverageDependentSurfPhase : public SurfPhase
AnyMap& speciesNode) const;
//! @name Methods calculating reference state thermodynamic properties
- //! Reference state properties are evaluated at \f$ T \text{ and }
- //! \theta^{ref} \f$. With coverage fixed at a reference value,
+ //! Reference state properties are evaluated at @f$ T \text{ and }
+ //! \theta^{ref} @f$. With coverage fixed at a reference value,
//! reference state properties are effectively only dependent on temperature.
//! @{
virtual void getEnthalpy_RT_ref(double* hrt) const;
@@ -339,131 +339,131 @@ class CoverageDependentSurfPhase : public SurfPhase
//! @}
//! @name Methods calculating standard state thermodynamic properties
- //! Standard state properties are evaluated at \f$ T \text{ and } \theta \f$,
+ //! Standard state properties are evaluated at @f$ T \text{ and } \theta @f$,
//! and thus are dependent both on temperature and coverage.
//! @{
//! Get the nondimensionalized standard state enthalpy vector.
/*!
- * \f[
+ * @f[
* \frac{h^o_k(T,\theta)}{RT}
* = \frac{h^{ref}_k(T) + h^{cov}_k(T,\theta)
* + \int_{298}^{T} c^{cov}_{p,k}(T,\theta)dT}{RT}
- * \f]
+ * @f]
*/
virtual void getEnthalpy_RT(double* hrt) const;
//! Get the nondimensionalized standard state entropy vector.
/*!
- * \f[
+ * @f[
* \frac{s^o_k(T,\theta)}{R}
* = \frac{s^{ref}_k(T) + s^{cov}_k(T,\theta)
* + \int_{298}^{T}\frac{c^{cov}_{p,k}(T,\theta)}{T}dT}{R}
* - \ln\left(\frac{1}{\theta_{ref}}\right)
- * \f]
+ * @f]
*/
virtual void getEntropy_R(double* sr) const;
//! Get the nondimensionalized standard state heat capacity vector.
/*!
- * \f[
+ * @f[
* \frac{c^o_{p,k}(T,\theta)}{RT}
* = \frac{c^{ref}_{p,k}(T) + c^{cov}_{p,k}(T,\theta)}{RT}
- * \f]
+ * @f]
*/
virtual void getCp_R(double* cpr) const;
//! Get the nondimensionalized standard state gibbs free energy vector.
/*!
- * \f[
+ * @f[
* \frac{g^o_k(T,\theta)}{RT}
* = \frac{h^o_k(T,\theta)}{RT} + \frac{s^o_k(T,\theta)}{R}
- * \f]
+ * @f]
*/
virtual void getGibbs_RT(double* grt) const;
//! Get the standard state gibbs free energy vector. Units: J/kmol.
/*!
- * \f[
+ * @f[
* g^o_k(T,\theta) = h^o_k(T,\theta) + Ts^o_k(T,\theta)
- * \f]
+ * @f]
*/
virtual void getPureGibbs(double* g) const;
//! Get the standard state chemical potential vector. Units: J/kmol.
/*!
- * \f[
+ * @f[
* \mu^o_k(T,\theta) = h^o_k(T,\theta) + Ts^o_k(T,\theta)
- * \f]
+ * @f]
*/
virtual void getStandardChemPotentials(double* mu0) const;
//! @}
//! @name Methods calculating partial molar thermodynamic properties
- //! Partial molar properties are evaluated at \f$ T \text{ and } \theta \f$,
+ //! Partial molar properties are evaluated at @f$ T \text{ and } \theta @f$,
//! and thus are dependent both on temperature and coverage.
//! @{
//! Get the partial molar enthalpy vector. Units: J/kmol.
/*!
- * \f[
+ * @f[
* \tilde{h}_k(T,\theta) = h^o_k(T,\theta)
- * \f]
+ * @f]
*/
virtual void getPartialMolarEnthalpies(double* hbar) const;
//! Get the partial molar entropy vector. Units: J/kmol/K.
/*!
- * \f[
+ * @f[
* \tilde{s}_k(T,\theta) = s^o_k(T,\theta) - R\ln(\theta_k)
- * \f]
+ * @f]
*/
virtual void getPartialMolarEntropies(double* sbar) const;
//! Get the partial molar heat capacity vector. Units: J/kmol/K.
/*!
- * \f[
+ * @f[
* \tilde{c}_{p,k}(T,\theta) = c^o_{p,k}(T,\theta)
- * \f]
+ * @f]
*/
virtual void getPartialMolarCp(double* cpbar) const;
//! Get the chemical potential vector. Units: J/kmol.
/*!
- * \f[
+ * @f[
* \mu_k(T,\theta) = \mu^o_k(T,\theta) + RT\ln(\theta_k)
- * \f]
+ * @f]
*/
virtual void getChemPotentials(double* mu) const;
//! @}
//! @name Methods calculating Phase thermodynamic properties
- //! Phase properties are evaluated at \f$ T \text{ and } \theta \f$,
+ //! Phase properties are evaluated at @f$ T \text{ and } \theta @f$,
//! and thus are dependent both on temperature and coverage.
//! @{
//! Return the solution's molar enthalpy. Units: J/kmol
/*!
- * \f[
+ * @f[
* \hat h(T,\theta) = \sum_k \theta_k \tilde{h}_k(T,\theta)
- * \f]
+ * @f]
*/
virtual double enthalpy_mole() const;
//! Return the solution's molar entropy. Units: J/kmol/K
/*!
- * \f[
+ * @f[
* \hat s(T,\theta) = \sum_k \theta_k \tilde{s}_k(T,\theta)
- * \f]
+ * @f]
*/
virtual double entropy_mole() const;
//! Return the solution's molar heat capacity. Units: J/kmol/K
/*!
- * \f[
+ * @f[
* \hat{c_p}(T,\theta) = \sum_k \theta_k \tilde{c_p}_k(T,\theta)
- * \f]
+ * @f]
*/
virtual double cp_mole() const;
//! @}
diff --git a/include/cantera/thermo/DebyeHuckel.h b/include/cantera/thermo/DebyeHuckel.h
index 110a0b9a19..05ade683d2 100644
--- a/include/cantera/thermo/DebyeHuckel.h
+++ b/include/cantera/thermo/DebyeHuckel.h
@@ -54,9 +54,9 @@ class PDSS_Water;
* ## Specification of Species Standard State Properties
*
* The standard states are on the unit molality basis. Therefore, in the
- * documentation below, the normal \f$ o \f$ superscript is replaced with the
- * \f$ \triangle \f$ symbol. The reference state symbol is now
- * \f$ \triangle, ref \f$.
+ * documentation below, the normal @f$ o @f$ superscript is replaced with the
+ * @f$ \triangle @f$ symbol. The reference state symbol is now
+ * @f$ \triangle, ref @f$.
*
* It is assumed that the reference state thermodynamics may be obtained by a
* pointer to a populated species thermodynamic property manager class (see
@@ -65,26 +65,26 @@ class PDSS_Water;
*
* For an incompressible, stoichiometric substance, the molar internal energy is
* independent of pressure. Since the thermodynamic properties are specified by
- * giving the standard-state enthalpy, the term \f$ P_0 \hat v\f$ is subtracted
+ * giving the standard-state enthalpy, the term @f$ P_0 \hat v @f$ is subtracted
* from the specified molar enthalpy to compute the molar internal energy. The
* entropy is assumed to be independent of the pressure.
*
* The enthalpy function is given by the following relation.
*
- * \f[
+ * @f[
* h^\triangle_k(T,P) = h^{\triangle,ref}_k(T)
* + \tilde v \left( P - P_{ref} \right)
- * \f]
+ * @f]
*
* For an incompressible, stoichiometric substance, the molar internal energy is
* independent of pressure. Since the thermodynamic properties are specified by
- * giving the standard-state enthalpy, the term \f$ P_{ref} \tilde v\f$ is
+ * giving the standard-state enthalpy, the term @f$ P_{ref} \tilde v @f$ is
* subtracted from the specified reference molar enthalpy to compute the molar
* internal energy.
*
- * \f[
+ * @f[
* u^\triangle_k(T,P) = h^{\triangle,ref}_k(T) - P_{ref} \tilde v
- * \f]
+ * @f]
*
* The standard state heat capacity and entropy are independent of pressure. The
* standard state Gibbs free energy is obtained from the enthalpy and entropy
@@ -99,18 +99,18 @@ class PDSS_Water;
*
* ## Specification of Solution Thermodynamic Properties
*
- * Chemical potentials of the solutes, \f$ \mu_k \f$, and the solvent, \f$ \mu_o
- * \f$, which are based on the molality form, have the following general format:
+ * Chemical potentials of the solutes, @f$ \mu_k @f$, and the solvent, @f$ \mu_o
+ * @f$, which are based on the molality form, have the following general format:
*
- * \f[
+ * @f[
* \mu_k = \mu^{\triangle}_k(T,P) + R T ln(\gamma_k^{\triangle} \frac{m_k}{m^\triangle})
- * \f]
- * \f[
+ * @f]
+ * @f[
* \mu_o = \mu^o_o(T,P) + RT ln(a_o)
- * \f]
+ * @f]
*
- * where \f$ \gamma_k^{\triangle} \f$ is the molality based activity coefficient
- * for species \f$k\f$.
+ * where @f$ \gamma_k^{\triangle} @f$ is the molality based activity coefficient
+ * for species @f$ k @f$.
*
* Individual activity coefficients of ions can not be independently measured.
* Instead, only binary pairs forming electroneutral solutions can be measured.
@@ -118,13 +118,13 @@ class PDSS_Water;
* ### Ionic Strength
*
* Most of the parameterizations within the model use the ionic strength as a
- * key variable. The ionic strength, \f$ I\f$ is defined as follows
+ * key variable. The ionic strength, @f$ I @f$ is defined as follows
*
- * \f[
+ * @f[
* I = \frac{1}{2} \sum_k{m_k z_k^2}
- * \f]
+ * @f]
*
- * \f$ m_k \f$ is the molality of the kth species. \f$ z_k \f$ is the charge of
+ * @f$ m_k @f$ is the molality of the kth species. @f$ z_k @f$ is the charge of
* the kth species. Note, the ionic strength is a defined units quantity. The
* molality has defined units of gmol kg-1, and therefore the ionic strength has
* units of sqrt( gmol kg-1).
@@ -139,38 +139,38 @@ class PDSS_Water;
* the ionic strength, then we will want to consider the associated weak acid as
* in effect being fully dissociated, when we calculate an effective value for
* the ionic strength. We will call this calculated value, the stoichiometric
- * ionic strength, \f$ I_s \f$, putting a subscript s to denote it from the more
- * straightforward calculation of \f$ I \f$.
+ * ionic strength, @f$ I_s @f$, putting a subscript s to denote it from the more
+ * straightforward calculation of @f$ I @f$.
*
- * \f[
+ * @f[
* I_s = \frac{1}{2} \sum_k{m_k^s z_k^2}
- * \f]
+ * @f]
*
- * Here, \f$ m_k^s \f$ is the value of the molalities calculated assuming that
+ * Here, @f$ m_k^s @f$ is the value of the molalities calculated assuming that
* all weak acid-base pairs are in their fully dissociated states. This
* calculation may be simplified by considering that the weakly associated acid
* may be made up of two charged species, k1 and k2, each with their own
* charges, obeying the following relationship:
*
- * \f[
+ * @f[
* z_k = z_{k1} + z_{k2}
- * \f]
- * Then, we may only need to specify one charge value, say, \f$ z_{k1}\f$, the
+ * @f]
+ * Then, we may only need to specify one charge value, say, @f$ z_{k1} @f$, the
* cation charge number, in order to get both numbers, since we have already
- * specified \f$ z_k \f$ in the definition of original species. Then, the
+ * specified @f$ z_k @f$ in the definition of original species. Then, the
* stoichiometric ionic strength may be calculated via the following formula.
*
- * \f[
+ * @f[
* I_s = \frac{1}{2} \left(\sum_{k,ions}{m_k z_k^2}+
* \sum_{k,weak_assoc}(m_k z_{k1}^2 + m_k z_{k2}^2) \right)
- * \f]
+ * @f]
*
* The specification of which species are weakly associated acids is made in YAML
- * input files by specifying the corresponding charge \f$k1\f$ as the `weak-acid-charge`
+ * input files by specifying the corresponding charge @f$ k1 @f$ as the `weak-acid-charge`
* parameter of the `Debye-Huckel` block in the corresponding species entry.
*
* Because we need the concept of a weakly associated acid in order to calculate
- * \f$ I_s \f$ we need to catalog all species in the phase. This is done using
+ * @f$ I_s @f$ we need to catalog all species in the phase. This is done using
* the following categories:
*
* - `cEST_solvent` Solvent species (neutral)
@@ -208,20 +208,20 @@ class PDSS_Water;
* DHFORM_DILUTE_LIMIT = 0
*
* This form assumes a dilute limit to DH, and is mainly for informational purposes:
- * \f[
+ * @f[
* \ln(\gamma_k^\triangle) = - z_k^2 A_{Debye} \sqrt{I}
- * \f]
- * where \f$ I\f$ is the ionic strength
- * \f[
+ * @f]
+ * where @f$ I @f$ is the ionic strength
+ * @f[
* I = \frac{1}{2} \sum_k{m_k z_k^2}
- * \f]
+ * @f]
*
- * The activity for the solvent water,\f$ a_o \f$, is not independent and must
+ * The activity for the solvent water,@f$ a_o @f$, is not independent and must
* be determined from the Gibbs-Duhem relation.
*
- * \f[
+ * @f[
* \ln(a_o) = \frac{X_o - 1.0}{X_o} + \frac{ 2 A_{Debye} \tilde{M}_o}{3} (I)^{3/2}
- * \f]
+ * @f]
*
* ### Bdot Formulation
*
@@ -229,28 +229,28 @@ class PDSS_Water;
*
* This form assumes Bethke's format for the Debye Huckel activity coefficient:
*
- * \f[
+ * @f[
* \ln(\gamma_k^\triangle) = -z_k^2 \frac{A_{Debye} \sqrt{I}}{ 1 + B_{Debye} a_k \sqrt{I}}
* + \log(10) B^{dot}_k I
- * \f]
+ * @f]
*
- * Note, this particular form where \f$ a_k \f$ can differ in multielectrolyte
+ * Note, this particular form where @f$ a_k @f$ can differ in multielectrolyte
* solutions has problems with respect to a Gibbs-Duhem analysis. However, we
* include it here because there is a lot of data fit to it.
*
- * The activity for the solvent water,\f$ a_o \f$, is not independent and must
+ * The activity for the solvent water,@f$ a_o @f$, is not independent and must
* be determined from the Gibbs-Duhem relation. Here, we use:
*
- * \f[
+ * @f[
* \ln(a_o) = \frac{X_o - 1.0}{X_o}
* + \frac{ 2 A_{Debye} \tilde{M}_o}{3} (I)^{1/2}
* \left[ \sum_k{\frac{1}{2} m_k z_k^2 \sigma( B_{Debye} a_k \sqrt{I} ) } \right]
* - \frac{\log(10)}{2} \tilde{M}_o I \sum_k{ B^{dot}_k m_k}
- * \f]
+ * @f]
* where
- * \f[
+ * @f[
* \sigma (y) = \frac{3}{y^3} \left[ (1+y) - 2 \ln(1 + y) - \frac{1}{1+y} \right]
- * \f]
+ * @f]
*
* Additionally, Helgeson's formulation for the water activity is offered as an
* alternative.
@@ -261,18 +261,18 @@ class PDSS_Water;
*
* This form assumes Bethke's format for the Debye-Huckel activity coefficient
*
- * \f[
+ * @f[
* \ln(\gamma_k^\triangle) = -z_k^2 \frac{A_{Debye} \sqrt{I}}{ 1 + B_{Debye} a \sqrt{I}}
* + \log(10) B^{dot}_k I
- * \f]
+ * @f]
*
* The value of a is determined at the beginning of the calculation, and not changed.
*
- * \f[
+ * @f[
* \ln(a_o) = \frac{X_o - 1.0}{X_o}
* + \frac{ 2 A_{Debye} \tilde{M}_o}{3} (I)^{3/2} \sigma( B_{Debye} a \sqrt{I} )
* - \frac{\log(10)}{2} \tilde{M}_o I \sum_k{ B^{dot}_k m_k}
- * \f]
+ * @f]
*
* ### Beta_IJ formulation
*
@@ -283,26 +283,26 @@ class PDSS_Water;
* beginning of more complex treatments for stronger electrolytes, fom Pitzer
* and from Harvey, Moller, and Weire.
*
- * \f[
+ * @f[
* \ln(\gamma_k^\triangle) = -z_k^2 \frac{A_{Debye} \sqrt{I}}{ 1 + B_{Debye} a \sqrt{I}}
* + 2 \sum_j \beta_{j,k} m_j
- * \f]
+ * @f]
*
- * In the current treatment the binary interaction coefficients, \f$
- * \beta_{j,k}\f$, are independent of temperature and pressure.
+ * In the current treatment the binary interaction coefficients, @f$
+ * \beta_{j,k} @f$, are independent of temperature and pressure.
*
- * \f[
+ * @f[
* \ln(a_o) = \frac{X_o - 1.0}{X_o}
* + \frac{ 2 A_{Debye} \tilde{M}_o}{3} (I)^{3/2} \sigma( B_{Debye} a \sqrt{I} )
* - \tilde{M}_o \sum_j \sum_k \beta_{j,k} m_j m_k
- * \f]
+ * @f]
*
- * In this formulation the ionic radius, \f$ a \f$, is a constant, specified as part
+ * In this formulation the ionic radius, @f$ a @f$, is a constant, specified as part
* of the species definition.
*
- * The \f$ \beta_{j,k} \f$ parameters are binary interaction parameters. There are in
- * principle \f$ N (N-1) /2 \f$ different, symmetric interaction parameters,
- * where \f$ N \f$ are the number of solute species in the mechanism.
+ * The @f$ \beta_{j,k} @f$ parameters are binary interaction parameters. There are in
+ * principle @f$ N (N-1) /2 @f$ different, symmetric interaction parameters,
+ * where @f$ N @f$ are the number of solute species in the mechanism.
*
* ### Pitzer Beta_IJ formulation
*
@@ -313,54 +313,54 @@ class PDSS_Water;
* the formulations above in the dilute limit, where rigorous theory may be
* applied.
*
- * \f[
+ * @f[
* \ln(\gamma_k^\triangle) = -z_k^2 \frac{A_{Debye}}{3} \frac{\sqrt{I}}{ 1 + B_{Debye} a \sqrt{I}}
* -2 z_k^2 \frac{A_{Debye}}{3} \frac{\ln(1 + B_{Debye} a \sqrt{I})}{ B_{Debye} a}
* + 2 \sum_j \beta_{j,k} m_j
- * \f]
- * \f[
+ * @f]
+ * @f[
* \ln(a_o) = \frac{X_o - 1.0}{X_o}
* + \frac{ 2 A_{Debye} \tilde{M}_o}{3} \frac{(I)^{3/2} }{1 + B_{Debye} a \sqrt{I} }
* - \tilde{M}_o \sum_j \sum_k \beta_{j,k} m_j m_k
- * \f]
+ * @f]
*
* ### Specification of the Debye Huckel Constants
*
- * In the equations above, the formulas for \f$ A_{Debye} \f$ and \f$
- * B_{Debye} \f$ are needed. The DebyeHuckel object uses two methods for
- * specifying these quantities. The default method is to assume that \f$
- * A_{Debye} \f$ is a constant, given in the initialization process, and stored
+ * In the equations above, the formulas for @f$ A_{Debye} @f$ and @f$
+ * B_{Debye} @f$ are needed. The DebyeHuckel object uses two methods for
+ * specifying these quantities. The default method is to assume that @f$
+ * A_{Debye} @f$ is a constant, given in the initialization process, and stored
* in the member double, m_A_Debye. Optionally, a full water treatment may be
- * employed that makes \f$ A_{Debye} \f$ a full function of *T* and *P*.
+ * employed that makes @f$ A_{Debye} @f$ a full function of *T* and *P*.
*
- * \f[
+ * @f[
* A_{Debye} = \frac{F e B_{Debye}}{8 \pi \epsilon R T} {\left( C_o \tilde{M}_o \right)}^{1/2}
- * \f]
+ * @f]
* where
- * \f[
+ * @f[
* B_{Debye} = \frac{F} {{(\frac{\epsilon R T}{2})}^{1/2}}
- * \f]
+ * @f]
* Therefore:
- * \f[
+ * @f[
* A_{Debye} = \frac{1}{8 \pi}
* {\left(\frac{2 N_a \rho_o}{1000}\right)}^{1/2}
* {\left(\frac{N_a e^2}{\epsilon R T }\right)}^{3/2}
- * \f]
+ * @f]
* where
- * - \f$ N_a \f$ is Avogadro's number
- * - \f$ \rho_w \f$ is the density of water
- * - \f$ e \f$ is the electronic charge
- * - \f$ \epsilon = K \epsilon_o \f$ is the permittivity of water
- * - \f$ K \f$ is the dielectric constant of water
- * - \f$ \epsilon_o \f$ is the permittivity of free space
- * - \f$ \rho_o \f$ is the density of the solvent in its standard state.
+ * - @f$ N_a @f$ is Avogadro's number
+ * - @f$ \rho_w @f$ is the density of water
+ * - @f$ e @f$ is the electronic charge
+ * - @f$ \epsilon = K \epsilon_o @f$ is the permittivity of water
+ * - @f$ K @f$ is the dielectric constant of water
+ * - @f$ \epsilon_o @f$ is the permittivity of free space
+ * - @f$ \rho_o @f$ is the density of the solvent in its standard state.
*
* Nominal value at 298 K and 1 atm = 1.172576 (kg/gmol)^(1/2) based on:
- * - \f$ \epsilon / \epsilon_0 \f$ = 78.54 (water at 25C)
+ * - @f$ \epsilon / \epsilon_0 @f$ = 78.54 (water at 25C)
* - T = 298.15 K
* - B_Debye = 3.28640E9 (kg/gmol)^(1/2) / m
*
- * Currently, \f$ B_{Debye} \f$ is a constant in the model, specified either by
+ * Currently, @f$ B_{Debye} @f$ is a constant in the model, specified either by
* a default water value, or through the input file. This may have to be looked
* at, in the future.
*
@@ -376,40 +376,40 @@ class PDSS_Water;
*
* For example, a bulk-phase binary reaction between liquid species j and k,
* producing a new liquid species l would have the following equation for its
- * rate of progress variable, \f$ R^1 \f$, which has units of kmol m-3 s-1.
+ * rate of progress variable, @f$ R^1 @f$, which has units of kmol m-3 s-1.
*
- * \f[
+ * @f[
* R^1 = k^1 C_j^a C_k^a = k^1 (C_o a_j) (C_o a_k)
- * \f]
+ * @f]
* where
- * \f[
+ * @f[
* C_j^a = C_o a_j \quad and \quad C_k^a = C_o a_k
- * \f]
+ * @f]
*
- * \f$ C_j^a \f$ is the activity concentration of species j, and
- * \f$ C_k^a \f$ is the activity concentration of species k. \f$ C_o \f$
- * is the concentration of water at 298 K and 1 atm. \f$ a_j \f$ is the activity
+ * @f$ C_j^a @f$ is the activity concentration of species j, and
+ * @f$ C_k^a @f$ is the activity concentration of species k. @f$ C_o @f$
+ * is the concentration of water at 298 K and 1 atm. @f$ a_j @f$ is the activity
* of species j at the current temperature and pressure and concentration of the
- * liquid phase. \f$k^1 \f$ has units of m3 kmol-1 s-1.
+ * liquid phase. @f$ k^1 @f$ has units of m3 kmol-1 s-1.
*
* The reverse rate constant can then be obtained from the law of microscopic
* reversibility and the equilibrium expression for the system.
*
- * \f[
+ * @f[
* \frac{a_j a_k}{ a_l} = K^{o,1} = \exp(\frac{\mu^o_l - \mu^o_j - \mu^o_k}{R T} )
- * \f]
+ * @f]
*
- * \f$ K^{o,1} \f$ is the dimensionless form of the equilibrium constant.
+ * @f$ K^{o,1} @f$ is the dimensionless form of the equilibrium constant.
*
- * \f[
+ * @f[
* R^{-1} = k^{-1} C_l^a = k^{-1} (C_o a_l)
- * \f]
+ * @f]
* where
- * \f[
+ * @f[
* k^{-1} = k^1 K^{o,1} C_o
- * \f]
+ * @f]
*
- * \f$k^{-1} \f$ has units of s-1.
+ * @f$ k^{-1} @f$ has units of s-1.
*/
class DebyeHuckel : public MolalityVPSSTP
{
@@ -442,12 +442,12 @@ class DebyeHuckel : public MolalityVPSSTP
/**
* For an ideal, constant partial molar volume solution mixture with
* pure species phases which exhibit zero volume expansivity:
- * \f[
+ * @f[
* \hat s(T, P, X_k) = \sum_k X_k \hat s^0_k(T)
* - \hat R \sum_k X_k log(X_k)
- * \f]
+ * @f]
* The reference-state pure-species entropies
- * \f$ \hat s^0_k(T,p_{ref}) \f$ are computed by the
+ * @f$ \hat s^0_k(T,p_{ref}) @f$ are computed by the
* species thermodynamic
* property manager. The pure species entropies are independent of
* temperature since the volume expansivities are equal to zero.
@@ -475,9 +475,9 @@ class DebyeHuckel : public MolalityVPSSTP
//! @}
//! @name Activities, Standard States, and Activity Concentrations
//!
- //! The activity \f$a_k\f$ of a species in solution is related to the
- //! chemical potential by \f[ \mu_k = \mu_k^0(T) + \hat R T \log a_k. \f] The
- //! quantity \f$\mu_k^0(T,P)\f$ is the chemical potential at unit activity,
+ //! The activity @f$ a_k @f$ of a species in solution is related to the
+ //! chemical potential by @f[ \mu_k = \mu_k^0(T) + \hat R T \log a_k. @f] The
+ //! quantity @f$ \mu_k^0(T,P) @f$ is the chemical potential at unit activity,
//! which depends only on temperature and the pressure. Activity is assumed
//! to be molality-based here.
//! @{
@@ -486,7 +486,7 @@ class DebyeHuckel : public MolalityVPSSTP
//! Return the standard concentration for the kth species
/*!
- * The standard concentration \f$ C^0_k \f$ used to normalize the activity
+ * The standard concentration @f$ C^0_k @f$ used to normalize the activity
* (that is, generalized) concentration in kinetics calculations.
*
* For the time being, we will use the concentration of pure solvent for the
@@ -532,9 +532,9 @@ class DebyeHuckel : public MolalityVPSSTP
* This function returns a vector of chemical potentials of the species in
* solution.
*
- * \f[
+ * @f[
* \mu_k = \mu^{\triangle}_k(T,P) + R T ln(\gamma_k^{\triangle} m_k)
- * \f]
+ * @f]
*
* @param mu Output vector of species chemical
* potentials. Length: m_kk. Units: J/kmol
@@ -548,13 +548,13 @@ class DebyeHuckel : public MolalityVPSSTP
* standard state enthalpies modified by the derivative of the
* molality-based activity coefficient wrt temperature
*
- * \f[
+ * @f[
* \bar h_k(T,P) = h^{\triangle}_k(T,P) - R T^2 \frac{d \ln(\gamma_k^\triangle)}{dT}
- * \f]
+ * @f]
* The solvent partial molar enthalpy is equal to
- * \f[
+ * @f[
* \bar h_o(T,P) = h^{o}_o(T,P) - R T^2 \frac{d \ln(a_o}{dT}
- * \f]
+ * @f]
*
* The temperature dependence of the activity coefficients currently
* only occurs through the temperature dependence of the Debye constant.
@@ -569,22 +569,22 @@ class DebyeHuckel : public MolalityVPSSTP
/**
* Maxwell's equations provide an insight in how to calculate this
* (p.215 Smith and Van Ness)
- * \f[
+ * @f[
* \frac{d\mu_i}{dT} = -\bar{s}_i
- * \f]
+ * @f]
*
* For this phase, the partial molar entropies are equal to the SS species
* entropies plus the ideal solution contribution:
- * \f[
+ * @f[
* \bar s_k(T,P) = \hat s^0_k(T) - R log(M0 * molality[k])
- * \f]
- * \f[
+ * @f]
+ * @f[
* \bar s_{solvent}(T,P) = \hat s^0_{solvent}(T)
* - R ((xmolSolvent - 1.0) / xmolSolvent)
- * \f]
+ * @f]
*
- * The reference-state pure-species entropies,\f$ \hat s^0_k(T) \f$, at the
- * reference pressure, \f$ P_{ref} \f$, are computed by the species
+ * The reference-state pure-species entropies,@f$ \hat s^0_k(T) @f$, at the
+ * reference pressure, @f$ P_{ref} @f$, are computed by the species
* thermodynamic property manager. They are polynomial functions of
* temperature.
* @see MultiSpeciesThermo
@@ -632,35 +632,35 @@ class DebyeHuckel : public MolalityVPSSTP
* The default is to assume that it is constant, given in the
* initialization process, and stored in the member double, m_A_Debye.
* Optionally, a full water treatment may be employed that makes
- * \f$ A_{Debye} \f$ a full function of T and P.
+ * @f$ A_{Debye} @f$ a full function of T and P.
*
- * \f[
+ * @f[
* A_{Debye} = \frac{F e B_{Debye}}{8 \pi \epsilon R T} {\left( C_o \tilde{M}_o \right)}^{1/2}
- * \f]
+ * @f]
* where
- * \f[
+ * @f[
* B_{Debye} = \frac{F} {{(\frac{\epsilon R T}{2})}^{1/2}}
- * \f]
+ * @f]
* Therefore:
- * \f[
+ * @f[
* A_{Debye} = \frac{1}{8 \pi}
* {\left(\frac{2 N_a \rho_o}{1000}\right)}^{1/2}
* {\left(\frac{N_a e^2}{\epsilon R T }\right)}^{3/2}
- * \f]
+ * @f]
*
* where
* - Units = sqrt(kg/gmol)
- * - \f$ N_a \f$ is Avogadro's number
- * - \f$ \rho_w \f$ is the density of water
- * - \f$ e \f$ is the electronic charge
- * - \f$ \epsilon = K \epsilon_o \f$ is the permittivity of water
- * - \f$ K \f$ is the dielectric constant of water,
- * - \f$ \epsilon_o \f$ is the permittivity of free space.
- * - \f$ \rho_o \f$ is the density of the solvent in its standard state.
+ * - @f$ N_a @f$ is Avogadro's number
+ * - @f$ \rho_w @f$ is the density of water
+ * - @f$ e @f$ is the electronic charge
+ * - @f$ \epsilon = K \epsilon_o @f$ is the permittivity of water
+ * - @f$ K @f$ is the dielectric constant of water,
+ * - @f$ \epsilon_o @f$ is the permittivity of free space.
+ * - @f$ \rho_o @f$ is the density of the solvent in its standard state.
*
* Nominal value at 298 K and 1 atm = 1.172576 (kg/gmol)^(1/2)
* based on:
- * - \f$ \epsilon / \epsilon_0 \f$ = 78.54 (water at 25C)
+ * - @f$ \epsilon / \epsilon_0 @f$ = 78.54 (water at 25C)
* - T = 298.15 K
* - B_Debye = 3.28640E9 (kg/gmol)^(1/2)/m
*
@@ -676,7 +676,7 @@ class DebyeHuckel : public MolalityVPSSTP
//! respect to temperature.
/*!
* This is a function of temperature and pressure. See A_Debye_TP() for
- * a definition of \f$ A_{Debye} \f$.
+ * a definition of @f$ A_{Debye} @f$.
*
* Units = sqrt(kg/gmol) K-1
*
@@ -692,7 +692,7 @@ class DebyeHuckel : public MolalityVPSSTP
//! respect to temperature as a function of temperature and pressure.
/*!
* This is a function of temperature and pressure. See A_Debye_TP() for
- * a definition of \f$ A_{Debye} \f$.
+ * a definition of @f$ A_{Debye} @f$.
*
* Units = sqrt(kg/gmol) K-2
*
@@ -708,7 +708,7 @@ class DebyeHuckel : public MolalityVPSSTP
//! respect to pressure, as a function of temperature and pressure.
/*!
* This is a function of temperature and pressure. See A_Debye_TP() for
- * a definition of \f$ A_{Debye} \f$.
+ * a definition of @f$ A_{Debye} @f$.
*
* Units = sqrt(kg/gmol) Pa-1
*
diff --git a/include/cantera/thermo/GibbsExcessVPSSTP.h b/include/cantera/thermo/GibbsExcessVPSSTP.h
index e319be94e6..00a656d360 100644
--- a/include/cantera/thermo/GibbsExcessVPSSTP.h
+++ b/include/cantera/thermo/GibbsExcessVPSSTP.h
@@ -43,15 +43,15 @@ namespace Cantera
* All of the Excess Gibbs free energy formulations in this area employ
* symmetrical formulations.
*
- * Chemical potentials of species k, \f$ \mu_o \f$, has the following general
+ * Chemical potentials of species k, @f$ \mu_o @f$, has the following general
* format:
*
- * \f[
+ * @f[
* \mu_k = \mu^o_k(T,P) + R T ln( \gamma_k X_k )
- * \f]
+ * @f]
*
- * where \f$ \gamma_k^{\triangle} \f$ is a molar based activity coefficient for
- * species \f$k\f$.
+ * where @f$ \gamma_k^{\triangle} @f$ is a molar based activity coefficient for
+ * species @f$ k @f$.
*
* GibbsExcessVPSSTP contains an internal vector with the current mole fraction
* vector. That's one of its primary usages. In order to keep the mole fraction
@@ -100,12 +100,12 @@ class GibbsExcessVPSSTP : public VPStandardStateTP
*
* The formula for this is
*
- * \f[
+ * @f[
* \rho = \frac{\sum_k{X_k W_k}}{\sum_k{X_k V_k}}
- * \f]
+ * @f]
*
- * where \f$X_k\f$ are the mole fractions, \f$W_k\f$ are the molecular
- * weights, and \f$V_k\f$ are the pure species molar volumes.
+ * where @f$ X_k @f$ are the mole fractions, @f$ W_k @f$ are the molecular
+ * weights, and @f$ V_k @f$ are the pure species molar volumes.
*
* Note, the basis behind this formula is that in an ideal solution the
* partial molar volumes are equal to the pure species molar volumes. We
@@ -121,9 +121,9 @@ class GibbsExcessVPSSTP : public VPStandardStateTP
//! @}
//! @name Activities, Standard States, and Activity Concentrations
//!
- //! The activity \f$a_k\f$ of a species in solution is related to the
- //! chemical potential by \f[ \mu_k = \mu_k^0(T) + \hat R T \log a_k. \f] The
- //! quantity \f$\mu_k^0(T,P)\f$ is the chemical potential at unit activity,
+ //! The activity @f$ a_k @f$ of a species in solution is related to the
+ //! chemical potential by @f[ \mu_k = \mu_k^0(T) + \hat R T \log a_k. @f] The
+ //! quantity @f$ \mu_k^0(T,P) @f$ is the chemical potential at unit activity,
//! which depends only on temperature and pressure.
//! @{
@@ -131,10 +131,10 @@ class GibbsExcessVPSSTP : public VPStandardStateTP
virtual void getActivityConcentrations(doublereal* c) const;
/**
- * The standard concentration \f$ C^0_k \f$ used to normalize the
+ * The standard concentration @f$ C^0_k @f$ used to normalize the
* generalized concentration. In many cases, this quantity will be the same
* for all species in a phase - for example, for an ideal gas
- * \f$ C^0_k = P/\hat R T \f$. For this reason, this method returns a single
+ * @f$ C^0_k = P/\hat R T @f$. For this reason, this method returns a single
* value, instead of an array. However, for phases in which the standard
* concentration is species-specific (for example, surface species of different
* sizes), this method may be called with an optional parameter indicating
@@ -152,9 +152,9 @@ class GibbsExcessVPSSTP : public VPStandardStateTP
//! class and classes that derive from it) at the current solution
//! temperature, pressure, and solution concentration.
/*!
- * \f[
+ * @f[
* a_i^\triangle = \gamma_k^{\triangle} \frac{m_k}{m^\triangle}
- * \f]
+ * @f]
*
* This function must be implemented in derived classes.
*
diff --git a/include/cantera/thermo/HMWSoln.h b/include/cantera/thermo/HMWSoln.h
index 2c2c87e5c1..989ac39bea 100644
--- a/include/cantera/thermo/HMWSoln.h
+++ b/include/cantera/thermo/HMWSoln.h
@@ -76,9 +76,9 @@ class WaterProps;
* #Cantera::WaterPropsIAPWS.
*
* The standard states for solutes are on the unit molality basis. Therefore, in
- * the documentation below, the normal \f$ o \f$ superscript is replaced with
- * the \f$ \triangle \f$ symbol. The reference state symbol is now
- * \f$ \triangle, ref \f$.
+ * the documentation below, the normal @f$ o @f$ superscript is replaced with
+ * the @f$ \triangle @f$ symbol. The reference state symbol is now
+ * @f$ \triangle, ref @f$.
*
* It is assumed that the reference state thermodynamics may be obtained by a
* pointer to a populated species thermodynamic property manager class (see
@@ -91,26 +91,26 @@ class WaterProps;
*
* For these incompressible, standard states, the molar internal energy is
* independent of pressure. Since the thermodynamic properties are specified by
- * giving the standard-state enthalpy, the term \f$ P_0 \hat v\f$ is subtracted
+ * giving the standard-state enthalpy, the term @f$ P_0 \hat v @f$ is subtracted
* from the specified molar enthalpy to compute the molar internal energy. The
* entropy is assumed to be independent of the pressure.
*
* The enthalpy function is given by the following relation.
*
- * \f[
+ * @f[
* h^\triangle_k(T,P) = h^{\triangle,ref}_k(T)
* + \tilde{v}_k \left( P - P_{ref} \right)
- * \f]
+ * @f]
*
* For an incompressible, stoichiometric substance, the molar internal energy is
* independent of pressure. Since the thermodynamic properties are specified by
- * giving the standard-state enthalpy, the term \f$ P_{ref} \tilde v\f$ is
+ * giving the standard-state enthalpy, the term @f$ P_{ref} \tilde v @f$ is
* subtracted from the specified reference molar enthalpy to compute the molar
* internal energy.
*
- * \f[
+ * @f[
* u^\triangle_k(T,P) = h^{\triangle,ref}_k(T) - P_{ref} \tilde{v}_k
- * \f]
+ * @f]
*
* The solute standard state heat capacity and entropy are independent of
* pressure. The solute standard state Gibbs free energy is obtained from the
@@ -125,18 +125,18 @@ class WaterProps;
*
* ## Specification of Solution Thermodynamic Properties
*
- * Chemical potentials of the solutes, \f$ \mu_k \f$, and the solvent, \f$ \mu_o
- * \f$, which are based on the molality form, have the following general format:
+ * Chemical potentials of the solutes, @f$ \mu_k @f$, and the solvent, @f$ \mu_o
+ * @f$, which are based on the molality form, have the following general format:
*
- * \f[
+ * @f[
* \mu_k = \mu^{\triangle}_k(T,P) + R T ln(\gamma_k^{\triangle} \frac{m_k}{m^\triangle})
- * \f]
- * \f[
+ * @f]
+ * @f[
* \mu_o = \mu^o_o(T,P) + RT ln(a_o)
- * \f]
+ * @f]
*
- * where \f$ \gamma_k^{\triangle} \f$ is the molality based activity coefficient
- * for species \f$k\f$.
