X-Git-Url: https://hackdaworld.org/gitweb/?p=lectures%2Flatex.git;a=blobdiff_plain;f=posic%2Ftalks%2Fupb-ua-xc.tex;h=7b953ffafa28429c1e0274314340d37373e7db7d;hp=2a976157077480c5126e854b425b280687b2ec1d;hb=e08a97849ebaf34c088eef126bf83fa8a4267119;hpb=79e206cc88cb4dfb6e04eb6574474d550ee401e1

diff --git a/posic/talks/upb-ua-xc.tex b/posic/talks/upb-ua-xc.tex
index 2a97615..7b953ff 100644
--- a/posic/talks/upb-ua-xc.tex
+++ b/posic/talks/upb-ua-xc.tex
@@ -20,6 +20,8 @@
 \usepackage{pstricks}
 \usepackage{pst-node}
 
+\usepackage{slashbox}
+
 %\usepackage{epic}
 %\usepackage{eepic}
 
@@ -1176,11 +1178,13 @@ POTIM = 0.1
  }
 
  Needed so often for input configurations ...\\[0.8cm]
- \begin{minipage}{7.7cm}
- \includegraphics[width=7cm]{100-c-si-db_light.eps}
- \hfill
+ \begin{minipage}{7.0cm}
+ \includegraphics[width=6.5cm]{100-c-si-db_light.eps}\\
+ Qualitative {\color{red}and} quantitative {\color{red}difference}!
  \end{minipage}
- \begin{minipage}{4.5cm}
+ \begin{minipage}{5.5cm}
+ \scriptsize
+ \begin{center}
  \begin{tabular}{|l|l|l|}
  \hline
   & a & b \\
@@ -1193,12 +1197,11 @@ POTIM = 0.1
  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{tabular}\\[0.2cm]
+ {\scriptsize\underline{PC (Vasp)}}
+ \includegraphics[width=6.1cm]{c_100_pc_vasp.ps}
  \end{center}
+ \end{minipage}
 
 \end{slide}
 
@@ -1208,7 +1211,8 @@ POTIM = 0.1
   Again: C \hkl<1 0 0> interstitial migration (VASP)
  }
 
- $\hkl<0 0 -1> \rightarrow \hkl<0 0 1>$ migration:
+ $\hkl<0 0 -1> \rightarrow \hkl<0 0 1>$ migration
+ ($3\times 3\times 3$ Type 2):
 
  \small
 
@@ -1256,7 +1260,8 @@ POTIM = 0.1
   Again: C \hkl<1 0 0> interstitial migration (VASP)
  }
 
- $\hkl<0 0 -1> \rightarrow \hkl<0 -1 0>$ migration:
+ $\hkl<0 0 -1> \rightarrow \hkl<0 -1 0>$ migration
+ ($3\times 3\times 3$ Type 2):
 
  \small
 
@@ -1285,41 +1290,1657 @@ POTIM = 0.1
  \Rightarrow \Delta E_{\text{f}} = E_{\text{mig}} = ?.?? \text{ eV}
  \]
 
