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}
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
\begin{slide}
{\large\bf\boldmath
- Once again: C \hkl<1 0 0> interstitial migration (VASP)
+ Again: C \hkl<1 0 0> interstitial migration (VASP)
}
- Method:
- \begin{itemize}
- \item Start in fully relaxed (assumed) saddle point configuration
- \item Move towards \hkl<1 0 0> cnfiguration using updated values
- for $\Delta x$, $\Delta y$ and $\Delta z$
- \item \hkl<1 1 0> constraints applied
- \end{itemize}
+ $\hkl<0 0 -1> \rightarrow \hkl<0 -1 0>$ migration
+ ($3\times 3\times 3$ Type 2):
- Results:
+ \small
+ \begin{minipage}[t]{4.1cm}
+ \underline{Starting configuration}\\
+ \includegraphics[height=3.2cm]{c_100_mig_vasp/start.eps}
+ \begin{center}
+ $E_{\text{f}}=3.154 \text{ eV}$
+ \end{center}
+ \end{minipage}
+ \begin{minipage}[t]{4.1cm}
+ \underline{Intermediate configuration}\\
in progress ...
+ \begin{center}
+ $E_{\text{f}}=?.?? \text{ eV}$
+ \end{center}
+ \end{minipage}
+ \begin{minipage}[t]{4.1cm}
+ \underline{Final configuration}\\
+ \includegraphics[height=3.2cm]{c_100_mig_vasp/0-10.eps}
+ \begin{center}
+ $E_{\text{f}}=3.157 \text{ eV}$
+ \end{center}
+ \end{minipage}\\[0.4cm]
+ \[
+ \Rightarrow \Delta E_{\text{f}} = E_{\text{mig}} = ?.?? \text{ eV}
+ \]
+ \vspace*{0.5cm}
+ {\large\bf
+ Intermediate configuration {\color{red}not found} by now!
+ }
+
\end{slide}
\begin{slide}
C in Si interstitial configurations (VASP)
}
- Check of Kohn-Sham eigenvalues
+ Check of Kohn-Sham eigenvalues\\
+
+ \small
- \underline{$4\times 4\times 3$ Type 1} with fixed border atoms\\
\begin{minipage}{6cm}
\hkl<1 0 0> interstitial\\
-383: 4.7371 - 2.00000\\
-384: 4.7691 - 2.00000\\
+ \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\\
-389: 5.5062 - 0.00000\\
-390: 5.5254 - 0.00000\\
-391: 5.5521 - 0.00000
+388: 5.4930 - 0.00000
\end{minipage}
\begin{minipage}{6cm}
- \hkl<1 0 0> interstitial\\
-383: 4.7270 - 2.00000\\
-384: 4.7779 - 2.00000\\
385: 4.8694 - 2.00000\\
-386: 4.9917 - 1.92603\\
-387: 5.1181 - 0.07397\\
-388: 5.4541 - 0.00000\\
-389: 5.4626 - 0.00000\\
-390: 5.4915 - 0.00000\\
-391: 5.5876 - 0.00000
- \end{minipage}
-
-\end{slide}
-
-\begin{slide}
-
- {\large\bf\boldmath
- C in Si interstitial configurations (VASP)
- }
-
- Check of Kohn-Sham eigenvalues
-
- \underline{$4\times 4\times 3$ Type 1} (no constraints)\\
+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}
- \hkl<1 0 0> interstitial\\
-383: 4.7381 - 2.00000\\
-384: 4.7689 - 2.00000\\
385: 4.8586 - 2.00000\\
386: 4.9458 - 2.00000\\
387: 5.3358 - 0.00000\\
-388: 5.4915 - 0.00000\\
-389: 5.5041 - 0.00000\\
-390: 5.5268 - 0.00000\\
-391: 5.5527 - 0.00000
+388: 5.4915 - 0.00000
\end{minipage}
\begin{minipage}{6cm}
- Saddle point configuration\\
-383: 4.7275 - 2.00000\\
-384: 4.7770 - 2.00000\\
385: 4.8693 - 2.00000\\
-386: 4.9879 - 1.92065\\
-387: 5.1120 - 0.07935\\
