\end{itemize}
\vspace*{0.2cm}
\underline{Param 2}\\
- After talking to the pros! Used for 'large' simulations.
+ After talking to the pros!
\begin{itemize}
\item $\Gamma$-point only
\item $E_{\text{cut-off}}=xyz\text{ eV}$
\item Gaussian smearing ($\sigma=0.05$)
\item Use symmetry
- \item Real space projection (Auto, Medium)
+ \item Real space projection (Auto, Medium) for 'large' simulations
\end{itemize}
\vspace*{0.2cm}
{\color{blue}
In both parameter sets the ultra soft pseudo potential method
- as well as the projector augmented wave method is used!
+ as well as the projector augmented wave method is used with both,
+ the LDA and GGA exchange correlation potential!
}
\end{slide}
\begin{slide}
+ \footnotesize
+
{\large\bf
Properties of Si, C and SiC using the new parameters\\
}
- $2\times 2\times 2$ Type 2 supercell, Param 1\\[0.2cm]
+ $2\times 2\times 2$ Type 2 supercell, Param 1, LDA, US PP\\[0.2cm]
\begin{tabular}{|l|l|l|l|}
\hline
& c-Si & c-C (diamond) & 3C-SiC \\
\hline
- Lattice constant [\AA] & 5.389 & 3.527 & \\
- Expt. [\AA] & 5.429 & 3.567 & \\
- Error [\%] & {\color{green}0.7} & 1.1 & \\
+ Lattice constant [\AA] & 5.389 & 3.527 & 4.319 \\
+ Expt. [\AA] & 5.429 & 3.567 & 4.359 \\
+ Error [\%] & {\color{green}0.7} & {\color{green}1.1} & {\color{green}0.9} \\
\hline
- Cohesive energy [eV] & -4.674 & -8.812 & \\
- Expt. [eV] & -4.63 & -7.374 & \\
- Error [\%] & {\color{green}1.0} & {\color{red}19.5} & \\
+ Cohesive energy [eV] & -5.277 & -8.812 & -7.318 \\
+ Expt. [eV] & -4.63 & -7.374 & -6.340 \\
+ Error [\%] & {\color{red}14.0} & {\color{red}19.5} & {\color{red}15.4} \\
\hline
\end{tabular}\\
+ \begin{minipage}{10cm}
+ $2\times 2\times 2$ Type 2 supercell, 3C-SiC, Param 1\\[0.2cm]
+ \begin{tabular}{|l|l|l|l|}
+ \hline
+ & {\color{magenta}US PP, GGA} & PAW, LDA & PAW, GGA \\
+ \hline
+ Lattice constant [\AA] & 4.370 & 4.330 & 4.379 \\
+ Error [\%] & {\color{green}0.3} & {\color{green}0.7} & {\color{green}0.5} \\
+ \hline
+ Cohesive energy [eV] & -6.426 & -7.371 & -6.491 \\
+ Error [\%] & {\color{green}1.4} & {\color{red}16.3} & {\color{green}2.4} \\
+ \hline
+ \end{tabular}
+ \end{minipage}
+ \begin{minipage}{3cm}
+ US PP, GGA\\[0.2cm]
+ \begin{tabular}{|l|l|}
+ \hline
+ c-Si & c-C \\
+ \hline
+ 5.455 & 3.567 \\
+ {\color{green}0.5} & {\color{green}0.01} \\
+ \hline
+ -4.591 & -7.703 \\
+ {\color{green}0.8} & {\color{orange}4.5} \\
+ \hline
+ \end{tabular}
+ \end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Energy cut-off for $\Gamma$-point only caclulations
+ }
+
+ $2\times 2\times 2$ Type 2 supercell, Param 2, US PP, LDA, 3C-SiC\\[0.2cm]
+ \includegraphics[width=5.5cm]{sic_32pc_gamma_cutoff.ps}
+ \includegraphics[width=5.5cm]{sic_32pc_gamma_cutoff_lc.ps}\\
+ $\Rightarrow$ Use 300 eV as energy cut-off?\\[0.2cm]
+ $2\times 2\times 2$ Type 2 supercell, Param 2, 300 eV, US PP, GGA\\[0.2cm]
+ \small
+ \begin{minipage}{10cm}
+ \begin{tabular}{|l|l|l|l|}
+ \hline
+ & c-Si & c-C (diamond) & 3C-SiC \\
+ \hline
+ Lattice constant [\AA] & 5.470 & 3.569 & 4.364 \\
+ Error [\%] & {\color{green}0.8} & {\color{green}0.1} & {\color{green}0.1} \\
+ \hline
+ Cohesive energy [eV] & -4.488 & -7.612 & -6.359 \\
+ Error [\%] & {\color{orange}3.1} & {\color{orange}3.2} & {\color{green}0.3} \\
+ \hline
+ \end{tabular}
+ \end{minipage}
+ \begin{minipage}{2cm}
+ {\LARGE
+ ${\color{green}\surd}$
+ }
+ \end{minipage}
+
\end{slide}
\begin{slide}
{\large\bf
- C interstitial in c-Si
+ C 100 interstitial migration along 110 in c-Si (Albe potential)
}
+ \small
+
+ \begin{minipage}[t]{4.2cm}
+ \underline{Starting configuration}\\
+ \includegraphics[width=4cm]{c_100_mig/start.eps}
+ \end{minipage}
+ \begin{minipage}[t]{4.0cm}
+ \vspace*{0.8cm}
+ $\Delta x=\frac{1}{4}a_{\text{Si}}=1.357\text{ \AA}$\\
+ $\Delta y=\frac{1}{4}a_{\text{Si}}=1.357\text{ \AA}$\\
+ $\Delta z=0.325\text{ \AA}$\\
+ \end{minipage}
+ \begin{minipage}[t]{4.2cm}
+ \underline{{\bf Expected} final configuration}\\
+ \includegraphics[width=4cm]{c_100_mig/final.eps}\\
+ \end{minipage}
+ \begin{minipage}{6cm}
+ \begin{itemize}
+ \item Fix border atoms of the simulation cell
+ \item Constraints and displacement of the C atom:
+ \begin{itemize}
+ \item along {\color{green}110 direction}\\
+ displaced by {\color{green} $\frac{1}{10}(\Delta x,\Delta y)$}