- Unexpected \& ({\color{red}more} or {\color{orange}less}) fatal:
+ \vspace*{0.5cm}
+ {\large\bf
+ Intermediate configuration {\color{red}not found} by now!
+ }
+ 
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  C in Si interstitial configurations (VASP)
+ }
+
+ Check of Kohn-Sham eigenvalues\\
+
+ \small
+
+ \begin{minipage}{6cm}
+ \hkl<1 0 0> interstitial\\
+ \end{minipage}
+ \begin{minipage}{6cm}
+ Saddle point configuration\\
+ \end{minipage}
+ \underline{$4\times 4\times 3$ Type 1 - fixed border atoms}\\
+ \begin{minipage}{6cm}
+385:      4.8567  -   2.00000\\
+386:      4.9510  -   2.00000\\
+387:      5.3437  -   0.00000\\
+388:      5.4930  -   0.00000
+ \end{minipage}
+ \begin{minipage}{6cm}
+385:      4.8694  -   2.00000\\
+386: {\color{red}4.9917}  -   1.92603\\
+387: {\color{red}5.1181}  -   0.07397\\
+388:      5.4541  -   0.00000
+ \end{minipage}\\[0.2cm]
+ \underline{$4\times 4\times 3$ Type 1 - no constraints}\\
+ \begin{minipage}{6cm}
+385:      4.8586   -  2.00000\\
+386:      4.9458   -  2.00000\\
+387:      5.3358   -  0.00000\\
+388:      5.4915   -  0.00000
+ \end{minipage}
+ \begin{minipage}{6cm}
+385:      4.8693   -  2.00000\\
+386: {\color{red}4.9879}   -  1.92065\\
+387: {\color{red}5.1120}   -  0.07935\\
+388:      5.4544   -  0.00000
+ \end{minipage}\\[0.2cm]
+ \underline{$3\times 3\times 3$ Type 2 - no constraints}\\
+ \begin{minipage}{6cm}
+433:       4.8054  -   2.00000\\
+434:       4.9027  -   2.00000\\
+435:       5.2543  -   0.00000\\
+436:       5.5718  -   0.00000
+ \end{minipage}
+ \begin{minipage}{6cm}
+433:       4.8160  -   2.00000\\
+434: {\color{green}5.0109}  -   1.00264\\
+435: {\color{green}5.0111}  -   0.99736\\
+436:       5.5364  -   0.00000
+ \end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Once again: C \hkl<1 0 0> interstitial migration (VASP)
+ }
+
+ Method:
  \begin{itemize}
-  \renewcommand\labelitemi{{\color{orange}$\bullet$}}
-  \item Difference in formation energy (0.02 eV)
-        of the initial and final configuration
-  \renewcommand\labelitemi{{\color{red}$\bullet$}}
-  \item Huge discrepancy (0.3 - 0.4 eV) to the migration barrier
-        of Type 1 (198+1 atoms) calculations
-  \renewcommand\labelitemi{{\color{black}$\bullet$}}
+  \item Start in fully relaxed (assumed) saddle point configuration
+  \item Move towards \hkl<1 0 0> configuration using updated values
+        for $\Delta x$, $\Delta y$ and $\Delta z$ (CRT)
+  \item \hkl<1 1 0> constraints applied, 1 Si atom fixed
+  \item $4\times 4\times 3$ Type 1 supercell
  \end{itemize}
- 
+
+ Results:
+
+ \begin{minipage}{6.2cm}
+ \includegraphics[width=6.0cm]{c_100_110sp-i_vasp.ps}
+ \end{minipage}
+ \begin{minipage}{6.2cm}
+ \includegraphics[width=6.0cm]{c_100_110sp-i_rc_vasp.ps}
+ \end{minipage}
+
+ Reaction coordinate:
+ $r_{i+1}=r_i+\sum_{\text{atoms j}} \left| r_{j,i+1}-r_{j,i} \right|$
+
 \end{slide}
 
 \begin{slide}
 
- {\large\bf
-  Molecular dynamics simulations (VASP)
+ {\large\bf\boldmath
+  Investigation of the migration path along \hkl<1 1 0> (VASP)
  }
 
  \small
 
+ \underline{Minimum:}\\
+ \begin{minipage}{4cm}
+   \includegraphics[width=3.5cm]{c_100_mig_vasp/110_c-si_split.eps}
+ \end{minipage}
+ \begin{minipage}{8cm}
+   \begin{itemize}
+    \item Starting conf: 35 \% displacement results (1443)
+    \item \hkl<1 1 0> constraint disabled
+   \end{itemize}
+   \begin{center}
+   $\Downarrow$
+   \end{center}
+   \begin{itemize}
+    \item C-Si \hkl<1 1 0> split interstitial
+    \item Stable configuration
+    \item $E_{\text{f}}=4.13\text{ eV}$
+   \end{itemize}
+ \end{minipage}\\[0.1cm]
+
+ \underline{Maximum:}\\
+ \begin{minipage}{6cm}
+   \begin{center}
+   \includegraphics[width=2.3cm]{c_100_mig_vasp/100-110_01.eps}
+   \includegraphics[width=2.3cm]{c_100_mig_vasp/100-110_02.eps}\\
+   20 \% $\rightarrow$ 25 \%\\
+   Breaking of Si-C bond
+   \end{center}
+ \end{minipage}
+ \begin{minipage}{6cm}
+  \includegraphics[width=6.2cm]{c_100_110sp-i_upd_vasp.ps}
+ \end{minipage}
+
 \end{slide}
 
 \begin{slide}
 
- {\large\bf
-  Density Functional Theory
+ {\large\bf\boldmath
+  Displacing the \hkl<1 1 0> Si-C split along \hkl<1 -1 0> (VASP)
  }
 