+ * where @f$ \gamma_k^{\triangle} @f$ is the molality based activity coefficient
+ * for species @f$ k @f$.
*
* Individual activity coefficients of ions can not be independently measured.
* Instead, only binary pairs forming electroneutral solutions can be measured.
@@ -150,13 +150,13 @@ class WaterProps;
* ### Ionic Strength
*
* Most of the parameterizations within the model use the ionic strength as a
- * key variable. The ionic strength, \f$ I\f$ is defined as follows
+ * key variable. The ionic strength, @f$ I @f$ is defined as follows
*
- * \f[
+ * @f[
* I = \frac{1}{2} \sum_k{m_k z_k^2}
- * \f]
+ * @f]
*
- * \f$ m_k \f$ is the molality of the kth species. \f$ z_k \f$ is the charge of
+ * @f$ m_k @f$ is the molality of the kth species. @f$ z_k @f$ is the charge of
* the kth species. Note, the ionic strength is a defined units quantity. The
* molality has defined units of gmol kg-1, and therefore the ionic strength has
* units of sqrt(gmol/kg).
@@ -164,19 +164,19 @@ class WaterProps;
* ### Specification of the Excess Gibbs Free Energy
*
* Pitzer's formulation may best be represented as a specification of the excess
- * Gibbs free energy, \f$ G^{ex} \f$, defined as the deviation of the total
+ * Gibbs free energy, @f$ G^{ex} @f$, defined as the deviation of the total
* Gibbs free energy from that of an ideal molal solution.
- * \f[
+ * @f[
* G = G^{id} + G^{ex}
- * \f]
+ * @f]
*
* The ideal molal solution contribution, not equal to an ideal solution
* contribution and in fact containing a singularity at the zero solvent mole
* fraction limit, is given below.
- * \f[
+ * @f[
* G^{id} = n_o \mu^o_o + \sum_{k\ne o} n_k \mu_k^{\triangle}
* + \tilde{M}_o n_o ( RT (\sum{m_i(\ln(m_i)-1)}))
- * \f]
+ * @f]
*
* From the excess Gibbs free energy formulation, the activity coefficient
* expression and the osmotic coefficient expression for the solvent may be
@@ -186,7 +186,7 @@ class WaterProps;
* Pitzer employs the following general expression for the excess Gibbs free
* energy
*
- * \f[
+ * @f[
* \begin{array}{cclc}
* \frac{G^{ex}}{\tilde{M}_o n_o RT} &= &
* \left( \frac{4A_{Debye}I}{3b} \right) \ln(1 + b \sqrt{I})
@@ -200,18 +200,18 @@ class WaterProps;
* + 2 \sum_{n < n'} \sum m_n m_{n'} \lambda_{n{n'}}
* + \sum_n m^2_n \lambda_{nn}
* \end{array}
- * \f]
+ * @f]
*
* *a* is a subscript over all anions, *c* is a subscript extending over all
* cations, and *i* is a subscript that extends over all anions and cations.
* *n* is a subscript that extends only over neutral solute molecules. The
* second line contains cross terms where cations affect cations and/or
* cation/anion pairs, and anions affect anions or cation/anion pairs. Note part
- * of the coefficients, \f$ \Phi_{c{c'}} \f$ and \f$ \Phi_{a{a'}} \f$ stem from
+ * of the coefficients, @f$ \Phi_{c{c'}} @f$ and @f$ \Phi_{a{a'}} @f$ stem from
* the theory of unsymmetrical mixing of electrolytes with different charges.
* This theory depends on the total ionic strength of the solution, and
- * therefore, \f$ \Phi_{c{c'}} \f$ and \f$ \Phi_{a{a'}} \f$ will depend on
- * *I*, the ionic strength. \f$ B_{ca}\f$ is a strong function of the
+ * therefore, @f$ \Phi_{c{c'}} @f$ and @f$ \Phi_{a{a'}} @f$ will depend on
+ * *I*, the ionic strength. @f$ B_{ca} @f$ is a strong function of the
* total ionic strength, *I*, of the electrolyte. The rest of the coefficients
* are assumed to be independent of the molalities or ionic strengths. However,
* all coefficients are potentially functions of the temperature and pressure
@@ -220,71 +220,71 @@ class WaterProps;
* *A* is the Debye-Huckel constant. Its specification is described in its
* own section below.
*
- * \f$ I\f$ is the ionic strength of the solution, and is given by:
+ * @f$ I @f$ is the ionic strength of the solution, and is given by:
*
- * \f[
+ * @f[
* I = \frac{1}{2} \sum_k{m_k z_k^2}
- * \f]
+ * @f]
*
* In contrast to several other Debye-Huckel implementations (see @ref
- * DebyeHuckel), the parameter \f$ b\f$ in the above equation is a constant that
+ * DebyeHuckel), the parameter @f$ b @f$ in the above equation is a constant that
* does not vary with respect to ion identity. This is an important
* simplification as it avoids troubles with satisfaction of the Gibbs-Duhem
* analysis.
*
- * The function \f$ Z \f$ is given by
+ * The function @f$ Z @f$ is given by
*
- * \f[
+ * @f[
* Z = \sum_i m_i \left| z_i \right|
- * \f]
+ * @f]
*
- * The value of \f$ B_{ca}\f$ is given by the following function
+ * The value of @f$ B_{ca} @f$ is given by the following function
*
- * \f[
+ * @f[
* B_{ca} = \beta^{(0)}_{ca} + \beta^{(1)}_{ca} g(\alpha^{(1)}_{ca} \sqrt{I})
* + \beta^{(2)}_{ca} g(\alpha^{(2)}_{ca} \sqrt{I})
- * \f]
+ * @f]
*
* where
*
- * \f[
+ * @f[
* g(x) = 2 \frac{(1 - (1 + x)\exp[-x])}{x^2}
- * \f]
+ * @f]
*
- * The formulation for \f$ B_{ca}\f$ combined with the formulation of the Debye-
+ * The formulation for @f$ B_{ca} @f$ combined with the formulation of the Debye-
* Huckel term in the eqn. for the excess Gibbs free energy stems essentially
* from an empirical fit to the ionic strength dependent data based over a wide
- * sampling of binary electrolyte systems. \f$ C_{ca} \f$, \f$ \lambda_{nc} \f$,
- * \f$ \lambda_{na} \f$, \f$ \lambda_{nn} \f$, \f$ \Psi_{c{c'}a} \f$, \f$
- * \Psi_{a{a'}c} \f$ are experimentally derived coefficients that may have
+ * sampling of binary electrolyte systems. @f$ C_{ca} @f$, @f$ \lambda_{nc} @f$,
+ * @f$ \lambda_{na} @f$, @f$ \lambda_{nn} @f$, @f$ \Psi_{c{c'}a} @f$, @f$
+ * \Psi_{a{a'}c} @f$ are experimentally derived coefficients that may have
* pressure and/or temperature dependencies.
*
- * The \f$ \Phi_{c{c'}} \f$ and \f$ \Phi_{a{a'}} \f$ formulations are slightly
- * more complicated. \f$ b \f$ is a universal constant defined to be equal to
- * \f$ 1.2\ kg^{1/2}\ gmol^{-1/2} \f$. The exponential coefficient \f$
- * \alpha^{(1)}_{ca} \f$ is usually fixed at \f$ \alpha^{(1)}_{ca} = 2.0\
- * kg^{1/2} gmol^{-1/2}\f$ except for 2-2 electrolytes, while other parameters
- * were fit to experimental data. For 2-2 electrolytes, \f$ \alpha^{(1)}_{ca} =
- * 1.4\ kg^{1/2}\ gmol^{-1/2}\f$ is used in combination with either \f$
- * \alpha^{(2)}_{ca} = 12\ kg^{1/2}\ gmol^{-1/2}\f$ or \f$ \alpha^{(2)}_{ca} = k
- * A_\psi \f$, where *k* is a constant. For electrolytes other than 2-2
- * electrolytes the \f$ \beta^{(2)}_{ca} g(\alpha^{(2)}_{ca} \sqrt{I}) \f$ term
+ * The @f$ \Phi_{c{c'}} @f$ and @f$ \Phi_{a{a'}} @f$ formulations are slightly
+ * more complicated. @f$ b @f$ is a universal constant defined to be equal to
+ * @f$ 1.2\ kg^{1/2}\ gmol^{-1/2} @f$. The exponential coefficient @f$
+ * \alpha^{(1)}_{ca} @f$ is usually fixed at @f$ \alpha^{(1)}_{ca} = 2.0\
+ * kg^{1/2} gmol^{-1/2} @f$ except for 2-2 electrolytes, while other parameters
+ * were fit to experimental data. For 2-2 electrolytes, @f$ \alpha^{(1)}_{ca} =
+ * 1.4\ kg^{1/2}\ gmol^{-1/2} @f$ is used in combination with either @f$
+ * \alpha^{(2)}_{ca} = 12\ kg^{1/2}\ gmol^{-1/2} @f$ or @f$ \alpha^{(2)}_{ca} = k
+ * A_\psi @f$, where *k* is a constant. For electrolytes other than 2-2
+ * electrolytes the @f$ \beta^{(2)}_{ca} g(\alpha^{(2)}_{ca} \sqrt{I}) @f$ term
* is not used in the fitting procedure; it is only used for divalent metal
* solfates and other high-valence electrolytes which exhibit significant
* association at low ionic strengths.
*
- * The \f$ \beta^{(0)}_{ca} \f$, \f$ \beta^{(1)}_{ca}\f$, \f$ \beta^{(2)}_{ca}
- * \f$, and \f$ C_{ca} \f$ binary coefficients are referred to as ion-
+ * The @f$ \beta^{(0)}_{ca} @f$, @f$ \beta^{(1)}_{ca} @f$, @f$ \beta^{(2)}_{ca}
+ * @f$, and @f$ C_{ca} @f$ binary coefficients are referred to as ion-
* interaction or Pitzer parameters. These Pitzer parameters may vary with
* temperature and pressure but they do not depend on the ionic strength. Their
* values and temperature derivatives of their values have been tabulated for a
* range of electrolytes
*
- * The \f$ \Phi_{c{c'}} \f$ and \f$ \Phi_{a{a'}} \f$ contributions, which
+ * The @f$ \Phi_{c{c'}} @f$ and @f$ \Phi_{a{a'}} @f$ contributions, which
* capture cation-cation and anion-anion interactions, also have an ionic
* strength dependence.
*
- * Ternary contributions \f$ \Psi_{c{c'}a} \f$ and \f$ \Psi_{a{a'}c} \f$ have
+ * Ternary contributions @f$ \Psi_{c{c'}a} @f$ and @f$ \Psi_{a{a'}c} @f$ have
* been measured also for some systems. The success of the Pitzer method lies in
* its ability to model nonlinear activity coefficients of complex
* multicomponent systems with just binary and minor ternary contributions,
@@ -296,9 +296,9 @@ class WaterProps;
* the following derivative of the excess Gibbs Free Energy formulation
* described above:
*
- * \f[
+ * @f[
* \ln(\gamma_k^\triangle) = \frac{d\left( \frac{G^{ex}}{M_o n_o RT} \right)}{d(m_k)}\Bigg|_{n_i}
- * \f]
+ * @f]
*
* In the formulas below the following conventions are used. The subscript *M*
* refers to a particular cation. The subscript X refers to a particular anion,
@@ -308,88 +308,88 @@ class WaterProps;
*
* The activity coefficient for a particular cation *M* is given by
*
- * \f[
+ * @f[
* \ln(\gamma_M^\triangle) = -z_M^2(F) + \sum_a m_a \left( 2 B_{Ma} + Z C_{Ma} \right)
* + z_M \left( \sum_a \sum_c m_a m_c C_{ca} \right)
* + \sum_c m_c \left[ 2 \Phi_{Mc} + \sum_a m_a \Psi_{Mca} \right]
* + \sum_{a < a'} \sum m_a m_{a'} \Psi_{Ma{a'}}
* + 2 \sum_n m_n \lambda_{nM}
- * \f]
+ * @f]
*
* The activity coefficient for a particular anion *X* is given by
*
- * \f[
+ * @f[
* \ln(\gamma_X^\triangle) = -z_X^2(F) + \sum_a m_c \left( 2 B_{cX} + Z C_{cX} \right)
* + \left|z_X \right| \left( \sum_a \sum_c m_a m_c C_{ca} \right)
* + \sum_a m_a \left[ 2 \Phi_{Xa} + \sum_c m_c \Psi_{cXa} \right]
* + \sum_{c < c'} \sum m_c m_{c'} \Psi_{c{c'}X}
* + 2 \sum_n m_n \lambda_{nM}
- * \f]
- * where the function \f$ F \f$ is given by
+ * @f]
+ * where the function @f$ F @f$ is given by
*
- * \f[
+ * @f[
* F = - A_{\phi} \left[ \frac{\sqrt{I}}{1 + b \sqrt{I}}
* + \frac{2}{b} \ln{\left(1 + b\sqrt{I}\right)} \right]
* + \sum_a \sum_c m_a m_c B'_{ca}
* + \sum_{c < c'} \sum m_c m_{c'} \Phi'_{c{c'}}
* + \sum_{a < a'} \sum m_a m_{a'} \Phi'_{a{a'}}
- * \f]
+ * @f]
*
- * We have employed the definition of \f$ A_{\phi} \f$, also used by Pitzer
+ * We have employed the definition of @f$ A_{\phi} @f$, also used by Pitzer
* which is equal to
*
- * \f[
+ * @f[
* A_{\phi} = \frac{A_{Debye}}{3}
- * \f]
+ * @f]
*
- * In the above formulas, \f$ \Phi'_{c{c'}} \f$ and \f$ \Phi'_{a{a'}} \f$ are the
- * ionic strength derivatives of \f$ \Phi_{c{c'}} \f$ and \f$ \Phi_{a{a'}} \f$,
+ * In the above formulas, @f$ \Phi'_{c{c'}} @f$ and @f$ \Phi'_{a{a'}} @f$ are the
+ * ionic strength derivatives of @f$ \Phi_{c{c'}} @f$ and @f$ \Phi_{a{a'}} @f$,
* respectively.
*
- * The function \f$ B'_{MX} \f$ is defined as:
+ * The function @f$ B'_{MX} @f$ is defined as:
*
- * \f[
+ * @f[
* B'_{MX} = \left( \frac{\beta^{(1)}_{MX} h(\alpha^{(1)}_{MX} \sqrt{I})}{I} \right)
* \left( \frac{\beta^{(2)}_{MX} h(\alpha^{(2)}_{MX} \sqrt{I})}{I} \right)
- * \f]
+ * @f]
*
- * where \f$ h(x) \f$ is defined as
+ * where @f$ h(x) @f$ is defined as
*
- * \f[
+ * @f[
* h(x) = g'(x) \frac{x}{2} =
* \frac{2\left(1 - \left(1 + x + \frac{x^2}{2} \right)\exp(-x) \right)}{x^2}
- * \f]
+ * @f]
*
* The activity coefficient for neutral species *N* is given by
*
- * \f[
+ * @f[
* \ln(\gamma_N^\triangle) = 2 \left( \sum_i m_i \lambda_{iN}\right)
- * \f]
+ * @f]
*
* ### Activity of the Water Solvent
*
- * The activity for the solvent water,\f$ a_o \f$, is not independent and must
+ * The activity for the solvent water,@f$ a_o @f$, is not independent and must
* be determined either from the Gibbs-Duhem relation or from taking the
* appropriate derivative of the same excess Gibbs free energy function as was
* used to formulate the solvent activity coefficients. Pitzer's description
* follows the later approach to derive a formula for the osmotic coefficient,
- * \f$ \phi \f$.
+ * @f$ \phi @f$.
*
- * \f[
+ * @f[
* \phi - 1 = - \left( \frac{d\left(\frac{G^{ex}}{RT} \right)}{d(\tilde{M}_o n_o)} \right)
* \frac{1}{\sum_{i \ne 0} m_i}
- * \f]
+ * @f]
*
* The osmotic coefficient may be related to the water activity by the following relation:
*
- * \f[
+ * @f[
* \phi = - \frac{1}{\tilde{M}_o \sum_{i \neq o} m_i} \ln(a_o)
* = - \frac{n_o}{\sum_{i \neq o}n_i} \ln(a_o)
- * \f]
+ * @f]
*
* The result is the following
*
- * \f[
+ * @f[
* \begin{array}{ccclc}
* \phi - 1 &= &
* \frac{2}{\sum_{i \ne 0} m_i}
@@ -405,28 +405,28 @@ class WaterProps;
* + \frac{1}{2} \left( \sum_n m^2_n \lambda_{nn}\right)
* \bigg]
* \end{array}
- * \f]
+ * @f]
*
* It can be shown that the expression
*
- * \f[
+ * @f[
* B^{\phi}_{ca} = \beta^{(0)}_{ca} + \beta^{(1)}_{ca} \exp{(- \alpha^{(1)}_{ca} \sqrt{I})}
* + \beta^{(2)}_{ca} \exp{(- \alpha^{(2)}_{ca} \sqrt{I} )}
- * \f]
+ * @f]
*
- * is consistent with the expression \f$ B_{ca} \f$ in the \f$ G^{ex} \f$
- * expression after carrying out the derivative wrt \f$ m_M \f$.
+ * is consistent with the expression @f$ B_{ca} @f$ in the @f$ G^{ex} @f$
+ * expression after carrying out the derivative wrt @f$ m_M @f$.
*
- * Also taking into account that \f$ {\Phi}_{c{c'}} \f$ and
- * \f$ {\Phi}_{a{a'}} \f$ has an ionic strength dependence.
+ * Also taking into account that @f$ {\Phi}_{c{c'}} @f$ and
+ * @f$ {\Phi}_{a{a'}} @f$ has an ionic strength dependence.
*
- * \f[
+ * @f[
* \Phi^{\phi}_{c{c'}} = {\Phi}_{c{c'}} + I \frac{d{\Phi}_{c{c'}}}{dI}
- * \f]
+ * @f]
*
- * \f[
+ * @f[
* \Phi^{\phi}_{a{a'}} = \Phi_{a{a'}} + I \frac{d\Phi_{a{a'}}}{dI}
- * \f]
+ * @f]
*
* ### Temperature and Pressure Dependence of the Pitzer Parameters
*
@@ -445,30 +445,30 @@ class WaterProps;
* form was used to fit the temperature dependence of the Pitzer Coefficients
* for each cation - anion pair, M X.
*
- * \f[
+ * @f[
* \beta^{(0)}_{MX} = q^{b0}_0
* + q^{b0}_1 \left( T - T_r \right)
* + q^{b0}_2 \left( T^2 - T_r^2 \right)
* + q^{b0}_3 \left( \frac{1}{T} - \frac{1}{T_r}\right)
* + q^{b0}_4 \ln \left( \frac{T}{T_r} \right)
- * \f]
- * \f[
+ * @f]
+ * @f[
* \beta^{(1)}_{MX} = q^{b1}_0 + q^{b1}_1 \left( T - T_r \right)
* + q^{b1}_{2} \left( T^2 - T_r^2 \right)
- * \f]
- * \f[
+ * @f]
+ * @f[
* C^{\phi}_{MX} = q^{Cphi}_0
* + q^{Cphi}_1 \left( T - T_r \right)
* + q^{Cphi}_2 \left( T^2 - T_r^2 \right)
* + q^{Cphi}_3 \left( \frac{1}{T} - \frac{1}{T_r}\right)
* + q^{Cphi}_4 \ln \left( \frac{T}{T_r} \right)
- * \f]
+ * @f]
*
* where
*
- * \f[
+ * @f[
* C^{\phi}_{MX} = 2 {\left| z_M z_X \right|}^{1/2} C_{MX}
- * \f]
+ * @f]
*
* In later papers, Pitzer has added additional temperature dependencies to all
* of the other remaining second and third order virial coefficients. Some of
@@ -485,90 +485,90 @@ class WaterProps;
* and pressure
* - PIZTER_TEMP_COMPLEX1 - string name "COMPLEX" or "COMPLEX1"
* - Uses the full temperature dependence for the
- * \f$\beta^{(0)}_{MX} \f$ (5 coeffs),
- * the \f$\beta^{(1)}_{MX} \f$ (3 coeffs),
- * and \f$ C^{\phi}_{MX} \f$ (5 coeffs) parameters described above.
+ * @f$ \beta^{(0)}_{MX} @f$ (5 coeffs),
+ * the @f$ \beta^{(1)}_{MX} @f$ (3 coeffs),
+ * and @f$ C^{\phi}_{MX} @f$ (5 coeffs) parameters described above.
* - PITZER_TEMP_LINEAR - string name "LINEAR"
* - Uses just the temperature dependence for the
- * \f$\beta^{(0)}_{MX} \f$, the \f$\beta^{(1)}_{MX} \f$,
- * and \f$ C^{\phi}_{MX} \f$ coefficients described above.
+ * @f$ \beta^{(0)}_{MX} @f$, the @f$ \beta^{(1)}_{MX} @f$,
+ * and @f$ C^{\phi}_{MX} @f$ coefficients described above.
* There are 2 coefficients for each term.
*
* The specification of the binary interaction between a cation and an anion is
- * given by the coefficients, \f$ B_{MX}\f$ and \f$ C_{MX}\f$ The specification
- * of \f$ B_{MX}\f$ is a function of \f$\beta^{(0)}_{MX} \f$,
- * \f$\beta^{(1)}_{MX} \f$, \f$\beta^{(2)}_{MX} \f$, \f$\alpha^{(1)}_{MX} \f$,
- * and \f$\alpha^{(2)}_{MX} \f$. \f$ C_{MX}\f$ is calculated from
- * \f$C^{\phi}_{MX} \f$ from the formula above.
+ * given by the coefficients, @f$ B_{MX} @f$ and @f$ C_{MX} @f$ The specification
+ * of @f$ B_{MX} @f$ is a function of @f$ \beta^{(0)}_{MX} @f$,
+ * @f$ \beta^{(1)}_{MX} @f$, @f$ \beta^{(2)}_{MX} @f$, @f$ \alpha^{(1)}_{MX} @f$,
+ * and @f$ \alpha^{(2)}_{MX} @f$. @f$ C_{MX} @f$ is calculated from
+ * @f$ C^{\phi}_{MX} @f$ from the formula above.
*
- * The parameters for \f$ \beta^{(0)}\f$ fit the following equation:
+ * The parameters for @f$ \beta^{(0)} @f$ fit the following equation:
*
- * \f[
+ * @f[
* \beta^{(0)} = q_0^{{\beta}0} + q_1^{{\beta}0} \left( T - T_r \right)
* + q_2^{{\beta}0} \left( T^2 - T_r^2 \right)
* + q_3^{{\beta}0} \left( \frac{1}{T} - \frac{1}{T_r} \right)
* + q_4^{{\beta}0} \ln \left( \frac{T}{T_r} \right)
- * \f]
+ * @f]
*
* This same `COMPLEX1` temperature dependence given above is used for the
* following parameters:
- * \f$ \beta^{(0)}_{MX} \f$, \f$ \beta^{(1)}_{MX} \f$,
- * \f$ \beta^{(2)}_{MX} \f$, \f$ \Theta_{cc'} \f$, \f$\Theta_{aa'} \f$,
- * \f$ \Psi_{c{c'}a} \f$ and \f$ \Psi_{ca{a'}} \f$.
+ * @f$ \beta^{(0)}_{MX} @f$, @f$ \beta^{(1)}_{MX} @f$,
+ * @f$ \beta^{(2)}_{MX} @f$, @f$ \Theta_{cc'} @f$, @f$ \Theta_{aa'} @f$,
+ * @f$ \Psi_{c{c'}a} @f$ and @f$ \Psi_{ca{a'}} @f$.
*
* ### Like-Charged Binary Ion Parameters and the Mixing Parameters
*
- * The previous section contained the functions, \f$ \Phi_{c{c'}} \f$,
- * \f$ \Phi_{a{a'}} \f$ and their derivatives wrt the ionic strength, \f$
- * \Phi'_{c{c'}} \f$ and \f$ \Phi'_{a{a'}} \f$. Part of these terms come from
+ * The previous section contained the functions, @f$ \Phi_{c{c'}} @f$,
+ * @f$ \Phi_{a{a'}} @f$ and their derivatives wrt the ionic strength, @f$
+ * \Phi'_{c{c'}} @f$ and @f$ \Phi'_{a{a'}} @f$. Part of these terms come from
* theory.
*
* Since like charged ions repel each other and are generally not near each
* other, the virial coefficients for same-charged ions are small. However,
* Pitzer doesn't ignore these in his formulation. Relatively larger and longer
* range terms between like-charged ions exist however, which appear only for
- * unsymmetrical mixing of same-sign charged ions with different charges. \f$
- * \Phi_{ij} \f$, where \f$ ij \f$ is either \f$ a{a'} \f$ or \f$ c{c'} \f$ is
+ * unsymmetrical mixing of same-sign charged ions with different charges. @f$
+ * \Phi_{ij} @f$, where @f$ ij @f$ is either @f$ a{a'} @f$ or @f$ c{c'} @f$ is
* given by
*
- * \f[
+ * @f[
* {\Phi}_{ij} = \Theta_{ij} + \,^E \Theta_{ij}(I)
- * \f]
+ * @f]
*
- * \f$ \Theta_{ij} \f$ is the small virial coefficient expansion term. Dependent
+ * @f$ \Theta_{ij} @f$ is the small virial coefficient expansion term. Dependent
* in general on temperature and pressure, its ionic strength dependence is
- * ignored in Pitzer's approach. \f$ \,^E\Theta_{ij}(I) \f$ accounts for the
+ * ignored in Pitzer's approach. @f$ \,^E\Theta_{ij}(I) @f$ accounts for the
* electrostatic unsymmetrical mixing effects and is dependent only on the
* charges of the ions i, j, the total ionic strength and on the dielectric
* constant and density of the solvent. This seems to be a relatively well-
* documented part of the theory. They theory below comes from Pitzer summation
* (Pitzer) in the appendix. It's also mentioned in Bethke's book (Bethke), and
- * the equations are summarized in Harvie & Weare (1980). Within the code, \f$
- * \,^E\Theta_{ij}(I) \f$ is evaluated according to the algorithm described in
+ * the equations are summarized in Harvie & Weare (1980). Within the code, @f$
+ * \,^E\Theta_{ij}(I) @f$ is evaluated according to the algorithm described in
* Appendix B [Pitzer] as
*
- * \f[
+ * @f[
* \,^E\Theta_{ij}(I) = \left( \frac{z_i z_j}{4I} \right)
* \left( J(x_{ij}) - \frac{1}{2} J(x_{ii})
* - \frac{1}{2} J(x_{jj}) \right)
- * \f]
+ * @f]
*
- * where \f$ x_{ij} = 6 z_i z_j A_{\phi} \sqrt{I} \f$ and
+ * where @f$ x_{ij} = 6 z_i z_j A_{\phi} \sqrt{I} @f$ and
*
- * \f[
+ * @f[
* J(x) = \frac{1}{x} \int_0^{\infty}{\left( 1 + q +
* \frac{1}{2} q^2 - e^q \right) y^2 dy}
- * \f]
+ * @f]
*
- * and \f$ q = - (\frac{x}{y}) e^{-y} \f$. \f$ J(x) \f$ is evaluated by
+ * and @f$ q = - (\frac{x}{y}) e^{-y} @f$. @f$ J(x) @f$ is evaluated by
* numerical integration.
*
- * The \f$ \Theta_{ij} \f$ term is a constant value, specified for pair of cations
+ * The @f$ \Theta_{ij} @f$ term is a constant value, specified for pair of cations
* or a pair of anions.
*
* ### Ternary Pitzer Parameters
*
- * The \f$ \Psi_{c{c'}a} \f$ and \f$ \Psi_{ca{a'}} \f$ terms represent ternary
+ * The @f$ \Psi_{c{c'}a} @f$ and @f$ \Psi_{ca{a'}} @f$ terms represent ternary
* interactions between two cations and an anion and two anions and a cation,
* respectively. In Pitzer's implementation these terms are usually small in
* absolute size.
@@ -576,7 +576,7 @@ class WaterProps;
* ### Treatment of Neutral Species
*
* Binary virial-coefficient-like interactions between two neutral species may
- * be specified in the \f$ \lambda_{mn} \f$ terms that appear in the formulas
+ * be specified in the @f$ \lambda_{mn} @f$ terms that appear in the formulas
* above. Currently these interactions are independent of pressure and ionic strength.
* Also, currently, the neutrality of the species are not checked. Therefore, this
* interaction may involve charged species in the solution as well.
@@ -587,44 +587,44 @@ class WaterProps;
*
* ### Specification of the Debye-Huckel Constant
*
- * In the equations above, the formula for \f$ A_{Debye} \f$ is needed. The
+ * In the equations above, the formula for @f$ A_{Debye} @f$ is needed. The
* HMWSoln object uses two methods for specifying these quantities. The default
- * method is to assume that \f$ A_{Debye} \f$ is a constant, given in the
+ * method is to assume that @f$ A_{Debye} @f$ is a constant, given in the
* initialization process, and stored in the member double, m_A_Debye.
* Optionally, a full water treatment may be employed that makes
- * \f$ A_{Debye} \f$ a full function of *T* and *P* and creates nontrivial
+ * @f$ A_{Debye} @f$ a full function of *T* and *P* and creates nontrivial
* entries for the excess heat capacity, enthalpy, and excess volumes of
* solution.
*
- * \f[
+ * @f[
* A_{Debye} = \frac{F e B_{Debye}}{8 \pi \epsilon R T} {\left( C_o \tilde{M}_o \right)}^{1/2}
- * \f]
+ * @f]
* where
*
- * \f[
+ * @f[
* B_{Debye} = \frac{F} {{(\frac{\epsilon R T}{2})}^{1/2}}
- * \f]
+ * @f]
* Therefore:
- * \f[
+ * @f[
* A_{Debye} = \frac{1}{8 \pi}
* {\left(\frac{2 N_a \rho_o}{1000}\right)}^{1/2}
* {\left(\frac{N_a e^2}{\epsilon R T }\right)}^{3/2}
- * \f]
+ * @f]
*
* Units = sqrt(kg/gmol)
*
* where
- * - \f$ N_a \f$ is Avogadro's number
- * - \f$ \rho_w \f$ is the density of water
- * - \f$ e \f$ is the electronic charge
- * - \f$ \epsilon = K \epsilon_o \f$ is the permittivity of water
- * - \f$ K \f$ is the dielectric constant of water,
- * - \f$ \epsilon_o \f$ is the permittivity of free space.
- * - \f$ \rho_o \f$ is the density of the solvent in its standard state.
+ * - @f$ N_a @f$ is Avogadro's number
+ * - @f$ \rho_w @f$ is the density of water
+ * - @f$ e @f$ is the electronic charge
+ * - @f$ \epsilon = K \epsilon_o @f$ is the permittivity of water
+ * - @f$ K @f$ is the dielectric constant of water,
+ * - @f$ \epsilon_o @f$ is the permittivity of free space.
+ * - @f$ \rho_o @f$ is the density of the solvent in its standard state.
*
* Nominal value at 298 K and 1 atm = 1.172576 (kg/gmol)^(1/2)
* based on:
- * - \f$ \epsilon / \epsilon_0 \f$ = 78.54 (water at 25C)
+ * - @f$ \epsilon / \epsilon_0 @f$ = 78.54 (water at 25C)
* - T = 298.15 K
* - B_Debye = 3.28640E9 (kg/gmol)^(1/2) / m
*
@@ -635,55 +635,55 @@ class WaterProps;
* molar enthalpies, entropies, and heat capacities are all non-trivial to
* compute. The following formulas are used.
*
- * The partial molar enthalpy, \f$ \bar s_k(T,P) \f$:
+ * The partial molar enthalpy, @f$ \bar s_k(T,P) @f$:
*
- * \f[
+ * @f[
* \bar h_k(T,P) = h^{\triangle}_k(T,P)
* - R T^2 \frac{d \ln(\gamma_k^\triangle)}{dT}
- * \f]
+ * @f]
* The solvent partial molar enthalpy is equal to
- * \f[
+ * @f[
* \bar h_o(T,P) = h^{o}_o(T,P) - R T^2 \frac{d \ln(a_o)}{dT}
* = h^{o}_o(T,P)
* + R T^2 (\sum_{k \neq o} m_k) \tilde{M_o} (\frac{d \phi}{dT})
- * \f]
+ * @f]
*
- * The partial molar entropy, \f$ \bar s_k(T,P) \f$:
+ * The partial molar entropy, @f$ \bar s_k(T,P) @f$:
*
- * \f[
+ * @f[
* \bar s_k(T,P) = s^{\triangle}_k(T,P)
* - R \ln( \gamma^{\triangle}_k \frac{m_k}{m^{\triangle}}))
* - R T \frac{d \ln(\gamma^{\triangle}_k) }{dT}
- * \f]
- * \f[
+ * @f]
+ * @f[
* \bar s_o(T,P) = s^o_o(T,P) - R \ln(a_o)
* - R T \frac{d \ln(a_o)}{dT}
- * \f]
+ * @f]
*
- * The partial molar heat capacity, \f$ C_{p,k}(T,P)\f$:
+ * The partial molar heat capacity, @f$ C_{p,k}(T,P) @f$:
*
- * \f[
+ * @f[
* \bar C_{p,k}(T,P) = C^{\triangle}_{p,k}(T,P)
* - 2 R T \frac{d \ln( \gamma^{\triangle}_k)}{dT}
* - R T^2 \frac{d^2 \ln(\gamma^{\triangle}_k) }{{dT}^2}
- * \f]
- * \f[
+ * @f]
+ * @f[
* \bar C_{p,o}(T,P) = C^o_{p,o}(T,P)
* - 2 R T \frac{d \ln(a_o)}{dT}
* - R T^2 \frac{d^2 \ln(a_o)}{{dT}^2}
- * \f]
+ * @f]
*
* The pressure dependence of the activity coefficients leads to non-zero terms
* for the excess Volume of the solution. Therefore, the partial molar volumes
* are functions of the pressure derivatives of the activity coefficients.
- * \f[
+ * @f[
* \bar V_k(T,P) = V^{\triangle}_k(T,P)
* + R T \frac{d \ln(\gamma^{\triangle}_k) }{dP}
- * \f]
- * \f[
+ * @f]
+ * @f[
* \bar V_o(T,P) = V^o_o(T,P)
* + R T \frac{d \ln(a_o)}{dP}
- * \f]
+ * @f]
*
* The majority of work for these functions take place in the internal routines
* that calculate the first and second derivatives of the log of the activity
@@ -707,70 +707,70 @@ class WaterProps;
*
* For example, a bulk-phase binary reaction between liquid solute species *j*
* and *k*, producing a new liquid solute species *l* would have the following
- * equation for its rate of progress variable, \f$ R^1 \f$, which has units of
+ * equation for its rate of progress variable, @f$ R^1 @f$, which has units of
* kmol m-3 s-1.
*
- * \f[
+ * @f[
* R^1 = k^1 C_j^a C_k^a = k^1 (C^o_o \tilde{M}_o a_j) (C^o_o \tilde{M}_o a_k)
- * \f]
+ * @f]
*
* where
*
- * \f[
+ * @f[
* C_j^a = C^o_o \tilde{M}_o a_j \quad and \quad C_k^a = C^o_o \tilde{M}_o a_k
- * \f]
+ * @f]
*
- * \f$ C_j^a \f$ is the activity concentration of species *j*, and
- * \f$ C_k^a \f$ is the activity concentration of species *k*. \f$ C^o_o \f$ is
- * the concentration of water at 298 K and 1 atm. \f$ \tilde{M}_o \f$ has units
+ * @f$ C_j^a @f$ is the activity concentration of species *j*, and
+ * @f$ C_k^a @f$ is the activity concentration of species *k*. @f$ C^o_o @f$ is
+ * the concentration of water at 298 K and 1 atm. @f$ \tilde{M}_o @f$ has units
* of kg solvent per gmol solvent and is equal to
*
- * \f[
+ * @f[
* \tilde{M}_o = \frac{M_o}{1000}
- * \f]
+ * @f]
*
- * \f$ a_j \f$ is the activity of species *j* at the current temperature and
+ * @f$ a_j @f$ is the activity of species *j* at the current temperature and
* pressure and concentration of the liquid phase is given by the molality based
* activity coefficient multiplied by the molality of the jth species.
*
- * \f[
+ * @f[
* a_j = \gamma_j^\triangle m_j = \gamma_j^\triangle \frac{n_j}{\tilde{M}_o n_o}
- * \f]
+ * @f]
*
- * \f$k^1 \f$ has units of m^3/kmol/s.
+ * @f$ k^1 @f$ has units of m^3/kmol/s.
*
* Therefore the generalized activity concentration of a solute species has the following form
*
- * \f[
+ * @f[
* C_j^a = C^o_o \frac{\gamma_j^\triangle n_j}{n_o}
- * \f]
+ * @f]
*
* The generalized activity concentration of the solvent has the same units, but it's a simpler form
*
- * \f[
+ * @f[
* C_o^a = C^o_o a_o
- * \f]
+ * @f]
*
* The reverse rate constant can then be obtained from the law of microscopic reversibility
* and the equilibrium expression for the system.
*
- * \f[
+ * @f[
* \frac{a_j a_k}{ a_l} = K^{o,1} = \exp(\frac{\mu^o_l - \mu^o_j - \mu^o_k}{R T} )
- * \f]
+ * @f]
*
- * \f$ K^{o,1} \f$ is the dimensionless form of the equilibrium constant.
+ * @f$ K^{o,1} @f$ is the dimensionless form of the equilibrium constant.
*
- * \f[
+ * @f[
* R^{-1} = k^{-1} C_l^a = k^{-1} (C_o \tilde{M}_o a_l)
- * \f]
+ * @f]
*
* where
*
- * \f[
+ * @f[
* k^{-1} = k^1 K^{o,1} C_o \tilde{M}_o
- * \f]
+ * @f]
*
- * \f$ k^{-1} \f$ has units of 1/s.
+ * @f$ k^{-1} @f$ has units of 1/s.
*
* @ingroup thermoprops
*/
@@ -833,11 +833,11 @@ class HMWSoln : public MolalityVPSSTP
* Molar entropy of the solution. Units: J/kmol/K. For an ideal, constant
* partial molar volume solution mixture with pure species phases which
* exhibit zero volume expansivity:
- * \f[
+ * @f[
* \hat s(T, P, X_k) = \sum_k X_k \hat s^0_k(T)
* - \hat R \sum_k X_k log(X_k)
- * \f]
- * The reference-state pure-species entropies \f$ \hat s^0_k(T,p_{ref}) \f$
+ * @f]
+ * The reference-state pure-species entropies @f$ \hat s^0_k(T,p_{ref}) @f$
* are computed by the species thermodynamic property manager. The pure
* species entropies are independent of temperature since the volume
* expansivities are equal to zero.
