\begin{slide}
{\large\bf
- C 100 interstitial migration along 110 in c-Si (Albe potential)\\
+ 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:}\\
+ {\color{blue}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\\
+ {\color{blue}Solution:}
+ \begin{itemize}
+ \item {\color{red}Slightly displace the Si atom}
+ (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}{$\rhd_{\text{remote url}}$})
+ \item {\color{green}Immediately quench the system}
+ (Video \href{../video/c_in_si_pqmig_albe.avi}{$\rhd_{\text{local}}$ } $|$
+ \href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/c_in_si_pqmig_albe.avi}{$\rhd_{\text{remote url}}$})
+ \end{itemize}
\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}
+ \includegraphics[width=6cm]{c_100_110pqmig_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 Jump in energy corresponds to the abrupt
+ structural change (as seen in the videos)
\item Due to the abrupt changes in structure and energy
this is {\color{red}not} the correct migration path and energy!?!
\end{itemize}
}
\small
- \vspace*{1cm}
- \ldots simulations running!
- \vspace*{1cm}
-
- \begin{minipage}{5cm}
- \end{minipage}
+ {\color{blue}Method:}
+ \begin{itemize}
+ \item Place interstitial carbon atom at the respective coordinates
+ into perfect c-Si
+ \item 110 direction fixed for the C atom
+ \item $4\times 4\times 3$ Type 1, $198+1$ atoms
+ \item Atoms with $x=0$ or $y=0$ or $z=0$ fixed
+ \end{itemize}
+ {\color{blue}Results:}
+ (Video \href{../video/c_in_si_pmig_vasp.avi}{$\rhd_{\text{local}}$ } $|$
+ \href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/c_in_si_pmig_vasp.avi}{$\rhd_{\text{remote url}}$})\\
\begin{minipage}{7cm}
+ \includegraphics[width=7cm]{c_100_110pmig_01_vasp.ps}
+ \end{minipage}
+ \begin{minipage}{5.5cm}
+ \begin{itemize}
+ \item Characteristics nearly equal to classical calulations
+ \item Approximately half of the classical energy
+ needed for migration
+ \end{itemize}
+ \end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ C 100 interstitial migration along 110 in c-Si (VASP)
+ }
+
+ \small
+
+ {\color{blue}Method:}
+ \begin{itemize}
+ \item Continue with atomic positions of the last run
+ \item Displace the C atom in 110 direction
+ \item 110 direction fixed for the C atom
+ \item $4\times 4\times 3$ Type 1, $198+1$ atoms
+ \item Atoms with $x=0$ or $y=0$ or $z=0$ fixed
+ \end{itemize}
+ \includegraphics[width=7cm]{c_100_110mig_01_vasp.ps}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Again: C 100 interstitial migration
+ }
+
+ \small
+
+ {\color{blue}The applied methods:}
+ \begin{enumerate}
+ \item Method
+ \begin{itemize}
+ \item Start in relaxed 100 interstitial configuration
+ \item Displace C atom along 110 direction
+ \item Relaxation (Berendsen thermostat)
+ \item Continue with configuration of the last run
+ \end{itemize}
+ \item Method
+ \begin{itemize}
+ \item Place interstitial carbon at the respective coordinates
+ into the perfect Si matrix
+ \item Quench the system
+ \end{itemize}
+ \end{enumerate}
+ {\color{blue}In both methods:}
+ \begin{itemize}
+ \item Fixed border atoms
+ \item Applied 110 constraint for the C atom
+ \end{itemize}
+ {\color{red}Pitfalls} and {\color{green}refinements}:
+ \begin{itemize}
+ \item {\color{red}Fixed border atoms} $\rightarrow$
+ Relaxation of stress not possible\\
+ $\Rightarrow$
+ {\color{green}Fix only one Si atom} (the one furthermost to the defect)
+ \item {\color{red}110 constraint not sufficient}\\
+ $\Rightarrow$ {\color{green}Apply 11x constraint}
+ (connecting line of initial and final C positions)
+ \end{itemize}
+
+\end{slide}
+
+\begin{slide}
+ {\large\bf
+ Again: C 100 interstitial migration
+ }
+
+ Defining the transformation for the Type 1 supercell (VASP)
+
+ \small
+
+ \begin{minipage}[t]{4.2cm}
+ \underline{Starting configuration}\\
+ \includegraphics[width=4cm]{c_100_mig_vasp/start.eps}
\end{minipage}
+ \begin{minipage}[t]{4.0cm}
+ \vspace*{0.8cm}
+ $\Delta x=\frac{1}{4}a_{\text{Si}}=1.368\text{ \AA}$\\
+ $\Delta y=\frac{1}{4}a_{\text{Si}}=1.368\text{ \AA}$\\
+ $\Delta z=0.888\text{ \AA}$\\
+ \end{minipage}
+ \begin{minipage}[t]{4.2cm}
+ \underline{{\bf Expected} final configuration}\\
+ \includegraphics[width=4cm]{c_100_mig_vasp/final.eps}\\
+ \end{minipage}\\
+ Angle of rotation about the 1-10 axis:
+ \[
+ \Theta=\arctan\frac{\Delta z}{\sqrt{2}\Delta x}=24.666^{\circ}
+ \]
+ Transformation of basis:
+ \[
+ T(\Theta)=\left(\begin{array}{ccc}
+ 1 & 0 & 0\\
+ 0 & \cos\Theta & -\sin\Theta \\
+ 0 & \sin\Theta & \cos\Theta
+ \end{array}\right)
+ \]
+ Transformation of atom coordinates: $T(-\Theta)$
+
+\end{slide}
+
+\begin{slide}
+ {\large\bf
+ Density Functional Theory
+ }
+
+ Hohenberg-Kohn theorem
+
+ \small
+
\end{slide}
projects / lectures / latex.git / blobdiff