- Hohenberg-Kohn theorem
+ \small
+
+ $4\times 4\times 3$ Type 1 supercell
+
+ \underline{Structures:}
+
+ \begin{minipage}[t]{4.1cm}
+  \includegraphics[height=3.0cm]{c_100_mig_vasp/start.eps}\\
+  \hkl<0 0 -1> dumbbell\\
+  $E_{\text{f}}={\color{orange}3.2254}\text{ eV}$
+ \end{minipage}
+ \begin{minipage}[t]{4.1cm}
+  \includegraphics[height=3.0cm]{c_100_mig_vasp/110_c-si_split.eps}\\
+  Assumed \hkl<1 1 0> C-Si split\\
+  $E_{\text{f}}=4.1314\text{ eV}$
+ \end{minipage}
+ \begin{minipage}[t]{4.1cm}
+  \includegraphics[height=3.0cm]{c_100_mig_vasp/110_dis_0-10.eps}\\
+  First guess: \hkl<0 -1 0> dumbbell\\
+  {\color{red}but:} $E_{\text{f}}={\color{orange}2.8924}\text{ eV}$\\
+  Third bond missing!
+ \end{minipage}\\
+
+ \underline{Occupancies:}
+
+ \scriptsize
+
+ \begin{minipage}{4.1cm}
+385:       4.8586  -  2.00000\\
+386:       4.9458  -  2.00000\\
+387:       5.3358  -  0.00000\\
+388:       5.4915  -  0.00000
+\hfill
+ \end{minipage}
+ \begin{minipage}{4.1cm}
+385:       4.7790  -  2.00000\\
+386:       4.8797  -  1.99964\\
+387:       5.1321  -  0.00036\\
+388:       5.4711  -  0.00000
+\hfill
+ \end{minipage}
+ \begin{minipage}{4.1cm}
+385:       4.7670  -  2.00000\\
+386:       4.9190  -  2.00000\\
+387:       5.2886  -  0.00000\\
+388:       5.4849  -  0.00000
+\hfill
+ \end{minipage}\\
+
+\small
+
+ \begin{center}
+ {\color{red}? ! ? ! ? ! ? ! ?}
+ \end{center}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  C \hkl<1 0 0> interstitial migration (VASP)
+ }
 
