}
Needed so often for input configurations ...\\[0.8cm]
- \begin{minipage}{7.7cm}
- \includegraphics[width=7cm]{100-c-si-db_light.eps}
- \hfill
+ \begin{minipage}{7.0cm}
+ \includegraphics[width=6.5cm]{100-c-si-db_light.eps}\\
+ Qualitative {\color{red}and} quantitative {\color{red}difference}!
\end{minipage}
- \begin{minipage}{4.5cm}
+ \begin{minipage}{5.5cm}
+ \scriptsize
+ \begin{center}
\begin{tabular}{|l|l|l|}
\hline
& a & b \\
fractional & 0.1547 & 0.1676 \\
in \AA & 0.84 & 0.91 \\
\hline
- \end{tabular}
+ \end{tabular}\\[0.2cm]
+ {\scriptsize\underline{PC (Vasp)}}
+ \includegraphics[width=6.1cm]{c_100_pc_vasp.ps}
+ \end{center}
\end{minipage}
- \begin{center}
- Qualitative {\color{red}and} quantitative {\color{red}difference}!
- \end{center}
\end{slide}
Again: C \hkl<1 0 0> interstitial migration (VASP)
}
- $\hkl<0 0 -1> \rightarrow \hkl<0 0 1>$ migration:
+ $\hkl<0 0 -1> \rightarrow \hkl<0 0 1>$ migration
+ ($3\times 3\times 3$ Type 2):
\small
Again: C \hkl<1 0 0> interstitial migration (VASP)
}
- $\hkl<0 0 -1> \rightarrow \hkl<0 -1 0>$ migration:
+ $\hkl<0 0 -1> \rightarrow \hkl<0 -1 0>$ migration
+ ($3\times 3\times 3$ Type 2):
\small
\Rightarrow \Delta E_{\text{f}} = E_{\text{mig}} = ?.?? \text{ eV}
\]
- Unexpected \& ({\color{red}more} or {\color{orange}less}) fatal:
+ \vspace*{0.5cm}
+ {\large\bf
+ Intermediate configuration {\color{red}not found} by now!
+ }
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ C in Si interstitial configurations (VASP)
+ }
+
+ Check of Kohn-Sham eigenvalues\\
+
+ \small
+
+ \begin{minipage}{6cm}
+ \hkl<1 0 0> interstitial\\
+ \end{minipage}
+ \begin{minipage}{6cm}
+ Saddle point configuration\\
+ \end{minipage}
+ \underline{$4\times 4\times 3$ Type 1 - fixed border atoms}\\
+ \begin{minipage}{6cm}
+385: 4.8567 - 2.00000\\
+386: 4.9510 - 2.00000\\
+387: 5.3437 - 0.00000\\
+388: 5.4930 - 0.00000
+ \end{minipage}
+ \begin{minipage}{6cm}
+385: 4.8694 - 2.00000\\
+386: {\color{red}4.9917} - 1.92603\\
+387: {\color{red}5.1181} - 0.07397\\
+388: 5.4541 - 0.00000
+ \end{minipage}\\[0.2cm]
+ \underline{$4\times 4\times 3$ Type 1 - no constraints}\\
+ \begin{minipage}{6cm}
+385: 4.8586 - 2.00000\\
+386: 4.9458 - 2.00000\\
+387: 5.3358 - 0.00000\\
+388: 5.4915 - 0.00000
+ \end{minipage}
+ \begin{minipage}{6cm}
+385: 4.8693 - 2.00000\\
+386: {\color{red}4.9879} - 1.92065\\
+387: {\color{red}5.1120} - 0.07935\\
+388: 5.4544 - 0.00000
+ \end{minipage}\\[0.2cm]
+ \underline{$3\times 3\times 3$ Type 2 - no constraints}\\
+ \begin{minipage}{6cm}
+433: 4.8054 - 2.00000\\
+434: 4.9027 - 2.00000\\
+435: 5.2543 - 0.00000\\
+436: 5.5718 - 0.00000
+ \end{minipage}
+ \begin{minipage}{6cm}
+433: 4.8160 - 2.00000\\
+434: {\color{green}5.0109} - 1.00264\\
+435: {\color{green}5.0111} - 0.99736\\
+436: 5.5364 - 0.00000
+ \end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ Once again: C \hkl<1 0 0> interstitial migration (VASP)
+ }
+
+ Method:
\begin{itemize}
- \renewcommand\labelitemi{{\color{orange}$\bullet$}}
- \item Difference in formation energy (0.02 eV)
- of the initial and final configuration
- \renewcommand\labelitemi{{\color{red}$\bullet$}}
- \item Huge discrepancy (0.3 - 0.4 eV) to the migration barrier
- of Type 1 (198+1 atoms) calculations
- \renewcommand\labelitemi{{\color{black}$\bullet$}}