@@ -878,12 +878,12 @@ class HMWSoln : public MolalityVPSSTP
*
* The formula for this is
*
- * \f[
+ * @f[
* \rho = \frac{\sum_k{X_k W_k}}{\sum_k{X_k V_k}}
- * \f]
+ * @f]
*
- * where \f$X_k\f$ are the mole fractions, \f$W_k\f$ are the molecular
- * weights, and \f$V_k\f$ are the pure species molar volumes.
+ * where @f$ X_k @f$ are the mole fractions, @f$ W_k @f$ are the molecular
+ * weights, and @f$ V_k @f$ are the pure species molar volumes.
*
* Note, the basis behind this formula is that in an ideal solution the
* partial molar volumes are equal to the pure species molar volumes. We
@@ -899,17 +899,17 @@ class HMWSoln : public MolalityVPSSTP
//! @}
//! @name Activities, Standard States, and Activity Concentrations
//!
- //! The activity \f$a_k\f$ of a species in solution is related to the
- //! chemical potential by \f[ \mu_k = \mu_k^0(T) + \hat R T \log a_k. \f] The
- //! quantity \f$\mu_k^0(T,P)\f$ is the chemical potential at unit activity,
+ //! The activity @f$ a_k @f$ of a species in solution is related to the
+ //! chemical potential by @f[ \mu_k = \mu_k^0(T) + \hat R T \log a_k. @f] The
+ //! quantity @f$ \mu_k^0(T,P) @f$ is the chemical potential at unit activity,
//! which depends only on temperature and the pressure. Activity is assumed
//! to be molality-based here.
//! @{
//! This method returns an array of generalized activity concentrations
/*!
- * The generalized activity concentrations, \f$ C_k^a\f$, are defined such
- * that \f$ a_k = C^a_k / C^0_k, \f$ where \f$ C^0_k \f$ is a standard
+ * The generalized activity concentrations, @f$ C_k^a @f$, are defined such
+ * that @f$ a_k = C^a_k / C^0_k, @f$ where @f$ C^0_k @f$ is a standard
* concentration defined below. These generalized concentrations are used
* by kinetics manager classes to compute the forward and reverse rates of
* elementary reactions.
@@ -917,16 +917,16 @@ class HMWSoln : public MolalityVPSSTP
* The generalized activity concentration of a solute species has the
* following form
*
- * \f[
+ * @f[
* C_j^a = C^o_o \frac{\gamma_j^\triangle n_j}{n_o}
- * \f]
+ * @f]
*
* The generalized activity concentration of the solvent has the same units,
* but it's a simpler form
*
- * \f[
+ * @f[
* C_o^a = C^o_o a_o
- * \f]
+ * @f]
*
* @param c Array of generalized concentrations. The
* units are kmol m-3 for both the solvent and the solute species
@@ -935,7 +935,7 @@ class HMWSoln : public MolalityVPSSTP
//! Return the standard concentration for the kth species
/*!
- * The standard concentration \f$ C^0_k \f$ used to normalize the activity
+ * The standard concentration @f$ C^0_k @f$ used to normalize the activity
* (that is, generalized) concentration for use
*
* We have set the standard concentration for all solute species in this
@@ -944,9 +944,9 @@ class HMWSoln : public MolalityVPSSTP
* solvent). The solvent standard concentration is just equal to its
* standard state concentration.
*
- * \f[
+ * @f[
* C_j^0 = C^o_o \tilde{M}_o \quad and C_o^0 = C^o_o
- * \f]
+ * @f]
*
* The consequence of this is that the standard concentrations have unequal
* units between the solvent and the solute. However, both the solvent and
@@ -960,52 +960,52 @@ class HMWSoln : public MolalityVPSSTP
*
* For example, a bulk-phase binary reaction between liquid solute species
* *j* and *k*, producing a new liquid solute species *l* would have the
- * following equation for its rate of progress variable, \f$ R^1 \f$, which
+ * following equation for its rate of progress variable, @f$ R^1 @f$, which
* has units of kmol m-3 s-1.
*
- * \f[
+ * @f[
* R^1 = k^1 C_j^a C_k^a = k^1 (C^o_o \tilde{M}_o a_j) (C^o_o \tilde{M}_o a_k)
- * \f]
+ * @f]
*
* where
*
- * \f[
+ * @f[
* C_j^a = C^o_o \tilde{M}_o a_j \quad and \quad C_k^a = C^o_o \tilde{M}_o a_k
- * \f]
+ * @f]
*
- * \f$ C_j^a \f$ is the activity concentration of species *j*, and
- * \f$ C_k^a \f$ is the activity concentration of species *k*. \f$ C^o_o \f$
- * is the concentration of water at 298 K and 1 atm. \f$ \tilde{M}_o \f$ has
+ * @f$ C_j^a @f$ is the activity concentration of species *j*, and
+ * @f$ C_k^a @f$ is the activity concentration of species *k*. @f$ C^o_o @f$
+ * is the concentration of water at 298 K and 1 atm. @f$ \tilde{M}_o @f$ has
* units of kg solvent per gmol solvent and is equal to
*
- * \f[
+ * @f[
* \tilde{M}_o = \frac{M_o}{1000}
- * \f]
+ * @f]
*
- * \f$ a_j \f$ is
+ * @f$ a_j @f$ is
* the activity of species *j* at the current temperature and pressure
* and concentration of the liquid phase is given by the molality based
* activity coefficient multiplied by the molality of the jth species.
*
- * \f[
+ * @f[
* a_j = \gamma_j^\triangle m_j = \gamma_j^\triangle \frac{n_j}{\tilde{M}_o n_o}
- * \f]
+ * @f]
*
- * \f$k^1 \f$ has units of m^3/kmol/s.
+ * @f$ k^1 @f$ has units of m^3/kmol/s.
*
* Therefore the generalized activity concentration of a solute species has
* the following form
*
- * \f[
+ * @f[
* C_j^a = C^o_o \frac{\gamma_j^\triangle n_j}{n_o}
- * \f]
+ * @f]
*
* The generalized activity concentration of the solvent has the same units,
* but it's a simpler form
*
- * \f[
+ * @f[
* C_o^a = C^o_o a_o
- * \f]
+ * @f]
*
* @param k Optional parameter indicating the species. The default is to
* assume this refers to species 0.
@@ -1037,9 +1037,9 @@ class HMWSoln : public MolalityVPSSTP
* This function returns a vector of chemical potentials of the
* species in solution.
*
- * \f[
+ * @f[
* \mu_k = \mu^{\triangle}_k(T,P) + R T ln(\gamma_k^{\triangle} m_k)
- * \f]
+ * @f]
*
* @param mu Output vector of species chemical
* potentials. Length: m_kk. Units: J/kmol
@@ -1053,16 +1053,16 @@ class HMWSoln : public MolalityVPSSTP
* state enthalpies modified by the derivative of the molality-based
* activity coefficient wrt temperature
*
- * \f[
+ * @f[
* \bar h_k(T,P) = h^{\triangle}_k(T,P)
* - R T^2 \frac{d \ln(\gamma_k^\triangle)}{dT}
- * \f]
+ * @f]
* The solvent partial molar enthalpy is equal to
- * \f[
+ * @f[
* \bar h_o(T,P) = h^{o}_o(T,P) - R T^2 \frac{d \ln(a_o)}{dT}
* = h^{o}_o(T,P)
* + R T^2 (\sum_{k \neq o} m_k) \tilde{M_o} (\frac{d \phi}{dT})
- * \f]
+ * @f]
*
* @param hbar Output vector of species partial molar enthalpies.
* Length: m_kk. units are J/kmol.
@@ -1081,15 +1081,15 @@ class HMWSoln : public MolalityVPSSTP
* entropies plus the ideal solution contribution plus complicated functions
* of the temperature derivative of the activity coefficients.
*
- * \f[
+ * @f[
* \bar s_k(T,P) = s^{\triangle}_k(T,P)
* - R \ln( \gamma^{\triangle}_k \frac{m_k}{m^{\triangle}}))
* - R T \frac{d \ln(\gamma^{\triangle}_k) }{dT}
- * \f]
- * \f[
+ * @f]
+ * @f[
* \bar s_o(T,P) = s^o_o(T,P) - R \ln(a_o)
* - R T \frac{d \ln(a_o)}{dT}
- * \f]
+ * @f]
*
* @param sbar Output vector of species partial molar entropies.
* Length = m_kk. units are J/kmol/K.
@@ -1102,14 +1102,14 @@ class HMWSoln : public MolalityVPSSTP
* For this solution, the partial molar volumes are functions of the
* pressure derivatives of the activity coefficients.
*
- * \f[
+ * @f[
* \bar V_k(T,P) = V^{\triangle}_k(T,P)
* + R T \frac{d \ln(\gamma^{\triangle}_k) }{dP}
- * \f]
- * \f[
+ * @f]
+ * @f[
* \bar V_o(T,P) = V^o_o(T,P)
* + R T \frac{d \ln(a_o)}{dP}
- * \f]
+ * @f]
*
* @param vbar Output vector of species partial molar volumes.
* Length = m_kk. units are m^3/kmol.
@@ -1121,16 +1121,16 @@ class HMWSoln : public MolalityVPSSTP
/*!
* The following formulas are implemented within the code.
*
- * \f[
+ * @f[
* \bar C_{p,k}(T,P) = C^{\triangle}_{p,k}(T,P)
* - 2 R T \frac{d \ln( \gamma^{\triangle}_k)}{dT}
* - R T^2 \frac{d^2 \ln(\gamma^{\triangle}_k) }{{dT}^2}
- * \f]
- * \f[
+ * @f]
+ * @f[
* \bar C_{p,o}(T,P) = C^o_{p,o}(T,P)
* - 2 R T \frac{d \ln(a_o)}{dT}
* - R T^2 \frac{d^2 \ln(a_o)}{{dT}^2}
- * \f]
+ * @f]
*
* @param cpbar Output vector of species partial molar heat capacities at
* constant pressure. Length = m_kk. units are J/kmol/K.
diff --git a/include/cantera/thermo/IdealGasPhase.h b/include/cantera/thermo/IdealGasPhase.h
index c4e5ab724b..c47f58987c 100644
--- a/include/cantera/thermo/IdealGasPhase.h
+++ b/include/cantera/thermo/IdealGasPhase.h
@@ -53,48 +53,48 @@ namespace Cantera
*
* The standard state enthalpy is independent of pressure:
*
- * \f[
+ * @f[
* h^o_k(T,P) = h^{ref}_k(T)
- * \f]
+ * @f]
*
* The standard state constant-pressure heat capacity is independent of pressure:
*
- * \f[
+ * @f[
* Cp^o_k(T,P) = Cp^{ref}_k(T)
- * \f]
+ * @f]
*
* The standard state entropy depends in the following fashion on pressure:
*
- * \f[
+ * @f[
* S^o_k(T,P) = S^{ref}_k(T) - R \ln(\frac{P}{P_{ref}})
- * \f]
+ * @f]
* The standard state Gibbs free energy is obtained from the enthalpy and entropy
* functions:
*
- * \f[
+ * @f[
* \mu^o_k(T,P) = h^o_k(T,P) - S^o_k(T,P) T
- * \f]
+ * @f]
*
- * \f[
+ * @f[
* \mu^o_k(T,P) = \mu^{ref}_k(T) + R T \ln( \frac{P}{P_{ref}})
- * \f]
+ * @f]
*
* where
- * \f[
+ * @f[
* \mu^{ref}_k(T) = h^{ref}_k(T) - T S^{ref}_k(T)
- * \f]
+ * @f]
*
* The standard state internal energy is obtained from the enthalpy function also
*
- * \f[
+ * @f[
* u^o_k(T,P) = h^o_k(T) - R T
- * \f]
+ * @f]
*
* The molar volume of a species is given by the ideal gas law
*
- * \f[
+ * @f[
* V^o_k(T,P) = \frac{R T}{P}
- * \f]
+ * @f]
*
* where R is the molar gas constant. For a complete list of physical constants
* used within %Cantera, see @ref physConstants .
@@ -102,142 +102,142 @@ namespace Cantera
* ## Specification of Solution Thermodynamic Properties
*
* The activity of a species defined in the phase is given by the ideal gas law:
- * \f[
+ * @f[
* a_k = X_k
- * \f]
- * where \f$ X_k \f$ is the mole fraction of species *k*. The chemical potential
+ * @f]
+ * where @f$ X_k @f$ is the mole fraction of species *k*. The chemical potential
* for species *k* is equal to
*
- * \f[
+ * @f[
* \mu_k(T,P) = \mu^o_k(T, P) + R T \log(X_k)
- * \f]
+ * @f]
*
* In terms of the reference state, the above can be rewritten
*
- * \f[
+ * @f[
* \mu_k(T,P) = \mu^{ref}_k(T, P) + R T \log(\frac{P X_k}{P_{ref}})
- * \f]
+ * @f]
*
* The partial molar entropy for species *k* is given by the following relation,
*
- * \f[
+ * @f[
* \tilde{s}_k(T,P) = s^o_k(T,P) - R \log(X_k) = s^{ref}_k(T) - R \log(\frac{P X_k}{P_{ref}})
- * \f]
+ * @f]
*
* The partial molar enthalpy for species *k* is
*
- * \f[
+ * @f[
* \tilde{h}_k(T,P) = h^o_k(T,P) = h^{ref}_k(T)
- * \f]
+ * @f]
*
* The partial molar Internal Energy for species *k* is
*
- * \f[
+ * @f[
* \tilde{u}_k(T,P) = u^o_k(T,P) = u^{ref}_k(T)
- * \f]
+ * @f]
*
* The partial molar Heat Capacity for species *k* is
*
- * \f[
+ * @f[
* \tilde{Cp}_k(T,P) = Cp^o_k(T,P) = Cp^{ref}_k(T)
- * \f]
+ * @f]
*
* ## Application within Kinetics Managers
*
- * \f$ C^a_k\f$ are defined such that \f$ a_k = C^a_k / C^s_k, \f$ where \f$
- * C^s_k \f$ is a standard concentration defined below and \f$ a_k \f$ are
+ * @f$ C^a_k @f$ are defined such that @f$ a_k = C^a_k / C^s_k, @f$ where @f$
+ * C^s_k @f$ is a standard concentration defined below and @f$ a_k @f$ are
* activities used in the thermodynamic functions. These activity (or
* generalized) concentrations are used by kinetics manager classes to compute
* the forward and reverse rates of elementary reactions. The activity
- * concentration,\f$ C^a_k \f$,is given by the following expression.
+ * concentration,@f$ C^a_k @f$,is given by the following expression.
*
- * \f[
+ * @f[
* C^a_k = C^s_k X_k = \frac{P}{R T} X_k
- * \f]
+ * @f]
*
* The standard concentration for species *k* is independent of *k* and equal to
*
- * \f[
+ * @f[
* C^s_k = C^s = \frac{P}{R T}
- * \f]
+ * @f]
*
* For example, a bulk-phase binary gas reaction between species j and k,
* producing a new gas species l would have the following equation for its rate
- * of progress variable, \f$ R^1 \f$, which has units of kmol m-3 s-1.
+ * of progress variable, @f$ R^1 @f$, which has units of kmol m-3 s-1.
*
- * \f[
+ * @f[
* R^1 = k^1 C_j^a C_k^a = k^1 (C^s a_j) (C^s a_k)
- * \f]
+ * @f]
* where
- * \f[
+ * @f[
* C_j^a = C^s a_j \quad \mbox{and} \quad C_k^a = C^s a_k
- * \f]
+ * @f]
*
- * \f$ C_j^a \f$ is the activity concentration of species j, and
- * \f$ C_k^a \f$ is the activity concentration of species k. \f$ C^s \f$ is the
- * standard concentration. \f$ a_j \f$ is the activity of species j which is
+ * @f$ C_j^a @f$ is the activity concentration of species j, and
+ * @f$ C_k^a @f$ is the activity concentration of species k. @f$ C^s @f$ is the
+ * standard concentration. @f$ a_j @f$ is the activity of species j which is
* equal to the mole fraction of j.
*
* The reverse rate constant can then be obtained from the law of microscopic
* reversibility and the equilibrium expression for the system.
*
- * \f[
+ * @f[
* \frac{a_j a_k}{ a_l} = K_a^{o,1} = \exp(\frac{\mu^o_l - \mu^o_j - \mu^o_k}{R T} )
- * \f]
+ * @f]
*
- * \f$ K_a^{o,1} \f$ is the dimensionless form of the equilibrium constant,
- * associated with the pressure dependent standard states \f$ \mu^o_l(T,P) \f$
- * and their associated activities, \f$ a_l \f$, repeated here:
+ * @f$ K_a^{o,1} @f$ is the dimensionless form of the equilibrium constant,
+ * associated with the pressure dependent standard states @f$ \mu^o_l(T,P) @f$
+ * and their associated activities, @f$ a_l @f$, repeated here:
*
- * \f[
+ * @f[
* \mu_l(T,P) = \mu^o_l(T, P) + R T \log(a_l)
- * \f]
+ * @f]
*
* We can switch over to expressing the equilibrium constant in terms of the
* reference state chemical potentials
*
- * \f[
+ * @f[
* K_a^{o,1} = \exp(\frac{\mu^{ref}_l - \mu^{ref}_j - \mu^{ref}_k}{R T} ) * \frac{P_{ref}}{P}
- * \f]
+ * @f]
*
- * The concentration equilibrium constant, \f$ K_c \f$, may be obtained by
+ * The concentration equilibrium constant, @f$ K_c @f$, may be obtained by
* changing over to activity concentrations. When this is done:
*
- * \f[
+ * @f[
* \frac{C^a_j C^a_k}{ C^a_l} = C^o K_a^{o,1} = K_c^1 =
* \exp(\frac{\mu^{ref}_l - \mu^{ref}_j - \mu^{ref}_k}{R T} ) * \frac{P_{ref}}{RT}
- * \f]
+ * @f]
*
* %Kinetics managers will calculate the concentration equilibrium constant,
- * \f$ K_c \f$, using the second and third part of the above expression as a
+ * @f$ K_c @f$, using the second and third part of the above expression as a
* definition for the concentration equilibrium constant.
*
* For completeness, the pressure equilibrium constant may be obtained as well
*
- * \f[
+ * @f[
* \frac{P_j P_k}{ P_l P_{ref}} = K_p^1 =
* \exp\left(\frac{\mu^{ref}_l - \mu^{ref}_j - \mu^{ref}_k}{R T} \right)
- * \f]
+ * @f]
*
- * \f$ K_p \f$ is the simplest form of the equilibrium constant for ideal gases.
+ * @f$ K_p @f$ is the simplest form of the equilibrium constant for ideal gases.
* However, it isn't necessarily the simplest form of the equilibrium constant
- * for other types of phases; \f$ K_c \f$ is used instead because it is
+ * for other types of phases; @f$ K_c @f$ is used instead because it is
* completely general.
*
* The reverse rate of progress may be written down as
- * \f[
+ * @f[
* R^{-1} = k^{-1} C_l^a = k^{-1} (C^o a_l)
- * \f]
+ * @f]
*
* where we can use the concept of microscopic reversibility to write the
* reverse rate constant in terms of the forward rate constant and the
- * concentration equilibrium constant, \f$ K_c \f$.
+ * concentration equilibrium constant, @f$ K_c @f$.
*
- * \f[
+ * @f[
* k^{-1} = k^1 K^1_c
- * \f]
+ * @f]
*
- * \f$k^{-1} \f$ has units of s-1.
+ * @f$ k^{-1} @f$ has units of s-1.
*
* ## YAML Example
*
@@ -283,11 +283,11 @@ class IdealGasPhase: public ThermoPhase
//! Return the Molar enthalpy. Units: J/kmol.
/*!
* For an ideal gas mixture,
- * \f[
+ * @f[
* \hat h(T) = \sum_k X_k \hat h^0_k(T),
- * \f]
+ * @f]
* and is a function only of temperature. The standard-state pure-species
- * enthalpies \f$ \hat h^0_k(T) \f$ are computed by the species
+ * enthalpies @f$ \hat h^0_k(T) @f$ are computed by the species
* thermodynamic property manager.
*
* \see MultiSpeciesThermo
@@ -299,10 +299,10 @@ class IdealGasPhase: public ThermoPhase
/**
* Molar entropy. Units: J/kmol/K.
* For an ideal gas mixture,
- * \f[
+ * @f[
* \hat s(T, P) = \sum_k X_k \hat s^0_k(T) - \hat R \log (P/P^0).
- * \f]
- * The reference-state pure-species entropies \f$ \hat s^0_k(T) \f$ are
+ * @f]
+ * The reference-state pure-species entropies @f$ \hat s^0_k(T) @f$ are
* computed by the species thermodynamic property manager.
* @see MultiSpeciesThermo
*/
@@ -311,10 +311,10 @@ class IdealGasPhase: public ThermoPhase
/**
* Molar heat capacity at constant pressure. Units: J/kmol/K.
* For an ideal gas mixture,
- * \f[
+ * @f[
* \hat c_p(t) = \sum_k \hat c^0_{p,k}(T).
- * \f]
- * The reference-state pure-species heat capacities \f$ \hat c^0_{p,k}(T) \f$
+ * @f]
+ * The reference-state pure-species heat capacities @f$ \hat c^0_{p,k}(T) @f$
* are computed by the species thermodynamic property manager.
* @see MultiSpeciesThermo
*/
@@ -323,7 +323,7 @@ class IdealGasPhase: public ThermoPhase
/**
* Molar heat capacity at constant volume. Units: J/kmol/K.
* For an ideal gas mixture,
- * \f[ \hat c_v = \hat c_p - \hat R. \f]
+ * @f[ \hat c_v = \hat c_p - \hat R. @f]
*/
virtual doublereal cv_mole() const;
@@ -334,7 +334,7 @@ class IdealGasPhase: public ThermoPhase
/**
* Pressure. Units: Pa.
* For an ideal gas mixture,
- * \f[ P = n \hat R T. \f]
+ * @f[ P = n \hat R T. @f]
*/
virtual doublereal pressure() const {
return GasConstant * molarDensity() * temperature();
@@ -344,9 +344,9 @@ class IdealGasPhase: public ThermoPhase
/*!
* Units: Pa.
* This method is implemented by setting the mass density to
- * \f[
+ * @f[
* \rho = \frac{P \overline W}{\hat R T }.
- * \f]
+ * @f]
*
* @param p Pressure (Pa)
*/
@@ -359,9 +359,9 @@ class IdealGasPhase: public ThermoPhase
* Units: kg/m^3, Pa.
* This method is implemented by setting the density to the input value and
* setting the temperature to
- * \f[
+ * @f[
* T = \frac{P \overline W}{\hat R \rho}.
- * \f]
+ * @f]
*
* @param rho Density (kg/m^3)
* @param p Pressure (Pa)
@@ -380,9 +380,9 @@ class IdealGasPhase: public ThermoPhase
//! Returns the isothermal compressibility. Units: 1/Pa.
/**
* The isothermal compressibility is defined as
- * \f[
+ * @f[
* \kappa_T = -\frac{1}{v}\left(\frac{\partial v}{\partial P}\right)_T
- * \f]
+ * @f]
* For ideal gases it's equal to the inverse of the pressure
*/
virtual doublereal isothermalCompressibility() const {
@@ -392,9 +392,9 @@ class IdealGasPhase: public ThermoPhase
//! Return the volumetric thermal expansion coefficient. Units: 1/K.
/*!
* The thermal expansion coefficient is defined as
- * \f[
+ * @f[
* \beta = \frac{1}{v}\left(\frac{\partial v}{\partial T}\right)_P
- * \f]
+ * @f]
* For ideal gases, it's equal to the inverse of the temperature.
*/
virtual doublereal thermalExpansionCoeff() const {
@@ -406,24 +406,24 @@ class IdealGasPhase: public ThermoPhase
//! @}
//! @name Chemical Potentials and Activities
//!
- //! The activity \f$a_k\f$ of a species in solution is
+ //! The activity @f$ a_k @f$ of a species in solution is
//! related to the chemical potential by
- //! \f[
+ //! @f[
//! \mu_k(T,P,X_k) = \mu_k^0(T,P)
//! + \hat R T \log a_k.
- //! \f]
- //! The quantity \f$\mu_k^0(T,P)\f$ is the standard state chemical potential
+ //! @f]
+ //! The quantity @f$ \mu_k^0(T,P) @f$ is the standard state chemical potential
//! at unit activity. It may depend on the pressure and the temperature.
//! However, it may not depend on the mole fractions of the species in the
//! solution.
//!
- //! The activities are related to the generalized concentrations, \f$\tilde
- //! C_k\f$, and standard concentrations, \f$C^0_k\f$, by the following
+ //! The activities are related to the generalized concentrations, @f$ \tilde
+ //! C_k @f$, and standard concentrations, @f$ C^0_k @f$, by the following
//! formula:
//!
- //! \f[
+ //! @f[
//! a_k = \frac{\tilde C_k}{C^0_k}
- //! \f]
+ //! @f]
//! The generalized concentrations are used in the kinetics classes to
//! describe the rates of progress of reactions involving the species. Their
//! formulation depends upon the specification of the rate constants for
@@ -445,14 +445,14 @@ class IdealGasPhase: public ThermoPhase
getConcentrations(c);
}
- //! Returns the standard concentration \f$ C^0_k \f$, which is used to
+ //! Returns the standard concentration @f$ C^0_k @f$, which is used to
//! normalize the generalized concentration.
/*!
* This is defined as the concentration by which the generalized
* concentration is normalized to produce the activity. In many cases, this
* quantity will be the same for all species in a phase. Since the activity
* for an ideal gas mixture is simply the mole fraction, for an ideal gas
- * \f$ C^0_k = P/\hat R T \f$.
+ * @f$ C^0_k = P/\hat R T @f$.
*
* @param k Optional parameter indicating the species. The default
* is to assume this refers to species 0.
diff --git a/include/cantera/thermo/IdealMolalSoln.h b/include/cantera/thermo/IdealMolalSoln.h
index 06b0bea87a..a57ceb9dae 100644
--- a/include/cantera/thermo/IdealMolalSoln.h
+++ b/include/cantera/thermo/IdealMolalSoln.h
@@ -50,8 +50,8 @@ namespace Cantera
* The standard concentrations can have three different forms.
* See setStandardConcentrationModel().
*
- * \f$ V^0_0 \f$ is the solvent standard molar volume. \f$ m^{\Delta} \f$ is a
- * constant equal to a molality of \f$ 1.0 \quad\mbox{gm kmol}^{-1} \f$.
+ * @f$ V^0_0 @f$ is the solvent standard molar volume. @f$ m^{\Delta} @f$ is a
+ * constant equal to a molality of @f$ 1.0 \quad\mbox{gm kmol}^{-1} @f$.
*
* The current default is to have mformGC = 2.
*
@@ -94,11 +94,11 @@ class IdealMolalSoln : public MolalityVPSSTP
/*!
* Returns the amount of enthalpy per mole of solution. For an ideal molal
* solution,
- * \f[
+ * @f[
* \bar{h}(T, P, X_k) = \sum_k X_k \bar{h}_k(T)
- * \f]
+ * @f]
* The formula is written in terms of the partial molar enthalpies.
- * \f$ \bar{h}_k(T, p, m_k) \f$.
+ * @f$ \bar{h}_k(T, p, m_k) @f$.
* See the partial molar enthalpy function, getPartialMolarEnthalpies(),
* for details.
*
@@ -110,11 +110,11 @@ class IdealMolalSoln : public MolalityVPSSTP
/*!
* Returns the amount of internal energy per mole of solution. For an ideal
* molal solution,
- * \f[
+ * @f[
* \bar{u}(T, P, X_k) = \sum_k X_k \bar{u}_k(T)
- * \f]
+ * @f]
* The formula is written in terms of the partial molar internal energy.
- * \f$ \bar{u}_k(T, p, m_k) \f$.
+ * @f$ \bar{u}_k(T, p, m_k) @f$.
*/
virtual doublereal intEnergy_mole() const;
@@ -122,11 +122,11 @@ class IdealMolalSoln : public MolalityVPSSTP
/*!
* Returns the amount of entropy per mole of solution. For an ideal molal
* solution,
- * \f[
+ * @f[
* \bar{s}(T, P, X_k) = \sum_k X_k \bar{s}_k(T)
- * \f]
+ * @f]
* The formula is written in terms of the partial molar entropies.
- * \f$ \bar{s}_k(T, p, m_k) \f$.
+ * @f$ \bar{s}_k(T, p, m_k) @f$.
* See the partial molar entropies function, getPartialMolarEntropies(),
* for details.
*
@@ -138,9 +138,9 @@ class IdealMolalSoln : public MolalityVPSSTP
/*!
* Returns the Gibbs free energy of the solution per mole of the solution.
*
- * \f[
+ * @f[
* \bar{g}(T, P, X_k) = \sum_k X_k \mu_k(T)
- * \f]
+ * @f]
*
* Units: J/kmol
*/
@@ -148,9 +148,9 @@ class IdealMolalSoln : public MolalityVPSSTP
//! Molar heat capacity of the solution at constant pressure. Units: J/kmol/K.
/*!
- * \f[
+ * @f[
* \bar{c}_p(T, P, X_k) = \sum_k X_k \bar{c}_{p,k}(T)
- * \f]
+ * @f]
*
* Units: J/kmol/K
*/
@@ -173,12 +173,12 @@ class IdealMolalSoln : public MolalityVPSSTP
*
* The formula for this is
*
- * \f[
+ * @f[
* \rho = \frac{\sum_k{X_k W_k}}{\sum_k{X_k V_k}}
- * \f]
+ * @f]
*
- * where \f$X_k\f$ are the mole fractions, \f$W_k\f$ are the molecular
- * weights, and \f$V_k\f$ are the pure species molar volumes.
+ * where @f$ X_k @f$ are the mole fractions, @f$ W_k @f$ are the molecular
+ * weights, and @f$ V_k @f$ are the pure species molar volumes.
*
* Note, the basis behind this formula is that in an ideal solution the
* partial molar volumes are equal to the pure species molar volumes. We
@@ -191,9 +191,9 @@ class IdealMolalSoln : public MolalityVPSSTP
//! The isothermal compressibility. Units: 1/Pa.
/*!
* The isothermal compressibility is defined as
- * \f[
+ * @f[
* \kappa_T = -\frac{1}{v}\left(\frac{\partial v}{\partial P}\right)_T
- * \f]
+ * @f]
*
* It's equal to zero for this model, since the molar volume doesn't change
* with pressure or temperature.
@@ -204,9 +204,9 @@ class IdealMolalSoln : public MolalityVPSSTP
/*!
* The thermal expansion coefficient is defined as
*
- * \f[
+ * @f[
* \beta = \frac{1}{v}\left(\frac{\partial v}{\partial T}\right)_P
- * \f]
+ * @f]
*
* It's equal to zero for this model, since the molar volume doesn't change
* with pressure or temperature.
@@ -216,9 +216,9 @@ class IdealMolalSoln : public MolalityVPSSTP
//! @}
//! @name Activities and Activity Concentrations
//!
- //! The activity \f$a_k\f$ of a species in solution is related to the
- //! chemical potential by \f[ \mu_k = \mu_k^0(T) + \hat R T \log a_k. \f] The
- //! quantity \f$\mu_k^0(T)\f$ is the chemical potential at unit activity,
+ //! The activity @f$ a_k @f$ of a species in solution is related to the
+ //! chemical potential by @f[ \mu_k = \mu_k^0(T) + \hat R T \log a_k. @f] The
+ //! quantity @f$ \mu_k^0(T) @f$ is the chemical potential at unit activity,
//! which depends only on temperature and the pressure.
//! @{
@@ -257,18 +257,18 @@ class IdealMolalSoln : public MolalityVPSSTP
* This function returns a vector of chemical potentials of the species in
* solution.
*
- * \f[
+ * @f[
* \mu_k = \mu^{o}_k(T,P) + R T \ln(\frac{m_k}{m^\Delta})
- * \f]
- * \f[
+ * @f]
+ * @f[
* \mu_w = \mu^{o}_w(T,P) +
* R T ((X_w - 1.0) / X_w)
- * \f]
+ * @f]
*
- * \f$ w \f$ refers to the solvent species.
- * \f$ X_w \f$ is the mole fraction of the solvent.
- * \f$ m_k \f$ is the molality of the kth solute.
- * \f$ m^\Delta \f$ is 1 gmol solute per kg solvent.
+ * @f$ w @f$ refers to the solvent species.
+ * @f$ X_w @f$ is the mole fraction of the solvent.
+ * @f$ m_k @f$ is the molality of the kth solute.
+ * @f$ m^\Delta @f$ is 1 gmol solute per kg solvent.
*
* Units: J/kmol.
*
@@ -281,11 +281,11 @@ class IdealMolalSoln : public MolalityVPSSTP
/*!
* Units (J/kmol). For this phase, the partial molar enthalpies are equal to
* the species standard state enthalpies.
- * \f[
+ * @f[
* \bar h_k(T,P) = \hat h^{ref}_k(T) + (P - P_{ref}) \hat V^0_k
- * \f]
- * The reference-state pure-species enthalpies, \f$ \hat h^{ref}_k(T) \f$,
- * at the reference pressure,\f$ P_{ref} \f$, are computed by the species
+ * @f]
+ * The reference-state pure-species enthalpies, @f$ \hat h^{ref}_k(T) @f$,
+ * at the reference pressure,@f$ P_{ref} @f$, are computed by the species
* thermodynamic property manager. They are polynomial functions of
* temperature.
* @see MultiSpeciesThermo
@@ -301,9 +301,9 @@ class IdealMolalSoln : public MolalityVPSSTP
* Units (J/kmol). For this phase, the partial molar internal energies are equal to
* the species standard state internal energies (which are equal to the reference
* state internal energies)
- * \f[
+ * @f[
* \bar u_k(T,P) = \hat u^{ref}_k(T)
- * \f]
+ * @f]
* @param hbar Output vector of partial molar internal energies, length #m_kk
*/
virtual void getPartialMolarIntEnergies(doublereal* hbar) const;
@@ -313,22 +313,22 @@ class IdealMolalSoln : public MolalityVPSSTP
/*!
* Maxwell's equations provide an insight in how to calculate this
* (p.215 Smith and Van Ness)
- * \f[
+ * @f[
* \frac{d(\mu_k)}{dT} = -\bar{s}_i
- * \f]
+ * @f]
* For this phase, the partial molar entropies are equal to the standard
* state species entropies plus the ideal molal solution contribution.
*
- * \f[
+ * @f[
* \bar{s}_k(T,P) = s^0_k(T) - R \ln( \frac{m_k}{m^{\triangle}} )
- * \f]
- * \f[
+ * @f]
+ * @f[
* \bar{s}_w(T,P) = s^0_w(T) - R ((X_w - 1.0) / X_w)
- * \f]
+ * @f]
*
- * The subscript, w, refers to the solvent species. \f$ X_w \f$ is the mole
- * fraction of solvent. The reference-state pure-species entropies,\f$
- * s^0_k(T) \f$, at the reference pressure, \f$ P_{ref} \f$, are computed by
+ * The subscript, w, refers to the solvent species. @f$ X_w @f$ is the mole
+ * fraction of solvent. The reference-state pure-species entropies,@f$
+ * s^0_k(T) @f$, at the reference pressure, @f$ P_{ref} @f$, are computed by
* the species thermodynamic property manager. They are polynomial functions
* of temperature.
* @see MultiSpeciesThermo
@@ -353,9 +353,9 @@ class IdealMolalSoln : public MolalityVPSSTP
* The kth partial molar heat capacity is equal to the temperature
* derivative of the partial molar enthalpy of the kth species in the
* solution at constant P and composition (p. 220 Smith and Van Ness).
- * \f[
+ * @f[
* \bar{Cp}_k(T,P) = {Cp}^0_k(T)
- * \f]
+ * @f]
*
* For this solution, this is equal to the reference state heat capacities.
*
@@ -383,9 +383,9 @@ class IdealMolalSoln : public MolalityVPSSTP
*
* | model | ActivityConc | StandardConc |
* | -------------------- | -------------------------------- | ------------------ |
- * | unity | \f$ {m_k}/ { m^{\Delta}}\f$ | \f$ 1.0 \f$ |
- * | species-molar-volume | \f$ m_k / (m^{\Delta} V_k)\f$ | \f$ 1.0 / V_k \f$ |
- * | solvent-molar-volume | \f$ m_k / (m^{\Delta} V^0_0)\f$ | \f$ 1.0 / V^0_0\f$ |
+ * | unity | @f$ {m_k}/ { m^{\Delta}} @f$ | @f$ 1.0 @f$ |
+ * | species-molar-volume | @f$ m_k / (m^{\Delta} V_k) @f$ | @f$ 1.0 / V_k @f$ |
+ * | solvent-molar-volume | @f$ m_k / (m^{\Delta} V^0_0) @f$ | @f$ 1.0 / V^0_0 @f$ |
*/
void setStandardConcentrationModel(const std::string& model);
@@ -394,7 +394,7 @@ class IdealMolalSoln : public MolalityVPSSTP
//! Report the molar volume of species k
/*!
- * units - \f$ m^3 kmol^{-1} \f$
+ * units - @f$ m^3 kmol^{-1} @f$
*
* @param k Species index.
*/
@@ -402,14 +402,14 @@ class IdealMolalSoln : public MolalityVPSSTP
/*!
* Fill in a return vector containing the species molar volumes
- * units - \f$ m^3 kmol^{-1} \f$
+ * units - @f$ m^3 kmol^{-1} @f$
*
* @param smv Output vector of species molar volumes.
*/
void getSpeciesMolarVolumes(double* smv) const;
protected:
- //! Species molar volume \f$ m^3 kmol^{-1} \f$
+ //! Species molar volume @f$ m^3 kmol^{-1} @f$
vector_fp m_speciesMolarVolume;
/**
diff --git a/include/cantera/thermo/IdealSolidSolnPhase.h b/include/cantera/thermo/IdealSolidSolnPhase.h
index d24c325956..7ea6f5c03d 100644
--- a/include/cantera/thermo/IdealSolidSolnPhase.h
+++ b/include/cantera/thermo/IdealSolidSolnPhase.h
@@ -75,11 +75,11 @@ class IdealSolidSolnPhase : public ThermoPhase
* Molar enthalpy of the solution. Units: J/kmol. For an ideal, constant
* partial molar volume solution mixture with pure species phases which
* exhibit zero volume expansivity and zero isothermal compressibility:
- * \f[
+ * @f[
* \hat h(T,P) = \sum_k X_k \hat h^0_k(T) + (P - P_{ref}) (\sum_k X_k \hat V^0_k)
- * \f]
+ * @f]
* The reference-state pure-species enthalpies at the reference pressure Pref
- * \f$ \hat h^0_k(T) \f$, are computed by the species thermodynamic
+ * @f$ \hat h^0_k(T) @f$, are computed by the species thermodynamic
* property manager. They are polynomial functions of temperature.