-388: 5.4544 - 0.00000\\
-389: 5.4629 - 0.00000\\
-390: 5.4919 - 0.00000\\
-391: 5.5878 - 0.00000
- \end{minipage}
-
-\end{slide}
-
-\begin{slide}
-
- {\large\bf\boldmath
- C in Si interstitial configurations (VASP)
- }
-
- Check of Kohn-Sham eigenvalues
-
- \underline{$3\times 3\times 3$ Type 2} (no constraints)\\
+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}
- \hkl<1 0 0> interstitial
-431: 4.7413 - 2.00000\\
-432: 4.8009 - 2.00000\\
433: 4.8054 - 2.00000\\
434: 4.9027 - 2.00000\\
435: 5.2543 - 0.00000\\
-436: 5.5718 - 0.00000\\
-437: 5.5842 - 0.00000\\
-438: 5.5861 - 0.00000\\
-439: 5.5871 - 0.00000\\
+436: 5.5718 - 0.00000
\end{minipage}
\begin{minipage}{6cm}
- Saddle point configuration\\
-432: 4.8157 - 2.00000\\
433: 4.8160 - 2.00000\\
-434: 5.0109 - 1.00264\\
-435: 5.0111 - 0.99736\\
-436: 5.5364 - 0.00000\\
-437: 5.5666 - 0.00000\\
-438: 5.5696 - 0.00000\\
-439: 5.5698 - 0.00000
+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
- Again: C \hkl<1 0 0> interstitial migration (VASP)
+ Once again: C \hkl<1 0 0> interstitial migration (VASP)
}
- $\hkl<0 0 -1> \rightarrow \hkl<0 -1 0>$ migration:
+ Method:
+ \begin{itemize}
+ \item Start in fully relaxed (assumed) saddle point configuration
+ \item Move towards \hkl<1 0 0> cnfiguration 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}
- \small
+ Results:
- \begin{minipage}[t]{4.1cm}
- \underline{Starting configuration}\\
- \includegraphics[height=3.2cm]{c_100_mig_vasp/start.eps}
- \begin{center}
- $E_{\text{f}}=3.154 \text{ eV}$
- \end{center}
+ \begin{minipage}{6.2cm}
+ \includegraphics[width=6.0cm]{c_100_110sp-i_vasp.ps}
\end{minipage}
- \begin{minipage}[t]{4.1cm}
- \underline{Intermediate configuration}\\
- in progress ...
- \begin{center}
- $E_{\text{f}}=?.?? \text{ eV}$
- \end{center}
+ \begin{minipage}{6.2cm}
+ \includegraphics[width=6.0cm]{c_100_110sp-i_rc_vasp.ps}
\end{minipage}
- \begin{minipage}[t]{4.1cm}
- \underline{Final configuration}\\
- \includegraphics[height=3.2cm]{c_100_mig_vasp/0-10.eps}
- \begin{center}
- $E_{\text{f}}=3.157 \text{ eV}$
- \end{center}
- \end{minipage}\\[0.4cm]
- \[
- \Rightarrow \Delta E_{\text{f}} = E_{\text{mig}} = ?.?? \text{ eV}
- \]
- Unexpected \& ({\color{red}more} or {\color{orange}less}) fatal:
- \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}$\bullet$}}
- \end{itemize}
-
+ Reaction coordinate:
+ $r_{i+1}=r_i+\sum_{\text{atoms j}} \left| r_{j,i+1}-r_{j,i} \right|$
+
\end{slide}
\begin{slide}
Molecular dynamics simulations (VASP)
}
- 2 C atoms in $2\times 2\times 2$ Type 2 supercell
+ 2 C atoms in $2\times 2\times 2$ Type 2 supercell at $450\,^{\circ}\text{C}$
\small
Molecular dynamics simulations (VASP)
}
- 10 C atoms in $3\times 3\times 3$ Type 2 supercell
+ 10 C atoms in $3\times 3\times 3$ Type 2 supercell at $450\,^{\circ}\text{C}$
\small
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