The basis is simple cubic.
In the following, an overview of the different simulation procedures and respective parameters is presented.
The basis is simple cubic.
In the following, an overview of the different simulation procedures and respective parameters is presented.
% todo - point defects are calculated for the neutral charge state.
Most of the parameter settings, as determined above, constitute a tradeoff regarding the tasks that need to be addressed.
% todo - point defects are calculated for the neutral charge state.
Most of the parameter settings, as determined above, constitute a tradeoff regarding the tasks that need to be addressed.
The choice of these parameters is considered to reflect a reasonable treatment with respect to both, computational efficiency and accuracy, as will be shown in the next sections.
Furthermore, criteria concerning the choice of the potential and the exchange-correlation (XC) functional are being outlined.
Finally, the utilized parameter set is tested by comparing the calculated values of the cohesive energy and the lattice constant to experimental data.
The choice of these parameters is considered to reflect a reasonable treatment with respect to both, computational efficiency and accuracy, as will be shown in the next sections.
Furthermore, criteria concerning the choice of the potential and the exchange-correlation (XC) functional are being outlined.
Finally, the utilized parameter set is tested by comparing the calculated values of the cohesive energy and the lattice constant to experimental data.
\caption{Defect formation energies of several defects in c-Si with respect to the size of the supercell.}
\label{fig:simulation:ef_ss}
\end{figure}
\caption{Defect formation energies of several defects in c-Si with respect to the size of the supercell.}
\label{fig:simulation:ef_ss}
\end{figure}
-To estimate a critical size the formation energies of several intrinsic defects in Si with respect to the system size are calculated.
-An energy cut-off of \unit[250]{eV} and a $4\times4\times4$ Monkhorst-Pack $k$-point mesh~\cite{monkhorst76} is used.
+To estimate a critical size, the formation energies of several intrinsic defects in Si with respect to the system size are calculated.
+An energy cut-off of \unit[250]{eV} and a $4\times4\times4$ Monkhorst-Pack $\vec{k}$-point mesh~\cite{monkhorst76} is used.
The results are displayed in Fig.~\ref{fig:simulation:ef_ss}.
The formation energies converge fast with respect to the system size.
Thus, investigating supercells containing more than 56 primitive cells or $112\pm1$ atoms should be reasonably accurate.
The results are displayed in Fig.~\ref{fig:simulation:ef_ss}.
The formation energies converge fast with respect to the system size.
Thus, investigating supercells containing more than 56 primitive cells or $112\pm1$ atoms should be reasonably accurate.
The calculation is usually two times faster and half of the storage needed for the wave functions can be saved since $c_{i,q}=c_{i,-q}^*$, where the $c_{i,q}$ are the Fourier coefficients of the wave function.
As discussed in section~\ref{subsection:basics:bzs}, this does not pose a severe limitation if the supercell is large enough.
Indeed, it was shown~\cite{dal_pino93} that already for calculations involving only 32 atoms, energy values obtained by sampling the $\Gamma$ point differ by less than \unit[0.02]{eV} from calculations using the Baldereschi point~\cite{baldereschi73}, which constitutes a mean-value point in the BZ.
The calculation is usually two times faster and half of the storage needed for the wave functions can be saved since $c_{i,q}=c_{i,-q}^*$, where the $c_{i,q}$ are the Fourier coefficients of the wave function.
As discussed in section~\ref{subsection:basics:bzs}, this does not pose a severe limitation if the supercell is large enough.
Indeed, it was shown~\cite{dal_pino93} that already for calculations involving only 32 atoms, energy values obtained by sampling the $\Gamma$ point differ by less than \unit[0.02]{eV} from calculations using the Baldereschi point~\cite{baldereschi73}, which constitutes a mean-value point in the BZ.
-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.
+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 $\vec{k}$-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}.
\begin{table}[t]
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]
To construct a spherical and topotactically aligned 3C-SiC precipitate in c-Si, the approach illustrated in the following is applied.
A total simulation volume $V$ consisting of 21 unit cells of c-Si in each direction is created.
To construct a spherical and topotactically aligned 3C-SiC precipitate in c-Si, the approach illustrated in the following is applied.
A total simulation volume $V$ consisting of 21 unit cells of c-Si in each direction is created.
This corresponds to a spherical 3C-SiC precipitate with a radius of approximately \unit[3]{nm}.
The initial precipitate configuration is constructed in two steps.
In the first step the surrounding Si matrix is created.
This corresponds to a spherical 3C-SiC precipitate with a radius of approximately \unit[3]{nm}.
The initial precipitate configuration is constructed in two steps.
In the first step the surrounding Si matrix is created.
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