* @see MultiSpeciesThermo
*/
@@ -89,11 +89,11 @@ class IdealSolidSolnPhase : public ThermoPhase
* Molar entropy of the solution. Units: J/kmol/K. For an ideal, constant
* partial molar volume solution mixture with pure species phases which
* exhibit zero volume expansivity:
- * \f[
+ * @f[
* \hat s(T, P, X_k) = \sum_k X_k \hat s^0_k(T) - \hat R \sum_k X_k log(X_k)
- * \f]
+ * @f]
* The reference-state pure-species entropies
- * \f$ \hat s^0_k(T,p_{ref}) \f$ are computed by the species thermodynamic
+ * @f$ \hat s^0_k(T,p_{ref}) @f$ are computed by the species thermodynamic
* property manager. The pure species entropies are independent of
* pressure since the volume expansivities are equal to zero.
* @see MultiSpeciesThermo
@@ -104,13 +104,13 @@ class IdealSolidSolnPhase : public ThermoPhase
* Molar Gibbs free energy of the solution. Units: J/kmol. For an ideal,
* constant partial molar volume solution mixture with pure species phases
* which exhibit zero volume expansivity:
- * \f[
+ * @f[
* \hat g(T, P) = \sum_k X_k \hat g^0_k(T,P) + \hat R T \sum_k X_k log(X_k)
- * \f]
+ * @f]
* The reference-state pure-species Gibbs free energies
- * \f$ \hat g^0_k(T) \f$ are computed by the species thermodynamic
+ * @f$ \hat g^0_k(T) @f$ are computed by the species thermodynamic
* property manager, while the standard state Gibbs free energies
- * \f$ \hat g^0_k(T,P) \f$ are computed by the member function, gibbs_RT().
+ * @f$ \hat g^0_k(T,P) @f$ are computed by the member function, gibbs_RT().
* @see MultiSpeciesThermo
*/
virtual doublereal gibbs_mole() const;
@@ -120,11 +120,11 @@ class IdealSolidSolnPhase : public ThermoPhase
* Units: J/kmol/K.
* For an ideal, constant partial molar volume solution mixture with
* pure species phases which exhibit zero volume expansivity:
- * \f[
+ * @f[
* \hat c_p(T,P) = \sum_k X_k \hat c^0_{p,k}(T) .
- * \f]
+ * @f]
* The heat capacity is independent of pressure. The reference-state pure-
- * species heat capacities \f$ \hat c^0_{p,k}(T) \f$ are computed by the
+ * species heat capacities @f$ \hat c^0_{p,k}(T) @f$ are computed by the
* species thermodynamic property manager.
* @see MultiSpeciesThermo
*/
@@ -134,7 +134,7 @@ class IdealSolidSolnPhase : public ThermoPhase
* Molar heat capacity at constant volume of the solution. Units: J/kmol/K.
* For an ideal, constant partial molar volume solution mixture with pure
* species phases which exhibit zero volume expansivity:
- * \f[ \hat c_v(T,P) = \hat c_p(T,P) \f]
+ * @f[ \hat c_v(T,P) = \hat c_p(T,P) @f]
* The two heat capacities are equal.
*/
virtual doublereal cv_mole() const {
@@ -174,12 +174,12 @@ class IdealSolidSolnPhase : public ThermoPhase
*
* The formula for this is
*
- * \f[
+ * @f[
* \rho = \frac{\sum_k{X_k W_k}}{\sum_k{X_k V_k}}
- * \f]
+ * @f]
*
- * where \f$X_k\f$ are the mole fractions, \f$W_k\f$ are the molecular
- * weights, and \f$V_k\f$ are the pure species molar volumes.
+ * where @f$ X_k @f$ are the mole fractions, @f$ W_k @f$ are the molecular
+ * weights, and @f$ V_k @f$ are the pure species molar volumes.
*
* Note, the basis behind this formula is that in an ideal solution the
* partial molar volumes are equal to the pure species molar volumes. We
@@ -191,24 +191,24 @@ class IdealSolidSolnPhase : public ThermoPhase
//! @}
//! @name Chemical Potentials and Activities
//!
- //! The activity \f$a_k\f$ of a species in solution is related to the
+ //! The activity @f$ a_k @f$ of a species in solution is related to the
//! chemical potential by
- //! \f[
+ //! @f[
//! \mu_k(T,P,X_k) = \mu_k^0(T,P)
//! + \hat R T \log a_k.
- //! \f]
- //! The quantity \f$\mu_k^0(T,P)\f$ is the standard state chemical potential
+ //! @f]
+ //! The quantity @f$ \mu_k^0(T,P) @f$ is the standard state chemical potential
//! at unit activity. It may depend on the pressure and the temperature.
//! However, it may not depend on the mole fractions of the species in the
//! solid solution.
//!
- //! The activities are related to the generalized concentrations, \f$\tilde
- //! C_k\f$, and standard concentrations, \f$C^0_k\f$, by the following
+ //! The activities are related to the generalized concentrations, @f$ \tilde
+ //! C_k @f$, and standard concentrations, @f$ C^0_k @f$, by the following
//! formula:
//!
- //! \f[
+ //! @f[
//! a_k = \frac{\tilde C_k}{C^0_k}
- //! \f]
+ //! @f]
//! The generalized concentrations are used in the kinetics classes to
//! describe the rates of progress of reactions involving the species. Their
//! formulation depends upon the specification of the rate constants for
@@ -258,7 +258,7 @@ class IdealSolidSolnPhase : public ThermoPhase
virtual void getActivityConcentrations(doublereal* c) const;
/**
- * The standard concentration \f$ C^0_k \f$ used to normalize the
+ * The standard concentration @f$ C^0_k @f$ used to normalize the
* generalized concentration. In many cases, this quantity will be the
* same for all species in a phase. However, for this case, we will return
* a distinct concentration for each species. This is the inverse of the
@@ -280,14 +280,14 @@ class IdealSolidSolnPhase : public ThermoPhase
*
* This function returns a vector of chemical potentials of the
* species in solution.
- * \f[
+ * @f[
* \mu_k = \mu^{ref}_k(T) + V_k * (p - p_o) + R T ln(X_k)
- * \f]
+ * @f]
* or another way to phrase this is
- * \f[
+ * @f[
* \mu_k = \mu^o_k(T,p) + R T ln(X_k)
- * \f]
- * where \f$ \mu^o_k(T,p) = \mu^{ref}_k(T) + V_k * (p - p_o)\f$
+ * @f]
+ * where @f$ \mu^o_k(T,p) = \mu^{ref}_k(T) + V_k * (p - p_o) @f$
*
* @param mu Output vector of chemical potentials.
*/
@@ -296,13 +296,13 @@ class IdealSolidSolnPhase : public ThermoPhase
/**
* Get the array of non-dimensional species solution
* chemical potentials at the current T and P
- * \f$\mu_k / \hat R T \f$.
- * \f[
+ * @f$ \mu_k / \hat R T @f$.
+ * @f[
* \mu^0_k(T,P) = \mu^{ref}_k(T) + (P - P_{ref}) * V_k + RT ln(X_k)
- * \f]
- * where \f$V_k\f$ is the molar volume of pure species *k*.
- * \f$ \mu^{ref}_k(T)\f$ is the chemical potential of pure
- * species *k* at the reference pressure, \f$P_{ref}\f$.
+ * @f]
+ * where @f$ V_k @f$ is the molar volume of pure species *k*.
+ * @f$ \mu^{ref}_k(T) @f$ is the chemical potential of pure
+ * species *k* at the reference pressure, @f$ P_{ref} @f$.
*
* @param mu Output vector of dimensionless chemical potentials.
* Length = m_kk.
@@ -319,11 +319,11 @@ class IdealSolidSolnPhase : public ThermoPhase
/*!
* Units (J/kmol). For this phase, the partial molar enthalpies are equal to
* the pure species enthalpies
- * \f[
+ * @f[
* \bar h_k(T,P) = \hat h^{ref}_k(T) + (P - P_{ref}) \hat V^0_k
- * \f]
- * The reference-state pure-species enthalpies, \f$ \hat h^{ref}_k(T) \f$,
- * at the reference pressure,\f$ P_{ref} \f$, are computed by the species
+ * @f]
+ * The reference-state pure-species enthalpies, @f$ \hat h^{ref}_k(T) @f$,
+ * at the reference pressure,@f$ P_{ref} @f$, are computed by the species
* thermodynamic property manager. They are polynomial functions of
* temperature.
* @see MultiSpeciesThermo
@@ -338,11 +338,11 @@ class IdealSolidSolnPhase : public ThermoPhase
* solution. Units: J/kmol/K. For this phase, the partial molar entropies
* are equal to the pure species entropies plus the ideal solution
* contribution.
- * \f[
+ * @f[
* \bar s_k(T,P) = \hat s^0_k(T) - R log(X_k)
- * \f]
- * The reference-state pure-species entropies,\f$ \hat s^{ref}_k(T) \f$, at
- * the reference pressure, \f$ P_{ref} \f$, are computed by the species
+ * @f]
+ * The reference-state pure-species entropies,@f$ \hat s^{ref}_k(T) @f$, at
+ * the reference pressure, @f$ P_{ref} @f$, are computed by the species
* thermodynamic property manager. They are polynomial functions of
* temperature.
* @see MultiSpeciesThermo
@@ -378,7 +378,7 @@ class IdealSolidSolnPhase : public ThermoPhase
/**
* Get the standard state chemical potentials of the species. This is the
- * array of chemical potentials at unit activity \f$ \mu^0_k(T,P) \f$. We
+ * array of chemical potentials at unit activity @f$ \mu^0_k(T,P) @f$. We
* define these here as the chemical potentials of the pure species at the
* temperature and pressure of the solution. This function is used in the
* evaluation of the equilibrium constant Kc. Therefore, Kc will also depend
@@ -397,12 +397,12 @@ class IdealSolidSolnPhase : public ThermoPhase
//! state species at the current *T* and *P* of the solution.
/*!
* We assume an incompressible constant partial molar volume here:
- * \f[
+ * @f[
* h^0_k(T,P) = h^{ref}_k(T) + (P - P_{ref}) * V_k
- * \f]
- * where \f$V_k\f$ is the molar volume of pure species *k*.
- * \f$ h^{ref}_k(T)\f$ is the enthalpy of the pure species *k* at the
- * reference pressure, \f$P_{ref}\f$.
+ * @f]
+ * where @f$ V_k @f$ is the molar volume of pure species *k*.
+ * @f$ h^{ref}_k(T) @f$ is the enthalpy of the pure species *k* at the
+ * reference pressure, @f$ P_{ref} @f$.
*
* @param hrt Vector of length m_kk, which on return hrt[k] will contain the
* nondimensional standard state enthalpy of species k.
@@ -424,12 +424,12 @@ class IdealSolidSolnPhase : public ThermoPhase
* Get the nondimensional Gibbs function for the species standard states at
* the current T and P of the solution.
*
- * \f[
+ * @f[
* \mu^0_k(T,P) = \mu^{ref}_k(T) + (P - P_{ref}) * V_k
- * \f]
- * where \f$V_k\f$ is the molar volume of pure species *k*.
- * \f$ \mu^{ref}_k(T)\f$ is the chemical potential of pure species *k*
- * at the reference pressure, \f$P_{ref}\f$.
+ * @f]
+ * where @f$ V_k @f$ is the molar volume of pure species *k*.
+ * @f$ \mu^{ref}_k(T) @f$ is the chemical potential of pure species *k*
+ * at the reference pressure, @f$ P_{ref} @f$.
*
* @param grt Vector of length m_kk, which on return sr[k] will contain the
* nondimensional standard state Gibbs function for species k.
@@ -440,12 +440,12 @@ class IdealSolidSolnPhase : public ThermoPhase
* Get the Gibbs functions for the pure species at the current *T* and *P*
* of the solution. We assume an incompressible constant partial molar
* volume here:
- * \f[
+ * @f[
* \mu^0_k(T,P) = \mu^{ref}_k(T) + (P - P_{ref}) * V_k
- * \f]
- * where \f$V_k\f$ is the molar volume of pure species *k*.
- * \f$ \mu^{ref}_k(T)\f$ is the chemical potential of pure species *k* at
- * the reference pressure, \f$P_{ref}\f$.
+ * @f]
+ * where @f$ V_k @f$ is the molar volume of pure species *k*.
+ * @f$ \mu^{ref}_k(T) @f$ is the chemical potential of pure species *k* at
+ * the reference pressure, @f$ P_{ref} @f$.
*
* @param gpure Output vector of Gibbs functions for species. Length: m_kk.
*/
@@ -456,12 +456,12 @@ class IdealSolidSolnPhase : public ThermoPhase
/**
* Get the nondimensional heat capacity at constant pressure function for
* the species standard states at the current T and P of the solution.
- * \f[
+ * @f[
* Cp^0_k(T,P) = Cp^{ref}_k(T)
- * \f]
- * where \f$V_k\f$ is the molar volume of pure species *k*.
- * \f$ Cp^{ref}_k(T)\f$ is the constant pressure heat capacity of species
- * *k* at the reference pressure, \f$p_{ref}\f$.
+ * @f]
+ * where @f$ V_k @f$ is the molar volume of pure species *k*.
+ * @f$ Cp^{ref}_k(T) @f$ is the constant pressure heat capacity of species
+ * *k* at the reference pressure, @f$ p_{ref} @f$.
*
* @param cpr Vector of length m_kk, which on return cpr[k] will contain the
* nondimensional constant pressure heat capacity for species k.
@@ -549,7 +549,7 @@ class IdealSolidSolnPhase : public ThermoPhase
/**
* Report the molar volume of species k
*
- * units - \f$ m^3 kmol^-1 \f$
+ * units - @f$ m^3 kmol^-1 @f$
*
* @param k species index
*/
@@ -558,7 +558,7 @@ class IdealSolidSolnPhase : public ThermoPhase
/**
* Fill in a return vector containing the species molar volumes.
*
- * units - \f$ m^3 kmol^-1 \f$
+ * units - @f$ m^3 kmol^-1 @f$
*
* @param smv output vector containing species molar volumes.
* Length: m_kk.
@@ -596,7 +596,7 @@ class IdealSolidSolnPhase : public ThermoPhase
//! Vector of molar volumes for each species in the solution
/**
- * Species molar volumes (\f$ m^3 kmol^-1 \f$) at the current mixture state.
+ * Species molar volumes (@f$ m^3 kmol^-1 @f$) at the current mixture state.
* For the IdealSolidSolnPhase class, these are constant.
*/
mutable vector_fp m_speciesMolarVolume;
diff --git a/include/cantera/thermo/IdealSolnGasVPSS.h b/include/cantera/thermo/IdealSolnGasVPSS.h
index ec5d6fac1f..8eff554026 100644
--- a/include/cantera/thermo/IdealSolnGasVPSS.h
+++ b/include/cantera/thermo/IdealSolnGasVPSS.h
@@ -67,12 +67,12 @@ class IdealSolnGasVPSS : public VPStandardStateTP
* Calculate the density of the mixture using the partial molar volumes and
* mole fractions as input. The formula for this is
*
- * \f[
+ * @f[
* \rho = \frac{\sum_k{X_k W_k}}{\sum_k{X_k V_k}}
- * \f]
+ * @f]
*
- * where \f$X_k\f$ are the mole fractions, \f$W_k\f$ are the molecular
- * weights, and \f$V_k\f$ are the pure species molar volumes.
+ * where @f$ X_k @f$ are the mole fractions, @f$ W_k @f$ are the molecular
+ * weights, and @f$ V_k @f$ are the pure species molar volumes.
*
* Note, the basis behind this formula is that in an ideal solution the
* partial molar volumes are equal to the species standard state molar
@@ -86,7 +86,7 @@ class IdealSolnGasVPSS : public VPStandardStateTP
virtual Units standardConcentrationUnits() const;
virtual void getActivityConcentrations(doublereal* c) const;
- //! Returns the standard concentration \f$ C^0_k \f$, which is used to
+ //! Returns the standard concentration @f$ C^0_k @f$, which is used to
//! normalize the generalized concentration.
/*!
* This is defined as the concentration by which the generalized
diff --git a/include/cantera/thermo/IonsFromNeutralVPSSTP.h b/include/cantera/thermo/IonsFromNeutralVPSSTP.h
index 24fff07301..05b860978f 100644
--- a/include/cantera/thermo/IonsFromNeutralVPSSTP.h
+++ b/include/cantera/thermo/IonsFromNeutralVPSSTP.h
@@ -108,9 +108,9 @@ class IonsFromNeutralVPSSTP : public GibbsExcessVPSSTP
//! @}
//! @name Activities, Standard States, and Activity Concentrations
//!
- //! The activity \f$a_k\f$ of a species in solution is
- //! related to the chemical potential by \f[ \mu_k = \mu_k^0(T)
- //! + \hat R T \log a_k. \f] The quantity \f$\mu_k^0(T,P)\f$ is
+ //! The activity @f$ a_k @f$ of a species in solution is
+ //! related to the chemical potential by @f[ \mu_k = \mu_k^0(T)
+ //! + \hat R T \log a_k. @f] The quantity @f$ \mu_k^0(T,P) @f$ is
//! the chemical potential at unit activity, which depends only
//! on temperature and pressure.
//! @{
@@ -132,9 +132,9 @@ class IonsFromNeutralVPSSTP : public GibbsExcessVPSSTP
* state enthalpies modified by the derivative of the molality-based
* activity coefficient wrt temperature
*
- * \f[
+ * @f[
* \bar h_k(T,P) = h^o_k(T,P) - R T^2 \frac{d \ln(\gamma_k)}{dT}
- * \f]
+ * @f]
*
* @param hbar Output vector of species partial molar enthalpies.
* Length: m_kk. Units: J/kmol
@@ -150,11 +150,11 @@ class IonsFromNeutralVPSSTP : public GibbsExcessVPSSTP
* state enthalpies modified by the derivative of the activity coefficient
* wrt temperature
*
- * \f[
+ * @f[
* \bar s_k(T,P) = s^o_k(T,P) - R T^2 \frac{d \ln(\gamma_k)}{dT}
* - R \ln( \gamma_k X_k)
* - R T \frac{d \ln(\gamma_k) }{dT}
- * \f]
+ * @f]
*
* @param sbar Output vector of species partial molar entropies.
* Length: m_kk. Units: J/kmol/K
diff --git a/include/cantera/thermo/LatticePhase.h b/include/cantera/thermo/LatticePhase.h
index 5cd7a606af..035effc06c 100644
--- a/include/cantera/thermo/LatticePhase.h
+++ b/include/cantera/thermo/LatticePhase.h
@@ -25,7 +25,7 @@ namespace Cantera
* standard states of the species are assumed to have zero volume expansivity
* and zero isothermal compressibility.
*
- * The density of matrix sites is given by the variable \f$ C_o \f$, which has
+ * The density of matrix sites is given by the variable @f$ C_o @f$, which has
* SI units of kmol m-3.
*
* ## Specification of Species Standard State Properties
@@ -39,22 +39,22 @@ namespace Cantera
* no effect on any quantities, as the molar concentration is a constant.
*
* The standard state enthalpy function is given by the following relation,
- * which has a weak dependence on the system pressure, \f$P\f$.
+ * which has a weak dependence on the system pressure, @f$ P @f$.
*
- * \f[
+ * @f[
* h^o_k(T,P) =
* h^{ref}_k(T) + \left( \frac{P - P_{ref}}{C_o} \right)
- * \f]
+ * @f]
*
* For an incompressible substance, the molar internal energy is independent of
* pressure. Since the thermodynamic properties are specified by giving the
- * standard-state enthalpy, the term \f$ \frac{P_{ref}}{C_o} \f$ is subtracted
+ * standard-state enthalpy, the term @f$ \frac{P_{ref}}{C_o} @f$ is subtracted
* from the specified reference molar enthalpy to compute the standard state
* molar internal energy:
*
- * \f[
+ * @f[
* u^o_k(T,P) = h^{ref}_k(T) - \frac{P_{ref}}{C_o}
- * \f]
+ * @f]
*
* The standard state heat capacity, internal energy, and entropy are
* independent of pressure. The standard state Gibbs free energy is obtained
@@ -63,56 +63,56 @@ namespace Cantera
* The standard state molar volume is independent of temperature, pressure, and
* species identity:
*
- * \f[
+ * @f[
* V^o_k(T,P) = \frac{1.0}{C_o}
- * \f]
+ * @f]
*
* ## Specification of Solution Thermodynamic Properties
*
- * The activity of species \f$ k \f$ defined in the phase, \f$ a_k \f$, is given
+ * The activity of species @f$ k @f$ defined in the phase, @f$ a_k @f$, is given
* by the ideal solution law:
*
- * \f[
+ * @f[
* a_k = X_k ,
- * \f]
+ * @f]
*
- * where \f$ X_k \f$ is the mole fraction of species *k*. The chemical potential
+ * where @f$ X_k @f$ is the mole fraction of species *k*. The chemical potential
* for species *k* is equal to
*
- * \f[
+ * @f[
* \mu_k(T,P) = \mu^o_k(T, P) + R T \log(X_k)
- * \f]
+ * @f]
*
* The partial molar entropy for species *k* is given by the following relation,
*
- * \f[
+ * @f[
* \tilde{s}_k(T,P) = s^o_k(T,P) - R \log(X_k) = s^{ref}_k(T) - R \log(X_k)
- * \f]
+ * @f]
*
* The partial molar enthalpy for species *k* is
*
- * \f[
+ * @f[
* \tilde{h}_k(T,P) = h^o_k(T,P) = h^{ref}_k(T) + \left( \frac{P - P_{ref}}{C_o} \right)
- * \f]
+ * @f]
*
* The partial molar Internal Energy for species *k* is
*
- * \f[
+ * @f[
* \tilde{u}_k(T,P) = u^o_k(T,P) = u^{ref}_k(T)
- * \f]
+ * @f]
*
* The partial molar Heat Capacity for species *k* is
*
- * \f[
+ * @f[
* \tilde{Cp}_k(T,P) = Cp^o_k(T,P) = Cp^{ref}_k(T)
- * \f]
+ * @f]
*
* The partial molar volume is independent of temperature, pressure, and species
* identity:
*
- * \f[
+ * @f[
* \tilde{V}_k(T,P) = V^o_k(T,P) = \frac{1.0}{C_o}
- * \f]
+ * @f]
*
* It is assumed that the reference state thermodynamics may be obtained by a
* pointer to a populated species thermodynamic property manager class (see
@@ -125,57 +125,57 @@ namespace Cantera
*
* ## Application within Kinetics Managers
*
- * \f$ C^a_k\f$ are defined such that \f$ C^a_k = a_k = X_k \f$. \f$ C^s_k \f$,
- * the standard concentration, is defined to be equal to one. \f$ a_k \f$ are
+ * @f$ C^a_k @f$ are defined such that @f$ C^a_k = a_k = X_k @f$. @f$ C^s_k @f$,
+ * the standard concentration, is defined to be equal to one. @f$ a_k @f$ are
* activities used in the thermodynamic functions. These activity (or
* generalized) concentrations are used by kinetics manager classes to compute
* the forward and reverse rates of elementary reactions. The activity
- * concentration,\f$ C^a_k \f$, is given by the following expression.
+ * concentration,@f$ C^a_k @f$, is given by the following expression.
*
- * \f[
+ * @f[
* C^a_k = C^s_k X_k = X_k
- * \f]
+ * @f]
*
* The standard concentration for species *k* is identically one
*
- * \f[
+ * @f[
* C^s_k = C^s = 1.0
- * \f]
+ * @f]
*
* For example, a bulk-phase binary gas reaction between species j and k,
* producing a new species l would have the following equation for its rate of
- * progress variable, \f$ R^1 \f$, which has units of kmol m-3 s-1.
+ * progress variable, @f$ R^1 @f$, which has units of kmol m-3 s-1.
*
- * \f[
+ * @f[
* R^1 = k^1 C_j^a C_k^a = k^1 X_j X_k
- * \f]
+ * @f]
*
* The reverse rate constant can then be obtained from the law of microscopic
* reversibility and the equilibrium expression for the system.
*
- * \f[
+ * @f[
* \frac{X_j X_k}{ X_l} = K_a^{o,1} = \exp(\frac{\mu^o_l - \mu^o_j - \mu^o_k}{R T} )
- * \f]
+ * @f]
*
- * \f$ K_a^{o,1} \f$ is the dimensionless form of the equilibrium constant,
- * associated with the pressure dependent standard states \f$ \mu^o_l(T,P) \f$
+ * @f$ K_a^{o,1} @f$ is the dimensionless form of the equilibrium constant,
+ * associated with the pressure dependent standard states @f$ \mu^o_l(T,P) @f$
* and their associated activities,
- * \f$ a_l \f$, repeated here:
+ * @f$ a_l @f$, repeated here:
*
- * \f[
+ * @f[
* \mu_l(T,P) = \mu^o_l(T, P) + R T \log(a_l)
- * \f]
+ * @f]
*
- * The concentration equilibrium constant, \f$ K_c \f$, may be obtained by
+ * The concentration equilibrium constant, @f$ K_c @f$, may be obtained by
* changing over to activity concentrations. When this is done:
*
- * \f[
+ * @f[
* \frac{C^a_j C^a_k}{ C^a_l} = C^o K_a^{o,1} = K_c^1 =
* \exp(\frac{\mu^{o}_l - \mu^{o}_j - \mu^{o}_k}{R T} )
- * \f]
+ * @f]
*
- * %Kinetics managers will calculate the concentration equilibrium constant, \f$
- * K_c \f$, using the second and third part of the above expression as a
+ * %Kinetics managers will calculate the concentration equilibrium constant, @f$
+ * K_c @f$, using the second and third part of the above expression as a
* definition for the concentration equilibrium constant.
*
* @ingroup thermoprops
@@ -211,11 +211,11 @@ class LatticePhase : public ThermoPhase
/*!
* For an ideal solution,
*
- * \f[
+ * @f[
* \hat h(T,P) = \sum_k X_k \hat h^0_k(T,P),
- * \f]
+ * @f]
*
- * The standard-state pure-species Enthalpies \f$ \hat h^0_k(T,P) \f$ are
+ * The standard-state pure-species Enthalpies @f$ \hat h^0_k(T,P) @f$ are
* computed first by the species reference state thermodynamic property
* manager and then a small pressure dependent term is added in.
*
@@ -227,10 +227,10 @@ class LatticePhase : public ThermoPhase
/*!
* For an ideal, constant partial molar volume solution mixture with
* pure species phases which exhibit zero volume expansivity:
- * \f[
+ * @f[
* \hat s(T, P, X_k) = \sum_k X_k \hat s^0_k(T) - \hat R \sum_k X_k log(X_k)
- * \f]
- * The reference-state pure-species entropies \f$ \hat s^0_k(T,p_{ref}) \f$
+ * @f]
+ * The reference-state pure-species entropies @f$ \hat s^0_k(T,p_{ref}) @f$
* are computed by the species thermodynamic property manager. The pure
* species entropies are independent of pressure since the volume
* expansivities are equal to zero.
@@ -246,11 +246,11 @@ class LatticePhase : public ThermoPhase
/*!
* For an ideal, constant partial molar volume solution mixture with
* pure species phases which exhibit zero volume expansivity:
- * \f[
+ * @f[
* \hat c_p(T,P) = \sum_k X_k \hat c^0_{p,k}(T) .
- * \f]
+ * @f]
* The heat capacity is independent of pressure. The reference-state pure-
- * species heat capacities \f$ \hat c^0_{p,k}(T) \f$ are computed by the
+ * species heat capacities @f$ \hat c^0_{p,k}(T) @f$ are computed by the
* species thermodynamic property manager.
*
* @see MultiSpeciesThermo
@@ -262,9 +262,9 @@ class LatticePhase : public ThermoPhase
/*!
* For an ideal, constant partial molar volume solution mixture with
* pure species phases which exhibit zero volume expansivity:
- * \f[
+ * @f[
* \hat c_v(T,P) = \hat c_p(T,P)
- * \f]
+ * @f]
*
* The two heat capacities are equal.
*/
@@ -304,12 +304,12 @@ class LatticePhase : public ThermoPhase
/*!
* The formula for this is
*
- * \f[
+ * @f[
* \rho = \frac{\sum_k{X_k W_k}}{\sum_k{X_k V_k}}
- * \f]
+ * @f]
*
- * where \f$X_k\f$ are the mole fractions, \f$W_k\f$ are the molecular
- * weights, and \f$V_k\f$ are the pure species molar volumes.
+ * where @f$ X_k @f$ are the mole fractions, @f$ W_k @f$ are the molecular
+ * weights, and @f$ V_k @f$ are the pure species molar volumes.
*
* Note, the basis behind this formula is that in an ideal solution the
* partial molar volumes are equal to the pure species molar volumes. We
@@ -321,9 +321,9 @@ class LatticePhase : public ThermoPhase
//! @}
//! @name Activities, Standard States, and Activity Concentrations
//!
- //! The activity \f$a_k\f$ of a species in solution is related to the
- //! chemical potential by \f[ \mu_k = \mu_k^0(T) + \hat R T \log a_k. \f] The
- //! quantity \f$\mu_k^0(T,P)\f$ is the chemical potential at unit activity,
+ //! The activity @f$ a_k @f$ of a species in solution is related to the
+ //! chemical potential by @f[ \mu_k = \mu_k^0(T) + \hat R T \log a_k. @f] The
+ //! quantity @f$ \mu_k^0(T,P) @f$ is the chemical potential at unit activity,
//! which depends only on temperature and the pressure. Activity is assumed
//! to be molality-based here.
//! @{
@@ -333,7 +333,7 @@ class LatticePhase : public ThermoPhase
//! Return the standard concentration for the kth species
/*!
- * The standard concentration \f$ C^0_k \f$ used to normalize
+ * The standard concentration @f$ C^0_k @f$ used to normalize
* the activity (that is, generalized) concentration for use
*
* For the time being, we will use the concentration of pure solvent for the
@@ -376,11 +376,11 @@ class LatticePhase : public ThermoPhase
* Returns an array of partial molar enthalpies for the species in the
* mixture. Units (J/kmol). For this phase, the partial molar enthalpies are
* equal to the pure species enthalpies
- * \f[
+ * @f[
* \bar h_k(T,P) = \hat h^{ref}_k(T) + (P - P_{ref}) \hat V^0_k
- * \f]
- * The reference-state pure-species enthalpies, \f$ \hat h^{ref}_k(T) \f$,
- * at the reference pressure,\f$ P_{ref} \f$, are computed by the species
+ * @f]
+ * The reference-state pure-species enthalpies, @f$ \hat h^{ref}_k(T) @f$,
+ * at the reference pressure,@f$ P_{ref} @f$, are computed by the species
* thermodynamic property manager. They are polynomial functions of
* temperature.
* @see MultiSpeciesThermo
@@ -395,11 +395,11 @@ class LatticePhase : public ThermoPhase
* solution. Units: J/kmol/K. For this phase, the partial molar entropies
* are equal to the pure species entropies plus the ideal solution
* contribution.
- * \f[
+ * @f[
* \bar s_k(T,P) = \hat s^0_k(T) - R log(X_k)
- * \f]
- * The reference-state pure-species entropies,\f$ \hat s^{ref}_k(T) \f$, at
- * the reference pressure, \f$ P_{ref} \f$, are computed by the species
+ * @f]
+ * The reference-state pure-species entropies,@f$ \hat s^{ref}_k(T) @f$, at
+ * the reference pressure, @f$ P_{ref} @f$, are computed by the species
* thermodynamic property manager. They are polynomial functions of
* temperature.
* @see MultiSpeciesThermo
@@ -433,9 +433,9 @@ class LatticePhase : public ThermoPhase
* A small pressure dependent term is added onto the reference state enthalpy
* to get the pressure dependence of this term.
*
- * \f[
+ * @f[
* h^o_k(T,P) = h^{ref}_k(T) + \left( \frac{P - P_{ref}}{C_o} \right)
- * \f]
+ * @f]
*
* The reference state thermodynamics is obtained by a pointer to a
* populated species thermodynamic property manager class (see
@@ -453,9 +453,9 @@ class LatticePhase : public ThermoPhase
* The entropy of the standard state is defined as independent of
* pressure here.
*
- * \f[
+ * @f[
* s^o_k(T,P) = s^{ref}_k(T)
- * \f]
+ * @f]
*
* The reference state thermodynamics is obtained by a pointer to a
* populated species thermodynamic property manager class (see
@@ -473,9 +473,9 @@ class LatticePhase : public ThermoPhase
* The standard Gibbs free energies are obtained from the enthalpy and
* entropy formulation.
*
- * \f[
+ * @f[
* g^o_k(T,P) = h^{o}_k(T,P) - T s^{o}_k(T,P)
- * \f]
+ * @f]
*
* @param grt Output vector of nondimensional standard state Gibbs free
* energies. Length: m_kk.
@@ -487,9 +487,9 @@ class LatticePhase : public ThermoPhase
/*!
* The heat capacity of the standard state is independent of pressure
*
- * \f[
+ * @f[
* Cp^o_k(T,P) = Cp^{ref}_k(T)
- * \f]
+ * @f]
*
* The reference state thermodynamics is obtained by a pointer to a
* populated species thermodynamic property manager class (see
@@ -589,7 +589,7 @@ class LatticePhase : public ThermoPhase
//! Vector of molar volumes for each species in the solution
/**
- * Species molar volumes \f$ m^3 kmol^-1 \f$
+ * Species molar volumes @f$ m^3 kmol^-1 @f$
*/
vector_fp m_speciesMolarVolume;
diff --git a/include/cantera/thermo/LatticeSolidPhase.h b/include/cantera/thermo/LatticeSolidPhase.h
index 3d434473fe..2941d4cec5 100644
--- a/include/cantera/thermo/LatticeSolidPhase.h
+++ b/include/cantera/thermo/LatticeSolidPhase.h
@@ -52,14 +52,14 @@ namespace Cantera
* contains a value for the molar density of the entire mixture. This is the
* same thing as saying that
*
- * \f[
+ * @f[
* L_i = L^{solid} \theta_i
- * \f]
+ * @f]
*
- * \f$ L_i \f$ is the molar volume of the ith lattice. \f$ L^{solid} \f$ is the
- * molar volume of the entire solid. \f$ \theta_i \f$ is a fixed weighting
+ * @f$ L_i @f$ is the molar volume of the ith lattice. @f$ L^{solid} @f$ is the
+ * molar volume of the entire solid. @f$ \theta_i @f$ is a fixed weighting
* factor for the ith lattice representing the lattice stoichiometric
- * coefficient. For this object the \f$ \theta_i \f$ values are fixed.
+ * coefficient. For this object the @f$ \theta_i @f$ values are fixed.
*
* Let's take FeS2 as an example, which may be thought of as a combination of
* two lattices: Fe and S lattice. The Fe sublattice has a molar density of 1
@@ -81,16 +81,16 @@ namespace Cantera
* The molar volume of the Lattice solid is calculated from the following
* formula
*
- * \f[
+ * @f[
* V = \sum_i{ \theta_i V_i^{lattice}}
- * \f]
+ * @f]
*
- * where \f$ V_i^{lattice} \f$ is the molar volume of the ith sublattice. This
+ * where @f$ V_i^{lattice} @f$ is the molar volume of the ith sublattice. This
* is calculated from the following standard formula.
*
- * \f[
+ * @f[
* V_i = \sum_k{ X_k V_k}
- * \f]
+ * @f]
*
* where k is a species in the ith sublattice.
*
@@ -143,14 +143,14 @@ class LatticeSolidPhase : public ThermoPhase
//! Return the Molar Enthalpy. Units: J/kmol.
/*!
- * The molar enthalpy is determined by the following formula, where \f$
- * \theta_n \f$ is the lattice stoichiometric coefficient of the nth lattice
+ * The molar enthalpy is determined by the following formula, where @f$
+ * \theta_n @f$ is the lattice stoichiometric coefficient of the nth lattice
*
- * \f[
+ * @f[
* \tilde h(T,P) = {\sum_n \theta_n \tilde h_n(T,P) }
- * \f]
+ * @f]
*
- * \f$ \tilde h_n(T,P) \f$ is the enthalpy of the nth lattice.
+ * @f$ \tilde h_n(T,P) @f$ is the enthalpy of the nth lattice.
*
* units J/kmol
*/
@@ -158,14 +158,14 @@ class LatticeSolidPhase : public ThermoPhase
//! Return the Molar Internal Energy. Units: J/kmol.
/*!
- * The molar enthalpy is determined by the following formula, where \f$
- * \theta_n \f$ is the lattice stoichiometric coefficient of the nth lattice
+ * The molar enthalpy is determined by the following formula, where @f$
+ * \theta_n @f$ is the lattice stoichiometric coefficient of the nth lattice
*
- * \f[
+ * @f[
* \tilde u(T,P) = {\sum_n \theta_n \tilde u_n(T,P) }
- * \f]
+ * @f]
*
- * \f$ \tilde u_n(T,P) \f$ is the internal energy of the nth lattice.
+ * @f$ \tilde u_n(T,P) @f$ is the internal energy of the nth lattice.
*
* units J/kmol
*/
@@ -173,14 +173,14 @@ class LatticeSolidPhase : public ThermoPhase
//! Return the Molar Entropy. Units: J/kmol/K.
/*!
- * The molar enthalpy is determined by the following formula, where \f$
- * \theta_n \f$ is the lattice stoichiometric coefficient of the nth lattice
+ * The molar enthalpy is determined by the following formula, where @f$
+ * \theta_n @f$ is the lattice stoichiometric coefficient of the nth lattice
*
- * \f[
+ * @f[
* \tilde s(T,P) = \sum_n \theta_n \tilde s_n(T,P)
- * \f]
+ * @f]
*
- * \f$ \tilde s_n(T,P) \f$ is the molar entropy of the nth lattice.
+ * @f$ \tilde s_n(T,P) @f$ is the molar entropy of the nth lattice.
*
* units J/kmol/K
*/
@@ -189,14 +189,14 @@ class LatticeSolidPhase : public ThermoPhase
//! Return the Molar Gibbs energy. Units: J/kmol.
/*!
* The molar Gibbs free energy is determined by the following formula, where
- * \f$ \theta_n \f$ is the lattice stoichiometric coefficient of the nth
+ * @f$ \theta_n @f$ is the lattice stoichiometric coefficient of the nth
* lattice
*
- * \f[
+ * @f[
* \tilde h(T,P) = {\sum_n \theta_n \tilde h_n(T,P) }
- * \f]
+ * @f]
*
- * \f$ \tilde h_n(T,P) \f$ is the enthalpy of the nth lattice.
+ * @f$ \tilde h_n(T,P) @f$ is the enthalpy of the nth lattice.
*
* units J/kmol
*/
@@ -205,14 +205,14 @@ class LatticeSolidPhase : public ThermoPhase
//! Return the constant pressure heat capacity. Units: J/kmol/K
/*!
* The molar constant pressure heat capacity is determined by the following
- * formula, where \f$ C_n \f$ is the lattice molar density of the nth
- * lattice, and \f$ C_T \f$ is the molar density of the solid compound.