+ \item Start in fully relaxed (assumed) saddle point configuration
+ \item Move towards \hkl<1 0 0> configuration using updated values
+ for $\Delta x$, $\Delta y$ and $\Delta z$
+ \item \hkl<1 1 0> constraints applied, 1 Si atom fixed
+ \item $4\times 4\times 3$ Type 1 supercell
\end{itemize}
-
+
+ Results:
+
+ \begin{minipage}{6.2cm}
+ \includegraphics[width=6.0cm]{c_100_110sp-i_vasp.ps}
+ \end{minipage}
+ \begin{minipage}{6.2cm}
+ \includegraphics[width=6.0cm]{c_100_110sp-i_rc_vasp.ps}
+ \end{minipage}
+
+ Reaction coordinate:
+ $r_{i+1}=r_i+\sum_{\text{atoms j}} \left| r_{j,i+1}-r_{j,i} \right|$
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ Investigation of the migration path along \hkl<1 1 0> (VASP)
+ }
+
+ \small
+
+ \underline{Minimum:}\\
+ \begin{minipage}{4cm}
+ \includegraphics[width=3.5cm]{c_100_mig_vasp/110_c-si_split.eps}
+ \end{minipage}
+ \begin{minipage}{8cm}
+ \begin{itemize}
+ \item Starting conf: 35 \% displacement results
+ \item \hkl<1 1 0> constraint disabled
+ \end{itemize}
+ \begin{center}
+ $\Downarrow$
+ \end{center}
+ \begin{itemize}
+ \item C-Si \hkl<1 1 0> split interstitial
+ \item Stable configuration
+ \item $E_{\text{f}}=4.13\text{ eV}$
+ \end{itemize}
+ \end{minipage}\\[0.1cm]
+
+ \underline{Maximum:}\\
+ \begin{minipage}{6cm}
+ \begin{center}
+ \includegraphics[width=2.3cm]{c_100_mig_vasp/100-110_01.eps}
+ \includegraphics[width=2.3cm]{c_100_mig_vasp/100-110_02.eps}\\
+ 20 \% $\rightarrow$ 25 \%\\
+ Breaking of Si-C bond
+ \end{center}
+ \end{minipage}
+ \begin{minipage}{6cm}
+ \includegraphics[width=6.2cm]{c_100_110sp-i_upd_vasp.ps}
+ \end{minipage}
+
\end{slide}
\begin{slide}
Molecular dynamics simulations (VASP)
}
+ 2 C atoms in $2\times 2\times 2$ Type 2 supercell at $450\,^{\circ}\text{C}$
+
\small
+ \begin{minipage}{7.6cm}
+ Radial distribution\\
+ \includegraphics[width=7.6cm]{md_02c_2222si_pc.ps}
+ \end{minipage}
+ \begin{minipage}{5.0cm}
+ \begin{center}
+ PC average from\\
+ $t_1=50$ ps to $t_2=50.93$ ps
+ \end{center}
+ \end{minipage}
+ Diffusion:
+ \begin{itemize}
+ \item $<(x(t)-x(0))^2>$ hard to determine due to missing info of
+ boundary crossings
+ \item No jumps recognized in the
+ Video \href{../video/md_02c_2222si_vasp.avi}{$\rhd_{\text{local}}$ } $|$
+ \href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/md_02c_2222si_vasp.avi}{$\rhd_{\text{remote url}}$}
+ \end{itemize}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Molecular dynamics simulations (VASP)
+ }
+
+ 10 C atoms in $3\times 3\times 3$ Type 2 supercell at $450\,^{\circ}\text{C}$
+
+ \small
+
+ \begin{minipage}{7.2cm}
+ Radial distribution (PC averaged over 1 ps)\\
+ \includegraphics[width=7.0cm]{md_10c_2333si_pc_vasp.ps}
+ \end{minipage}
+ \begin{minipage}{5.0cm}
+ \includegraphics[width=6.0cm]{md_10c_2333si_pcc_vasp.ps}
+ \end{minipage}
+ Diffusion:
+ (Video \href{../video/md_10c_2333si_vasp.avi}{$\rhd_{\text{local}}$ } $|$
+ \href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/md_10c_2333si_vasp.avi}{$\rhd_{\text{remote url}}$})
+ \begin{itemize}
+ \item $<(x(t)-x(0))^2>$ hard to determine due to missing info of
+ boundary crossings
+ \item Agglomeration of C? (Video)
+ \end{itemize}
+
\end{slide}
\begin{slide}
projects / lectures / latex.git / blobdiff