  \small
+
+ \begin{minipage}{6.2cm}
+ \begin{itemize}
+  \item $3\times 3\times 3$ Type 2 supercell
+  \item \hkl<1 1 0> constraints applied
+        (\href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/sd_rot.patch}{Patch})
+  \item Move from \hkl<1 0 0> towards\\
+        bond centered configuration
+ \end{itemize}
+ \underline{Sd Rot usage (POSCAR):}
+\begin{verbatim}
+cubic diamond                           
+5.480
+ 3.0 0.0 0.0
+ 0.0 3.0 0.0
+ 0.0 0.0 3.0
+216 1
+Transformed selective dynamics
+45.0 0.0
+Direct
+ ...
+\end{verbatim}
+Only works in direct mode!\\
+$z,x'$-axis rotation: $45.0^{\circ}$, $0.0^{\circ}$
+ \end{minipage}
+ \begin{minipage}{6.2cm}
+ \includegraphics[width=5cm]{c_100_110sp-i_2333_vasp.ps}
+ \includegraphics[width=5cm]{c_100_110sp-i_2333_rc_vasp.ps}\\
+ {\color{red}One fixed Si atom not enough!}\\
+ Video: \href{../video/c_in_si_233_110mig_vasp.avi}{$\rhd_{\text{local}}$ } $|$
+ \href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/c_in_si_233_110mig_vasp.avi}{$\rhd_{\text{remote url}}$}\\
+ \end{minipage}
+
+ {\color{blue}
+  Next: Migration calculation in 2333 using CRT
+  (\hkl<0 0 -1> $\rightarrow$ \hkl<0 0 1> and \hkl<0 -1 0>)
+ }
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Defect configurations in $4\times 4\times 3$ Type 1 supercells revisited
+ }
+
+ \footnotesize
+
+ \begin{tabular}{l|p{2.5cm}|p{2.5cm}|p{4cm}|}
+  & \hkl<0 0 -1> interstitial
+  & local minimum\newline
+    \hkl<1 1 0> C-Si split
+  & intermediate configuration\newline
+    (bond centered conf)\\
+ \hline
+ default & $E_{\text{f}}=3.3254\text{ eV}$\newline
+           {\tiny
+           386: 4.9458 - 2.00000\newline
+           387: 5.3358 - 0.00000}
+         & $E_{\text{f}}=4.1314\text{ eV}$\newline
+           {\tiny
+           386: 4.8797 - 1.99964\newline
+           387: 5.1321 - 0.00036}
+         & $E_{\text{f}}=4.2434\text{ eV}$\newline
+           {\tiny
+           386: 4.9879 - 1.92065\newline
+           387: 5.1120 - 0.07935} \\
+ \hline
+ No symmetry & $E_{\text{f}}=3.3154\text{ eV}$\newline
+               {\tiny
+               386: 4.9456 - 2.00000\newline
+               387: 5.3366 - 0.00000}
+             & $E_{\text{f}}=4.1314\text{ eV}$\newline
+               {\tiny
+               386: 4.8798 - 1.99961\newline
+               387: 5.1307 - 0.00039}
+             & $E_{\text{f}}=4.2454\text{ eV}$\newline
+               {\tiny
+               386: 4.9841 - 1.92147\newline
+               387: 5.1085 - 0.07853} \\
+ \hline
+ $+$ spin polarized & $E_{\text{f}}=3.3154\text{ eV}$\newline
+                      {\tiny
+                      {\color{blue}
+                      386: 4.9449 - 1.00000\newline
+                      387: 5.3365 - 0.00000\newline%
+                      }%
+                      {\color{green}%
+                      386: 4.9449 - 1.00000\newline
+                      387: 5.3365 - 0.00000}}
+                    & $E_{\text{f}}={\color{red}4.1314}\text{ eV}$\newline
+                      {\tiny
+                      {\color{blue}
+                      386: 4.8799 - 0.99980\newline
+                      387: 5.1307 - 0.00020\newline%
+                      }%
+                      {\color{green}%
+                      386: 4.8799 - 0.99980\newline
+                      387: 5.1306 - 0.00020}}
+                    & $E_{\text{f}}=4.0254\text{ eV}$\newline
+                      {\tiny
+                      {\color{blue}
+                      387: 4.8581 - 1.00000\newline
+                      388: 5.4662 - 0.00000\newline%
+                      }%
+                      {\color{green}%
+                      385: 4.8620 - 1.00000\newline
+                      386: 5.2951 - 0.00000}} \\
+ \hline
+ $+$ spin difference 2 & $E_{\text{f}}=3.6394\text{ eV}$\newline
+                         {\tiny
+                         {\color{blue}
+                         387: 5.2704 - 0.99891\newline
+                         388: 5.4886 - 0.00095\newline
+                         389: 5.5094 - 0.00011\newline
+                         390: 5.5206 - 0.00003\newline%
+                         }%
+                         {\color{green}%
+                         385: 4.8565 - 0.98603\newline
+                         386: 5.0119 - 0.01397}}