+ * formula, where @f$ C_n @f$ is the lattice molar density of the nth
+ * lattice, and @f$ C_T @f$ is the molar density of the solid compound.
*
- * \f[
+ * @f[
* \tilde c_{p,n}(T,P) = \frac{\sum_n C_n \tilde c_{p,n}(T,P) }{C_T},
- * \f]
+ * @f]
*
- * \f$ \tilde c_{p,n}(T,P) \f$ is the heat capacity of the nth lattice.
+ * @f$ \tilde c_{p,n}(T,P) @f$ is the heat capacity of the nth lattice.
*
* units J/kmol/K
*/
@@ -221,14 +221,14 @@ class LatticeSolidPhase : public ThermoPhase
//! Return the constant volume heat capacity. Units: J/kmol/K
/*!
* The molar constant volume heat capacity is determined by the following
- * formula, where \f$ C_n \f$ is the lattice molar density of the nth
- * lattice, and \f$ C_T \f$ is the molar density of the solid compound.
+ * formula, where @f$ C_n @f$ is the lattice molar density of the nth
+ * lattice, and @f$ C_T @f$ is the molar density of the solid compound.
*
- * \f[
+ * @f[
* \tilde c_{v,n}(T,P) = \frac{\sum_n C_n \tilde c_{v,n}(T,P) }{C_T},
- * \f]
+ * @f]
*
- * \f$ \tilde c_{v,n}(T,P) \f$ is the heat capacity of the nth lattice.
+ * @f$ \tilde c_{v,n}(T,P) @f$ is the heat capacity of the nth lattice.
*
* units J/kmol/K
*/
@@ -254,11 +254,11 @@ class LatticeSolidPhase : public ThermoPhase
/*!
* The formula for this is
*
- * \f[
+ * @f[
* \rho = \sum_n{ \rho_n \theta_n }
- * \f]
+ * @f]
*
- * where \f$ \rho_n \f$ is the density of the nth sublattice
+ * where @f$ \rho_n @f$ is the density of the nth sublattice
*/
doublereal calcDensity();
@@ -344,11 +344,11 @@ class LatticeSolidPhase : public ThermoPhase
/*!
* Units (J/kmol). For this phase, the partial molar enthalpies are equal to
* the pure species enthalpies
- * \f[
+ * @f[
* \bar h_k(T,P) = \hat h^{ref}_k(T) + (P - P_{ref}) \hat V^0_k
- * \f]
- * The reference-state pure-species enthalpies, \f$ \hat h^{ref}_k(T) \f$,
- * at the reference pressure,\f$ P_{ref} \f$, are computed by the species
+ * @f]
+ * The reference-state pure-species enthalpies, @f$ \hat h^{ref}_k(T) @f$,
+ * at the reference pressure,@f$ P_{ref} @f$, are computed by the species
* thermodynamic property manager. They are polynomial functions of
* temperature.
* @see MultiSpeciesThermo
@@ -363,11 +363,11 @@ class LatticeSolidPhase : public ThermoPhase
* solution. Units: J/kmol/K. For this phase, the partial molar entropies
* are equal to the pure species entropies plus the ideal solution
* contribution.
- * \f[
+ * @f[
* \bar s_k(T,P) = \hat s^0_k(T) - R log(X_k)
- * \f]
- * The reference-state pure-species entropies,\f$ \hat s^{ref}_k(T) \f$, at
- * the reference pressure, \f$ P_{ref} \f$, are computed by the species
+ * @f]
+ * The reference-state pure-species entropies,@f$ \hat s^{ref}_k(T) @f$, at
+ * the reference pressure, @f$ P_{ref} @f$, are computed by the species
* thermodynamic property manager. They are polynomial functions of
* temperature.
* @see MultiSpeciesThermo
@@ -401,7 +401,7 @@ class LatticeSolidPhase : public ThermoPhase
//! the species at their standard states at the current *T* and *P* of the
//! solution.
/*!
- * These are the standard state chemical potentials \f$ \mu^0_k(T,P) \f$.
+ * These are the standard state chemical potentials @f$ \mu^0_k(T,P) @f$.
* The values are evaluated at the current temperature and pressure of the
* solution.
*
@@ -428,7 +428,7 @@ class LatticeSolidPhase : public ThermoPhase
//! Add a lattice to this phase
void addLattice(shared_ptr lattice);
- //! Set the lattice stoichiometric coefficients, \f$ \theta_i \f$
+ //! Set the lattice stoichiometric coefficients, @f$ \theta_i @f$
void setLatticeStoichiometry(const compositionMap& comp);
virtual void setParameters(const AnyMap& phaseNode,
diff --git a/include/cantera/thermo/MargulesVPSSTP.h b/include/cantera/thermo/MargulesVPSSTP.h
index 9a80ac59a6..c43620699c 100644
--- a/include/cantera/thermo/MargulesVPSSTP.h
+++ b/include/cantera/thermo/MargulesVPSSTP.h
@@ -41,173 +41,173 @@ namespace Cantera
* the generalization of the Margules formulation for a phase that has more than
* 2 species.
*
- * \f[
+ * @f[
* G^E = \sum_i \left( H_{Ei} - T S_{Ei} \right)
- * \f]
- * \f[
+ * @f]
+ * @f[
* H^E_i = n X_{Ai} X_{Bi} \left( h_{o,i} + h_{1,i} X_{Bi} \right)
- * \f]
- * \f[
+ * @f]
+ * @f[
* S^E_i = n X_{Ai} X_{Bi} \left( s_{o,i} + s_{1,i} X_{Bi} \right)
- * \f]
+ * @f]
*
* where n is the total moles in the solution.
*
* The activity of a species defined in the phase is given by an excess Gibbs
* free energy formulation.
*
- * \f[
+ * @f[
* a_k = \gamma_k X_k
- * \f]
+ * @f]
*
* where
*
- * \f[
+ * @f[
* R T \ln( \gamma_k )= \frac{d(n G^E)}{d(n_k)}\Bigg|_{n_i}
- * \f]
+ * @f]
*
* Taking the derivatives results in the following expression
*
- * \f[
+ * @f[
* R T \ln( \gamma_k )= \sum_i \left( \left( \delta_{Ai,k} X_{Bi} + \delta_{Bi,k} X_{Ai} - X_{Ai} X_{Bi} \right)
* \left( g^E_{o,i} + g^E_{1,i} X_{Bi} \right) +
* \left( \delta_{Bi,k} - X_{Bi} \right) X_{Ai} X_{Bi} g^E_{1,i} \right)
- * \f]
+ * @f]
* where
- * \f$ g^E_{o,i} = h_{o,i} - T s_{o,i} \f$ and
- * \f$ g^E_{1,i} = h_{1,i} - T s_{1,i} \f$ and where
- * \f$ X_k \f$ is the mole fraction of species *k*.
+ * @f$ g^E_{o,i} = h_{o,i} - T s_{o,i} @f$ and
+ * @f$ g^E_{1,i} = h_{1,i} - T s_{1,i} @f$ and where
+ * @f$ X_k @f$ is the mole fraction of species *k*.
*
* This object inherits from the class VPStandardStateTP. Therefore, the
* specification and calculation of all standard state and reference state
* values are handled at that level. Various functional forms for the standard
* state are permissible. The chemical potential for species *k* is equal to
*
- * \f[
+ * @f[
* \mu_k(T,P) = \mu^o_k(T, P) + R T \ln(\gamma_k X_k)
- * \f]
+ * @f]
*
* The partial molar entropy for species *k* is given by
*
- * \f[
+ * @f[
* \tilde{s}_k(T,P) = s^o_k(T,P) - R \ln( \gamma_k X_k )
* - R T \frac{d \ln(\gamma_k) }{dT}
- * \f]
+ * @f]
*
* The partial molar enthalpy for species *k* is given by
*
- * \f[
+ * @f[
* \tilde{h}_k(T,P) = h^o_k(T,P) - R T^2 \frac{d \ln(\gamma_k)}{dT}
- * \f]
+ * @f]
*
* The partial molar volume for species *k* is
*
- * \f[
+ * @f[
* \tilde V_k(T,P) = V^o_k(T,P) + R T \frac{d \ln(\gamma_k) }{dP}
- * \f]
+ * @f]
*
* The partial molar Heat Capacity for species *k* is
*
- * \f[
+ * @f[
* \tilde{C}_{p,k}(T,P) = C^o_{p,k}(T,P) - 2 R T \frac{d \ln( \gamma_k )}{dT}
* - R T^2 \frac{d^2 \ln(\gamma_k) }{{dT}^2}
- * \f]
+ * @f]
*
* ## Application within Kinetics Managers
*
- * \f$ C^a_k\f$ are defined such that \f$ a_k = C^a_k / C^s_k, \f$ where
- * \f$ C^s_k \f$ is a standard concentration defined below and \f$ a_k \f$ are
+ * @f$ C^a_k @f$ are defined such that @f$ a_k = C^a_k / C^s_k, @f$ where
+ * @f$ C^s_k @f$ is a standard concentration defined below and @f$ a_k @f$ are
* activities used in the thermodynamic functions. These activity (or
* generalized) concentrations are used by kinetics manager classes to compute
* the forward and reverse rates of elementary reactions. The activity
- * concentration,\f$ C^a_k \f$,is given by the following expression.
+ * concentration,@f$ C^a_k @f$,is given by the following expression.
*
- * \f[
+ * @f[
* C^a_k = C^s_k X_k = \frac{P}{R T} X_k
- * \f]
+ * @f]
*
* The standard concentration for species *k* is independent of *k* and equal to
*
- * \f[
+ * @f[
* C^s_k = C^s = \frac{P}{R T}
- * \f]
+ * @f]
*
* For example, a bulk-phase binary gas reaction between species j and k,
* producing a new gas species l would have the following equation for its rate
- * of progress variable, \f$ R^1 \f$, which has units of kmol m-3 s-1.
+ * of progress variable, @f$ R^1 @f$, which has units of kmol m-3 s-1.
*
- * \f[
+ * @f[
* R^1 = k^1 C_j^a C_k^a = k^1 (C^s a_j) (C^s a_k)
- * \f]
+ * @f]
* where
- * \f[
+ * @f[
* C_j^a = C^s a_j \mbox{\quad and \quad} C_k^a = C^s a_k
- * \f]
+ * @f]
*
- * \f$ C_j^a \f$ is the activity concentration of species j, and \f$ C_k^a \f$
- * is the activity concentration of species k. \f$ C^s \f$ is the standard
- * concentration. \f$ a_j \f$ is the activity of species j which is equal to the
+ * @f$ C_j^a @f$ is the activity concentration of species j, and @f$ C_k^a @f$
+ * is the activity concentration of species k. @f$ C^s @f$ is the standard
+ * concentration. @f$ a_j @f$ is the activity of species j which is equal to the
* mole fraction of j.
*
* The reverse rate constant can then be obtained from the law of microscopic
* reversibility and the equilibrium expression for the system.
*
- * \f[
+ * @f[
* \frac{a_j a_k}{ a_l} = K_a^{o,1} = \exp(\frac{\mu^o_l - \mu^o_j - \mu^o_k}{R T} )
- * \f]
+ * @f]
*
- * \f$ K_a^{o,1} \f$ is the dimensionless form of the equilibrium constant,
- * associated with the pressure dependent standard states \f$ \mu^o_l(T,P) \f$
- * and their associated activities, \f$ a_l \f$, repeated here:
+ * @f$ K_a^{o,1} @f$ is the dimensionless form of the equilibrium constant,
+ * associated with the pressure dependent standard states @f$ \mu^o_l(T,P) @f$
+ * and their associated activities, @f$ a_l @f$, repeated here:
*
- * \f[
+ * @f[
* \mu_l(T,P) = \mu^o_l(T, P) + R T \log(a_l)
- * \f]
+ * @f]
*
* We can switch over to expressing the equilibrium constant in terms of the
* reference state chemical potentials
*
- * \f[
+ * @f[
* K_a^{o,1} = \exp(\frac{\mu^{ref}_l - \mu^{ref}_j - \mu^{ref}_k}{R T} ) * \frac{P_{ref}}{P}
- * \f]
+ * @f]
*
- * The concentration equilibrium constant, \f$ K_c \f$, may be obtained by
+ * The concentration equilibrium constant, @f$ K_c @f$, may be obtained by
* changing over to activity concentrations. When this is done:
*
- * \f[
+ * @f[
* \frac{C^a_j C^a_k}{ C^a_l} = C^o K_a^{o,1} = K_c^1 =
* \exp(\frac{\mu^{ref}_l - \mu^{ref}_j - \mu^{ref}_k}{R T} ) * \frac{P_{ref}}{RT}
- * \f]
+ * @f]
*
- * %Kinetics managers will calculate the concentration equilibrium constant, \f$
- * K_c \f$, using the second and third part of the above expression as a
+ * %Kinetics managers will calculate the concentration equilibrium constant, @f$
+ * K_c @f$, using the second and third part of the above expression as a
* definition for the concentration equilibrium constant.
*
* For completeness, the pressure equilibrium constant may be obtained as well
*
- * \f[
+ * @f[
* \frac{P_j P_k}{ P_l P_{ref}} = K_p^1 = \exp(\frac{\mu^{ref}_l - \mu^{ref}_j - \mu^{ref}_k}{R T} )
- * \f]
+ * @f]
*
- * \f$ K_p \f$ is the simplest form of the equilibrium constant for ideal gases.
+ * @f$ K_p @f$ is the simplest form of the equilibrium constant for ideal gases.
* However, it isn't necessarily the simplest form of the equilibrium constant
- * for other types of phases; \f$ K_c \f$ is used instead because it is
+ * for other types of phases; @f$ K_c @f$ is used instead because it is
* completely general.
*
* The reverse rate of progress may be written down as
- * \f[
+ * @f[
* R^{-1} = k^{-1} C_l^a = k^{-1} (C^o a_l)
- * \f]
+ * @f]
*
* where we can use the concept of microscopic reversibility to write the
* reverse rate constant in terms of the forward rate constant and the
- * concentration equilibrium constant, \f$ K_c \f$.
+ * concentration equilibrium constant, @f$ K_c @f$.
*
- * \f[
+ * @f[
* k^{-1} = k^1 K^1_c
- * \f]
+ * @f]
*
- * \f$k^{-1} \f$ has units of s-1.
+ * @f$ k^{-1} @f$ has units of s-1.
*
* @ingroup thermoprops
*/
@@ -239,9 +239,9 @@ class MargulesVPSSTP : public GibbsExcessVPSSTP
//! @}
//! @name Activities, Standard States, and Activity Concentrations
//!
- //! The activity \f$a_k\f$ of a species in solution is related to the
- //! chemical potential by \f[ \mu_k = \mu_k^0(T) + \hat R T \log a_k. \f] The
- //! quantity \f$\mu_k^0(T,P)\f$ is the chemical potential at unit activity,
+ //! The activity @f$ a_k @f$ of a species in solution is related to the
+ //! chemical potential by @f[ \mu_k = \mu_k^0(T) + \hat R T \log a_k. @f] The
+ //! quantity @f$ \mu_k^0(T,P) @f$ is the chemical potential at unit activity,
//! which depends only on temperature and pressure.
//! @{
@@ -262,9 +262,9 @@ class MargulesVPSSTP : public GibbsExcessVPSSTP
* state enthalpies modified by the derivative of the molality-based
* activity coefficient wrt temperature
*
- * \f[
+ * @f[
* \bar h_k(T,P) = h^o_k(T,P) - R T^2 \frac{d \ln(\gamma_k)}{dT}
- * \f]
+ * @f]
*
* @param hbar Vector of returned partial molar enthalpies
* (length m_kk, units = J/kmol)
@@ -280,11 +280,11 @@ class MargulesVPSSTP : public GibbsExcessVPSSTP
* state enthalpies modified by the derivative of the activity coefficient
* wrt temperature
*
- * \f[
+ * @f[
* \bar s_k(T,P) = s^o_k(T,P) - R T^2 \frac{d \ln(\gamma_k)}{dT}
* - R \ln( \gamma_k X_k)
* - R T \frac{d \ln(\gamma_k) }{dT}
- * \f]
+ * @f]
*
* @param sbar Vector of returned partial molar entropies
* (length m_kk, units = J/kmol/K)
@@ -300,13 +300,13 @@ class MargulesVPSSTP : public GibbsExcessVPSSTP
* state enthalpies modified by the derivative of the activity coefficient
* wrt temperature
*
- * \f[
+ * @f[
* ???????????????
* \bar s_k(T,P) = s^o_k(T,P) - R T^2 \frac{d \ln(\gamma_k)}{dT}
* - R \ln( \gamma_k X_k)
* - R T \frac{d \ln(\gamma_k) }{dT}
* ???????????????
- * \f]
+ * @f]
*
* @param cpbar Vector of returned partial molar heat capacities
* (length m_kk, units = J/kmol/K)
diff --git a/include/cantera/thermo/MixtureFugacityTP.h b/include/cantera/thermo/MixtureFugacityTP.h
index b258077c01..2d468d8e1d 100644
--- a/include/cantera/thermo/MixtureFugacityTP.h
+++ b/include/cantera/thermo/MixtureFugacityTP.h
@@ -128,7 +128,7 @@ class MixtureFugacityTP : public ThermoPhase
//! Get the array of non-dimensional species chemical potentials
//! These are partial molar Gibbs free energies.
/*!
- * \f$ \mu_k / \hat R T \f$.
+ * @f$ \mu_k / \hat R T @f$.
* Units: unitless
*
* We close the loop on this function, here, calling getChemPotentials() and
@@ -151,8 +151,8 @@ class MixtureFugacityTP : public ThermoPhase
//! Get the array of chemical potentials at unit activity.
/*!
- * These are the standard state chemical potentials \f$ \mu^0_k(T,P)
- * \f$. The values are evaluated at the current temperature and pressure.
+ * These are the standard state chemical potentials @f$ \mu^0_k(T,P)
+ * @f$. The values are evaluated at the current temperature and pressure.
*
* For all objects with the Mixture Fugacity approximation, we define the
* standard state as an ideal gas at the current temperature and pressure
@@ -217,9 +217,9 @@ class MixtureFugacityTP : public ThermoPhase
* standard state as an ideal gas at the current temperature and pressure
* of the solution.
*
- * \f[
+ * @f[
* u^{ss}_k(T,P) = h^{ss}_k(T) - P * V^{ss}_k
- * \f]
+ * @f]
*
* @param urt Output vector of nondimensional standard state internal
* energies. length = m_kk.
@@ -342,9 +342,9 @@ class MixtureFugacityTP : public ThermoPhase
//! Calculate the value of z
/*!
- * \f[
+ * @f[
* z = \frac{P v}{R T}
- * \f]
+ * @f]
*
* returns the value of z
*/
diff --git a/include/cantera/thermo/MolalityVPSSTP.h b/include/cantera/thermo/MolalityVPSSTP.h
index ecd9e26580..9df7005b7d 100644
--- a/include/cantera/thermo/MolalityVPSSTP.h
+++ b/include/cantera/thermo/MolalityVPSSTP.h
@@ -34,10 +34,10 @@ namespace Cantera
* Activity coefficients for species k may be altered between scales s1 to s2
* using the following formula
*
- * \f[
+ * @f[
* ln(\gamma_k^{s2}) = ln(\gamma_k^{s1})
* + \frac{z_k}{z_j} \left( ln(\gamma_j^{s2}) - ln(\gamma_j^{s1}) \right)
- * \f]
+ * @f]
*
* where j is any one species.
*/
@@ -51,17 +51,17 @@ const int PHSCALE_PITZER = 0;
* Activity coefficients for species k may be altered between scales s1 to s2
* using the following formula
*
- * \f[
+ * @f[
* ln(\gamma_k^{s2}) = ln(\gamma_k^{s1})
* + \frac{z_k}{z_j} \left( ln(\gamma_j^{s2}) - ln(\gamma_j^{s1}) \right)
- * \f]
+ * @f]
*
* where j is any one species. For the NBS scale, j is equal to the Cl- species
* and
*
- * \f[
+ * @f[
* ln(\gamma_{Cl-}^{s2}) = \frac{-A_{\phi} \sqrt{I}}{1.0 + 1.5 \sqrt{I}}
- * \f]
+ * @f]
*
* This is the NBS pH scale, which is used in all conventional pH measurements.
* and is based on the Bates-Guggenheim equations.
@@ -83,88 +83,88 @@ const int PHSCALE_NBS = 1;
* MolalityVPSSTP class return `cAC_CONVENTION_MOLALITY` from this member
* function.
*
- * The molality of a solute, \f$ m_i \f$, is defined as
+ * The molality of a solute, @f$ m_i @f$, is defined as
*
- * \f[
+ * @f[
* m_i = \frac{n_i}{\tilde{M}_o n_o}
- * \f]
+ * @f]
* where
- * \f[
+ * @f[
* \tilde{M}_o = \frac{M_o}{1000}
- * \f]
+ * @f]
*
- * where \f$ M_o \f$ is the molecular weight of the solvent. The molality has
+ * where @f$ M_o @f$ is the molecular weight of the solvent. The molality has
* units of gmol/kg. For the solute, the molality may be considered
* as the amount of gmol's of solute per kg of solvent, a natural experimental
* quantity.
*
* The formulas for calculating mole fractions if given the molalities of the
- * solutes is stated below. First calculate \f$ L^{sum} \f$, an intermediate
+ * solutes is stated below. First calculate @f$ L^{sum} @f$, an intermediate
* quantity.
*
- * \f[
+ * @f[
* L^{sum} = \frac{1}{\tilde{M}_o X_o} = \frac{1}{\tilde{M}_o} + \sum_{i\ne o} m_i
- * \f]
+ * @f]
* Then,
- * \f[
+ * @f[
* X_o = \frac{1}{\tilde{M}_o L^{sum}}
- * \f]
- * \f[
+ * @f]
+ * @f[
* X_i = \frac{m_i}{L^{sum}}
- * \f]
- * where \f$ X_o \f$ is the mole fraction of solvent, and \f$ X_o \f$ is the
+ * @f]
+ * where @f$ X_o @f$ is the mole fraction of solvent, and @f$ X_o @f$ is the
* mole fraction of solute *i*. Thus, the molality scale and the mole fraction
* scale offer a one-to-one mapping between each other, except in the limit of a
* zero solvent mole fraction.
*
* The standard states for thermodynamic objects that derive from MolalityVPSSTP
- * are on the unit molality basis. Chemical potentials of the solutes, \f$ \mu_k
- * \f$, and the solvent, \f$ \mu_o \f$, which are based on the molality form,
+ * are on the unit molality basis. Chemical potentials of the solutes, @f$ \mu_k
+ * @f$, and the solvent, @f$ \mu_o @f$, which are based on the molality form,
* have the following general format:
*
- * \f[
+ * @f[
* \mu_k = \mu^{\triangle}_k(T,P) + R T ln(\gamma_k^{\triangle} \frac{m_k}{m^\triangle})
- * \f]
- * \f[
+ * @f]
+ * @f[
* \mu_o = \mu^o_o(T,P) + RT ln(a_o)
- * \f]
+ * @f]
*
- * where \f$ \gamma_k^{\triangle} \f$ is the molality based activity coefficient
- * for species \f$k\f$.
+ * where @f$ \gamma_k^{\triangle} @f$ is the molality based activity coefficient
+ * for species @f$ k @f$.
*
* The chemical potential of the solvent is thus expressed in a different format
* than the chemical potential of the solutes. Additionally, the activity of the
- * solvent, \f$ a_o \f$, is further reexpressed in terms of an osmotic
- * coefficient, \f$ \phi \f$.
- * \f[
+ * solvent, @f$ a_o @f$, is further reexpressed in terms of an osmotic
+ * coefficient, @f$ \phi @f$.
+ * @f[
* \phi = \frac{- ln(a_o)}{\tilde{M}_o \sum_{i \ne o} m_i}
- * \f]
+ * @f]
*
- * MolalityVPSSTP::osmoticCoefficient() returns the value of \f$ \phi \f$. Note
+ * MolalityVPSSTP::osmoticCoefficient() returns the value of @f$ \phi @f$. Note
* there are a few of definitions of the osmotic coefficient floating around. We
* use the one defined in (Activity Coefficients in Electrolyte Solutions, K. S.
* Pitzer CRC Press, Boca Raton, 1991, p. 85, Eqn. 28). This definition is most
* clearly related to theoretical calculation.
*
- * The molar-based activity coefficients \f$ \gamma_k \f$ may be calculated from
- * the molality-based activity coefficients, \f$ \gamma_k^\triangle \f$ by the
+ * The molar-based activity coefficients @f$ \gamma_k @f$ may be calculated from
+ * the molality-based activity coefficients, @f$ \gamma_k^\triangle @f$ by the
* following formula.
- * \f[
+ * @f[
* \gamma_k = \frac{\gamma_k^\triangle}{X_o}
- * \f]
+ * @f]
* For purposes of establishing a convention, the molar activity coefficient of
* the solvent is set equal to the molality-based activity coefficient of the
* solvent:
- * \f[
+ * @f[
* \gamma_o = \gamma_o^\triangle
- * \f]
+ * @f]
*
* The molality-based and molarity-based standard states may be related to one
* another by the following formula.
*
- * \f[
+ * @f[
* \mu_k^\triangle(T,P) = \mu_k^o(T,P) + R T \ln(\tilde{M}_o m^\triangle)
- * \f]
+ * @f]
*
* An important convention is followed in all routines that derive from
* MolalityVPSSTP. Standard state thermodynamic functions and reference state
@@ -194,17 +194,17 @@ const int PHSCALE_NBS = 1;
* Activity coefficients for species k may be altered between scales s1 to s2
* using the following formula
*
- * \f[
+ * @f[
* ln(\gamma_k^{s2}) = ln(\gamma_k^{s1})
* + \frac{z_k}{z_j} \left( ln(\gamma_j^{s2}) - ln(\gamma_j^{s1}) \right)
- * \f]
+ * @f]
*
* where j is any one species. For the NBS scale, j is equal to the Cl- species
* and
*
- * \f[
+ * @f[
* ln(\gamma_{Cl-}^{s2}) = \frac{-A_{\phi} \sqrt{I}}{1.0 + 1.5 \sqrt{I}}
- * \f]
+ * @f]
*
* The Pitzer scale doesn't actually change anything. The pitzer scale is
* defined as the raw unscaled activity coefficients produced by the underlying
@@ -289,15 +289,15 @@ class MolalityVPSSTP : public VPStandardStateTP
/*!
* We calculate the vector of molalities of the species in the phase and
* store the result internally:
- * \f[
+ * @f[
* m_i = \frac{X_i}{1000 * M_o * X_{o,p}}
- * \f]
+ * @f]
* where
- * - \f$ M_o \f$ is the molecular weight of the solvent
- * - \f$ X_o \f$ is the mole fraction of the solvent
- * - \f$ X_i \f$ is the mole fraction of the solute.
- * - \f$ X_{o,p} = \max (X_{o}^{min}, X_o) \f$
- * - \f$ X_{o}^{min} \f$ = minimum mole fraction of solvent allowed
+ * - @f$ M_o @f$ is the molecular weight of the solvent
+ * - @f$ X_o @f$ is the mole fraction of the solvent
+ * - @f$ X_i @f$ is the mole fraction of the solute.
+ * - @f$ X_{o,p} = \max (X_{o}^{min}, X_o) @f$
+ * - @f$ X_{o}^{min} @f$ = minimum mole fraction of solvent allowed
* in the denominator.
*/
void calcMolalities() const;
@@ -305,15 +305,15 @@ class MolalityVPSSTP : public VPStandardStateTP
//! This function will return the molalities of the species.
/*!
* We calculate the vector of molalities of the species in the phase
- * \f[
+ * @f[
* m_i = \frac{X_i}{1000 * M_o * X_{o,p}}
- * \f]
+ * @f]
* where
- * - \f$ M_o \f$ is the molecular weight of the solvent
- * - \f$ X_o \f$ is the mole fraction of the solvent
- * - \f$ X_i \f$ is the mole fraction of the solute.
- * - \f$ X_{o,p} = \max (X_{o}^{min}, X_o) \f$
- * - \f$ X_{o}^{min} \f$ = minimum mole fraction of solvent allowed
+ * - @f$ M_o @f$ is the molecular weight of the solvent
+ * - @f$ X_o @f$ is the mole fraction of the solvent
+ * - @f$ X_i @f$ is the mole fraction of the solute.
+ * - @f$ X_{o,p} = \max (X_{o}^{min}, X_o) @f$
+ * - @f$ X_{o}^{min} @f$ = minimum mole fraction of solvent allowed
* in the denominator.
*
* @param molal Output vector of molalities. Length: m_kk.
@@ -325,30 +325,30 @@ class MolalityVPSSTP : public VPStandardStateTP
* Note, the entry for the solvent is not used. We are supplied with the
* molalities of all of the solute species. We then calculate the mole
* fractions of all species and update the ThermoPhase object.
- * \f[
+ * @f[
* m_i = \frac{X_i}{M_o/1000 * X_{o,p}}
- * \f]
+ * @f]
* where
- * - \f$M_o\f$ is the molecular weight of the solvent
- * - \f$X_o\f$ is the mole fraction of the solvent
- * - \f$X_i\f$ is the mole fraction of the solute.
- * - \f$X_{o,p} = \max(X_o^{min}, X_o)\f$
- * - \f$X_o^{min}\f$ = minimum mole fraction of solvent allowed
+ * - @f$ M_o @f$ is the molecular weight of the solvent
+ * - @f$ X_o @f$ is the mole fraction of the solvent
+ * - @f$ X_i @f$ is the mole fraction of the solute.
+ * - @f$ X_{o,p} = \max(X_o^{min}, X_o) @f$
+ * - @f$ X_o^{min} @f$ = minimum mole fraction of solvent allowed
* in the denominator.
*
* The formulas for calculating mole fractions are
- * \f[
+ * @f[
* L^{sum} = \frac{1}{\tilde{M}_o X_o} = \frac{1}{\tilde{M}_o} + \sum_{i\ne o} m_i
- * \f]
+ * @f]
* Then,
- * \f[
+ * @f[
* X_o = \frac{1}{\tilde{M}_o L^{sum}}
- * \f]
- * \f[
+ * @f]
+ * @f[
* X_i = \frac{m_i}{L^{sum}}
- * \f]
+ * @f]
* It is currently an error if the solvent mole fraction is attempted to be
- * set to a value lower than \f$ X_o^{min} \f$.
+ * set to a value lower than @f$ X_o^{min} @f$.
*
* @param molal Input vector of molalities. Length: m_kk.
*/
@@ -375,9 +375,9 @@ class MolalityVPSSTP : public VPStandardStateTP
//! @}
//! @name Activities, Standard States, and Activity Concentrations
//!
- //! The activity \f$a_k\f$ of a species in solution is related to the
- //! chemical potential by \f[ \mu_k = \mu_k^0(T) + \hat R T \log a_k. \f] The
- //! quantity \f$\mu_k^0(T,P)\f$ is the chemical potential at unit activity,
+ //! The activity @f$ a_k @f$ of a species in solution is related to the
+ //! chemical potential by @f[ \mu_k = \mu_k^0(T) + \hat R T \log a_k. @f] The
+ //! quantity @f$ \mu_k^0(T,P) @f$ is the chemical potential at unit activity,
//! which depends only on temperature and pressure.
//! @{
@@ -397,9 +397,9 @@ class MolalityVPSSTP : public VPStandardStateTP
* consistent with the molality scale. Therefore, this function must return
* molality-based activities.
*
- * \f[
+ * @f[
* a_i^\triangle = \gamma_k^{\triangle} \frac{m_k}{m^\triangle}
- * \f]
+ * @f]
*
* This function must be implemented in derived classes.
*
@@ -415,20 +415,20 @@ class MolalityVPSSTP : public VPStandardStateTP
* of the molality-based activity coefficients.
* See Denbigh p. 278 for a thorough discussion.
*
- * The molar-based activity coefficients \f$ \gamma_k \f$ may be calculated
- * from the molality-based activity coefficients, \f$ \gamma_k^\triangle \f$
+ * The molar-based activity coefficients @f$ \gamma_k @f$ may be calculated
+ * from the molality-based activity coefficients, @f$ \gamma_k^\triangle @f$
* by the following formula.
- * \f[
+ * @f[
* \gamma_k = \frac{\gamma_k^\triangle}{X_o}
- * \f]
+ * @f]
*
* For purposes of establishing a convention, the molar activity coefficient of the
* solvent is set equal to the molality-based activity coefficient of the
* solvent:
*
- * \f[
+ * @f[
* \gamma_o = \gamma_o^\triangle
- * \f]
+ * @f]
*
* Derived classes don't need to overload this function. This function is
* handled at this level.
@@ -452,17 +452,17 @@ class MolalityVPSSTP : public VPStandardStateTP
* Activity coefficients for species k may be altered between scales s1 to
* s2 using the following formula
*
- * \f[
+ * @f[
* ln(\gamma_k^{s2}) = ln(\gamma_k^{s1})
* + \frac{z_k}{z_j} \left( ln(\gamma_j^{s2}) - ln(\gamma_j^{s1}) \right)
- * \f]
+ * @f]
*
* where j is any one species. For the NBS scale, j is equal to the Cl-
* species and
*
- * \f[
+ * @f[
* ln(\gamma_{Cl-}^{s2}) = \frac{-A_{\phi} \sqrt{I}}{1.0 + 1.5 \sqrt{I}}
- * \f]
+ * @f]
*
* @param acMolality Output vector containing the molality based activity
* coefficients. length: m_kk.
@@ -471,9 +471,9 @@ class MolalityVPSSTP : public VPStandardStateTP
//! Calculate the osmotic coefficient
/*!
- * \f[
+ * @f[
* \phi = \frac{- ln(a_o)}{\tilde{M}_o \sum_{i \ne o} m_i}
- * \f]
+ * @f]
*
* Note there are a few of definitions of the osmotic coefficient floating
* around. We use the one defined in (Activity Coefficients in Electrolyte
diff --git a/include/cantera/thermo/Mu0Poly.h b/include/cantera/thermo/Mu0Poly.h
index a85368859a..71529106d3 100644
--- a/include/cantera/thermo/Mu0Poly.h
+++ b/include/cantera/thermo/Mu0Poly.h
@@ -24,7 +24,7 @@ namespace Cantera
* The Mu0Poly class implements a piecewise constant heat capacity
* approximation. of the standard state chemical potential of one species at a
* single reference pressure. The chemical potential is input as a series of
- * (\f$T\f$, \f$ \mu^o(T)\f$) values. The first temperature is assumed to be
+ * (@f$ T @f$, @f$ \mu^o(T) @f$) values. The first temperature is assumed to be
* equal to 298.15 K; however, this may be relaxed in the future. This
* information, and an assumption of a constant heat capacity within each
* interval is enough to calculate all thermodynamic functions.
@@ -32,37 +32,37 @@ namespace Cantera
* The piece-wise constant heat capacity is calculated from the change in the
* chemical potential over each interval. Once the heat capacity is known, the
* other thermodynamic functions may be determined. The basic equation for going
- * from temperature point 1 to temperature point 2 are as follows for \f$ T \f$,
- * \f$ T_1 <= T <= T_2 \f$
+ * from temperature point 1 to temperature point 2 are as follows for @f$ T @f$,
+ * @f$ T_1 <= T <= T_2 @f$
*
- * \f[
+ * @f[
* \mu^o(T_1) = h^o(T_1) - T_1 * s^o(T_1)
- * \f]
- * \f[
+ * @f]
+ * @f[
* \mu^o(T_2) - \mu^o(T_1) = Cp^o(T_1)(T_2 - T_1) - Cp^o(T_1)(T_2)ln(\frac{T_2}{T_1}) - s^o(T_1)(T_2 - T_1)
- * \f]
- * \f[
+ * @f]
+ * @f[
* s^o(T_2) = s^o(T_1) + Cp^o(T_1)ln(\frac{T_2}{T_1})
- * \f]
- * \f[
+ * @f]
+ * @f[
* h^o(T_2) = h^o(T_1) + Cp^o(T_1)(T_2 - T_1)
- * \f]
+ * @f]
*
- * Within each interval the following relations are used. For \f$ T \f$, \f$
- * T_1 <= T <= T_2 \f$
+ * Within each interval the following relations are used. For @f$ T @f$, @f$
+ * T_1 <= T <= T_2 @f$
*
- * \f[
+ * @f[
* \mu^o(T) = \mu^o(T_1) + Cp^o(T_1)(T - T_1) - Cp^o(T_1)(T_2)ln(\frac{T}{T_1}) - s^o(T_1)(T - T_1)
- * \f]
- * \f[
+ * @f]
+ * @f[
* s^o(T) = s^o(T_1) + Cp^o(T_1)ln(\frac{T}{T_1})
- * \f]
- * \f[
+ * @f]
+ * @f[
* h^o(T) = h^o(T_1) + Cp^o(T_1)(T - T_1)
- * \f]
+ * @f]
*
- * Notes about temperature interpolation for \f$ T < T_1 \f$ and \f$ T >
- * T_{npoints} \f$: These are achieved by assuming a constant heat capacity
+ * Notes about temperature interpolation for @f$ T < T_1 @f$ and @f$ T >
+ * T_{npoints} @f$: These are achieved by assuming a constant heat capacity
* equal to the value in the closest temperature interval. No error is thrown.
*
* @note In the future, a better assumption about the heat capacity may be
@@ -81,23 +81,23 @@ class Mu0Poly: public SpeciesThermoInterpType
* @param thigh Maximum temperature
* @param pref reference pressure (Pa).
* @param coeffs Vector of coefficients used to set the parameters for the
- * standard state for species n. There are \f$ 2+npoints*2
- * \f$ coefficients, where \f$ npoints \f$ are the number of
+ * standard state for species n. There are @f$ 2+npoints*2
+ * @f$ coefficients, where @f$ npoints @f$ are the number of
* temperature points. Their identity is further broken down:
* - coeffs[0] = number of points (integer)
- * - coeffs[1] = \f$ h^o(298.15 K) \f$ (J/kmol)
- * - coeffs[2] = \f$ T_1 \f$ (Kelvin)
- * - coeffs[3] = \f$ \mu^o(T_1) \f$ (J/kmol)
- * - coeffs[4] = \f$ T_2 \f$ (Kelvin)
- * - coeffs[5] = \f$ \mu^o(T_2) \f$ (J/kmol)
- * - coeffs[6] = \f$ T_3 \f$ (Kelvin)
- * - coeffs[7] = \f$ \mu^o(T_3) \f$ (J/kmol)
+ * - coeffs[1] = @f$ h^o(298.15 K) @f$ (J/kmol)
+ * - coeffs[2] = @f$ T_1 @f$ (Kelvin)
+ * - coeffs[3] = @f$ \mu^o(T_1) @f$ (J/kmol)
+ * - coeffs[4] = @f$ T_2 @f$ (Kelvin)
+ * - coeffs[5] = @f$ \mu^o(T_2) @f$ (J/kmol)
+ * - coeffs[6] = @f$ T_3 @f$ (Kelvin)
+ * - coeffs[7] = @f$ \mu^o(T_3) @f$ (J/kmol)
* - ........
