Merge pull request #28 from RemDelaporteMathurin/rewrite_chapter3

Chapter 3 remake

chapters/chapter2/model_description.tex

@@ -194,7 +194,7 @@ \subsubsection{Analytical simplification for an implanted source of H} \label{tr
 In this expression, $R_i = (p / (k c_\mathrm{max}) + 1)^{-1}$ represents the maximum filling ratio of the trap $i$ and $n_i$ is the trap density.
 When $t \gg \tau$, $c_\mathrm{max}(t) \approx \frac{R_p \varphi_\mathrm{imp}}{D} + \sqrt{\frac{\varphi_\mathrm{imp}}{K_r}}$
 
-\subsection{Interface condition: conservation of chemical potential}
+\subsection{Interface condition: conservation of chemical potential}\labsec{conservation of chemical potential}
 % According to Krom \textit{et al} \sidecite{krom_hydrogen_2000}, since the solubility of hydrogen atoms in solids is low, the chemical potential of solute hydrogen $\mu$ is expressed by:
 % \begin{equation}
 %     \mu = \mu_0 + RT \ln\left( \frac{c_\mathrm{m}}{N_L}\right)

chapters/chapter2/verification_and_validation/comparison_with_tmap7.tex

@@ -1,9 +1,9 @@
 The FESTIM code was compared to TMAP7 \sidecite{longhurst_tmap7_2008} on a 1D case.
 
-The 1D simulation case is a \SI{8.5}{mm}-thick composite slab made of W, Cu and CuCrZr (see Figure \ref{fig: monoblock 1D geometry}).
+The 1D simulation case is a \SI{8.5}{mm}-thick composite slab made of W, Cu and CuCrZr (see \reffig{monoblock 1D geometry}).
 The plasma facing surface $\Gamma_\mathrm{top}$ is located at $x=\SI{0}{mm}$ and the surface cooled by water $\Gamma_\mathrm{coolant}$ is located at $x=\SI{8.5}{mm}$.
-The trapping parameters are detailed in Table \ref{tab:materials properties_1}.
-The boundary conditions are detailed in Equation \ref{eq: code comparison BCs}.
+The trapping parameters are detailed in \reftab{traps comparison tmap}.
+The boundary conditions are detailed in \refeq{code comparison BCs}.
 
 \begin{figure}
     \begin{overpic}[width=0.75\linewidth]{Figures/Chapter3/monoblocks/interface_condition/iter case/Monoblock 1D.pdf}
@@ -16,25 +16,46 @@
         \put(6, 25){\large$\Gamma_\mathrm{top}$}
         \put(85, 25){\large$\Gamma_\mathrm{coolant}$}
     \end{overpic}
-     \caption{TMAP7 - FESTIM comparison 1D geometry showing W \cruleme[grey]{0.3cm}{0.3cm}, Cu \cruleme[orange]{0.3cm}{0.3cm}, CuCrZr \cruleme[yellow]{0.3cm}{0.3cm}}
-     \label{fig: monoblock 1D geometry}
+    \caption{TMAP7 - FESTIM comparison 1D geometry showing W \cruleme[grey]{0.3cm}{0.3cm}, Cu \cruleme[orange]{0.3cm}{0.3cm}, CuCrZr \cruleme[yellow]{0.3cm}{0.3cm}}
+    \labfig{monoblock 1D geometry}
 \end{figure}
 
+\begin{table*}
+    \centering
+    \begin{tabular}{L{1.5cm} L{1.5cm} R{1.7cm} R{1.1cm} R{1.6cm} R{1.1cm} R{1.9cm}}
+         & Material & $k_0 (\si{m^3.s^{-1}})$ &  $E_k (\si{eV})$ & $p_0 (\si{s^{-1}})$ & $E_p (\si{eV})$ & $n_i (\si{at.fr.})$ \\
+        \hline
+        \\
+        Trap 1 & W & $3.8 \times 10^{-17}$ & 0.39 & $8.4 \times 10^{12}$& 1.20 & $5.0 \times 10^{-4}$ \\
+        \\
+        Trap 2 & W & $3.8 \times 10^{-17}$ & 0.39 & $8.4 \times 10^{12}$& 1.40 & $5.0 \times 10^{-3}$ \\
+        \\
+        Trap 3 & Cu & $6.0 \times 10^{-17}$ & 0.39 & $8.0 \times 10^{13}$ & 0.50 &$5.0 \times 10^{-5}$\\
+        \\
+        Trap 4 & CuCrZr & $1.2\times 10^{-16}$ & 0.42 & $8.0 \times 10^{13}$ & 0.50 &$5.0 \times 10^{-5}$\\
+        \\
+        Trap 5 & CuCrZr & $1.2\times 10^{-16}$ & 0.42 & $8.0 \times 10^{13}$ & 0.83 &$4.0 \times 10^{-2}$\\
+        \\
+    \end{tabular}
+    \caption{Traps properties used in the comparison with TMAP7.}
+    \labtab{traps comparison tmap}
+\end{table*}
+
 \begin{subequations}
     \begin{align}
     T &= \SI{1200}{K}\quad \text { on } \Gamma_\mathrm{top}\\
     c_\mathrm{m} &=  \frac{\varphi_\mathrm{imp} \cdot R_p}{D} \quad \text { on } \Gamma_\mathrm{top}\\
     T &= \SI{373}{K} \quad \text { on } \Gamma_\mathrm{coolant}\\
     -D \nabla c_\mathrm{m} \cdot \mathbf{n} &= K_\mathrm{CuCrZr} \cdot c_\mathrm{m}^{2} \quad \text { on } \Gamma_\mathrm{coolant}  
     \end{align}
-    \label{eq: code comparison BCs}
+    \labeq{code comparison BCs}
 \end{subequations}
 with $\varphi_\mathrm{imp} = \SI{5e23}{m^{-2}.s^{-1}}$ the implanted particle flux, $R_p = \SI{1.25}{nm}$ the implantation depth, $\mathbf{n}$ the normal vector and $K_\mathrm{CuCrZr} = 2.9 \times 10^{-14}\cdot \exp{(-1.92/(k_B\cdot T))}$ the recombination coefficient of the CuCrZr (in vacuum) expressed in \si{m^4.s^{-1}} \sidecite{anderl_deuterium_1999}.
 
 The Dirichlet boundary condition on $\Gamma_\mathrm{top}$ for the hydrogen transport corresponds to a flux balance between the implanted flux and the flux that is retro-desorbed at the surface (see Section \ref{triangle model}).
 The temperature profile in TMAP7 was fixed on the temperature profile produced by FESTIM (see \reffig{temperature}).
 
-TMAP7 and FESTIM were found to be in very good agreement (see Figure \ref{fig: code comparison}).
+TMAP7 and FESTIM were found to be in very good agreement (see Figure \reffig{code comparison}).
 
 \begin{figure*} [h]
     \centering
@@ -47,6 +68,6 @@
     \centering
     \includegraphics[width=\linewidth]{Figures/Chapter3/monoblocks/interface_condition/iter case/comparison_codes.pdf}
     \caption{Comparison of results provided by FESTIM and TMAP7}
-    \label{fig: code comparison}
+    \labfig{code comparison}
 \end{figure}