+                       & Relaxation into\newline
+                         bond centered\newline
+                         configuration\newline
+                         $\rightarrow$
+                       & $E_{\text{f}}=4.0254\text{ eV}$\newline
+                         {\tiny
+                         {\color{blue}
+                         387: 4.8578 - 1.00000\newline
+                         388: 5.4661 - 0.00000\newline%
+                         }%
+                         {\color{green}%
+                         385: 4.8618 - 1.00000\newline
+                         386: 5.2950 - 0.00000}} \\
+ \hline
+ \end{tabular}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Defect configurations in $3\times 3\times 3$ Type 2 supercells revisited\\
+ }
+
+ \footnotesize
+
+ \begin{tabular}{l|p{2.5cm}|p{2.5cm}|p{4cm}|}
+  & \hkl<0 0 -1> interstitial
+  & local minimum\newline
+    \hkl<1 1 0> C-Si split
+  & intermediate configuration\newline
+    (bond centered conf)\\
+ \hline
+ default & $E_{\text{f}}=3.15407\text{ eV}$\newline
+           {\tiny
+           434: 4.9027 - 2.00000\newline
+           435: 5.2543 - 0.00000}
+         & $E_{\text{f}}=??\text{ eV}$\newline
+           {\tiny
+           ??\newline
+           ??}
+         & $E_{\text{f}}=4.40907\text{ eV}$\newline
+           {\tiny
+           434: 5.0109 - 1.00264\newline
+           435: 5.0111 - 0.99736}\\
+ \hline
+ No symmetry & $E_{\text{f}}=3.16107\text{ eV}$\newline
+               {\tiny
+               434: 4.9032 - 2.00000\newline
+               435: 5.2547 - 0.00000}
+             & $E_{\text{f}}=??\text{ eV}$\newline
+               {\tiny
+               ??\newline
+               ??}
+             & $E_{\text{f}}=4.41507\text{ eV}$\newline
+               {\tiny
+               434: 5.0113 - 1.00140\newline
+               435: 5.0114 - 0.99860} \\
+ \hline
+ $+$ spin polarized & $E_{\text{f}}=3.16107\text{ eV}$\newline
+                      {\tiny
+                      {\color{blue}
+                      434: 4.9033 - 1.00000\newline
+                      435: 5.2544 - 0.00000\newline%
+                      }%
+                      {\color{green}%
+                      434: 4.9035 - 1.00000\newline
+                      435: 5.2550 - 0.00000}}
+                    & $E_{\text{f}}=??\text{ eV}$\newline
+                      {\tiny
+                      {\color{blue}
+                      ??\newline
+                      ??\newline%
+                      }%
+                      {\color{green}%
+                      ??\newline
+                      ??}}
+                    & $E_{\text{f}}=4.10307\text{ eV}$\newline
+                      {\tiny
+                      {\color{blue}
+                      435: 4.8118 - 1.00000\newline
+                      436: 5.5360 - 0.00000\newline%
+                      }%
+                      {\color{green}%
+                      433: 4.8151 - 1.00000\newline
+                      434: 5.3475 - 0.00000}} \\
+ \hline
+ \end{tabular}
+
+ \normalsize
+
+ \vspace*{0.3cm}
+
+ {\color{blue}Tracer:}\\
+ Smearing of electrons over two or more (degenerated) energy levels\\
+ $\Rightarrow$ use spin polarized calculations!
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Bond centered configuration revisited ($3\times 3\times 3$ Type 2)
+ }
+
+ Spin polarized calculations
+
+ {\small
+ \begin{minipage}[t]{5.8cm}
+ \underline{Kohn-Sham eigenvalues}\\
+  \begin{minipage}{2.8cm}
+  Spin up:\\
+  430: 4.2639 - 1\newline
+  431: 4.7332 - 1\newline
+  432: 4.7354 - 1\newline
+  433: 4.7700 - 1\newline
+  434: 4.8116 - 1\newline
+  435: 4.8118 - 1\newline
+  436: 5.5360 - 0\newline
+  437: 5.5623 - 0
+  \end{minipage}
+  \begin{minipage}{2.8cm}
+  Spin down:\\
+  430: 4.2682 - 1\newline
+  431: 4.7738 - 1\newline
+  432: 4.8150 - 1\newline
+  433: 4.8151 - 1\newline
+  434: 5.3475 - 0\newline
+  435: 5.3476 - 0\newline
+  436: 5.5455 - 0\newline
+  437: 5.5652 - 0
+  \end{minipage}\\[0.3cm]
+ \begin{itemize}
+  \item linear Si-C-Si bond
+  \item Each Si has another 3 Si neighbours
+ \end{itemize}
+ \begin{center}
+ {\color{blue}Spin polarized calculations necessary!}\\[0.3cm]
+ \end{center}
+ {\scriptsize Charge density isosurface of