* .
*/
Mu0Poly(double tlow, double thigh, double pref, const double* coeffs);
- //! Set parameters for \f$ \mu^o(T) \f$
+ //! Set parameters for @f$ \mu^o(T) @f$
/*!
* Calculates and stores the piecewise linear approximation to the
* thermodynamic functions.
diff --git a/include/cantera/thermo/Nasa9Poly1.h b/include/cantera/thermo/Nasa9Poly1.h
index 2230df04ed..eb0ec52c2b 100644
--- a/include/cantera/thermo/Nasa9Poly1.h
+++ b/include/cantera/thermo/Nasa9Poly1.h
@@ -29,24 +29,24 @@ namespace Cantera
* Individual Species," B. J. McBride, M. J. Zehe, S. Gordon
* NASA/TP-2002-211556, Sept. 2002
*
- * Nine coefficients \f$(a_0,\dots,a_8)\f$ are used to represent
- * \f$ C_p^0(T)\f$, \f$ H^0(T)\f$, and \f$ S^0(T) \f$ as
- * polynomials in \f$ T \f$ :
- * \f[
+ * Nine coefficients @f$ (a_0,\dots,a_8) @f$ are used to represent
+ * @f$ C_p^0(T) @f$, @f$ H^0(T) @f$, and @f$ S^0(T) @f$ as
+ * polynomials in @f$ T @f$ :
+ * @f[
* \frac{C_p^0(T)}{R} = a_0 T^{-2} + a_1 T^{-1} + a_2 + a_3 T
* + a_4 T^2 + a_5 T^3 + a_6 T^4
- * \f]
+ * @f]
*
- * \f[
+ * @f[
* \frac{H^0(T)}{RT} = - a_0 T^{-2} + a_1 \frac{\ln T}{T} + a_2
* + \frac{a_3}{2} T + \frac{a_4}{3} T^2 + \frac{a_5}{4} T^3 +
* \frac{a_6}{5} T^4 + \frac{a_7}{T}
- * \f]
+ * @f]
*
- * \f[
+ * @f[
* \frac{s^0(T)}{R} = - \frac{a_0}{2} T^{-2} - a_1 T^{-1} + a_2 \ln T
* + a_3 T + \frac{a_4}{2} T^2 + \frac{a_5}{3} T^3 + \frac{a_6}{4} T^4 + a_8
- * \f]
+ * @f]
*
* The standard state is assumed to be an ideal gas at the standard pressure of
* 1 bar, for gases. For condensed species, the standard state is the pure
diff --git a/include/cantera/thermo/NasaPoly1.h b/include/cantera/thermo/NasaPoly1.h
index 04f12deb05..cb9902bbed 100644
--- a/include/cantera/thermo/NasaPoly1.h
+++ b/include/cantera/thermo/NasaPoly1.h
@@ -27,20 +27,20 @@ namespace Cantera
* the Chemkin software package, but differs from the form used in the more
* recent NASA equilibrium program.
*
- * Seven coefficients \f$(a_0,\dots,a_6)\f$ are used to represent
- * \f$ c_p^0(T)\f$, \f$ h^0(T)\f$, and \f$ s^0(T) \f$ as
- * polynomials in \f$ T \f$ :
- * \f[
+ * Seven coefficients @f$ (a_0,\dots,a_6) @f$ are used to represent
+ * @f$ c_p^0(T) @f$, @f$ h^0(T) @f$, and @f$ s^0(T) @f$ as
+ * polynomials in @f$ T @f$ :
+ * @f[
* \frac{c_p(T)}{R} = a_0 + a_1 T + a_2 T^2 + a_3 T^3 + a_4 T^4
- * \f]
- * \f[
+ * @f]
+ * @f[
* \frac{h^0(T)}{RT} = a_0 + \frac{a_1}{2} T + \frac{a_2}{3} T^2
* + \frac{a_3}{4} T^3 + \frac{a_4}{5} T^4 + \frac{a_5}{T}.
- * \f]
- * \f[
+ * @f]
+ * @f[
* \frac{s^0(T)}{R} = a_0\ln T + a_1 T + \frac{a_2}{2} T^2
* + \frac{a_3}{3} T^3 + \frac{a_4}{4} T^4 + a_6.
- * \f]
+ * @f]
*
* @ingroup spthermo
*/
diff --git a/include/cantera/thermo/NasaPoly2.h b/include/cantera/thermo/NasaPoly2.h
index 47d3bdb1bf..9df7e2062d 100644
--- a/include/cantera/thermo/NasaPoly2.h
+++ b/include/cantera/thermo/NasaPoly2.h
@@ -26,20 +26,20 @@ namespace Cantera
* the Chemkin software package, but differs from the form used in the more
* recent NASA equilibrium program.
*
- * Seven coefficients \f$(a_0,\dots,a_6)\f$ are used to represent
- * \f$ c_p^0(T)\f$, \f$ h^0(T)\f$, and \f$ s^0(T) \f$ as
- * polynomials in \f$ T \f$ :
- * \f[
+ * Seven coefficients @f$ (a_0,\dots,a_6) @f$ are used to represent
+ * @f$ c_p^0(T) @f$, @f$ h^0(T) @f$, and @f$ s^0(T) @f$ as
+ * polynomials in @f$ T @f$ :
+ * @f[
* \frac{c_p(T)}{R} = a_0 + a_1 T + a_2 T^2 + a_3 T^3 + a_4 T^4
- * \f]
- * \f[
+ * @f]
+ * @f[
* \frac{h^0(T)}{RT} = a_0 + \frac{a_1}{2} T + \frac{a_2}{3} T^2
* + \frac{a_3}{4} T^3 + \frac{a_4}{5} T^4 + \frac{a_5}{T}.
- * \f]
- * \f[
+ * @f]
+ * @f[
* \frac{s^0(T)}{R} = a_0\ln T + a_1 T + \frac{a_2}{2} T^2
* + \frac{a_3}{3} T^3 + \frac{a_4}{4} T^4 + a_6.
- * \f]
+ * @f]
*
* This class is designed specifically for use by the class MultiSpeciesThermo.
*
diff --git a/include/cantera/thermo/PDSS.h b/include/cantera/thermo/PDSS.h
index 9717b7b444..410b3e8b5a 100644
--- a/include/cantera/thermo/PDSS.h
+++ b/include/cantera/thermo/PDSS.h
@@ -337,9 +337,9 @@ class PDSS
//! Return the volumetric thermal expansion coefficient. Units: 1/K.
/*!
* The thermal expansion coefficient is defined as
- * \f[
+ * @f[
* \beta = \frac{1}{v}\left(\frac{\partial v}{\partial T}\right)_P
- * \f]
+ * @f]
*/
virtual doublereal thermalExpansionCoeff() const;
//! @}
diff --git a/include/cantera/thermo/PDSS_IonsFromNeutral.h b/include/cantera/thermo/PDSS_IonsFromNeutral.h
index 7da4aeb0bc..391a608fa3 100644
--- a/include/cantera/thermo/PDSS_IonsFromNeutral.h
+++ b/include/cantera/thermo/PDSS_IonsFromNeutral.h
@@ -52,13 +52,13 @@ class PDSS_IonsFromNeutral : public PDSS_Nondimensional
/*!
* @copydoc PDSS::gibbs_RT()
*
- * \f[
+ * @f[
* \frac{\mu^o_k}{RT} = \sum_{m}{ \alpha_{m , k} \frac{\mu^o_{m}}{RT}} + ( 1 - \delta_{k,sp}) 2.0 \ln{2.0}
- * \f]
+ * @f]
*
- * *m* is the neutral molecule species index. \f$ \alpha_{m , k} \f$ is the
+ * *m* is the neutral molecule species index. @f$ \alpha_{m , k} @f$ is the
* stoichiometric coefficient for the neutral molecule, *m*, that creates the
- * thermodynamics for the ionic species *k*. A factor \f$ 2.0 \ln{2.0} \f$
+ * thermodynamics for the ionic species *k*. A factor @f$ 2.0 \ln{2.0} @f$
* is added to all ions except for the species ionic species, which in this
* case is the single anion species, with species index *sp*.
*/
diff --git a/include/cantera/thermo/PDSS_SSVol.h b/include/cantera/thermo/PDSS_SSVol.h
index a3f34f7337..9aaa1ff381 100644
--- a/include/cantera/thermo/PDSS_SSVol.h
+++ b/include/cantera/thermo/PDSS_SSVol.h
@@ -45,61 +45,61 @@ namespace Cantera
* - Temperature polynomial for the standard state volume
* - This standard state model is invoked with the keyword "temperature_polynomial".
* The standard state volume is considered a function of temperature only.
- * \f[
+ * @f[
* V^o_k(T,P) = a_0 + a_1 T + a_2 T^2 + a_3 T^3
- * \f]
+ * @f]
*
* - Temperature polynomial for the standard state density
* - This standard state model is invoked with the keyword "density_temperature_polynomial".
* The standard state density, which is the inverse of the volume,
* is considered a function of temperature only.
- * \f[
+ * @f[
* {\rho}^o_k(T,P) = \frac{M_k}{V^o_k(T,P)} = a_0 + a_1 T + a_2 T^2 + a_3 T^3
- * \f]
+ * @f]
*
* ## Specification of Species Standard State Properties
*
* The standard molar Gibbs free energy for species *k* is determined from
* the enthalpy and entropy expressions
*
- * \f[
+ * @f[
* G^o_k(T,P) = H^o_k(T,P) - S^o_k(T,P)
- * \f]
+ * @f]
*
* The enthalpy is calculated mostly from the MultiSpeciesThermo object's enthalpy
* evaluator. The dependence on pressure originates from the Maxwell relation
*
- * \f[
+ * @f[
* {\left(\frac{dH^o_k}{dP}\right)}_T = T {\left(\frac{dS^o_k}{dP}\right)}_T + V^o_k
- * \f]
+ * @f]
* which is equal to
*
- * \f[
+ * @f[
* {\left(\frac{dH^o_k}{dP}\right)}_T = V^o_k - T {\left(\frac{dV^o_k}{dT}\right)}_P
- * \f]
+ * @f]
*
* The entropy is calculated mostly from the MultiSpeciesThermo objects entropy
* evaluator. The dependence on pressure originates from the Maxwell relation:
*
- * \f[
+ * @f[
* {\left(\frac{dS^o_k}{dP}\right)}_T = - {\left(\frac{dV^o_k}{dT}\right)}_P
- * \f]
+ * @f]
*
* The standard state constant-pressure heat capacity expression is obtained
* from taking the temperature derivative of the Maxwell relation involving the
* enthalpy given above to yield an expression for the pressure dependence of
* the heat capacity.
*
- * \f[
+ * @f[
* {\left(\frac{d{C}^o_{p,k}}{dP}\right)}_T = - T {\left(\frac{{d}^2{V}^o_k}{{dT}^2}\right)}_T
- * \f]
+ * @f]
*
* The standard molar Internal Energy for species *k* is determined from the
* following relation.
*
- * \f[
+ * @f[
* U^o_k(T,P) = H^o_k(T,P) - p V^o_k
- * \f]
+ * @f]
*
* An example of the specification of a standard state using a temperature dependent
* standard state volume is given in the
diff --git a/include/cantera/thermo/PDSS_Water.h b/include/cantera/thermo/PDSS_Water.h
index 01ff1d9b24..4ecef0d72e 100644
--- a/include/cantera/thermo/PDSS_Water.h
+++ b/include/cantera/thermo/PDSS_Water.h
@@ -110,22 +110,22 @@ class PDSS_Water : public PDSS_Molar
//! Units: 1/K2.
/*!
* The thermal expansion coefficient is defined as
- * \f[
+ * @f[
* \beta = \frac{1}{v}\left(\frac{\partial v}{\partial T}\right)_P
- * \f]
+ * @f]
*/
virtual doublereal dthermalExpansionCoeffdT() const;
//! Returns the isothermal compressibility. Units: 1/Pa.
/*!
* The isothermal compressibility is defined as
- * \f[
+ * @f[
* \kappa_T = -\frac{1}{v}\left(\frac{\partial v}{\partial P}\right)_T
- * \f]
+ * @f]
* or
- * \f[
+ * @f[
* \kappa_T = \frac{1}{\rho}\left(\frac{\partial \rho}{\partial P}\right)_T
- * \f]
+ * @f]
*/
virtual doublereal isothermalCompressibility() const;
diff --git a/include/cantera/thermo/PengRobinson.h b/include/cantera/thermo/PengRobinson.h
index 78917f6499..3a129d7fab 100644
--- a/include/cantera/thermo/PengRobinson.h
+++ b/include/cantera/thermo/PengRobinson.h
@@ -49,56 +49,56 @@ class PengRobinson : public MixtureFugacityTP
/*!
* Since the mass density, temperature, and mass fractions are stored,
* this method uses these values to implement the
- * mechanical equation of state \f$ P(T, \rho, Y_1, \dots, Y_K) \f$.
+ * mechanical equation of state @f$ P(T, \rho, Y_1, \dots, Y_K) @f$.
*
- * \f[
+ * @f[
* P = \frac{RT}{v-b_{mix}}
* - \frac{\left(\alpha a\right)_{mix}}{v^2 + 2b_{mix}v - b_{mix}^2}
- * \f]
+ * @f]
*
* where:
*
- * \f[
+ * @f[
* \alpha = \left[ 1 + \kappa \left(1-T_r^{0.5}\right)\right]^2
- * \f]
+ * @f]
*
* and
*
- * \f[
+ * @f[
* \kappa = \left(0.37464 + 1.54226\omega - 0.26992\omega^2\right),
* \qquad \qquad \text{For } \omega <= 0.491 \\
*
* \kappa = \left(0.379642 + 1.487503\omega - 0.164423\omega^2 + 0.016667\omega^3 \right),
* \qquad \text{For } \omega > 0.491
- * \f]
+ * @f]
*
- * Coefficients \f$ a_{mix}, b_{mix} \f$ and \f$(a \alpha)_{mix}\f$ are calculated as
+ * Coefficients @f$ a_{mix}, b_{mix} @f$ and @f$ (a \alpha)_{mix} @f$ are calculated as
*
- * \f[
+ * @f[
* a_{mix} = \sum_i \sum_j X_i X_j a_{i, j} = \sum_i \sum_j X_i X_j \sqrt{a_i a_j}
- * \f]
+ * @f]
*
- * \f[
+ * @f[
* b_{mix} = \sum_i X_i b_i
- * \f]
+ * @f]
*
- * \f[
+ * @f[
* {a \alpha}_{mix} = \sum_i \sum_j X_i X_j {a \alpha}_{i, j}
* = \sum_i \sum_j X_i X_j \sqrt{a_i a_j} \sqrt{\alpha_i \alpha_j}
- * \f]
+ * @f]
*/
virtual double pressure() const;
//! @}
- //! Returns the standard concentration \f$ C^0_k \f$, which is used to
+ //! Returns the standard concentration @f$ C^0_k @f$, which is used to
//! normalize the generalized concentration.
/*!
* This is defined as the concentration by which the generalized
* concentration is normalized to produce the activity.
* The ideal gas mixture is considered as the standard or reference state here.
* Since the activity for an ideal gas mixture is simply the mole fraction,
- * for an ideal gas, \f$ C^0_k = P/\hat R T \f$.
+ * for an ideal gas, @f$ C^0_k = P/\hat R T @f$.
*
* @param k Optional parameter indicating the species. The default is to
* assume this refers to species 0.
@@ -136,7 +136,7 @@ class PengRobinson : public MixtureFugacityTP
//! Calculate species-specific critical temperature
/*!
* The temperature dependent parameter in P-R EoS is calculated as
- * \f[ T_{crit} = (0.0778 a)/(0.4572 b R) \f]
+ * @f[ T_{crit} = (0.0778 a)/(0.4572 b R) @f]
* Units: Kelvin
*
* @param a species-specific coefficients used in P-R EoS
@@ -160,8 +160,8 @@ class PengRobinson : public MixtureFugacityTP
//! Set the pure fluid interaction parameters for a species
/*!
* @param species Name of the species
- * @param a \f$a\f$ parameter in the Peng-Robinson model [Pa-m^6/kmol^2]
- * @param b \f$a\f$ parameter in the Peng-Robinson model [m^3/kmol]
+ * @param a @f$ a @f$ parameter in the Peng-Robinson model [Pa-m^6/kmol^2]
+ * @param b @f$ a @f$ parameter in the Peng-Robinson model [m^3/kmol]
* @param w acentric factor
*/
void setSpeciesCoeffs(const std::string& species, double a, double b,
@@ -171,7 +171,7 @@ class PengRobinson : public MixtureFugacityTP
/*!
* @param species_i Name of one species
* @param species_j Name of the other species
- * @param a \f$a\f$ parameter in the Peng-Robinson model [Pa-m^6/kmol^2]
+ * @param a @f$ a @f$ parameter in the Peng-Robinson model [Pa-m^6/kmol^2]
*/
void setBinaryCoeffs(const std::string& species_i,
const std::string& species_j, double a);
@@ -191,13 +191,13 @@ class PengRobinson : public MixtureFugacityTP
// Special functions not inherited from MixtureFugacityTP
- //! Calculate temperature derivative \f$d(a \alpha)/dT\f$
+ //! Calculate temperature derivative @f$ d(a \alpha)/dT @f$
/*!
* These are stored internally.
*/
double daAlpha_dT() const;
- //! Calculate second derivative \f$d^2(a \alpha)/dT^2\f$
+ //! Calculate second derivative @f$ d^2(a \alpha)/dT^2 @f$
/*!
* These are stored internally.
*/
@@ -209,21 +209,21 @@ class PengRobinson : public MixtureFugacityTP
virtual double thermalExpansionCoeff() const;
virtual double soundSpeed() const;
- //! Calculate \f$dp/dV\f$ and \f$dp/dT\f$ at the current conditions
+ //! Calculate @f$ dp/dV @f$ and @f$ dp/dT @f$ at the current conditions
/*!
* These are stored internally.
*/
void calculatePressureDerivatives() const;
- //! Update the \f$a\f$, \f$b\f$, and \f$\alpha\f$ parameters
+ //! Update the @f$ a @f$, @f$ b @f$, and @f$ \alpha @f$ parameters
/*!
- * The \f$a\f$ and the \f$b\f$ parameters depend on the mole fraction and the
- * parameter \f$\alpha\f$ depends on the temperature. This function updates
+ * The @f$ a @f$ and the @f$ b @f$ parameters depend on the mole fraction and the
+ * parameter @f$ \alpha @f$ depends on the temperature. This function updates
* the internal numbers based on the state of the object.
*/
virtual void updateMixingExpressions();
- //! Calculate the \f$a\f$, \f$b\f$, and \f$\alpha\f$ parameters given the temperature
+ //! Calculate the @f$ a @f$, @f$ b @f$, and @f$ \alpha @f$ parameters given the temperature
/*!
* This function doesn't change the internal state of the object, so it is a
* const function. It does use the stored mole fractions in the object.
@@ -240,19 +240,19 @@ class PengRobinson : public MixtureFugacityTP
int solveCubic(double T, double pres, double a, double b, double aAlpha,
double Vroot[3]) const;
protected:
- //! Value of \f$b\f$ in the equation of state
+ //! Value of @f$ b @f$ in the equation of state
/*!
* `m_b` is a function of the mole fractions and species-specific b values.
*/
double m_b = 0.0;
- //! Value of \f$a\f$ in the equation of state
+ //! Value of @f$ a @f$ in the equation of state
/*!
* `m_a` depends only on the mole fractions.
*/
double m_a = 0.0;
- //! Value of \f$a \alpha\f$ in the equation of state
+ //! Value of @f$ a \alpha @f$ in the equation of state
/*!
* `m_aAlpha_mix` is a function of the temperature and the mole fractions.
*/
diff --git a/include/cantera/thermo/Phase.h b/include/cantera/thermo/Phase.h
index de549766b1..e688198404 100644
--- a/include/cantera/thermo/Phase.h
+++ b/include/cantera/thermo/Phase.h
@@ -47,7 +47,7 @@ class Species;
* It also stores an array of species molecular weights, which are used to
* convert between mole and mass representations of the composition. For
* efficiency in mass/mole conversion, the vector of mass fractions divided
- * by molecular weight \f$ Y_k/M_k \f$ is also stored.
+ * by molecular weight @f$ Y_k/M_k @f$ is also stored.
*
* Class Phase is not usually used directly. Its primary use is as a base class
* for class ThermoPhase. It is not generally necessary to overloaded any of
@@ -599,15 +599,15 @@ class Phase
//! Elemental mass fraction of element m
/*!
- * The elemental mass fraction \f$Z_{\mathrm{mass},m}\f$ of element \f$m\f$
+ * The elemental mass fraction @f$ Z_{\mathrm{mass},m} @f$ of element @f$ m @f$
* is defined as
- * \f[
+ * @f[
* Z_{\mathrm{mass},m} = \sum_k \frac{a_{m,k} M_m}{M_k} Y_k
- * \f]
- * with \f$a_{m,k}\f$ being the number of atoms of element \f$m\f$ in
- * species \f$k\f$, \f$M_m\f$ the atomic weight of element \f$m\f$,
- * \f$M_k\f$ the molecular weight of species \f$k\f$, and \f$Y_k\f$
- * the mass fraction of species \f$k\f$.
+ * @f]
+ * with @f$ a_{m,k} @f$ being the number of atoms of element @f$ m @f$ in
+ * species @f$ k @f$, @f$ M_m @f$ the atomic weight of element @f$ m @f$,
+ * @f$ M_k @f$ the molecular weight of species @f$ k @f$, and @f$ Y_k @f$
+ * the mass fraction of species @f$ k @f$.
*
* @param[in] m Index of the element within the phase. If m is outside
* the valid range, an exception will be thrown.
@@ -618,17 +618,17 @@ class Phase
//! Elemental mole fraction of element m
/*!
- * The elemental mole fraction \f$Z_{\mathrm{mole},m}\f$ of element \f$m\f$
+ * The elemental mole fraction @f$ Z_{\mathrm{mole},m} @f$ of element @f$ m @f$
* is the number of atoms of element *m* divided by the total number of
* atoms. It is defined as:
*
- * \f[
+ * @f[
* Z_{\mathrm{mole},m} = \frac{\sum_k a_{m,k} X_k}
* {\sum_k \sum_j a_{j,k} X_k}
- * \f]
- * with \f$a_{m,k}\f$ being the number of atoms of element \f$m\f$ in
- * species \f$k\f$, \f$\sum_j\f$ being a sum over all elements, and
- * \f$X_k\f$ being the mole fraction of species \f$k\f$.
+ * @f]
+ * with @f$ a_{m,k} @f$ being the number of atoms of element @f$ m @f$ in
+ * species @f$ k @f$, @f$ \sum_j @f$ being a sum over all elements, and
+ * @f$ X_k @f$ being the mole fraction of species @f$ k @f$.
*
* @param[in] m Index of the element within the phase. If m is outside the
* valid range, an exception will be thrown.
@@ -685,8 +685,8 @@ class Phase
* This method must be overloaded in derived classes. Within %Cantera, the
* independent variable is either density or pressure. If the state is
* defined by temperature, density, and mass fractions, this method should
- * use these values to implement the mechanical equation of state \f$ P(T,
- * \rho, Y_1, \dots, Y_K) \f$. Alternatively, it returns a stored value.
+ * use these values to implement the mechanical equation of state @f$ P(T,
+ * \rho, Y_1, \dots, Y_K) @f$. Alternatively, it returns a stored value.
*/
virtual double pressure() const {
throw NotImplementedError("Phase::pressure",
@@ -758,7 +758,7 @@ class Phase
//! @{
//! Evaluate the mole-fraction-weighted mean of an array Q.
- //! \f[ \sum_k X_k Q_k. \f]
+ //! @f[ \sum_k X_k Q_k. @f]
//! Q should contain pure-species molar property values.
//! @param[in] Q Array of length m_kk that is to be averaged.
//! @return mole-fraction-weighted mean of Q
@@ -772,7 +772,7 @@ class Phase
return m_mmw;
}
- //! Evaluate \f$ \sum_k X_k \log X_k \f$.
+ //! Evaluate @f$ \sum_k X_k \log X_k @f$.
//! @return The indicated sum. Dimensionless.
doublereal sum_xlogx() const;
diff --git a/include/cantera/thermo/PlasmaPhase.h b/include/cantera/thermo/PlasmaPhase.h
index 8dbe7cebb9..6903a3b114 100644
--- a/include/cantera/thermo/PlasmaPhase.h
+++ b/include/cantera/thermo/PlasmaPhase.h
@@ -24,25 +24,25 @@ namespace Cantera
* distribution with isotropic-velocity model. The generalized electron
* energy distribution for isotropic-velocity distribution can be
* expressed as [1,2],
- * \f[
+ * @f[
* f(\epsilon) = c_1 \frac{\sqrt{\epsilon}}{\epsilon_m^{3/2}}
* \exp(-c_2 (\frac{\epsilon}{\epsilon_m})^x),
- * \f]
- * where \f$ x = 1 \f$ and \f$ x = 2 \f$ correspond to the Maxwellian and
+ * @f]
+ * where @f$ x = 1 @f$ and @f$ x = 2 @f$ correspond to the Maxwellian and
* Druyvesteyn (default) electron energy distribution, respectively.
- * \f$ \epsilon_m = 3/2 T_e \f$ [eV] (mean electron energy). The second
+ * @f$ \epsilon_m = 3/2 T_e @f$ [eV] (mean electron energy). The second
* method uses setDiscretizedElectronEnergyDist() to manually set electron
* energy distribution and calculate electron temperature from mean electron
* energy, which is calculated as [3],
- * \f[
+ * @f[
* \epsilon_m = \int_0^{\infty} \epsilon^{3/2} f(\epsilon) d\epsilon,
- * \f]
+ * @f]
* which can be calculated using trapezoidal rule,
- * \f[
+ * @f[
* \epsilon_m = \sum_i (\epsilon^{5/2}_{i+1} - \epsilon^{5/2}_i)
* (f(\epsilon_{i+1}) + f(\epsilon_i)) / 2,
- * \f]
- * where \f$ i \f$ is the index of energy levels.
+ * @f]
+ * where @f$ i @f$ is the index of energy levels.
*
* For references, see Gudmundsson @cite gudmundsson2001; Khalilpour and Foroutan
* @cite khalilpour2020; Hagelaar and Pitchford @cite hagelaar2005, and BOLOS
@@ -108,7 +108,7 @@ class PlasmaPhase: public IdealGasPhase
}
//! Set the shape factor of isotropic electron energy distribution.
- //! Note that \f$ x = 1 \f$ and \f$ x = 2 \f$ correspond to the
+ //! Note that @f$ x = 1 @f$ and @f$ x = 2 @f$ correspond to the
//! Maxwellian and Druyvesteyn distribution, respectively.
//! @param x The shape factor
void setIsotropicShapeFactor(double x);
@@ -180,7 +180,7 @@ class PlasmaPhase: public IdealGasPhase
/**
* Electron pressure. Units: Pa.
- * \f[P = n_{k_e} R T_e\f]
+ * @f[P = n_{k_e} R T_e @f]
*/
virtual double electronPressure() const {
return GasConstant * concentration(m_electronSpeciesIndex) *
@@ -200,11 +200,11 @@ class PlasmaPhase: public IdealGasPhase
//! Return the Molar enthalpy. Units: J/kmol.
/*!
* For an ideal gas mixture with additional electron,
- * \f[
+ * @f[
* \hat h(T) = \sum_{k \neq k_e} X_k \hat h^0_k(T) + X_{k_e} \hat h^0_{k_e}(T_e),
- * \f]
+ * @f]
* and is a function only of temperature. The standard-state pure-species
- * enthalpies \f$ \hat h^0_k(T) \f$ are computed by the species
+ * enthalpies @f$ \hat h^0_k(T) @f$ are computed by the species
* thermodynamic property manager.
*
* \see MultiSpeciesThermo
diff --git a/include/cantera/thermo/RedlichKisterVPSSTP.h b/include/cantera/thermo/RedlichKisterVPSSTP.h
index 70a318836d..ab52a61d1e 100644
--- a/include/cantera/thermo/RedlichKisterVPSSTP.h
+++ b/include/cantera/thermo/RedlichKisterVPSSTP.h
@@ -41,191 +41,191 @@ namespace Cantera
* the generalization of the Redlich-Kister formulation for a phase that has
* more than 2 species.
*
- * \f[
+ * @f[
* G^E = \sum_{i} G^E_{i}
- * \f]
+ * @f]
*
* where
*
- * \f[
+ * @f[
* G^E_{i} = n X_{Ai} X_{Bi} \sum_m \left( A^{i}_m {\left( X_{Ai} - X_{Bi} \right)}^m \right)
- * \f]
+ * @f]
*
* where n is the total moles in the solution and where we can break down the Gibbs free
* energy contributions into enthalpy and entropy contributions by defining
- * \f$ A^i_m = H^i_m - T S^i_m \f$ :
+ * @f$ A^i_m = H^i_m - T S^i_m @f$ :
*
- * \f[
+ * @f[
* H^E_i = n X_{Ai} X_{Bi} \sum_m \left( H^{i}_m {\left( X_{Ai} - X_{Bi} \right)}^m \right)
- * \f]
+ * @f]
*
- * \f[
+ * @f[
* S^E_i = n X_{Ai} X_{Bi} \sum_m \left( S^{i}_m {\left( X_{Ai} - X_{Bi} \right)}^m \right)
- * \f]
+ * @f]
*
* The activity of a species defined in the phase is given by an excess Gibbs free
* energy formulation:
*
- * \f[
+ * @f[
* a_k = \gamma_k X_k
- * \f]
+ * @f]
*
* where
*
- * \f[
+ * @f[
* R T \ln( \gamma_k )= \frac{d(n G^E)}{d(n_k)}\Bigg|_{n_i}
- * \f]
+ * @f]
*
* Taking the derivatives results in the following expression
- * \f[
+ * @f[
* R T \ln( \gamma_k )= \sum_i \delta_{Ai,k} (1 - X_{Ai}) X_{Bi} \sum_m \left( A^{i}_m {\left( X_{Ai} - X_{Bi} \right)}^m \right)
* + \sum_i \delta_{Ai,k} X_{Ai} X_{Bi} \sum_m \left( A^{i}_0 + A^{i}_m {\left( X_{Ai} - X_{Bi} \right)}^{m-1} (1 - X_{Ai} + X_{Bi}) \right)
- * \f]
+ * @f]
*
* Evaluating thermodynamic properties requires the following derivatives of
- * \f$ \ln(\gamma_k) \f$:
+ * @f$ \ln(\gamma_k) @f$:
*
- * \f[
+ * @f[
* \frac{d \ln( \gamma_k )}{dT} = - \frac{1}{RT^2} \left( \sum_i \delta_{Ai,k} (1 - X_{Ai}) X_{Bi} \sum_m \left( H^{i}_m {\left( X_{Ai} - X_{Bi} \right)}^m \right)
* + \sum_i \delta_{Ai,k} X_{Ai} X_{Bi} \sum_m \left( H^{i}_0 + H^{i}_m {\left( X_{Ai} - X_{Bi} \right)}^{m-1} (1 - X_{Ai} + X_{Bi}) \right) \right)
- * \f]
+ * @f]
*
* and
*
- * \f[
+ * @f[
* \frac{d^2 \ln( \gamma_k )}{dT^2} = -\frac{2}{T} \frac{d \ln( \gamma_k )}{dT}
- * \f]
+ * @f]
*
* This object inherits from the class VPStandardStateTP. Therefore, the
* specification and calculation of all standard state and reference state
* values are handled at that level. Various functional forms for the standard
* state are permissible. The chemical potential for species *k* is equal to
*
- * \f[
+ * @f[
* \mu_k(T,P) = \mu^o_k(T, P) + R T \ln(\gamma_k X_k)
- * \f]
+ * @f]
*
* The partial molar entropy for species *k* is given by the following relation,
*
- * \f[
+ * @f[
* \tilde{s}_k(T,P) = s^o_k(T,P) - R \ln( \gamma_k X_k )
* - R T \frac{d \ln(\gamma_k) }{dT}
- * \f]
+ * @f]
*
* The partial molar enthalpy for species *k* is given by
*
- * \f[
+ * @f[
* \tilde{h}_k(T,P) = h^o_k(T,P) - R T^2 \frac{d \ln(\gamma_k)}{dT}
- * \f]
+ * @f]
*
* The partial molar volume for species *k* is
*
- * \f[
+ * @f[
* \tilde V_k(T,P) = V^o_k(T,P) + R T \frac{d \ln(\gamma_k) }{dP}
- * \f]
+ * @f]
*
* The partial molar Heat Capacity for species *k* is
*
- * \f[
+ * @f[
* \tilde{C}_{p,k}(T,P) = C^o_{p,k}(T,P) - 2 R T \frac{d \ln( \gamma_k )}{dT}
* - R T^2 \frac{d^2 \ln(\gamma_k) }{{dT}^2} = C^o_{p,k}(T,P)
- * \f]
+ * @f]
*
* ## Application within Kinetics Managers
*
- * \f$ C^a_k\f$ are defined such that \f$ a_k = C^a_k / C^s_k, \f$ where
- * \f$ C^s_k \f$ is a standard concentration defined below and \f$ a_k \f$ are
+ * @f$ C^a_k @f$ are defined such that @f$ a_k = C^a_k / C^s_k, @f$ where
+ * @f$ C^s_k @f$ is a standard concentration defined below and @f$ a_k @f$ are
* activities used in the thermodynamic functions. These activity (or
* generalized) concentrations are used by kinetics manager classes to compute
* the forward and reverse rates of elementary reactions. The activity
- * concentration,\f$ C^a_k \f$,is given by the following expression.
+ * concentration,@f$ C^a_k @f$,is given by the following expression.
*
- * \f[
+ * @f[
* C^a_k = C^s_k X_k = \frac{P}{R T} X_k
- * \f]
+ * @f]
*
* The standard concentration for species *k* is independent of *k* and equal to
*
- * \f[
+ * @f[
* C^s_k = C^s = \frac{P}{R T}
- * \f]
+ * @f]
*
* For example, a bulk-phase binary gas reaction between species j and k,
* producing a new gas species l would have the following equation for its rate
- * of progress variable, \f$ R^1 \f$, which has units of kmol m-3 s-1.
+ * of progress variable, @f$ R^1 @f$, which has units of kmol m-3 s-1.
*
- * \f[
+ * @f[
* R^1 = k^1 C_j^a C_k^a = k^1 (C^s a_j) (C^s a_k)
- * \f]
+ * @f]
* where
- * \f[
+ * @f[
* C_j^a = C^s a_j \mbox{\quad and \quad} C_k^a = C^s a_k
- * \f]
+ * @f]
*
- * \f$ C_j^a \f$ is the activity concentration of species j, and \f$ C_k^a \f$
- * is the activity concentration of species k. \f$ C^s \f$ is the standard
- * concentration. \f$ a_j \f$ is the activity of species j which is equal to the
+ * @f$ C_j^a @f$ is the activity concentration of species j, and @f$ C_k^a @f$
+ * is the activity concentration of species k. @f$ C^s @f$ is the standard
+ * concentration. @f$ a_j @f$ is the activity of species j which is equal to the
* mole fraction of j.
*
* The reverse rate constant can then be obtained from the law of microscopic
* reversibility and the equilibrium expression for the system.
*
- * \f[
+ * @f[
* \frac{a_j a_k}{ a_l} = K_a^{o,1} = \exp(\frac{\mu^o_l - \mu^o_j - \mu^o_k}{R T} )
- * \f]
+ * @f]
*
- * \f$ K_a^{o,1} \f$ is the dimensionless form of the equilibrium constant,
- * associated with the pressure dependent standard states \f$ \mu^o_l(T,P) \f$
- * and their associated activities, \f$ a_l \f$, repeated here:
+ * @f$ K_a^{o,1} @f$ is the dimensionless form of the equilibrium constant,
+ * associated with the pressure dependent standard states @f$ \mu^o_l(T,P) @f$
+ * and their associated activities, @f$ a_l @f$, repeated here:
*
- * \f[
+ * @f[
* \mu_l(T,P) = \mu^o_l(T, P) + R T \log(a_l)
- * \f]
+ * @f]
*
* We can switch over to expressing the equilibrium constant in terms of the
* reference state chemical potentials
*
- * \f[
+ * @f[
* K_a^{o,1} = \exp(\frac{\mu^{ref}_l - \mu^{ref}_j - \mu^{ref}_k}{R T} ) * \frac{P_{ref}}{P}
- * \f]
+ * @f]
*
- * The concentration equilibrium constant, \f$ K_c \f$, may be obtained by
+ * The concentration equilibrium constant, @f$ K_c @f$, may be obtained by
* changing over to activity concentrations. When this is done:
*
- * \f[
+ * @f[
* \frac{C^a_j C^a_k}{ C^a_l} = C^o K_a^{o,1} = K_c^1 =
* \exp(\frac{\mu^{ref}_l - \mu^{ref}_j - \mu^{ref}_k}{R T} ) * \frac{P_{ref}}{RT}
- * \f]
+ * @f]
*
- * %Kinetics managers will calculate the concentration equilibrium constant, \f$
- * K_c \f$, using the second and third part of the above expression as a
+ * %Kinetics managers will calculate the concentration equilibrium constant, @f$
+ * K_c @f$, using the second and third part of the above expression as a
* definition for the concentration equilibrium constant.
*
* For completeness, the pressure equilibrium constant may be obtained as well
*
- * \f[
+ * @f[
* \frac{P_j P_k}{ P_l P_{ref}} = K_p^1 = \exp(\frac{\mu^{ref}_l - \mu^{ref}_j - \mu^{ref}_k}{R T} )
- * \f]
+ * @f]
*
- * \f$ K_p \f$ is the simplest form of the equilibrium constant for ideal gases.
+ * @f$ K_p @f$ is the simplest form of the equilibrium constant for ideal gases.
* However, it isn't necessarily the simplest form of the equilibrium constant
- * for other types of phases; \f$ K_c \f$ is used instead because it is
+ * for other types of phases; @f$ K_c @f$ is used instead because it is
* completely general.
*
* The reverse rate of progress may be written down as
- * \f[
+ * @f[
* R^{-1} = k^{-1} C_l^a = k^{-1} (C^o a_l)
- * \f]
+ * @f]
*
* where we can use the concept of microscopic reversibility to write the
* reverse rate constant in terms of the forward rate constant and the
- * concentration equilibrium constant, \f$ K_c \f$.
+ * concentration equilibrium constant, @f$ K_c @f$.
*
- * \f[
+ * @f[
* k^{-1} = k^1 K^1_c
- * \f]
+ * @f]
*
- * \f$k^{-1} \f$ has units of s-1.
+ * @f$ k^{-1} @f$ has units of s-1.
*
* @ingroup thermoprops
*/
@@ -257,9 +257,9 @@ class RedlichKisterVPSSTP : public GibbsExcessVPSSTP
//! @}
//! @name Activities, Standard States, and Activity Concentrations
//!
