\section{DFT calculations}
\label{section:simulation:dft_calc}
-The first-principles DFT calculations are performed with the plane-wave-based Vienna {\em ab initio} simulation package ({\textsc vasp}) \cite{kresse96}.
+The first-principles DFT calculations are performed with the plane-wave-based Vienna {\em ab initio} simulation package (\textsc{vasp}) \cite{kresse96}.
The Kohn-Sham equations are solved using the GGA utilizing the exchange-correlation functional proposed by Perdew and Wang (GGA-PW91) \cite{perdew86,perdew92}.
-The electron-ion interaction is described by norm-conserving ultra-soft pseudopotentials as implemented in {\textsc vasp} \cite{vanderbilt90}.
+The electron-ion interaction is described by norm-conserving ultra-soft pseudopotentials as implemented in \textsc{vasp} \cite{vanderbilt90}.
An energy cut-off of \unit[300]{eV} is used to expand the wave functions into the plane-wave basis.
Sampling of the Brillouin zone is restricted to the $\Gamma$ point.
Spin polarization has been fully accounted for.
The conjugate gradient algorithm is used for ionic relaxation.
Migration paths are determined by the modified version of the CRT method as explained in section \ref{section:basics:migration}.
The cell volume and shape is allowed to change using the pressure control algorithm of Parrinello and Rahman \cite{parrinello81} in order to realize constant pressure simulations.
-Due to restrictions by the {\textsc vasp} code, {\em ab initio} MD could only be performed at constant volume.
+Due to restrictions by the \textsc{vasp} code, {\em ab initio} MD could only be performed at constant volume.
In MD simulations the equations of motion are integrated by a fourth order predictor corrector algorithm for a time step of \unit[1]{fs}.
% todo - point defects are calculated for the neutral charge state.
To find the most suitable combination of potential and XC functional for the C/Si system a $2\times2\times2$ supercell of type 3 of Si and C, both in the diamond structure, as well as 3C-SiC is equilibrated for different combinations of the available potentials and XC functionals.
To exclude a possibly corrupting influence of the other parameters highly accurate calculations are performed, i.e. an energy cut-off of \unit[650]{eV} and a $6\times6\times6$ Monkhorst-Pack $k$-point mesh is used.
-Next to the ultra-soft pseudopotentials \cite{vanderbilt90} {\textsc vasp} offers the projector augmented-wave method (PAW) \cite{bloechl94} to describe the ion-electron interaction.
-The two XC functionals included in the test are of the LDA \cite{ceperley80,perdew81} and GGA \cite{perdew86,perdew92} type as implemented in {\textsc vasp}.
+Next to the ultra-soft pseudopotentials \cite{vanderbilt90} \textsc{vasp} offers the projector augmented-wave method (PAW) \cite{bloechl94} to describe the ion-electron interaction.
+The two XC functionals included in the test are of the LDA \cite{ceperley80,perdew81} and GGA \cite{perdew86,perdew92} type as implemented in \textsc{vasp}.
\begin{table}[t]
\begin{center}
An interfacial energy of \unit[2267.28]{eV} is obtained.
The amount of C atoms together with the observed lattice constant of the precipitate leads to a precipitate radius of \unit[29.93]{\AA}.
Thus, the interface tension, given by the energy of the interface divided by the surface area of the precipitate is \unit[20.15]{eV/nm$^2$} or \unit[$3.23\times 10^{-4}$]{J/cm$^2$}.
-This value perfectly fits within the experimentally estimated range of \unit[$2-8\times10^{-4}$]{J/cm$^2$} \cite{taylor93}.
+This value perfectly fits within the experimentally estimated range of \unit[2--8$\times10^{-4}$]{J/cm$^2$} \cite{taylor93}.
Thus, the EA potential is considered an appropriate choice for the current study concerning the accurate description of the energetics of interfaces.
Furthermore, since the calculated interfacial energy is located in the lower part of the experimental range, the obtained interface structure might resemble an authentic configuration of an energetically favorable interface structure of a 3C-SiC precipitate in c-Si.
projects / lectures / latex.git / blobdiff