From ae16e2c0d5eb1f261c1f3fbf2f53712d0b723615 Mon Sep 17 00:00:00 2001
From: hackbard <hackbard@sage.physik.uni-augsburg.de>
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