+              {\color{gray}spin up}, {\color{green}spin down} and
+              the {\color{blue}resulting spin up} electrons.\\
+              Two {\color{yellow} Si} atoms and one {\color{red}C}
+              atom are shown.
+ }
+ \end{minipage}
+ \begin{minipage}[t]{6.5cm}
+ \underline{MO diagram}\\
+  \begin{minipage}[t]{1.2cm}
+  {\color{red}Si}\\
+  {\tiny sp$^3$}\\[0.8cm]
+  \underline{${\color{red}\uparrow}$}
+  \underline{${\color{red}\uparrow}$}
+  \underline{${\color{red}\uparrow}$}
+  \underline{${\color{red}\uparrow}$}\\
+  sp$^3$
+  \end{minipage}
+  \begin{minipage}[t]{1.4cm}
+  \begin{center}
+  {\color{red}M}{\color{blue}O}\\[1.0cm]
+  \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
+  $\sigma_{\text{ab}}$\\[0.5cm]
+  \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
+  $\sigma_{\text{b}}$
+  \end{center}
+  \end{minipage}
+  \begin{minipage}[t]{1.0cm}
+  \begin{center}
+  {\color{blue}C}\\
+  {\tiny sp}\\[0.2cm]
+  \underline{${\color{white}\uparrow\uparrow}$}
+  \underline{${\color{white}\uparrow\uparrow}$}\\
+  2p\\[0.4cm]
+  \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
+  \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\
+  sp
+  \end{center}
+  \end{minipage}
+  \begin{minipage}[t]{1.4cm}
+  \begin{center}
+  {\color{blue}M}{\color{green}O}\\[1.0cm]
+  \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
+  $\sigma_{\text{ab}}$\\[0.5cm]
+  \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\
+  $\sigma_{\text{b}}$
+  \end{center}
+  \end{minipage}
+  \begin{minipage}[t]{1.2cm}
+  \begin{flushright}
+  {\color{green}Si}\\
+  {\tiny sp$^3$}\\[0.8cm]
+  \underline{${\color{green}\uparrow}$}
+  \underline{${\color{green}\uparrow}$}
+  \underline{${\color{green}\uparrow}$}
+  \underline{${\color{green}\uparrow}$}\\
+  sp$^3$
+  \end{flushright}
+  \end{minipage}\\[0.4cm]
+ \begin{flushright}
+ \includegraphics[width=6cm]{c_100_mig_vasp/im_spin_diff.eps}
+ \end{flushright}
+ \end{minipage}
+ }
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  \hkl<0 0 -1> configuration revisited ($3\times 3\times 3$ Type 2)
+ }
+
+ Spin polarized calculations
+
+ {\small
+ \begin{minipage}[t]{5.8cm}
+ \underline{Kohn-Sham eigenvalues}\\
+  \begin{minipage}{2.8cm}
+  Spin up:\\
+  430: 4.3317 - 1\newline
+  431: 4.7418 - 1\newline
+  432: 4.8014 - 1\newline
+  433: 4.8060 - 1\newline
+  434: 4.9033 - 1\newline
+  435: 5.2544 - 0\newline
+  436: 5.5723 - 0\newline
+  437: 5.5848 - 0
+  \end{minipage}
+  \begin{minipage}{2.8cm}
+  Spin down:\\
+  430: 4.3317 - 1\newline
+  431: 4.7420 - 1\newline
+  432: 4.8013 - 1\newline
+  433: 4.8059 - 1\newline
+  434: 4.9035 - 1\newline
+  435: 5.2550 - 0\newline
+  436: 5.5724 - 0\newline
+  437: 5.5846 - 0
+  \end{minipage}
+ \end{minipage}
+ \begin{minipage}[t]{6.5cm}
+ \underline{MO diagram}\\
+  \begin{minipage}[t]{1.2cm}
+  {\color{red}Si}\\
+  {\tiny sp$^2$}\\[0.1cm]
+  \underline{${\color{white}\uparrow}$}\\
+  p\\[0.4cm]
+  \underline{${\color{red}\uparrow\downarrow}$}
+  \underline{${\color{red}\uparrow}{\color{white}\downarrow}$}
+  \underline{${\color{red}\uparrow}{\color{white}\downarrow}$}\\
+  sp$^2$
+  \end{minipage}
+  \begin{minipage}[t]{1.2cm}
+  \begin{flushright}
+  {\color{red}M}\\[1.0cm]
+  \underline{${\color{white}\uparrow}{\color{white}\downarrow}$}\\
+  $\sigma_{\text{ab}}$\\[0.5cm]
+  \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
+  $\sigma_{\text{b}}$
+  \end{flushright}
+  \end{minipage}
+  \begin{minipage}[t]{1.2cm}
+  \begin{flushleft}
+  {\color{blue}O}\\[0.4cm]
+  \underline{${\color{white}\uparrow}{\color{white}\downarrow}$}\\
+  $\pi_{\text{ab}}$\\[0.5cm]
+  \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
+  $\pi_{\text{b}}$
+  \end{flushleft}
+  \end{minipage}
+  \begin{minipage}[t]{2.0cm}
+  \begin{center}
+  {\color{blue}C}\\
+  {\tiny sp$^2$}\\[0.5cm]
+  \underline{${\color{white}\uparrow\uparrow}$}\\
+  p\\[0.4cm]
+  \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
+  \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}
+  \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
+  sp$^2$
+  \end{center}
+  \end{minipage}
+ \end{minipage}
+ }
+
+ \vspace*{0.4cm}
+
+ \begin{itemize}
+  \item Si-C double bond
+  \item Si and C atom have another 2 Si neighbours
+ \end{itemize}
  
