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}
-
\end{slide}
\begin{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 $\Delta z$ (CRT)
+ \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 (1443)
+ \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}
+
+ {\large\bf\boldmath
+ Displacing the \hkl<1 1 0> Si-C split along \hkl<1 -1 0> (VASP)
+ }
+
+ \small
+
+ $4\times 4\times 3$ Type 1 supercell
+
+ \underline{Structures:}
+
+ \begin{minipage}[t]{4.1cm}
+ \includegraphics[height=3.0cm]{c_100_mig_vasp/start.eps}\\
+ \hkl<0 0 -1> dumbbell\\
+ $E_{\text{f}}={\color{orange}3.2254}\text{ eV}$
+ \end{minipage}
+ \begin{minipage}[t]{4.1cm}
+ \includegraphics[height=3.0cm]{c_100_mig_vasp/110_c-si_split.eps}\\
+ Assumed \hkl<1 1 0> C-Si split\\
+ $E_{\text{f}}=4.1314\text{ eV}$
+ \end{minipage}
+ \begin{minipage}[t]{4.1cm}
+ \includegraphics[height=3.0cm]{c_100_mig_vasp/110_dis_0-10.eps}\\
+ First guess: \hkl<0 -1 0> dumbbell\\
+ {\color{red}but:} $E_{\text{f}}={\color{orange}2.8924}\text{ eV}$\\
+ Third bond missing!
+ \end{minipage}\\
+
+ \underline{Occupancies:}
+
+ \scriptsize
+
+ \begin{minipage}{4.1cm}
+385: 4.8586 - 2.00000\\
+386: 4.9458 - 2.00000\\
+387: 5.3358 - 0.00000\\
+388: 5.4915 - 0.00000
+\hfill
+ \end{minipage}
+ \begin{minipage}{4.1cm}
+385: 4.7790 - 2.00000\\
+386: 4.8797 - 1.99964\\
+387: 5.1321 - 0.00036\\
+388: 5.4711 - 0.00000
+\hfill
+ \end{minipage}
+ \begin{minipage}{4.1cm}
+385: 4.7670 - 2.00000\\
+386: 4.9190 - 2.00000\\
+387: 5.2886 - 0.00000\\
+388: 5.4849 - 0.00000
+\hfill
+ \end{minipage}\\
+
+\small
+
+ \begin{center}
+ {\color{red}? ! ? ! ? ! ? ! ?}
+ \end{center}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ C \hkl<1 0 0> interstitial migration (VASP)
+ }
+
+ \small
+
+ \begin{minipage}{6.2cm}
+ \begin{itemize}
+ \item $3\times 3\times 3$ Type 2 supercell
+ \item \hkl<1 1 0> constraints applied
+ (\href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/sd_rot.patch}{Patch})
+ \item Move from \hkl<1 0 0> towards\\
+ bond centered configuration
+ \end{itemize}
+ \underline{Sd Rot usage (POSCAR):}
+\begin{verbatim}
+cubic diamond
+5.480
+ 3.0 0.0 0.0
+ 0.0 3.0 0.0
+ 0.0 0.0 3.0
+216 1
+Transformed selective dynamics
+45.0 0.0
+Direct
+ ...
+\end{verbatim}
+Only works in direct mode!\\
+$z,x'$-axis rotation: $45.0^{\circ}$, $0.0^{\circ}$
+ \end{minipage}
+ \begin{minipage}{6.2cm}
+ \includegraphics[width=6cm]{c_100_110sp-i_2333_vasp.ps}
+ \includegraphics[width=6cm]{c_100_110sp-i_2333_rc_vasp.ps}
+ \end{minipage}
+
+ {\color{blue}
+ Next: Migration calculation in 2333 using CRT
+ (\hkl<0 0 -1> $\rightarrow$ \hkl<0 0 1> and \hkl<0 -1 0>)
+ }
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ Defect configurations revisited
+ }
+
+ \underline{$4\times 4\times 3$ Type 1}
+
+ \small
+
+ \begin{tabular}{l|l|p{2.5cm}|p{4cm}|}
+ & \hkl<0 0 -1> interstitial
+ & local minimum\newline
+ \hkl<1 1 0> C-Si split
+ & intermediate configuration\newline
+ (bond centered conf)\\
+ \hline
+ default & $E_{\text{f}}=3.3254\text{ eV}$
+ & $E_{\text{f}}=4.1314\text{ eV}$
+ & $E_{\text{f}}=4.2434\text{ eV}$ \\
+ \hline
+ No symmetry & $E_{\text{f}}=3.3154\text{ eV}$
+ & TODO
+ & $E_{\text{f}}=4.2454\text{ eV}$ \\
+ \hline
+ $+$ spin polarized & $E_{\text{f}}=3.3154\text{ eV}$
+ & TODO
+ & $E_{\text{f}}=4.0254\text{ eV}$ \\
+ \hline
+ $+$ spin difference 2 & in progress & TODO & in progress \\
+ \hline
+ \end{tabular}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ \hkl<0 0 -1> to \hkl <0 0 1> migration
+ in the $3\times 3\times 3$ Type 2 supercell
+ }
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ \hkl<0 0 -1> to \hkl <0 -1 0> migration
+ in the $3\times 3\times 3$ Type 2 supercell
+ }
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ Defect configurations in $3\times 3\times 3$ Type 2 supercells revisited
+ }
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ Combination of defects
+ }
+
+ TODO: introduce some Si self-interstitials and C interstitials before\\
+ BUT: Concentrate on 100 C interstitial combinations and 100 C + vacancy\\
+ Agglomeration of 100 defects energetically favorable?
+
\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
\end{slide}
+\begin{slide}
+
+ {\large\bf
+ Molecular dynamics simulations (VASP)
+ }
+
+ 1 C atom in $3\times 3\times 3$ Type 2 supercell at $900\,^{\circ}\text{C}$
+
+ in progress ...
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Molecular dynamics simulations (VASP)
+ }
+
+ 10 C atoms in $3\times 3\times 3$ Type 2 supercell at $900\,^{\circ}\text{C}$
+
+ in progress ...
+
+\end{slide}
+
\begin{slide}
{\large\bf
Hohenberg-Kohn theorem
\small
-
\end{slide}
+\begin{slide}
+
+ {\large\bf
+ More theory ...
+ }
+
+ Transition state theory\\
+ ART,NEB ...
+
+ Group theory
+
+ \small
+
+\end{slide}
+
+\end{document}
\end{document}
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