YouPlot: preview data immediately in terminal
Python Numba, Fortran, and CUDA in scientific computing
Use jupyter notebook on Hoffman2
How do I configure my neovim lazily
Read ab initio data from ALAMODE output files
In order to perform a fully ab initio calculation, for
example, the VRMC simulation that we did in the last post, ab initio
data, such as specific heat (spectral), phonon dispersion, and phonon
lifetime, is needed. ALAMODE
is a powerful tool to calculate these data, but the official
documentation is not very clear about the formats...
Variance-reduced Monte Carlo simulation of phonon transport in silicon films
The variance-reduced Monte Carlo simulation of phonon transport solves the following equation:
\[ \frac{\partial e^{\text{d}}}{\partial t} + \boldsymbol{v}_{\mathrm{g}} \cdot \nabla e^{\text{d}} = -\frac{e^{\mathrm{d}} - (e^{\mathrm{eq}}(T)-e^{\mathrm{eq}}(T_{\mathrm{eq}}))}{\tau} \]
Here, relaxation time approximation is used, and \(\tau\) takes ab initio calculated value, see the previous post. In this equation, \(e^{\mathrm{d}} = \hbar\omega (f(\omega)-f_{\mathrm{BE}}(\omega, T_{\mathrm{eq}}))\) for each phonon mode, where \(f\) is the distribution function (not necessarily equilibrium). While \(e^{\mathrm{eq}}(T)=\hbar\omega (f_{\mathrm{BE}}(\omega, T)-f_{\mathrm{BE}}(\omega, T_{\mathrm{eq}}))\) follows the Bose-Einstein distribution. Note that here \(T_{\mathrm{eq}}\) is a reference temperature, and \(T\) is the local temperature that deviates from \(T_{\mathrm{eq}}\).
Ab initio determination of thermal conductivity of Silicon
Overview
The ab inito calculation of thermal conductivity is very complex and needs several softwares to work together. The basic idea is to calculate the interatomic force constants (IFCs) for both the harmonic and anharmonic terms, and then use the IFCs to calculate the phonon dispersion relation and phonon scattering time using knowledges that are summarized in the previous posts about anharmonicity and phonon dispersion.
Workflow
Overall, we use the following open-source softwares:
- phonopy that helps to generate the supercell we want.
- Quantum Espresso that carries out the ab initio calculation of electronic structures.
- alamode which fits the IFCs from the ab initio calculation and calculates the phonon dispersion relation and phonon scattering time and finally thermal conductivity.