+ \begin{center}
+ {\color{blue}Spin polarized calculations {\color{red}not} necessary!}
+ \end{center}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Kohn-Sham levels visualized
+ }
+
+ \begin{minipage}{6cm}
+ \underline{\hkl<0 0 -1> configuration}
+ \begin{center}
+ \includegraphics[height=8cm]{c_100_mig_vasp/100_ksl.ps}
+ \end{center}
+ \end{minipage}
+ \begin{minipage}{6cm}
+ \underline{Saddle point configuration}
+ \begin{center}
+ \includegraphics[height=8cm]{c_100_mig_vasp/im_ksl.ps}
+ \end{center}
+ \end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Saddle point configuration check
+ }
+
+ Simulations:
+ \begin{itemize}
+  \item Displacing the C atom in the BC configuration
+        \begin{itemize}
+         \item in \hkl<1 -1 0> direction\\
+               $(0.1240, 0.1240, 0.0409) \rightarrow
+                (0.1340, 0.1140, 0.0409)$
+         \item in \hkl<1 0 0> direction\\
+               $(0.1240, 0.1240, 0.0409) \rightarrow
+                (0.1440, 0.1240, 0.0409)$
+        \end{itemize}
+  \item Full relaxation of the configuration
+ \end{itemize}
+
+ Results:
+ \begin{itemize}
+  \item Both displacement simulations relax to
+        the BC configuration
+  \item Obviously the second derivative with respect to the
+        migration direction is also positive
+ \end{itemize}
+
+ \begin{center}
+ $\Downarrow$\\
+ Bond centered configuration is a
+ {\color{blue}real local minimum}
+ and  {\color{red}not} a saddle point configuration
+ \end{center}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  New default parameter set\\[1cm]
+ }
+
+ Since some defect configurations need spin polarized calculations ...\\[1cm]
+
+ from now on the default parameter set\\
+ {\bf\color{blue}
+ $+$ no symmetry\\
+ $+$ spin polarized\\
+ }
+ \ldots is used!\\[1cm]
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  BC to \hkl<0 0 -1> migration
+   in the $3\times 3\times 3$ Type 2 supercell
+ }
+
+ \begin{minipage}{6cm}
+ Method:
+ \begin{itemize}
+  \item Starting configuration:\\
+        C bond centered
+  \item CRT towards \hkl<0 0 -1> configuration
+  \item Spin polarized calculations
+ \end{itemize}
+ Results:\\
+ Video \href{../video/c_im_00-1_vasp.avi}{$\rhd_{\text{local}}$ } $|$
+ \href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/c_im_00-1_vasp.avi}{$\rhd_{\text{remote url}}$}
+ \begin{itemize}
+  \item Still abrupt changes in configuration and energy 
+  \item Migration barrier $>$ 1 eV
+ \end{itemize} 
+ \end{minipage}
+ \begin{minipage}{6cm}
+ \includegraphics[width=6cm]{c_im_001_mig_vasp.ps}
+ \includegraphics[width=6cm]{c_im_001_mig_rc_vasp.ps}
+ \end{minipage}
 