- //! The activity \f$a_k\f$ of a species in solution is
- //! related to the chemical potential by \f[ \mu_k = \mu_k^0(T)
- //! + \hat R T \log a_k. \f] The quantity \f$\mu_k^0(T,P)\f$ is
+ //! The activity @f$ a_k @f$ of a species in solution is
+ //! related to the chemical potential by @f[ \mu_k = \mu_k^0(T)
+ //! + \hat R T \log a_k. @f] The quantity @f$ \mu_k^0(T,P) @f$ is
//! the chemical potential at unit activity, which depends only
//! on temperature and pressure.
//! @{
@@ -281,9 +281,9 @@ class RedlichKisterVPSSTP : public GibbsExcessVPSSTP
* state enthalpies modified by the derivative of the molality-based
* activity coefficient wrt temperature
*
- * \f[
+ * @f[
* \bar h_k(T,P) = h^o_k(T,P) - R T^2 \frac{d \ln(\gamma_k)}{dT}
- * \f]
+ * @f]
*
* @param hbar Vector of returned partial molar enthalpies
* (length m_kk, units = J/kmol)
@@ -297,10 +297,10 @@ class RedlichKisterVPSSTP : public GibbsExcessVPSSTP
* state entropies modified by the derivative of the activity coefficient
* with respect to temperature:
*
- * \f[
+ * @f[
* \bar s_k(T,P) = s^o_k(T,P) - R \ln( \gamma_k X_k)
* - R T \frac{d \ln(\gamma_k) }{dT}
- * \f]
+ * @f]
*
* @param sbar Vector of returned partial molar entropies
* (length m_kk, units = J/kmol/K)
@@ -315,9 +315,9 @@ class RedlichKisterVPSSTP : public GibbsExcessVPSSTP
* For this phase, the partial molar heat capacities are equal to the standard
* state heat capacities:
*
- * \f[
+ * @f[
* \tilde{C}_{p,k}(T,P) = C^o_{p,k}(T,P)
- * \f]
+ * @f]
*
* @param cpbar Vector of returned partial molar heat capacities
* (length m_kk, units = J/kmol/K)
diff --git a/include/cantera/thermo/RedlichKwongMFTP.h b/include/cantera/thermo/RedlichKwongMFTP.h
index 8f33be3faf..5b550cb982 100644
--- a/include/cantera/thermo/RedlichKwongMFTP.h
+++ b/include/cantera/thermo/RedlichKwongMFTP.h
@@ -45,11 +45,11 @@ class RedlichKwongMFTP : public MixtureFugacityTP
/*!
* Since the mass density, temperature, and mass fractions are stored,
* this method uses these values to implement the
- * mechanical equation of state \f$ P(T, \rho, Y_1, \dots, Y_K) \f$.
+ * mechanical equation of state @f$ P(T, \rho, Y_1, \dots, Y_K) @f$.
*
- * \f[
+ * @f[
* P = \frac{RT}{v-b_{mix}} - \frac{a_{mix}}{T^{0.5} v \left( v + b_{mix} \right) }
- * \f]
+ * @f]
*/
virtual doublereal pressure() const;
@@ -57,14 +57,14 @@ class RedlichKwongMFTP : public MixtureFugacityTP
public:
- //! Returns the standard concentration \f$ C^0_k \f$, which is used to
+ //! Returns the standard concentration @f$ C^0_k @f$, which is used to
//! normalize the generalized concentration.
/*!
* This is defined as the concentration by which the generalized
* concentration is normalized to produce the activity. In many cases, this
* quantity will be the same for all species in a phase. Since the activity
* for an ideal gas mixture is simply the mole fraction, for an ideal gas
- * \f$ C^0_k = P/\hat R T \f$.
+ * @f$ C^0_k = P/\hat R T @f$.
*
* @param k Optional parameter indicating the species. The default is to
* assume this refers to species 0.
@@ -90,7 +90,7 @@ class RedlichKwongMFTP : public MixtureFugacityTP
//! Get the array of non-dimensional species chemical potentials.
//! These are partial molar Gibbs free energies.
/*!
- * \f$ \mu_k / \hat R T \f$.
+ * @f$ \mu_k / \hat R T @f$.
* Units: unitless
*
* We close the loop on this function, here, calling getChemPotentials() and
@@ -130,7 +130,7 @@ class RedlichKwongMFTP : public MixtureFugacityTP
/*!
* The "a" parameter for species *i* in the Redlich-Kwong model is assumed
* to be a linear function of temperature:
- * \f[ a = a_0 + a_1 T \f]
+ * @f[ a = a_0 + a_1 T @f]
*
* @param species Name of the species
* @param a0 constant term in the expression for the "a" parameter
@@ -146,10 +146,10 @@ class RedlichKwongMFTP : public MixtureFugacityTP
/*!
* The "a" parameter for interactions between species *i* and *j* is
* assumed by default to be computed as:
- * \f[ a_{ij} = \sqrt(a_{i,0} a_{j,0}) + \sqrt(a_{i,1} a_{j,1}) T \f]
+ * @f[ a_{ij} = \sqrt(a_{i,0} a_{j,0}) + \sqrt(a_{i,1} a_{j,1}) T @f]
*
* This function overrides the defaults with the specified parameters:
- * \f[ a_{ij} = a_{ij,0} + a_{ij,1} T \f]
+ * @f[ a_{ij} = a_{ij,0} + a_{ij,1} T @f]
*
* @param species_i Name of one species
* @param species_j Name of the other species
diff --git a/include/cantera/thermo/ShomatePoly.h b/include/cantera/thermo/ShomatePoly.h
index ce5c4b5229..e7755da815 100644
--- a/include/cantera/thermo/ShomatePoly.h
+++ b/include/cantera/thermo/ShomatePoly.h
@@ -22,30 +22,30 @@ namespace Cantera
//! The Shomate polynomial parameterization for one temperature range for one
//! species
/*!
- * Seven coefficients \f$(A,\dots,G)\f$ are used to represent
- * \f$ c_p^0(T)\f$, \f$ h^0(T)\f$, and \f$ s^0(T) \f$ as
- * polynomials in the temperature, \f$ T \f$ :
+ * Seven coefficients @f$ (A,\dots,G) @f$ are used to represent
+ * @f$ c_p^0(T) @f$, @f$ h^0(T) @f$, and @f$ s^0(T) @f$ as
+ * polynomials in the temperature, @f$ T @f$ :
*
- * \f[
+ * @f[
* \tilde{c}_p^0(T) = A + B t + C t^2 + D t^3 + \frac{E}{t^2}
- * \f]
- * \f[
+ * @f]
+ * @f[
* \tilde{h}^0(T) = A t + \frac{B t^2}{2} + \frac{C t^3}{3}
* + \frac{D t^4}{4} - \frac{E}{t} + F.
- * \f]
- * \f[
+ * @f]
+ * @f[
* \tilde{s}^0(T) = A\ln t + B t + \frac{C t^2}{2}
* + \frac{D t^3}{3} - \frac{E}{2t^2} + G.
- * \f]
+ * @f]
*
* In the above expressions, the thermodynamic polynomials are expressed in
- * dimensional units, but the temperature,\f$ t \f$, is divided by 1000. The
+ * dimensional units, but the temperature,@f$ t @f$, is divided by 1000. The
* following dimensions are assumed in the above expressions:
*
- * - \f$ \tilde{c}_p^0(T)\f$ = Heat Capacity (J/gmol*K)
- * - \f$ \tilde{h}^0(T) \f$ = standard Enthalpy (kJ/gmol)
- * - \f$ \tilde{s}^0(T) \f$= standard Entropy (J/gmol*K)
- * - \f$ t \f$= temperature (K) / 1000.
+ * - @f$ \tilde{c}_p^0(T) @f$ = Heat Capacity (J/gmol*K)
+ * - @f$ \tilde{h}^0(T) @f$ = standard Enthalpy (kJ/gmol)
+ * - @f$ \tilde{s}^0(T) @f$= standard Entropy (J/gmol*K)
+ * - @f$ t @f$= temperature (K) / 1000.
*
* For more information about Shomate polynomials, see the NIST website,
* http://webbook.nist.gov/
@@ -69,7 +69,7 @@ class ShomatePoly : public SpeciesThermoInterpType
* the parameters for the species standard state.
*
* See the class description for the polynomial representation of the
- * thermo functions in terms of \f$ A, \dots, G \f$.
+ * thermo functions in terms of @f$ A, \dots, G @f$.
*/
ShomatePoly(double tlow, double thigh, double pref, const double* coeffs) :
SpeciesThermoInterpType(tlow, thigh, pref),
@@ -195,30 +195,30 @@ class ShomatePoly : public SpeciesThermoInterpType
//! The Shomate polynomial parameterization for two temperature ranges for one
//! species
/*!
- * Seven coefficients \f$(A,\dots,G)\f$ are used to represent
- * \f$ c_p^0(T)\f$, \f$ h^0(T)\f$, and \f$ s^0(T) \f$ as
- * polynomials in the temperature, \f$ T \f$, in one temperature region:
+ * Seven coefficients @f$ (A,\dots,G) @f$ are used to represent
+ * @f$ c_p^0(T) @f$, @f$ h^0(T) @f$, and @f$ s^0(T) @f$ as
+ * polynomials in the temperature, @f$ T @f$, in one temperature region:
*
- * \f[
+ * @f[
* \tilde{c}_p^0(T) = A + B t + C t^2 + D t^3 + \frac{E}{t^2}
- * \f]
- * \f[
+ * @f]
+ * @f[
* \tilde{h}^0(T) = A t + \frac{B t^2}{2} + \frac{C t^3}{3}
* + \frac{D t^4}{4} - \frac{E}{t} + F.
- * \f]
- * \f[
+ * @f]
+ * @f[
* \tilde{s}^0(T) = A\ln t + B t + \frac{C t^2}{2}
* + \frac{D t^3}{3} - \frac{E}{2t^2} + G.
- * \f]
+ * @f]
*
* In the above expressions, the thermodynamic polynomials are expressed
- * in dimensional units, but the temperature,\f$ t \f$, is divided by 1000. The
+ * in dimensional units, but the temperature,@f$ t @f$, is divided by 1000. The
* following dimensions are assumed in the above expressions:
*
- * - \f$ \tilde{c}_p^0(T)\f$ = Heat Capacity (J/gmol*K)
- * - \f$ \tilde{h}^0(T) \f$ = standard Enthalpy (kJ/gmol)
- * - \f$ \tilde{s}^0(T) \f$= standard Entropy (J/gmol*K)
- * - \f$ t \f$= temperature (K) / 1000.
+ * - @f$ \tilde{c}_p^0(T) @f$ = Heat Capacity (J/gmol*K)
+ * - @f$ \tilde{h}^0(T) @f$ = standard Enthalpy (kJ/gmol)
+ * - @f$ \tilde{s}^0(T) @f$= standard Entropy (J/gmol*K)
+ * - @f$ t @f$= temperature (K) / 1000.
*
* For more information about Shomate polynomials, see the NIST website,
* http://webbook.nist.gov/
diff --git a/include/cantera/thermo/SingleSpeciesTP.h b/include/cantera/thermo/SingleSpeciesTP.h
index 5b7bf778b1..5e124cce4d 100644
--- a/include/cantera/thermo/SingleSpeciesTP.h
+++ b/include/cantera/thermo/SingleSpeciesTP.h
@@ -84,9 +84,9 @@ class SingleSpeciesTP : public ThermoPhase
//! @}
//! @name Activities, Standard State, and Activity Concentrations
//!
- //! The activity \f$a_k\f$ of a species in solution is related to the
- //! chemical potential by \f[ \mu_k = \mu_k^0(T) + \hat R T \log a_k. \f]
- //! The quantity \f$\mu_k^0(T)\f$ is the chemical potential at unit activity,
+ //! The activity @f$ a_k @f$ of a species in solution is related to the
+ //! chemical potential by @f[ \mu_k = \mu_k^0(T) + \hat R T \log a_k. @f]
+ //! The quantity @f$ \mu_k^0(T) @f$ is the chemical potential at unit activity,
//! which depends only on temperature.
//! @{
@@ -119,7 +119,7 @@ class SingleSpeciesTP : public ThermoPhase
/*!
* These are the phase, partial molar, and the standard state dimensionless
* chemical potentials.
- * \f$ \mu_k / \hat R T \f$.
+ * @f$ \mu_k / \hat R T @f$.
*
* Units: unitless
*
@@ -133,7 +133,7 @@ class SingleSpeciesTP : public ThermoPhase
/*!
* These are the phase, partial molar, and the standard state chemical
* potentials.
- * \f$ \mu(T,P) = \mu^0_k(T,P) \f$.
+ * @f$ \mu(T,P) = \mu^0_k(T,P) @f$.
*
* @param mu On return, Contains the chemical potential of the single
* species and the phase. Units are J / kmol . Length = 1
@@ -142,7 +142,7 @@ class SingleSpeciesTP : public ThermoPhase
//! Get the species partial molar enthalpies. Units: J/kmol.
/*!
- * These are the phase enthalpies. \f$ h_k \f$.
+ * These are the phase enthalpies. @f$ h_k @f$.
*
* @param hbar Output vector of species partial molar enthalpies.
* Length: 1. units are J/kmol.
@@ -151,7 +151,7 @@ class SingleSpeciesTP : public ThermoPhase
//! Get the species partial molar internal energies. Units: J/kmol.
/*!
- * These are the phase internal energies. \f$ u_k \f$.
+ * These are the phase internal energies. @f$ u_k @f$.
*
* @param ubar On return, Contains the internal energy of the single species
* and the phase. Units are J / kmol . Length = 1
@@ -160,7 +160,7 @@ class SingleSpeciesTP : public ThermoPhase
//! Get the species partial molar entropy. Units: J/kmol K.
/*!
- * This is the phase entropy. \f$ s(T,P) = s_o(T,P) \f$.
+ * This is the phase entropy. @f$ s(T,P) = s_o(T,P) @f$.
*
* @param sbar On return, Contains the entropy of the single species and the
* phase. Units are J / kmol / K . Length = 1
@@ -169,7 +169,7 @@ class SingleSpeciesTP : public ThermoPhase
//! Get the species partial molar Heat Capacities. Units: J/ kmol /K.
/*!
- * This is the phase heat capacity. \f$ Cp(T,P) = Cp_o(T,P) \f$.
+ * This is the phase heat capacity. @f$ Cp(T,P) = Cp_o(T,P) @f$.
*
* @param cpbar On return, Contains the heat capacity of the single species
* and the phase. Units are J / kmol / K . Length = 1
@@ -178,7 +178,7 @@ class SingleSpeciesTP : public ThermoPhase
//! Get the species partial molar volumes. Units: m^3/kmol.
/*!
- * This is the phase molar volume. \f$ V(T,P) = V_o(T,P) \f$.
+ * This is the phase molar volume. @f$ V(T,P) = V_o(T,P) @f$.
*
* @param vbar On return, Contains the molar volume of the single species
* and the phase. Units are m^3 / kmol. Length = 1
diff --git a/include/cantera/thermo/StoichSubstance.h b/include/cantera/thermo/StoichSubstance.h
index 689c3fbaf8..b902ad0edf 100644
--- a/include/cantera/thermo/StoichSubstance.h
+++ b/include/cantera/thermo/StoichSubstance.h
@@ -33,26 +33,26 @@ namespace Cantera
*
* For an incompressible, stoichiometric substance, the molar internal energy is
* independent of pressure. Since the thermodynamic properties are specified by
- * giving the standard-state enthalpy, the term \f$ P_0 \hat v\f$ is subtracted
+ * giving the standard-state enthalpy, the term @f$ P_0 \hat v @f$ is subtracted
* from the specified molar enthalpy to compute the molar internal energy. The
* entropy is assumed to be independent of the pressure.
*
* The enthalpy function is given by the following relation.
*
- * \f[
+ * @f[
* h^o_k(T,P) =
* h^{ref}_k(T) + \tilde v \left( P - P_{ref} \right)
- * \f]
+ * @f]
*
* For an incompressible, stoichiometric substance, the molar internal energy is
* independent of pressure. Since the thermodynamic properties are specified by
- * giving the standard-state enthalpy, the term \f$ P_{ref} \tilde v\f$ is
+ * giving the standard-state enthalpy, the term @f$ P_{ref} \tilde v @f$ is
* subtracted from the specified reference molar enthalpy to compute the molar
* internal energy.
*
- * \f[
+ * @f[
* u^o_k(T,P) = h^{ref}_k(T) - P_{ref} \tilde v
- * \f]
+ * @f]
*
* The standard state heat capacity and entropy are independent of pressure. The
* standard state Gibbs free energy is obtained from the enthalpy and entropy
@@ -73,12 +73,12 @@ namespace Cantera
* An example of a reaction using this is a sticking coefficient reaction of a
* substance in an ideal gas phase on a surface with a bulk phase species in
* this phase. In this case, the rate of progress for this reaction,
- * \f$ R_s \f$, may be expressed via the following equation:
- * \f[
+ * @f$ R_s @f$, may be expressed via the following equation:
+ * @f[
* R_s = k_s C_{gas}
- * \f]
- * where the units for \f$ R_s \f$ are kmol m-2 s-1. \f$ C_{gas} \f$ has units
- * of kmol m-3. Therefore, the kinetic rate constant, \f$ k_s \f$, has units of
+ * @f]
+ * where the units for @f$ R_s @f$ are kmol m-2 s-1. @f$ C_{gas} @f$ has units
+ * of kmol m-3. Therefore, the kinetic rate constant, @f$ k_s @f$, has units of
* m s-1. Nowhere does the concentration of the bulk phase appear in the rate
* constant expression, since it's a stoichiometric phase and the activity is
* always equal to 1.0.
@@ -141,8 +141,8 @@ class StoichSubstance : public SingleSpeciesTP
//! This method returns an array of generalized concentrations
/*!
- * \f$ C^a_k\f$ are defined such that \f$ a_k = C^a_k / C^0_k, \f$ where
- * \f$ C^0_k \f$ is a standard concentration defined below and \f$ a_k \f$
+ * @f$ C^a_k @f$ are defined such that @f$ a_k = C^a_k / C^0_k, @f$ where
+ * @f$ C^0_k @f$ is a standard concentration defined below and @f$ a_k @f$
* are activities used in the thermodynamic functions. These activity (or
* generalized) concentrations are used by kinetics manager classes to
* compute the forward and reverse rates of elementary reactions.
@@ -158,7 +158,7 @@ class StoichSubstance : public SingleSpeciesTP
//! Return the standard concentration for the kth species
/*!
- * The standard concentration \f$ C^0_k \f$ used to normalize the activity
+ * The standard concentration @f$ C^0_k @f$ used to normalize the activity
* (that is, generalized) concentration. This phase assumes that the kinetics
* operator works on an dimensionless basis. Thus, the standard
* concentration is equal to 1.0.
@@ -178,7 +178,7 @@ class StoichSubstance : public SingleSpeciesTP
* potential expression, and therefore the standard chemical potential and
* the chemical potential are both equal to the molar Gibbs function.
*
- * These are the standard state chemical potentials \f$ \mu^0_k(T,P) \f$.
+ * These are the standard state chemical potentials @f$ \mu^0_k(T,P) @f$.
* The values are evaluated at the current temperature and pressure of the
* solution
*
@@ -202,7 +202,7 @@ class StoichSubstance : public SingleSpeciesTP
* For an incompressible, stoichiometric substance, the molar internal
* energy is independent of pressure. Since the thermodynamic properties
* are specified by giving the standard-state enthalpy, the term
- * \f$ P_{ref} \hat v\f$ is subtracted from the specified reference molar
+ * @f$ P_{ref} \hat v @f$ is subtracted from the specified reference molar
* enthalpy to compute the standard state molar internal energy.
*
* @param urt output vector of nondimensional standard state
diff --git a/include/cantera/thermo/SurfPhase.h b/include/cantera/thermo/SurfPhase.h
index 0efacdc970..8940e56cef 100644
--- a/include/cantera/thermo/SurfPhase.h
+++ b/include/cantera/thermo/SurfPhase.h
@@ -24,7 +24,7 @@ namespace Cantera
* defined to occupy one or more sites. The surface species are assumed to be
* independent, and thus the species form an ideal solution.
*
- * The density of surface sites is given by the variable \f$ n_0 \f$,
+ * The density of surface sites is given by the variable @f$ n_0 @f$,
* which has SI units of kmol m-2.
*
* ## Specification of Species Standard State Properties
@@ -40,9 +40,9 @@ namespace Cantera
* Therefore, The standard state internal energy for species *k* is equal to the
* enthalpy for species *k*.
*
- * \f[
+ * @f[
* u^o_k = h^o_k
- * \f]
+ * @f]
*
* Also, the standard state chemical potentials, entropy, and heat capacities
* are independent of pressure. The standard state Gibbs free energy is obtained
@@ -51,43 +51,43 @@ namespace Cantera
* ## Specification of Solution Thermodynamic Properties
*
* The activity of species defined in the phase is given by
- * \f[
+ * @f[
* a_k = \theta_k
- * \f]
+ * @f]
*
* The chemical potential for species *k* is equal to
- * \f[
+ * @f[
* \mu_k(T,P) = \mu^o_k(T) + R T \log(\theta_k)
- * \f]
+ * @f]
*
* Pressure is defined as an independent variable in this phase. However, it has
* no effect on any quantities, as the molar concentration is a constant.
*
* The internal energy for species k is equal to the enthalpy for species *k*
- * \f[
+ * @f[
* u_k = h_k
- * \f]
+ * @f]
*
* The entropy for the phase is given by the following relation, which is
* independent of the pressure:
*
- * \f[
+ * @f[
* s_k(T,P) = s^o_k(T) - R \log(\theta_k)
- * \f]
+ * @f]
*
* ## Application within Kinetics Managers
*
- * The activity concentration,\f$ C^a_k \f$, used by the kinetics manager, is equal to
- * the actual concentration, \f$ C^s_k \f$, and is given by the following
+ * The activity concentration,@f$ C^a_k @f$, used by the kinetics manager, is equal to
+ * the actual concentration, @f$ C^s_k @f$, and is given by the following
* expression.
- * \f[
+ * @f[
* C^a_k = C^s_k = \frac{\theta_k n_0}{s_k}
- * \f]
+ * @f]
*
* The standard concentration for species *k* is:
- * \f[
+ * @f[
* C^0_k = \frac{n_0}{s_k}
- * \f]
+ * @f]
*
* An example phase definition is given in the
* YAML API Reference.
@@ -117,11 +117,11 @@ class SurfPhase : public ThermoPhase
//! Return the Molar Enthalpy. Units: J/kmol.
/*!
* For an ideal solution,
- * \f[
+ * @f[
* \hat h(T,P) = \sum_k X_k \hat h^0_k(T),
- * \f]
+ * @f]
* and is a function only of temperature. The standard-state pure-species
- * Enthalpies \f$ \hat h^0_k(T) \f$ are computed by the species
+ * Enthalpies @f$ \hat h^0_k(T) @f$ are computed by the species
* thermodynamic property manager.
*
* \see MultiSpeciesThermo
@@ -137,9 +137,9 @@ class SurfPhase : public ThermoPhase
//! Return the Molar Entropy. Units: J/kmol-K
/**
- * \f[
+ * @f[
* \hat s(T,P) = \sum_k X_k (\hat s^0_k(T) - R \log(\theta_k))
- * \f]
+ * @f]
*/
virtual doublereal entropy_mole() const;
@@ -155,21 +155,21 @@ class SurfPhase : public ThermoPhase
//! Return a vector of activity concentrations for each species
/*!
- * For this phase the activity concentrations,\f$ C^a_k \f$, are defined to
- * be equal to the actual concentrations, \f$ C^s_k \f$. Activity
+ * For this phase the activity concentrations,@f$ C^a_k @f$, are defined to
+ * be equal to the actual concentrations, @f$ C^s_k @f$. Activity
* concentrations are
*
- * \f[
+ * @f[
* C^a_k = C^s_k = \frac{\theta_k n_0}{s_k}
- * \f]
+ * @f]
*
- * where \f$ \theta_k \f$ is the surface site fraction for species k,
- * \f$ n_0 \f$ is the surface site density for the phase, and
- * \f$ s_k \f$ is the surface size of species k.
+ * where @f$ \theta_k @f$ is the surface site fraction for species k,
+ * @f$ n_0 @f$ is the surface site density for the phase, and
+ * @f$ s_k @f$ is the surface size of species k.
*
- * \f$ C^a_k\f$ that are defined such that \f$ a_k = C^a_k / C^0_k, \f$
- * where \f$ C^0_k \f$ is a standard concentration defined below and \f$ a_k
- * \f$ are activities used in the thermodynamic functions. These activity
+ * @f$ C^a_k @f$ that are defined such that @f$ a_k = C^a_k / C^0_k, @f$
+ * where @f$ C^0_k @f$ is a standard concentration defined below and @f$ a_k
+ * @f$ are activities used in the thermodynamic functions. These activity
* concentrations are used by kinetics manager classes to compute the
* forward and reverse rates of elementary reactions. Note that they may or
* may not have units of concentration --- they might be partial pressures,
@@ -181,15 +181,15 @@ class SurfPhase : public ThermoPhase
//! Return the standard concentration for the kth species
/*!
- * The standard concentration \f$ C^0_k \f$ used to normalize the activity
+ * The standard concentration @f$ C^0_k @f$ used to normalize the activity
* (that is, generalized) concentration. For this phase, the standard
* concentration is species- specific
*
- * \f[
+ * @f[
* C^0_k = \frac{n_0}{s_k}
- * \f]
+ * @f]
*
- * This definition implies that the activity is equal to \f$ \theta_k \f$.
+ * This definition implies that the activity is equal to @f$ \theta_k @f$.
*
* @param k Optional parameter indicating the species. The default
* is to assume this refers to species 0.
diff --git a/include/cantera/thermo/ThermoPhase.h b/include/cantera/thermo/ThermoPhase.h
index d117a1e46d..2f344fb3e1 100644
--- a/include/cantera/thermo/ThermoPhase.h
+++ b/include/cantera/thermo/ThermoPhase.h
@@ -269,13 +269,13 @@ class ThermoPhase : public Phase
//! Returns the isothermal compressibility. Units: 1/Pa.
/*!
* The isothermal compressibility is defined as
- * \f[
+ * @f[
* \kappa_T = -\frac{1}{v}\left(\frac{\partial v}{\partial P}\right)_T
- * \f]
+ * @f]
* or
- * \f[
+ * @f[
* \kappa_T = \frac{1}{\rho}\left(\frac{\partial \rho}{\partial P}\right)_T
- * \f]
+ * @f]
*/
virtual doublereal isothermalCompressibility() const {
throw NotImplementedError("ThermoPhase::isothermalCompressibility");
@@ -284,9 +284,9 @@ class ThermoPhase : public Phase
//! Return the volumetric thermal expansion coefficient. Units: 1/K.
/*!
* The thermal expansion coefficient is defined as
- * \f[
+ * @f[
* \beta = \frac{1}{v}\left(\frac{\partial v}{\partial T}\right)_P
- * \f]
+ * @f]
*/
virtual doublereal thermalExpansionCoeff() const {
throw NotImplementedError("ThermoPhase::thermalExpansionCoeff");
@@ -295,9 +295,9 @@ class ThermoPhase : public Phase
//! Return the speed of sound. Units: m/s.
/*!
* The speed of sound is defined as
- * \f[
+ * @f[
* c = \sqrt{\left(\frac{\partial P}{\partial\rho}\right)_s}
- * \f]
+ * @f]
*/
virtual double soundSpeed() const {
throw NotImplementedError("ThermoPhase::soundSpeed");
@@ -336,9 +336,9 @@ class ThermoPhase : public Phase
//! @}
//! @name Activities, Standard States, and Activity Concentrations
//!
- //! The activity \f$a_k\f$ of a species in solution is related to the
- //! chemical potential by \f[ \mu_k = \mu_k^0(T,P) + \hat R T \log a_k. \f]
- //! The quantity \f$\mu_k^0(T,P)\f$ is the standard chemical potential at
+ //! The activity @f$ a_k @f$ of a species in solution is related to the
+ //! chemical potential by @f[ \mu_k = \mu_k^0(T,P) + \hat R T \log a_k. @f]
+ //! The quantity @f$ \mu_k^0(T,P) @f$ is the standard chemical potential at
//! unit activity, which depends on temperature and pressure, but not on
//! composition. The activity is dimensionless.
//! @{
@@ -393,8 +393,8 @@ class ThermoPhase : public Phase
//! This method returns an array of generalized concentrations
/*!
- * \f$ C^a_k\f$ are defined such that \f$ a_k = C^a_k / C^0_k, \f$ where
- * \f$ C^0_k \f$ is a standard concentration defined below and \f$ a_k \f$
+ * @f$ C^a_k @f$ are defined such that @f$ a_k = C^a_k / C^0_k, @f$ where
+ * @f$ C^0_k @f$ is a standard concentration defined below and @f$ a_k @f$
* are activities used in the thermodynamic functions. These activity (or
* generalized) concentrations are used by kinetics manager classes to
* compute the forward and reverse rates of elementary reactions. Note that
@@ -411,10 +411,10 @@ class ThermoPhase : public Phase
//! Return the standard concentration for the kth species
/*!
- * The standard concentration \f$ C^0_k \f$ used to normalize the activity
+ * The standard concentration @f$ C^0_k @f$ used to normalize the activity
* (that is, generalized) concentration. In many cases, this quantity will be
- * the same for all species in a phase - for example, for an ideal gas \f$
- * C^0_k = P/\hat R T \f$. For this reason, this method returns a single
+ * the same for all species in a phase - for example, for an ideal gas @f$
+ * C^0_k = P/\hat R T @f$. For this reason, this method returns a single
* value, instead of an array. However, for phases in which the standard
* concentration is species-specific (such as surface species of different
* sizes), this method may be called with an optional parameter indicating
@@ -477,7 +477,7 @@ class ThermoPhase : public Phase
/**
* Get the array of non-dimensional species chemical potentials
* These are partial molar Gibbs free energies.
- * \f$ \mu_k / \hat R T \f$.
+ * @f$ \mu_k / \hat R T @f$.
* Units: unitless
*
* @param mu Output vector of dimensionless chemical potentials.
@@ -504,14 +504,14 @@ class ThermoPhase : public Phase
//! Get the species electrochemical potentials.
/*!
- * These are partial molar quantities. This method adds a term \f$ F z_k
- * \phi_p \f$ to each chemical potential. The electrochemical potential of
- * species k in a phase p, \f$ \zeta_k \f$, is related to the chemical
+ * These are partial molar quantities. This method adds a term @f$ F z_k
+ * \phi_p @f$ to each chemical potential. The electrochemical potential of
+ * species k in a phase p, @f$ \zeta_k @f$, is related to the chemical
* potential via the following equation,
*
- * \f[
+ * @f[
* \zeta_{k}(T,P) = \mu_{k}(T,P) + F z_k \phi_p
- * \f]
+ * @f]
*
* @param mu Output vector of species electrochemical
* potentials. Length: m_kk. Units: J/kmol
@@ -576,8 +576,8 @@ class ThermoPhase : public Phase
//! Get the array of chemical potentials at unit activity for the species at
//! their standard states at the current *T* and *P* of the solution.
/*!
- * These are the standard state chemical potentials \f$ \mu^0_k(T,P)
- * \f$. The values are evaluated at the current temperature and pressure of
+ * These are the standard state chemical potentials @f$ \mu^0_k(T,P)
+ * @f$. The values are evaluated at the current temperature and pressure of
* the solution
*
* @param mu Output vector of chemical potentials.
@@ -1256,20 +1256,20 @@ class ThermoPhase : public Phase
* Fuel and oxidizer compositions are given either as
* mole fractions or mass fractions (specified by `basis`)
* and do not need to be normalized.
- * The mixture fraction \f$ Z \f$ can be computed from a single element
- * \f[ Z_m = \frac{Z_{\mathrm{mass},m}-Z_{\mathrm{mass},m,\mathrm{ox}}}
- * {Z_{\mathrm{mass},\mathrm{fuel}}-Z_{\mathrm{mass},m,\mathrm{ox}}} \f] where
- * \f$ Z_{\mathrm{mass},m} \f$ is the elemental mass fraction of element m
- * in the mixture, and \f$ Z_{\mathrm{mass},m,\mathrm{ox}} \f$ and
- * \f$ Z_{\mathrm{mass},m,\mathrm{fuel}} \f$ are the elemental mass fractions
+ * The mixture fraction @f$ Z @f$ can be computed from a single element
+ * @f[ Z_m = \frac{Z_{\mathrm{mass},m}-Z_{\mathrm{mass},m,\mathrm{ox}}}
+ * {Z_{\mathrm{mass},\mathrm{fuel}}-Z_{\mathrm{mass},m,\mathrm{ox}}} @f] where
+ * @f$ Z_{\mathrm{mass},m} @f$ is the elemental mass fraction of element m
+ * in the mixture, and @f$ Z_{\mathrm{mass},m,\mathrm{ox}} @f$ and
+ * @f$ Z_{\mathrm{mass},m,\mathrm{fuel}} @f$ are the elemental mass fractions
* of the oxidizer and fuel, or from the Bilger mixture fraction,
* which considers the elements C, S, H and O (R. W. Bilger, "Turbulent jet
* diffusion flames," Prog. Energy Combust. Sci., 109-131 (1979))
- * \f[ Z_{\mathrm{Bilger}} = \frac{\beta-\beta_{\mathrm{ox}}}
- * {\beta_{\mathrm{fuel}}-\beta_{\mathrm{ox}}} \f]
- * with \f$ \beta = 2\frac{Z_C}{M_C}+2\frac{Z_S}{M_S}+\frac{1}{2}\frac{Z_H}{M_H}
- * -\frac{Z_O}{M_O} \f$
- * and \f$ M_m \f$ the atomic weight of element \f$ m \f$.
+ * @f[ Z_{\mathrm{Bilger}} = \frac{\beta-\beta_{\mathrm{ox}}}
+ * {\beta_{\mathrm{fuel}}-\beta_{\mathrm{ox}}} @f]
+ * with @f$ \beta = 2\frac{Z_C}{M_C}+2\frac{Z_S}{M_S}+\frac{1}{2}\frac{Z_H}{M_H}
+ * -\frac{Z_O}{M_O} @f$
+ * and @f$ M_m @f$ the atomic weight of element @f$ m @f$.
*
* @param fuelComp composition of the fuel
* @param oxComp composition of the oxidizer
@@ -1327,11 +1327,11 @@ class ThermoPhase : public Phase
//! Compute the equivalence ratio for the current mixture
//! given the compositions of fuel and oxidizer
/*!
- * The equivalence ratio \f$ \phi \f$ is computed from
- * \f[ \phi = \frac{Z}{1-Z}\frac{1-Z_{\mathrm{st}}}{Z_{\mathrm{st}}} \f]
- * where \f$ Z \f$ is the Bilger mixture fraction of the mixture
+ * The equivalence ratio @f$ \phi @f$ is computed from
+ * @f[ \phi = \frac{Z}{1-Z}\frac{1-Z_{\mathrm{st}}}{Z_{\mathrm{st}}} @f]
+ * where @f$ Z @f$ is the Bilger mixture fraction of the mixture
* given the specified fuel and oxidizer compositions
- * \f$ Z_{\mathrm{st}} \f$ is the mixture fraction at stoichiometric
+ * @f$ Z_{\mathrm{st}} @f$ is the mixture fraction at stoichiometric
* conditions. Fuel and oxidizer compositions are given either as
* mole fractions or mass fractions (specified by `basis`)
* and do not need to be normalized.
@@ -1346,7 +1346,7 @@ class ThermoPhase : public Phase
* as mole or mass fractions (default: molar)
* @returns equivalence ratio
* @see mixtureFraction for the definition of the Bilger mixture fraction
- * @see equivalenceRatio() for the computation of \f$ \phi \f$ without arguments
+ * @see equivalenceRatio() for the computation of @f$ \phi @f$ without arguments
*/
double equivalenceRatio(const double* fuelComp, const double* oxComp,
ThermoBasis basis=ThermoBasis::molar) const;
@@ -1361,12 +1361,12 @@ class ThermoPhase : public Phase
//! Compute the equivalence ratio for the current mixture
//! from available oxygen and required oxygen
/*!
- * Computes the equivalence ratio \f$ \phi \f$ from
- * \f[ \phi =
+ * Computes the equivalence ratio @f$ \phi @f$ from
+ * @f[ \phi =
* \frac{Z_{\mathrm{mole},C} + Z_{\mathrm{mole},S} + \frac{1}{4}Z_{\mathrm{mole},H}}
- * {\frac{1}{2}Z_{\mathrm{mole},O}} \f]
- * where \f$ Z_{\mathrm{mole},m} \f$ is the elemental mole fraction
- * of element \f$ m \f$. In this special case, the equivalence ratio
+ * {\frac{1}{2}Z_{\mathrm{mole},O}} @f]
+ * where @f$ Z_{\mathrm{mole},m} @f$ is the elemental mole fraction
+ * of element @f$ m @f$. In this special case, the equivalence ratio
* is independent of a fuel or oxidizer composition because it only
* considers the locally available oxygen compared to the required oxygen
* for complete oxidation. It is the same as assuming that the oxidizer
@@ -1391,10 +1391,10 @@ class ThermoPhase : public Phase
* mole fractions or mass fractions (specified by `basis`)
* and do not need to be normalized.
* Elements C, S, H and O are considered for the oxidation.
- * Note that the stoichiometric air to fuel ratio \f$ \mathit{AFR}_{\mathrm{st}} \f$
+ * Note that the stoichiometric air to fuel ratio @f$ \mathit{AFR}_{\mathrm{st}} @f$
* does not depend on the current mixture composition. The current air to fuel ratio
- * can be computed from \f$ \mathit{AFR} = \mathit{AFR}_{\mathrm{st}}/\phi \f$
- * where \f$ \phi \f$ is the equivalence ratio of the current mixture
+ * can be computed from @f$ \mathit{AFR} = \mathit{AFR}_{\mathrm{st}}/\phi @f$
+ * where @f$ \phi @f$ is the equivalence ratio of the current mixture
*
* @param fuelComp composition of the fuel
* @param oxComp composition of the oxidizer
@@ -1502,9 +1502,9 @@ class ThermoPhase : public Phase
//!This method is used by the ChemEquil equilibrium solver.
/*!
* It sets the state such that the chemical potentials satisfy
- * \f[ \frac{\mu_k}{\hat R T} = \sum_m A_{k,m}
- * \left(\frac{\lambda_m} {\hat R T}\right) \f] where
- * \f$ \lambda_m \f$ is the element potential of element m. The
+ * @f[ \frac{\mu_k}{\hat R T} = \sum_m A_{k,m}
+ * \left(\frac{\lambda_m} {\hat R T}\right) @f] where
+ * @f$ \lambda_m @f$ is the element potential of element m. The
* temperature is unchanged. Any phase (ideal or not) that
* implements this method can be equilibrated by ChemEquil.
*
@@ -1777,9 +1777,9 @@ class ThermoPhase : public Phase
* act_coeff for the *m*-th species with respect to the number of moles of
* the *k*-th species.
