From: hackbard <hackbard@sage.physik.uni-augsburg.de>
Date: Wed, 9 Sep 2009 15:28:29 +0000 (+0200)
Subject: new migration stuff etc ...
X-Git-Url: https://hackdaworld.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=49e043bbb553452f41f1d1b73d6f0d69273dbcf8;p=lectures%2Flatex.git

new migration stuff etc ...
---

diff --git a/posic/talks/upb-ua-xc.tex b/posic/talks/upb-ua-xc.tex
index 2d7db85..c0e0aca 100644
--- a/posic/talks/upb-ua-xc.tex
+++ b/posic/talks/upb-ua-xc.tex
@@ -1000,6 +1000,9 @@ POTIM = 0.1
   \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_smig_vasp.avi}{$\rhd_{\text{local}}$ } $|$
+ \href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/c_in_si_smig_vasp.avi}{$\rhd_{\text{remote url}}$})\\
  \includegraphics[width=7cm]{c_100_110mig_01_vasp.ps} 
 
 \end{slide}
@@ -1049,40 +1052,146 @@ POTIM = 0.1
 \begin{slide}
 
  {\large\bf
-  Again: C 100 interstitial migration
+  Again: C 100 interstitial migration (Albe)
+ }
+
+ Constraint applied by modyfing the Velocity Verlet algorithm
+
+ {\color{blue}Results:}
+ (Video \href{../video/c_in_si_fmig_albe.avi}{$\rhd_{\text{local}}$ } $|$
+ \href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/c_in_si_fmig_albe.avi}{$\rhd_{\text{remote url}}$})\\
+ \begin{minipage}{6.3cm}
+ \includegraphics[width=6cm]{c_100_110fmig_01_albe.ps}
+ \end{minipage}
+ \begin{minipage}{6cm}
+ \begin{center}
+  Again there are jumps in energy corresponding to abrupt
+  structural changes as seen in the video
+ \end{center}
+ \end{minipage}
+ \begin{itemize}
+  \item Expected final configuration not obtained
+  \item Bonds to neighboured silicon atoms persist
+  \item C and neighboured Si atoms move along the direction of displacement
+  \item Even the bond to the lower left silicon atom persists
+ \end{itemize}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Again: C 100 interstitial migration (VASP)
  }
 
- Defining the transformation for the Type 1 supercell (VASP)
+ Transformation for the Type 2 supercell
 
  \small
 
  \begin{minipage}[t]{4.2cm}
  \underline{Starting configuration}\\
- \includegraphics[width=4cm]{c_100_mig_vasp/start.eps}
+ \includegraphics[width=3cm]{c_100_mig_vasp/start.eps}
  \end{minipage}
  \begin{minipage}[t]{4.0cm}
- \vspace*{0.8cm}
- $\Delta x=\frac{1}{4}a_{\text{Si}}=1.368\text{ \AA}$\\
- $\Delta y=\frac{1}{4}a_{\text{Si}}=1.368\text{ \AA}$\\
- $\Delta z=0.888\text{ \AA}$\\
+ \vspace*{1.0cm}
+ $\Delta x=1.367\text{ \AA}$\\
+ $\Delta y=1.367\text{ \AA}$\\
+ $\Delta z=0.787\text{ \AA}$\\
  \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:
+ \includegraphics[width=3cm]{c_100_mig_vasp/final.eps}\\
+ \end{minipage}
+ \begin{minipage}{6.2cm}
+ Rotation angles:
  \[
- \Theta=\arctan\frac{\Delta z}{\sqrt{2}\Delta x}=24.666^{\circ}
+ \alpha=45^{\circ}
+ \textrm{ , }
+ \beta=\arctan\frac{\Delta z}{\sqrt{2}\Delta x}=22.165^{\circ}
  \]
+ \end{minipage}
+ \begin{minipage}{6.2cm}
+ Length of migration path:
+ \[
+ l=\sqrt{\Delta x^2+\Delta y^2+\Delta z^2}=2.087\text{ \AA}
+ \]
+ \end{minipage}\\[0.3cm]
  Transformation of basis:
  \[
- T(\Theta)=\left(\begin{array}{ccc}
+ T=ABA^{-1}A=AB \textrm{, mit }
+ A=\left(\begin{array}{ccc}
+ \cos\alpha & -\sin\alpha & 0\\
+ \sin\alpha & \cos\alpha & 0\\
+ 0 & 0 & 1
+ \end{array}\right)
+ \textrm{, }
+ B=\left(\begin{array}{ccc}
  1 & 0 & 0\\
- 0 & \cos\Theta & -\sin\Theta \\
- 0 & \sin\Theta & \cos\Theta
+ 0 & \cos\beta & \sin\beta \\
+ 0 & -\sin\beta & \cos\beta
  \end{array}\right)
  \]
- Transformation of atom coordinates: $T(-\Theta)$
+ Atom coordinates transformed by: $T^{-1}=B^{-1}A^{-1}$
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Again: C 100 interstitial migration\\
+ }
+
+ {\color{blue}Reminder:}\\
+ Transformation needed since in VASP constraints can only be applied to
+ the basis vectors!\\
+ {\color{red}Problem:} (stupid me!)\\
+ Transformation of supercell 'destroys' the correct periodicity!\\
+ {\color{green}Solution:}\\
+ Find a supercell with one basis vector forming the correct constraint\\
+ {\color{red}Problem:}\\
+ Hard to find a supercell for the $22.165^{\circ}$ rotation\\
+
+ Another method to {\color{blue}\underline{estimate}} the migration energy:
+ \begin{itemize}
+  \item Assume an intermediate saddle point configuration during migration
+  \item Determine the energy of the saddle point configuration
+  \item Substract the saddle point configuration energy by
+        the energy of the initial (final) defect configuration
+ \end{itemize}
+ 
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  The C 100 defect configuration
+ }
+
+ Needed so often for input configurations ...\\[0.8cm]
+ \begin{minipage}{7.7cm}
+ \includegraphics[width=7cm]{100-c-si-db_light.eps}
+ \hfill
+ \end{minipage}
+ \begin{minipage}{4.5cm}
+ \begin{tabular}{|l|l|l|}
+ \hline
+  & a & b \\
+ \hline
+ \underline{VASP} & & \\
+ fractional & 0.1969 & 0.1211 \\
+ in \AA & 1.08 & 0.66 \\
+ \hline
+ \underline{Albe} & & \\
+ fractional & 0.1547 & 0.1676 \\
+ in \AA & 0.84 & 0.91 \\
+ \hline
+ \end{tabular}
+ \end{minipage}
+
+ \begin{center}
+ Qualitative {\color{red}and} quantitative {\color{red}difference}!
+ \end{center}
 
 \end{slide}