+ \item C atom {\color{red}entirely fixed in position}\\
+ displaced by
+ {\color{red}$\frac{1}{10}(\Delta x,\Delta y,\Delta z)$}
+ \end{itemize}
+ \item Berendsen thermostat applied
+ \end{itemize}
+ {\bf\color{blue}Expected configuration not obtained!}
+ \end{minipage}
+ \begin{minipage}{0.5cm}
+ \hfill
+ \end{minipage}
+ \begin{minipage}{6cm}
+ \includegraphics[width=6.0cm]{c_100_110mig_01_albe.ps}
+ \end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ C 100 interstitial migration along 110 in c-Si (Albe potential)
+ }
+
+ \footnotesize
+
+ \begin{minipage}{3.2cm}
+ \includegraphics[width=3cm]{c_100_mig/fixmig_50.eps}
+ \begin{center}
+ 50 \%
+ \end{center}
+ \end{minipage}
+ \begin{minipage}{3.2cm}
+ \includegraphics[width=3cm]{c_100_mig/fixmig_80.eps}
+ \begin{center}
+ 80 \%
+ \end{center}
+ \end{minipage}
+ \begin{minipage}{3.2cm}
+ \includegraphics[width=3cm]{c_100_mig/fixmig_90.eps}
+ \begin{center}
+ 90 \%
+ \end{center}
+ \end{minipage}
+ \begin{minipage}{3.2cm}
+ \includegraphics[width=3cm]{c_100_mig/fixmig_99.eps}
+ \begin{center}
+ 100 \%
+ \end{center}
+ \end{minipage}
+
+ Open questions ...
+ \begin{enumerate}
+ \item Why is the expected configuration not obtained?
+ \item How to find a migration path preceding to the expected configuration?
+ \end{enumerate}
+
+ Answers ...
+ \begin{enumerate}
+ \item Simple: it is not the right migration path!
+ \begin{itemize}
+ \item (Surrounding) atoms settle into a local minimum configuration
+ \item A possibly existing more favorable configuration is not achieved
+ \end{itemize}
+ \item \begin{itemize}
+ \item Search global minimum in each step (by simulated annealing)\\
+ {\color{red}But:}
+ Loss of the correct energy needed for migration
+ \item Smaller displacements\\
+ A more favorable configuration might be achieved
+ possibly preceding to the expected configuration
+ \end{itemize}
+ \end{enumerate}
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ C 100 interstitial migration along 110 in c-Si (Albe potential)\\
+ }
+
+ Displacement step size decreased to
+ $\frac{1}{100} (\Delta x,\Delta y)$\\[0.2cm]
+
+ \begin{minipage}{7.5cm}
+ Result: (Video \href{../video/c_in_si_smig_albe.avi}{$\rhd_{\text{local}}$ } $|$
+ \href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/c_in_si_smig_albe.avi}{$\rhd_{\text{remote url}}$})
+ \begin{itemize}
+ \item Expected final configuration not obtained
+ \item Bonds to neighboured silicon atoms persist
+ \item C and neighboured Si atoms move along the direction of displacement
+ \item Even the bond to the lower left silicon atom persists
+ \end{itemize}
+ {\color{red}
+ Obviously: overestimated bond strength
+ }
+ \end{minipage}
+ \begin{minipage}{5cm}
+ \includegraphics[width=6cm]{c_100_110smig_01_albe.ps}
+ \end{minipage}\\[0.4cm]
+ New approach to find the migration path:\\
+ {\color{blue}
+ Place interstitial carbon atom at the respective coordinates
+ into a perfect c-Si matrix!
+ }
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ C 100 interstitial migration along 110 in c-Si (Albe potential)\\
+ }
+
+ {\color{blue}New approach:}\\
+ Place interstitial carbon atom at the respective coordinates
+ into a perfect c-Si matrix!\\
+ {\color{red}Problem:}\\
+ Too high forces due to the small distance of the C atom to the Si
+ atom sharing the lattice site.\\
+ {\color{green}Solution:}
+ Slightly displace the Si atom\\
+
+ \begin{minipage}{6.5cm}
+ Result:
+ (Video \href{../video/c_in_si_pmig_albe.avi}{$\rhd_{\text{local}}$ } $|$
+ \href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/c_in_si_pmig_albe.avi}{$\rhd_{\text{remote url}}$})\\
+ \includegraphics[width=6cm]{c_100_110pmig_01_albe.ps}
+ \end{minipage}
+ \begin{minipage}{6cm}
+ \begin{itemize}
+ \item Jump in energy (25 and 75 \%) corresponds to the abrupt
+ structural change (as seen in the video)
+ \item Due to the abrupt changes in structure and energy
+ this is {\color{red}not} the correct migration path and energy!?!
+ \end{itemize}
+ \end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ C 100 interstitial migration along 110 in c-Si (VASP)
+ }
+
+ \small
+ \vspace*{1cm}
+ \ldots simulations running!
+ \vspace*{1cm}
+
+ \begin{minipage}{5cm}
+
+ \end{minipage}
+ \begin{minipage}{7cm}
+
+ \end{minipage}
+
+
\end{slide}
\end{document}