*
- * \f[
+ * @f[
* \frac{d \ln(\gamma_m) }{d \ln( n_k ) }\Bigg|_{n_i}
- * \f]
+ * @f]
*
* When implemented, this method is used within the VCS equilibrium solver to
* calculate the Jacobian elements, which accelerates convergence of the algorithm.
diff --git a/include/cantera/thermo/VPStandardStateTP.h b/include/cantera/thermo/VPStandardStateTP.h
index c15c771c8a..e1691b55dd 100644
--- a/include/cantera/thermo/VPStandardStateTP.h
+++ b/include/cantera/thermo/VPStandardStateTP.h
@@ -65,7 +65,7 @@ class VPStandardStateTP : public ThermoPhase
//! Get the array of non-dimensional species chemical potentials.
/*!
- * These are partial molar Gibbs free energies, \f$ \mu_k / \hat R T \f$.
+ * These are partial molar Gibbs free energies, @f$ \mu_k / \hat R T @f$.
*
* We close the loop on this function, here, calling getChemPotentials() and
* then dividing by RT. No need for child classes to handle.
@@ -168,12 +168,12 @@ class VPStandardStateTP : public ThermoPhase
*
* The formula for this is
*
- * \f[
+ * @f[
* \rho = \frac{\sum_k{X_k W_k}}{\sum_k{X_k V_k}}
- * \f]
+ * @f]
*
- * where \f$X_k\f$ are the mole fractions, \f$W_k\f$ are the molecular
- * weights, and \f$V_k\f$ are the pure species molar volumes.
+ * where @f$ X_k @f$ are the mole fractions, @f$ W_k @f$ are the molecular
+ * weights, and @f$ V_k @f$ are the pure species molar volumes.
*
* Note, the basis behind this formula is that in an ideal solution the
* partial molar volumes are equal to the pure species molar volumes. We
diff --git a/include/cantera/thermo/WaterProps.h b/include/cantera/thermo/WaterProps.h
index 81f19eaaca..aaeffb4b66 100644
--- a/include/cantera/thermo/WaterProps.h
+++ b/include/cantera/thermo/WaterProps.h
@@ -26,17 +26,17 @@ class PDSS_Water;
*
* ### Treatment of the phase potential and the electrochemical potential of a species
*
- * The electrochemical potential of species \f$k\f$ in a phase \f$p\f$, \f$ \zeta_k \f$,
+ * The electrochemical potential of species @f$ k @f$ in a phase @f$ p @f$, @f$ \zeta_k @f$,
* is related to the chemical potential via the following equation,
*
- * \f[
+ * @f[
* \zeta_{k}(T,P) = \mu_{k}(T,P) + z_k \phi_p
- * \f]
+ * @f]
*
- * where \f$ \nu_k \f$ is the charge of species \f$k\f$, and \f$ \phi_p \f$ is
- * the electric potential of phase \f$p\f$.
+ * where @f$ \nu_k @f$ is the charge of species @f$ k @f$, and @f$ \phi_p @f$ is
+ * the electric potential of phase @f$ p @f$.
*
- * The potential \f$ \phi_p \f$ is tracked and internally stored within the
+ * The potential @f$ \phi_p @f$ is tracked and internally stored within the
* base ThermoPhase object. It constitutes a specification of the internal state
* of the phase; it's the third state variable, the first two being temperature
* and density (or, pressure, for incompressible equations of state). It may be
@@ -46,9 +46,9 @@ class PDSS_Water;
* Note, the overall electrochemical potential of a phase may not be changed
* by the potential because many phases enforce charge neutrality:
*
- * \f[
+ * @f[
* 0 = \sum_k z_k X_k
- * \f]
+ * @f]
*
* Whether charge neutrality is necessary for a phase is also specified within
* the ThermoPhase object, by the function call
@@ -57,7 +57,7 @@ class PDSS_Water;
* such as DebyeHuckel and HMWSoln for the proper specification of the chemical
* potentials.
*
- * This equation, when applied to the \f$ \zeta_k \f$ equation described
+ * This equation, when applied to the @f$ \zeta_k @f$ equation described
* above, results in a zero net change in the effective Gibbs free energy of
* the phase. However, specific charged species in the phase may increase or
* decrease their electrochemical potentials, which will have an effect on
@@ -176,10 +176,10 @@ class WaterProps
* And, therefore, most be recalculated whenever T or P changes. The units
* returned by this expression are sqrt(kg/gmol).
*
- * \f[
+ * @f[
* A_{Debye} = \frac{1}{8 \pi} \sqrt{\frac{2 N_{Avog} \rho_w}{1000}}
* {\left(\frac{e^2}{\epsilon k_{boltz} T}\right)}^{\frac{3}{2}}
- * \f]
+ * @f]
*
* Nominal value at 25C and 1atm = 1.172576 sqrt(kg/gmol).
*
diff --git a/include/cantera/thermo/WaterPropsIAPWS.h b/include/cantera/thermo/WaterPropsIAPWS.h
index 721201badd..8d0bd6a15d 100644
--- a/include/cantera/thermo/WaterPropsIAPWS.h
+++ b/include/cantera/thermo/WaterPropsIAPWS.h
@@ -48,28 +48,28 @@ namespace Cantera
* This class provides a very complicated polynomial for the specific
* Helmholtz free energy of water, as a function of temperature and density.
*
- * \f[
+ * @f[
* \frac{M\hat{f}(\rho,T)}{R T} = \phi(\delta, \tau) =
* \phi^o(\delta, \tau) + \phi^r(\delta, \tau)
- * \f]
+ * @f]
*
* where
*
- * \f[
+ * @f[
* \delta = \rho / \rho_c \quad \mathrm{and} \quad \tau = T_c / T
- * \f]
+ * @f]
*
* The following constants are assumed
*
- * \f[
+ * @f[
* T_c = 647.096\mathrm{\;K}
- * \f]
- * \f[
+ * @f]
+ * @f[
* \rho_c = 322 \mathrm{\;kg\,m^{-3}}
- * \f]
- * \f[
+ * @f]
+ * @f[
* R/M = 0.46151805 \mathrm{\;kJ\,kg^{-1}\,K^{-1}}
- * \f]
+ * @f]
*
* The free energy is a unique single-valued function of the temperature and
* density over its entire range.
@@ -98,8 +98,8 @@ namespace Cantera
* then calculating the correction factor.
*
* This class provides an interface to the WaterPropsIAPWSphi class, which
- * actually calculates the \f$ \phi^o(\delta, \tau) \f$ and the
- * \f$ \phi^r(\delta, \tau) \f$ polynomials in dimensionless form.
+ * actually calculates the @f$ \phi^o(\delta, \tau) @f$ and the
+ * @f$ \phi^r(\delta, \tau) @f$ polynomials in dimensionless form.
*
* All thermodynamic results from this class are returned in dimensional form.
* This is because the gas constant (and molecular weight) used within this
@@ -110,12 +110,12 @@ namespace Cantera
*
* This class is not a ThermoPhase. However, it does maintain an internal
* state of the object that is dependent on temperature and density. The
- * internal state is characterized by an internally stored \f$ \tau\f$ and a
- * \f$ \delta \f$ value, and an iState value, which indicates whether the
+ * internal state is characterized by an internally stored @f$ \tau @f$ and a
+ * @f$ \delta @f$ value, and an iState value, which indicates whether the
* point is a liquid, a gas, or a supercritical fluid. Along with that the
- * \f$ \tau\f$ and a \f$ \delta \f$ values are polynomials of \f$ \tau\f$ and
- * a \f$ \delta \f$ that are kept by the WaterPropsIAPWSphi class. Therefore,
- * whenever \f$ \tau\f$ or \f$ \delta \f$ is changed, the function setState()
+ * @f$ \tau @f$ and a @f$ \delta @f$ values are polynomials of @f$ \tau @f$ and
+ * a @f$ \delta @f$ that are kept by the WaterPropsIAPWSphi class. Therefore,
+ * whenever @f$ \tau @f$ or @f$ \delta @f$ is changed, the function setState()
* must be called in order for the internal state to be kept up to date.
*
* The class is pretty straightforward. However, one function deserves
diff --git a/include/cantera/transport/DustyGasTransport.h b/include/cantera/transport/DustyGasTransport.h
index aff66f9206..50914fcb6a 100644
--- a/include/cantera/transport/DustyGasTransport.h
+++ b/include/cantera/transport/DustyGasTransport.h
@@ -26,20 +26,20 @@ namespace Cantera
* of species due to a pressure gradient that is part of Darcy's law.
*
* The dusty gas model expresses the value of the molar flux of species
- * \f$ k \f$, \f$ J_k \f$ by the following formula.
+ * @f$ k @f$, @f$ J_k @f$ by the following formula.
*
- * \f[
+ * @f[
* \sum_{j \ne k}{\frac{X_j J_k - X_k J_j}{D^e_{kj}}} + \frac{J_k}{\mathcal{D}^{e}_{k,knud}} =
* - \nabla C_k - \frac{C_k}{\mathcal{D}^{e}_{k,knud}} \frac{\kappa}{\mu} \nabla p
- * \f]
+ * @f]
*
- * \f$ j \f$ is a sum over all species in the gas.
+ * @f$ j @f$ is a sum over all species in the gas.
*
* The effective Knudsen diffusion coefficients are given by the following form
*
- * \f[
+ * @f[
* \mathcal{D}^e_{k,knud} = \frac{2}{3} \frac{r_{pore} \phi}{\tau} \left( \frac{8 R T}{\pi W_k} \right)^{1/2}
- * \f]
+ * @f]
*
* The effective knudsen diffusion coefficients take into account the effects of
* collisions of gas-phase molecules with the wall.
@@ -71,9 +71,9 @@ class DustyGasTransport : public Transport
//! Get the molar fluxes [kmol/m^2/s], given the thermodynamic state at two nearby points.
/*!
- * \f[
+ * @f[
* J_k = - \sum_{j = 1, N} \left[D^{multi}_{kj}\right]^{-1} \left( \nabla C_j + \frac{C_j}{\mathcal{D}^{knud}_j} \frac{\kappa}{\mu} \nabla p \right)
- * \f]
+ * @f]
*
* @param state1 Array of temperature, density, and mass fractions for state 1.
* @param state2 Array of temperature, density, and mass fractions for state 2.
@@ -120,9 +120,9 @@ class DustyGasTransport : public Transport
* The value for close-packed spheres is given below, where p is the
* porosity, t is the tortuosity, and d is the diameter of the sphere
*
- * \f[
+ * @f[
* \kappa = \frac{p^3 d^2}{72 t (1 - p)^2}
- * \f]
+ * @f]
*
* @param B set the permeability of the media (units = m^2)
*/
@@ -173,15 +173,15 @@ class DustyGasTransport : public Transport
//! Private routine to update the dusty gas binary diffusion coefficients
/*!
- * The dusty gas binary diffusion coefficients \f$ D^{dg}_{i,j} \f$ are
- * evaluated from the binary gas-phase diffusion coefficients \f$
- * D^{bin}_{i,j} \f$ using the following formula
+ * The dusty gas binary diffusion coefficients @f$ D^{dg}_{i,j} @f$ are
+ * evaluated from the binary gas-phase diffusion coefficients @f$
+ * D^{bin}_{i,j} @f$ using the following formula
*
- * \f[
+ * @f[
* D^{dg}_{i,j} = \frac{\phi}{\tau} D^{bin}_{i,j}
- * \f]
+ * @f]
*
- * where \f$ \phi \f$ is the porosity of the media and \f$ \tau \f$ is the
+ * where @f$ \phi @f$ is the porosity of the media and @f$ \tau @f$ is the
* tortuosity of the media.
*/
void updateBinaryDiffCoeffs();
@@ -197,22 +197,22 @@ class DustyGasTransport : public Transport
/*!
* The Knudsen diffusion coefficients are given by the following form
*
- * \f[
+ * @f[
* \mathcal{D}^{knud}_k = \frac{2}{3} \frac{r_{pore} \phi}{\tau} \left( \frac{8 R T}{\pi W_k} \right)^{1/2}
- * \f]
+ * @f]
*/
void updateKnudsenDiffCoeffs();
//! Calculate the H matrix
/*!
- * The multicomponent diffusion H matrix \f$ H_{k,l} \f$ is given by the following form
+ * The multicomponent diffusion H matrix @f$ H_{k,l} @f$ is given by the following form
*
- * \f[
+ * @f[
* H_{k,l} = - \frac{X_k}{D_{k,l}}
- * \f]
- * \f[
+ * @f]
+ * @f[
* H_{k,k} = \frac{1}{\mathcal(D)^{knud}_{k}} + \sum_{j \ne k}^N{ \frac{X_j}{D_{k,j}} }
- * \f]
+ * @f]
*/
void eval_H_matrix();
@@ -273,11 +273,11 @@ class DustyGasTransport : public Transport
* The permeability is the proportionality constant for Darcy's law which
* relates discharge rate and viscosity to the applied pressure gradient.
*
- * Below is Darcy's law, where \f$ \kappa \f$ is the permeability
+ * Below is Darcy's law, where @f$ \kappa @f$ is the permeability
*
- * \f[
+ * @f[
* v = \frac{\kappa}{\mu} \frac{\delta P}{\delta x}
- * \f]
+ * @f]
*
* units are m2
*/
diff --git a/include/cantera/transport/GasTransport.h b/include/cantera/transport/GasTransport.h
index 34666fd4cd..1378097ad5 100644
--- a/include/cantera/transport/GasTransport.h
+++ b/include/cantera/transport/GasTransport.h
@@ -29,17 +29,17 @@ class GasTransport : public Transport
/*!
* The viscosity is computed using the Wilke mixture rule (kg /m /s)
*
- * \f[
+ * @f[
* \mu = \sum_k \frac{\mu_k X_k}{\sum_j \Phi_{k,j} X_j}.
- * \f]
+ * @f]
*
- * Here \f$ \mu_k \f$ is the viscosity of pure species \e k, and
+ * Here @f$ \mu_k @f$ is the viscosity of pure species \e k, and
*
- * \f[
+ * @f[
* \Phi_{k,j} = \frac{\left[1
* + \sqrt{\left(\frac{\mu_k}{\mu_j}\sqrt{\frac{M_j}{M_k}}\right)}\right]^2}
* {\sqrt{8}\sqrt{1 + M_k/M_j}}
- * \f]
+ * @f]
*
* @returns the viscosity of the mixture (units = Pa s = kg /m /s)
*
@@ -74,11 +74,11 @@ class GasTransport : public Transport
*
* This is Eqn. 12.180 from "Chemically Reacting Flow"
*
- * \f[
+ * @f[
* D_{km}' = \frac{\left( \bar{M} - X_k M_k \right)}{ \bar{\qquad M \qquad } } {\left( \sum_{j \ne k} \frac{X_j}{D_{kj}} \right) }^{-1}
- * \f]
+ * @f]
*
- * @param[out] d Vector of mixture diffusion coefficients, \f$ D_{km}' \f$ ,
+ * @param[out] d Vector of mixture diffusion coefficients, @f$ D_{km}' @f$ ,
* for each species (m^2/s). length m_nsp
*/
virtual void getMixDiffCoeffs(doublereal* const d);
@@ -88,7 +88,7 @@ class GasTransport : public Transport
//! from the species mole fraction gradients, computed according to
//! Eq. 12.176 in "Chemically Reacting Flow":
//!
- //! \f[ D_{km}^* = \frac{1-X_k}{\sum_{j \ne k}^K X_j/\mathcal{D}_{kj}} \f]
+ //! @f[ D_{km}^* = \frac{1-X_k}{\sum_{j \ne k}^K X_j/\mathcal{D}_{kj}} @f]
//!
//! @param[out] d vector of mixture-averaged diffusion coefficients for
//! each species, length m_nsp.
@@ -100,10 +100,10 @@ class GasTransport : public Transport
* from the species mass fraction gradients, computed according to
* Eq. 12.178 in "Chemically Reacting Flow":
*
- * \f[
+ * @f[
* \frac{1}{D_{km}} = \sum_{j \ne k}^K \frac{X_j}{\mathcal{D}_{kj}} +
* \frac{X_k}{1-Y_k} \sum_{j \ne k}^K \frac{Y_j}{\mathcal{D}_{kj}}
- * \f]
+ * @f]
*
* @param[out] d vector of mixture-averaged diffusion coefficients for
* each species, length m_nsp.
@@ -169,10 +169,10 @@ class GasTransport : public Transport
*
* The formula for the weighting function is from Poling and Prausnitz,
* Eq. (9-5.14):
- * \f[
+ * @f[
* \phi_{ij} = \frac{ \left[ 1 + \left( \mu_i / \mu_j \right)^{1/2} \left( M_j / M_i \right)^{1/4} \right]^2 }
* {\left[ 8 \left( 1 + M_i / M_j \right) \right]^{1/2}}
- * \f]
+ * @f]
*/
virtual void updateViscosity_T();
@@ -228,25 +228,25 @@ class GasTransport : public Transport
*/
void fitCollisionIntegrals(MMCollisionInt& integrals);
- //! Generate polynomial fits to the viscosity \f$ \eta \f$ and conductivity
- //! \f$ \lambda \f$.
+ //! Generate polynomial fits to the viscosity @f$ \eta @f$ and conductivity
+ //! @f$ \lambda @f$.
/*!
* If CK_mode, then the fits are of the form
- * \f[
+ * @f[
* \log(\eta(i)) = \sum_{n=0}^3 a_n(i) \, (\log T)^n
- * \f]
+ * @f]
* and
- * \f[
+ * @f[
* \log(\lambda(i)) = \sum_{n=0}^3 b_n(i) \, (\log T)^n
- * \f]
+ * @f]
* Otherwise the fits are of the form
- * \f[
+ * @f[
* \left(\eta(i)\right)^{1/2} = T^{1/4} \sum_{n=0}^4 a_n(i) \, (\log T)^n
- * \f]
+ * @f]
* and
- * \f[
+ * @f[
* \lambda(i) = T^{1/2} \sum_{n=0}^4 b_n(i) \, (\log T)^n
- * \f]
+ * @f]
*
* @param integrals interpolator for the collision integrals
*/
@@ -255,13 +255,13 @@ class GasTransport : public Transport
//! Generate polynomial fits to the binary diffusion coefficients
/*!
* If CK_mode, then the fits are of the form
- * \f[
+ * @f[
* \log(D(i,j)) = \sum_{n=0}^3 c_n(i,j) \, (\log T)^n
- * \f]
+ * @f]
* Otherwise the fits are of the form
- * \f[
+ * @f[
* D(i,j) = T^{3/2} \sum_{n=0}^4 c_n(i,j) \, (\log T)^n
- * \f]
+ * @f]
*
* @param integrals interpolator for the collision integrals
*/
diff --git a/include/cantera/transport/IonGasTransport.h b/include/cantera/transport/IonGasTransport.h
index 0780e98b38..27b99f8098 100644
--- a/include/cantera/transport/IonGasTransport.h
+++ b/include/cantera/transport/IonGasTransport.h
@@ -59,9 +59,9 @@ class IonGasTransport : public MixTransport
virtual void getMixDiffCoeffs(double* const d);
/*! The electrical conductivity (Siemens/m).
- * \f[
+ * @f[
* \sigma = \sum_k{\left|C_k\right| \mu_k \frac{X_k P}{k_b T}}
- * \f]
+ * @f]
*/
virtual double electricalConductivity();
diff --git a/include/cantera/transport/MixTransport.h b/include/cantera/transport/MixTransport.h
index 7321143a9a..39c4e2d937 100644
--- a/include/cantera/transport/MixTransport.h
+++ b/include/cantera/transport/MixTransport.h
@@ -23,28 +23,28 @@ namespace Cantera
*
* The viscosity is computed using the Wilke mixture rule (kg /m /s)
*
- * \f[
+ * @f[
* \mu = \sum_k \frac{\mu_k X_k}{\sum_j \Phi_{k,j} X_j}.
- * \f]
+ * @f]
*
- * Here \f$ \mu_k \f$ is the viscosity of pure species \e k, and
+ * Here @f$ \mu_k @f$ is the viscosity of pure species \e k, and
*
- * \f[
+ * @f[
* \Phi_{k,j} = \frac{\left[1
* + \sqrt{\left(\frac{\mu_k}{\mu_j}\sqrt{\frac{M_j}{M_k}}\right)}\right]^2}
* {\sqrt{8}\sqrt{1 + M_k/M_j}}
- * \f]
+ * @f]
*
* The thermal conductivity is computed from the following mixture rule:
- * \f[
+ * @f[
* \lambda = 0.5 \left( \sum_k X_k \lambda_k + \frac{1}{\sum_k X_k/\lambda_k} \right)
- * \f]
+ * @f]
*
* It's used to compute the flux of energy due to a thermal gradient
*
- * \f[
+ * @f[
* j_T = - \lambda \nabla T
- * \f]
+ * @f]
*
* The flux of energy has units of energy (kg m2 /s2) per second per area.
*
@@ -72,15 +72,15 @@ class MixTransport : public GasTransport
//! Returns the mixture thermal conductivity (W/m /K)
/*!
* The thermal conductivity is computed from the following mixture rule:
- * \f[
+ * @f[
* \lambda = 0.5 \left( \sum_k X_k \lambda_k + \frac{1}{\sum_k X_k/\lambda_k} \right)
- * \f]
+ * @f]
*
* It's used to compute the flux of energy due to a thermal gradient
*
- * \f[
+ * @f[
* j_T = - \lambda \nabla T
- * \f]
+ * @f]
*
* The flux of energy has units of energy (kg m2 /s2) per second per area.
*
@@ -98,9 +98,9 @@ class MixTransport : public GasTransport
* Here, the mobility is calculated from the diffusion coefficient using the
* Einstein relation
*
- * \f[
+ * @f[
* \mu^e_k = \frac{F D_k}{R T}
- * \f]
+ * @f]
*
* @param mobil Returns the mobilities of the species in array \c mobil.
* The array must be dimensioned at least as large as the
@@ -128,9 +128,9 @@ class MixTransport : public GasTransport
* Units for the returned fluxes are kg m-2 s-1.
*
* The diffusive mass flux of species \e k is computed from
- * \f[
+ * @f[
* \vec{j}_k = -n M_k D_k \nabla X_k.
- * \f]
+ * @f]
*
* @param ndim Number of dimensions in the flux expressions
* @param grad_T Gradient of the temperature (length = ndim)
diff --git a/include/cantera/transport/Transport.h b/include/cantera/transport/Transport.h
index c3c00d32a4..1524127016 100644
--- a/include/cantera/transport/Transport.h
+++ b/include/cantera/transport/Transport.h
@@ -335,9 +335,9 @@ class Transport
* Frequently, but not always, the mobility is calculated from the diffusion
* coefficient using the Einstein relation
*
- * \f[
+ * @f[
* \mu^e_k = \frac{F D_k}{R T}
- * \f]
+ * @f]
*
* @param mobil_e Returns the mobilities of the species in array \c
* mobil_e. The array must be dimensioned at least as large as
@@ -357,9 +357,9 @@ class Transport
* Frequently, but not always, the mobility is calculated from the diffusion
* coefficient using the Einstein relation
*
- * \f[
+ * @f[
* \mu^f_k = \frac{D_k}{R T}
- * \f]
+ * @f]
*
* @param mobil_f Returns the mobilities of the species in array \c mobil.
* The array must be dimensioned at least as large as the
@@ -377,12 +377,12 @@ class Transport
//! Compute the mixture electrical conductivity (S m-1) at the current
//! conditions of the phase (Siemens m-1)
/*!
- * The electrical conductivity, \f$ \sigma \f$, relates the electric current
+ * The electrical conductivity, @f$ \sigma @f$, relates the electric current
* density, J, to the electric field, E.
*
- * \f[
+ * @f[
* \vec{J} = \sigma \vec{E}
- * \f]
+ * @f]
*
* We assume here that the mixture electrical conductivity is an isotropic
* quantity, at this stage. Tensors may be included at a later time.
@@ -579,13 +579,13 @@ class Transport
//! Return a vector of Thermal diffusion coefficients [kg/m/sec].
/*!
- * The thermal diffusion coefficient \f$ D^T_k \f$ is defined so that the
+ * The thermal diffusion coefficient @f$ D^T_k @f$ is defined so that the
* diffusive mass flux of species *k* induced by the local temperature
* gradient is given by the following formula:
*
- * \f[
+ * @f[
* M_k J_k = -D^T_k \nabla \ln T.
- * \f]
+ * @f]
*
* The thermal diffusion coefficient can be either positive or negative.
*
diff --git a/include/cantera/transport/UnityLewisTransport.h b/include/cantera/transport/UnityLewisTransport.h
index 2f8328247a..7bf500d6e4 100644
--- a/include/cantera/transport/UnityLewisTransport.h
+++ b/include/cantera/transport/UnityLewisTransport.h
@@ -39,16 +39,16 @@ class UnityLewisTransport : public MixTransport
* with respect to the mass averaged velocity using gradients of the mole
* fraction.
*
- * \f[
+ * @f[
* D^\prime_{km} = \frac{\lambda}{\rho c_p}
- * \f]
+ * @f]
*
* In order to obtain the expected behavior from a unity Lewis number model,
* this formulation requires that the correction velocity be computed as
*
- * \f[
+ * @f[
* V_c = \sum \frac{W_k}{\overline{W}} D^\prime_{km} \nabla X_k
- * \f]
+ * @f]
*
* @param[out] d Vector of diffusion coefficients for each species (m^2/s).
* length m_nsp.
@@ -71,9 +71,9 @@ class UnityLewisTransport : public MixTransport
* These are the coefficients for calculating the diffusive mass fluxes
* from the species mass fraction gradients, computed as
*
- * \f[
+ * @f[
* D_{km} = \frac{\lambda}{\rho c_p}
- * \f]
+ * @f]
*
* @param[out] d Vector of diffusion coefficients for each species (m^2/s).
* length m_nsp.
diff --git a/include/cantera/zeroD/ReactorNet.h b/include/cantera/zeroD/ReactorNet.h
index bac308c02d..9b21a54d53 100644
--- a/include/cantera/zeroD/ReactorNet.h
+++ b/include/cantera/zeroD/ReactorNet.h
@@ -168,10 +168,10 @@ class ReactorNet : public FuncEval
//! Return the sensitivity of the *k*-th solution component with respect to
//! the *p*-th sensitivity parameter.
/*!
- * The sensitivity coefficient \f$ S_{ki} \f$ of solution variable \f$ y_k
- * \f$ with respect to sensitivity parameter \f$ p_i \f$ is defined as:
+ * The sensitivity coefficient @f$ S_{ki} @f$ of solution variable @f$ y_k
+ * @f$ with respect to sensitivity parameter @f$ p_i @f$ is defined as:
*
- * \f[ S_{ki} = \frac{1}{y_k} \frac{\partial y_k}{\partial p_i} \f]
+ * @f[ S_{ki} = \frac{1}{y_k} \frac{\partial y_k}{\partial p_i} @f]
*
* For reaction sensitivities, the parameter is a multiplier on the forward
* rate constant (and implicitly on the reverse rate constant for
diff --git a/include/cantera/zeroD/Wall.h b/include/cantera/zeroD/Wall.h
index 3e73f23cff..43c302c83d 100644
--- a/include/cantera/zeroD/Wall.h
+++ b/include/cantera/zeroD/Wall.h
@@ -147,11 +147,11 @@ class Wall : public WallBase
return "Wall";
}
- //! Wall velocity \f$ v(t) \f$ at current reactor network time.
+ //! Wall velocity @f$ v(t) @f$ at current reactor network time.
//! @since New in %Cantera 3.0.
double velocity() const;
- //! Set the wall velocity to a specified function of time, \f$ v(t) \f$.
+ //! Set the wall velocity to a specified function of time, @f$ v(t) @f$.
void setVelocity(Func1* f=0) {
if (f) {
m_vf = f;
@@ -161,9 +161,9 @@ class Wall : public WallBase
//! Rate of volume change (m^3/s) for the adjacent reactors.
/*!
* The volume rate of change is given by
- * \f[
+ * @f[
* \dot V = K A (P_{left} - P_{right}) + F(t)
- * \f]
+ * @f]
* where *K* is the specified expansion rate coefficient, *A* is the wall
* area, and *F(t)* is a specified function of time. Positive values for
* `vdot` correspond to increases in the volume of reactor on left, and
@@ -176,9 +176,9 @@ class Wall : public WallBase
//! Rate of volume change (m^3/s) for the adjacent reactors.
/*!
* The volume rate of change is given by
- * \f[
+ * @f[
* \dot V = K A (P_{left} - P_{right}) + F(t)
- * \f]
+ * @f]
* where *K* is the specified expansion rate coefficient, *A* is the wall area,
* and and *F(t)* is a specified function evaluated at the current network time.
* Positive values for `expansionRate` correspond to increases in the volume of
@@ -187,11 +187,11 @@ class Wall : public WallBase
*/
virtual double expansionRate();
- //! Heat flux function \f$ q_0(t) \f$ evaluated at current reactor network time.
+ //! Heat flux function @f$ q_0(t) @f$ evaluated at current reactor network time.
//! @since New in %Cantera 3.0.
double heatFlux() const;
- //! Specify the heat flux function \f$ q_0(t) \f$.
+ //! Specify the heat flux function @f$ q_0(t) @f$.
void setHeatFlux(Func1* q) {
m_qf = q;
}
@@ -199,9 +199,9 @@ class Wall : public WallBase
//! Heat flow rate through the wall (W).
/*!
* The heat flux is given by
- * \f[
+ * @f[
* Q = h A (T_{left} - T_{right}) + A G(t)
- * \f]
+ * @f]
* where *h* is the heat transfer coefficient, *A* is the wall area, and
* *G(t)* is a specified function of time. Positive values denote a flux
* from left to right.
@@ -212,9 +212,9 @@ class Wall : public WallBase
//! Heat flow rate through the wall (W).
/*!
* The heat flux is given by
- * \f[
+ * @f[
* Q = h A (T_{left} - T_{right}) + A G(t)
- * \f]
+ * @f]
* where *h* is the heat transfer coefficient, *A* is the wall area, and
* *G(t)* is a specified function of time evaluated at the current network
* time. Positive values denote a flux from left to right.
diff --git a/include/cantera/zeroD/flowControllers.h b/include/cantera/zeroD/flowControllers.h
index 88513db918..5b9398baaf 100644
--- a/include/cantera/zeroD/flowControllers.h
+++ b/include/cantera/zeroD/flowControllers.h
@@ -32,10 +32,10 @@ class MassFlowController : public FlowDevice
//! Set the mass flow coefficient.
/*!
* *m* has units of kg/s. The mass flow rate is computed as:
- * \f[\dot{m} = m g(t) \f]
+ * @f[\dot{m} = m g(t) @f]
* where *g* is a function of time that is set by `setTimeFunction`.
* If no function is specified, the mass flow rate defaults to:
- * \f[\dot{m} = m \f]
+ * @f[\dot{m} = m @f]
*/
void setMassFlowCoeff(double m) {
m_coeff = m;
@@ -94,11 +94,11 @@ class PressureController : public FlowDevice
//! rate
/*!
* *c* has units of kg/s/Pa. The mass flow rate is computed as:
- * \f[\dot{m} = \dot{m}_{primary} + c f(\Delta P) \f]
+ * @f[\dot{m} = \dot{m}_{primary} + c f(\Delta P) @f]
* where *f* is a functions of pressure drop that is set by
* `setPressureFunction`. If no functions is specified, the mass flow
* rate defaults to:
- * \f[\dot{m} = \dot{m}_{primary} + c \Delta P \f]
+ * @f[\dot{m} = \dot{m}_{primary} + c \Delta P @f]
*/
void setPressureCoeff(double c) {
m_coeff = c;
@@ -136,11 +136,11 @@ class Valve : public FlowDevice
//! rate
/*!
* *c* has units of kg/s/Pa. The mass flow rate is computed as:
- * \f[\dot{m} = c g(t) f(\Delta P) \f]
+ * @f[\dot{m} = c g(t) f(\Delta P) @f]
* where *g* and *f* are functions of time and pressure drop that are set
* by `setTimeFunction` and `setPressureFunction`, respectively. If no functions are
* specified, the mass flow rate defaults to:
- * \f[\dot{m} = c \Delta P \f]
+ * @f[\dot{m} = c \Delta P @f]
*/
void setValveCoeff(double c) {
m_coeff = c;
diff --git a/interfaces/dotnet/Cantera/src/Consts.cs b/interfaces/dotnet/Cantera/src/Consts.cs
index 860f05ab24..b41a422897 100644
--- a/interfaces/dotnet/Cantera/src/Consts.cs
+++ b/interfaces/dotnet/Cantera/src/Consts.cs
@@ -9,47 +9,47 @@ namespace Cantera;
public static class Consts
{
///
- /// Avogadro's Number \f$ N_{\mathrm{A}} \f$ [number/kmol]
+ /// Avogadro's Number @f$ N_{\mathrm{A}} @f$ [number/kmol]
///
public const double Avogadro = 6.02214076e26;
///
- /// Boltzmann constant \f$ k \f$ [J/K]
+ /// Boltzmann constant @f$ k @f$ [J/K]
///
public const double Boltzmann = 1.380649e-23;
///
- /// Planck constant \f$ h \f$ [J-s]
+ /// Planck constant @f$ h @f$ [J-s]
///
public const double Planck = 6.62607015e-34;
///
- /// Elementary charge \f$ e \f$ [C]
+ /// Elementary charge @f$ e @f$ [C]
///
public const double ElectronCharge = 1.602176634e-19;
///
- /// Speed of Light in a vacuum \f$ c \f$ [m/s]
+ /// Speed of Light in a vacuum @f$ c @f$ [m/s]
///
public const double LightSpeed = 299792458.0;
///
- /// Electron Mass \f$ m_e \f$ [kg]
+ /// Electron Mass @f$ m_e @f$ [kg]
///
public const double ElectronMass = 9.1093837015e-31;
///
- /// Universal Gas Constant \f$ R_u \f$ [J/kmol/K]
+ /// Universal Gas Constant @f$ R_u @f$ [J/kmol/K]
///
public const double GasConstant = Avogadro * Boltzmann;
///
- /// Faraday constant \f$ F \f$ [C/kmol]
+ /// Faraday constant @f$ F @f$ [C/kmol]
///
public const double Faraday = ElectronCharge * Avogadro;
///
- /// Stefan-Boltzmann constant \f$ \sigma \f$ [W/m2/K4]
+ /// Stefan-Boltzmann constant @f$ \sigma @f$ [W/m2/K4]
///
public const double StefanBoltzmann = 5.670374419e-8;
diff --git a/samples/cxx/bvp/blasius.cpp b/samples/cxx/bvp/blasius.cpp
index e65c8a10ee..4e3970673a 100644
--- a/samples/cxx/bvp/blasius.cpp
+++ b/samples/cxx/bvp/blasius.cpp
@@ -20,16 +20,16 @@ using Cantera::npos;
/**
* This class solves the Blasius boundary value problem on the domain (0,L):
- * \f[
+ * @f[
* \frac{d\zeta}{dz} = u.
- * \f]
- * \f[
+ * @f]
+ * @f[
* \frac{d^2u}{dz^2} + 0.5\zeta \frac{du}{dz} = 0.
- * \f]
+ * @f]
* with boundary conditions
- * \f[
+ * @f[
* \zeta(0) = 0, u(0) = 0, u(L) = 1.
- * \f]
+ * @f]
* Note that this is formulated as a system of two equations, with maximum
* order of 2, rather than as a single third-order boundary value problem.
* For reasons having to do with the band structure of the Jacobian, no
diff --git a/src/oneD/MultiNewton.cpp b/src/oneD/MultiNewton.cpp
index 38ef5e40b3..683273326f 100644
--- a/src/oneD/MultiNewton.cpp
+++ b/src/oneD/MultiNewton.cpp
@@ -87,16 +87,16 @@ doublereal bound_step(const doublereal* x, const doublereal* step,
* number of components, and number of points.
*
* The return value is
- * \f[
+ * @f[
* \sum_{n,j} \left(\frac{s_{n,j}}{w_n}\right)^2
- * \f]
- * where the error weight for solution component \f$n\f$ is given by
- * \f[
+ * @f]
+ * where the error weight for solution component @f$ n @f$ is given by
+ * @f[
* w_n = \epsilon_{r,n} \frac{\sum_j |x_{n,j}|}{J} + \epsilon_{a,n}.
- * \f]
- * Here \f$\epsilon_{r,n} \f$ is the relative error tolerance for component n,
+ * @f]
+ * Here @f$ \epsilon_{r,n} @f$ is the relative error tolerance for component n,
* and multiplies the average magnitude of solution component n in the domain.
- * The second term, \f$\epsilon_{a,n}\f$, is the absolute error tolerance for
+ * The second term, @f$ \epsilon_{a,n} @f$, is the absolute error tolerance for
* component n.
*/
doublereal norm_square(const doublereal* x,
diff --git a/src/transport/MultiTransport.cpp b/src/transport/MultiTransport.cpp
index f9e2584026..9f594f4525 100644
--- a/src/transport/MultiTransport.cpp
+++ b/src/transport/MultiTransport.cpp
@@ -21,7 +21,7 @@ namespace Cantera
/**
* The Parker temperature correction to the rotational collision number.
*
- * @param tr Reduced temperature \f$ \epsilon/kT \f$
+ * @param tr Reduced temperature @f$ \epsilon/kT @f$
* @param sqtr square root of tr.
*/
doublereal Frot(doublereal tr, doublereal sqtr)
@@ -387,7 +387,7 @@ void MultiTransport::getMultiDiffCoeffs(const size_t ld, doublereal* const d)
(m_Lmatrix(i,j) - m_Lmatrix(i,i));
}
}
-
+
}
void MultiTransport::update_T()
diff --git a/src/zeroD/MoleReactor.cpp b/src/zeroD/MoleReactor.cpp
index 6a2effcb2d..b6147f4396 100644
--- a/src/zeroD/MoleReactor.cpp
+++ b/src/zeroD/MoleReactor.cpp
@@ -242,9 +242,9 @@ void MoleReactor::eval(double time, double* LHS, double* RHS)
}
// Energy equation.
- // \f[
+ // @f[
// \dot U = -P\dot V + A \dot q + \dot m_{in} h_{in} - \dot m_{out} h.
- // \f]
+ // @f]
if (m_energy) {
RHS[0] = - m_thermo->pressure() * m_vdot + m_Qdot;
} else {
diff --git a/src/zeroD/Reactor.cpp b/src/zeroD/Reactor.cpp
index 014d9627d2..9be81e215b 100644
--- a/src/zeroD/Reactor.cpp
+++ b/src/zeroD/Reactor.cpp
@@ -239,9 +239,9 @@ void Reactor::eval(double time, double* LHS, double* RHS)
}
// Energy equation.
- // \f[
+ // @f[
// \dot U = -P\dot V + A \dot q + \dot m_{in} h_{in} - \dot m_{out} h.
- // \f]
+ // @f]
if (m_energy) {
RHS[2] = - m_thermo->pressure() * m_vdot + m_Qdot;
} else {