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Si.html
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<html> <head>
<title>MCViNE example: Single Crystal Phonon Scattering</title>
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<h1>Single Crystal Phonon Scattering - Si in diamond structure</h1>
The differential cross section is given by
$$
\begin{aligned}
{\left(\frac{d^2\sigma}{d\Omega dE_f}\right)}_{\rm{coh}+1}
= &
\frac{k_f}{k_i} \frac{(2\pi)^3}{2v_0}
\sum_s \sum_{\mathbf{\tau}}
\frac{1}{E_s}
\left| \sum_d \frac{\overline{b_d}}{\sqrt{M_d}} exp(-W_d)
exp(i\mathbf(Q) . \mathbf{d}) \right|^2 \\
&
\times (n_s + 1) \delta(\omega - \omega_s) \delta(\mathbf{Q}-\mathbf{q}-\mathbf{\tau})
\end{aligned}
$$
<h3>Experimental data</h3>
<img class="figure" src="Si/exp-IxE.jpg" width="500px">
<h3>Simple modeling</h3>
Phonon energies and polarizations were computed from VASP and phonopy.
<img class="figure" src="Si/modeled-IxE.jpg" width="500px">
<h3>Modeling convoluted with resolution function computed using MCViNE</h3>
This is similar to the previous result.
The improvement was achieved by a convolution of the modeled intensity
with a resolution function computed from a MCViNE simulation,
in which a "$\delta$-function kernel" was used.
<img class="figure" src="Si/IxE-pppointcloud-eps0.3.jpg" width="500px">
<h3>Full Monte Carlo ray-tracing simulation using MCViNE</h3>
This simulation includes two kernels: one for coherent single-phonon
scattering, and one for multiphonon scattering in incoherent approximation.
<img class="figure" src="Si/fullsim-withMP-100K-IxE-n5e7.jpg" width="500px">
<div>
Collaborators: Dennis Kim and Brent Fultz from Caltech.
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