X-Git-Url: https://hackdaworld.org/gitweb/?a=blobdiff_plain;f=posic%2Ftalks%2Fupb-ua-xc.tex;h=2d7db856fd219613306f2fd9dce4fcea0c030a8f;hb=ae16e2c0d5eb1f261c1f3fbf2f53712d0b723615;hp=8561eb37f694e487841bc06454b1fd8ec3652294;hpb=a14f12a9addac7366d8065ac82188867df2c1d38;p=lectures%2Flatex.git

diff --git a/posic/talks/upb-ua-xc.tex b/posic/talks/upb-ua-xc.tex
index 8561eb3..2d7db85 100644
--- a/posic/talks/upb-ua-xc.tex
+++ b/posic/talks/upb-ua-xc.tex
@@ -916,6 +916,42 @@ POTIM = 0.1
 
 \end{slide}
 
+\begin{slide}
+
+ {\large\bf
+  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{blue}Problem:}\\
+ Too high forces due to the small distance of the C atom to the Si
+ atom sharing the lattice site.\\
+ {\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}
+ \includegraphics[width=6cm]{c_100_110pqmig_01_albe.ps}
+ \end{minipage}
+ \begin{minipage}{6cm}
+ \begin{itemize}
+  \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}
+ \end{minipage}
+
+\end{slide}
+
 \begin{slide}
 
  {\large\bf
@@ -923,17 +959,143 @@ POTIM = 0.1
  }
 
  \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}