From ae16e2c0d5eb1f261c1f3fbf2f53712d0b723615 Mon Sep 17 00:00:00 2001 From: hackbard Date: Wed, 12 Aug 2009 20:00:56 +0200 Subject: [PATCH] begin trafo --- posic/talks/upb-ua-xc.tex | 118 +++++++++++++++++++++++++++++++++++++- 1 file changed, 115 insertions(+), 3 deletions(-) diff --git a/posic/talks/upb-ua-xc.tex b/posic/talks/upb-ua-xc.tex index 87d30d1..2d7db85 100644 --- a/posic/talks/upb-ua-xc.tex +++ b/posic/talks/upb-ua-xc.tex @@ -980,12 +980,124 @@ POTIM = 0.1 \item Approximately half of the classical energy needed for migration \end{itemize} - \begin{center} - Preliminary: 20 \% calculation still running - \end{center} \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} + \end{document} -- 2.39.2