 \end{slide}
 
+\begin{slide}
+
+ {\large\bf\boldmath
+  \hkl<0 0 -1> to \hkl<0 -1 0> migration
+  in the $3\times 3\times 3$ Type 2 supercell
+ }
+
+ \includegraphics[width=6cm]{c_00-1_0-10_mig_vasp.ps}
+ \includegraphics[width=6cm]{c_00-1_0-10_mig_dis_vasp.ps}
+
+ Calculations without spin:\\
+ Video \href{../video/c_00-1_0-10_vasp.avi}{$\rhd_{\text{local}}$ } $|$
+ \href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/c_00-1_0-10_vasp.avi}{$\rhd_{\text{remote url}}$} ... WAAAAH!!!
+ \begin{itemize}
+  \item Refined starting from 70\% due to
+        abrubt jumps in energy and configuration 
+  \item Displacement from 80 to 85\% disastrous
+  \item Subsequent displacements too large
+ \end{itemize}
+
+ Waiting for spin polarized calculations before deciding what to do ...
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  C \hkl<1 0 0> migration - yet another method!
+ }
+
+ {\color{red}Problem:}
+
+ Abrubt changes in atomic configurations (and energy)
+ in consecutive steps.
+ In addition - sometimes - the final configuration is not obtained!
+
+ {\color{blue}New method:}
+
+ Displace {\color{red}all} atoms towards the final configuration
+ and apply corresponding constraints for each atom.
+
+ Usage: 
+ (\href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/sd_rot_all-atoms.patch}{Patch})
+
+\footnotesize 
+
+\begin{verbatim}
+cubic diamond                           
+   5.48000000000000     
+     2.9909698580839312    0.0039546630279804   -0.0039658085666586
+     0.0039548953566878    2.9909698596656376   -0.0039660323646892
+    -0.0039680658132861   -0.0039674231313905    2.9909994291263242
+ 216   1
+Transformed selective dynamics
+Direct
+ 0.994174 0.994174 -0.000408732 T F T 45 36.5145
+ 0.182792 0.182792 0.981597 T F T -135 -5.95043
+ ...
+ 0.119896 0.119896 0.0385525 T F T -135 21.8036
+\end{verbatim}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  BC to \hkl<0 0 -1> migration (all atoms CRT)
+ }
+
+ \includegraphics[width=6cm]{im_00-1_nosym_sp_fullct.ps}
+ \includegraphics[width=6cm]{im_00-1_nosym_sp_fullct_rc.ps}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  \hkl<0 0 -1> to \hkl<0 -1 0> migration (all atoms CRT)
+ }
+
+ \includegraphics[width=6cm]{00-1_0-10_nosym_sp_fullct.ps}
+ \includegraphics[width=6cm]{00-1_0-10_nosym_sp_fullct_rc.ps}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  \hkl<0 0 -1> to \hkl<0 -1 0> migration in place (all atoms CRT)
+ }
+
+ \includegraphics[width=6cm]{00-1_ip0-10_nosym_sp_fullct.ps}
+ \includegraphics[width=6cm]{00-1_ip0-10_nosym_sp_fullct_rc.ps}
+
+ in progress ...
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Combination of defects
+ }
+
+ TODO: introduce some Si self-interstitials and C interstitials before\\
+ BUT: Concentrate on 100 C interstitial combinations and 100 C + vacancy\\
+ 
+ Agglomeration of 100 defects energetically favorable?
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Silicon point defects
+ }
+
+ \begin{minipage}{3.2cm}
+ \underline{Vacancy}
+ \begin{itemize}
+  \item $E_{\text{f}}=3.63\text{ eV}$
+ \end{itemize}
+ \includegraphics[width=3cm]{si_pd_vasp/vac_2333.eps}\\
+ \underline{\hkl<1 1 0> interstitial}
+ \begin{itemize}
+  \item $E_{\text{f}}=3.39\text{ eV}$
+ \end{itemize}
+ \includegraphics[width=3cm]{si_pd_vasp/110_2333.eps}
+ \end{minipage}
+ \begin{minipage}{4.5cm}
+ \begin{center}
+ \includegraphics[height=8cm]{si_pd_vasp/vac_2333_ksl.ps}\\
+ {\scriptsize Vacancy}
+ \end{center}
+ \end{minipage}
+ \begin{minipage}{4.5cm}
+ \begin{center}
+ \includegraphics[height=8cm]{si_pd_vasp/110_2333_ksl.ps}
+ {\scriptsize \hkl<1 1 0> interstitial}
+ \end{center}
+ \end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Silicon point defects
+ }
+
+ \begin{minipage}{3.1cm}
+ \underline{Hexagonal}
+ \begin{itemize}
+  \item $E_{\text{f}}=3.42\text{ eV}$
+ \end{itemize}
+ \includegraphics[width=3cm]{si_pd_vasp/hex_2333.eps}\\
+ \underline{Tetrahedral}
+ \begin{itemize}
+  \item $E_{\text{f}}=3.77\text{ eV}$
+ \end{itemize}
+ \includegraphics[width=3cm]{si_pd_vasp/tet_2333.eps}
+ \end{minipage}
+ \begin{minipage}{3.7cm}
+ \begin{center}
+ \includegraphics[height=8cm]{si_pd_vasp/hex_2333_ksl.ps}\\
+ {\scriptsize Hexagonal}
+ \end{center}
+ \end{minipage}
+ \begin{minipage}{3.7cm}
+ \begin{center}
+ \includegraphics[height=8cm]{si_pd_vasp/tet_2333_ksl.ps}
+ {\scriptsize Tetrahedral}
+ \end{center}
+ \end{minipage}
+ \begin{minipage}[c]{0.1cm}
+ \hfill
+ \end{minipage}
+ \begin{minipage}[c]{1.9cm}
+{\tiny
+\underline{Energy - Occup.}\\
+5.5063 - 0.32840\\
+5.5064 - 0.32793\\
+5.5064 - 0.32764\\
+5.5777 - 0.00691\\
+5.5777 - 0.00691\\
+5.6031 - 0.00074\\
+5.6031 - 0.00074\\
+5.6035 - 0.00071\\
+5.6357 - 0.00002\\
+5.6453 - 0.00001\\
+5.6453 - 0.00001
+}
+ \end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Silicon point defects
+ }
+
+ \begin{minipage}{3.1cm}
+ \underline{\hkl<1 0 0> interstitial}
+ \begin{itemize}
+  \item $E_{\text{f}}=4.41\text{ eV}$
+ \end{itemize}
+ \includegraphics[width=3cm]{si_pd_vasp/100_2333.eps}\\
+ \end{minipage}
+ \begin{minipage}{3.7cm}
+ \begin{center}
+ \includegraphics[height=8cm]{si_pd_vasp/100_2333_ksl.ps}\\
+ {\scriptsize \hkl<1 0 0> interstitial}
+ \end{center}
+ \end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Carbon point defects in silicon
+ }
+ 
+ \begin{minipage}{3.2cm}
+ \underline{C substitutional}
+ \begin{itemize}
+  \item $E_{\text{f}}=1.39\text{ eV}$
+ \end{itemize}
+ \includegraphics[width=3cm]{c_pd_vasp/sub_2333.eps}\\
+ \underline{\hkl<1 0 0> interstitial}
+ \begin{itemize}
+  \item $E_{\text{f}}=3.15\text{ eV}$
+ \end{itemize}
+ \includegraphics[width=3cm]{c_pd_vasp/100_2333.eps}
+ \end{minipage}
+ \begin{minipage}{4.5cm}
+ \begin{center}
+ \includegraphics[height=8cm]{c_pd_vasp/sub_2333_ksl.ps}\\
+ {\scriptsize C substitutional}
+ \end{center}
+ \end{minipage}
+ \begin{minipage}{4.5cm}
+ \begin{center}
+ \includegraphics[height=8cm]{c_pd_vasp/100_2333_ksl.ps}
+ {\scriptsize \hkl<1 0 0> interstitial}
+ \end{center}
+ \end{minipage}
+ 
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Carbon point defects in silicon
+ }
+ 
+ \begin{minipage}{3.2cm}
+ \underline{C bond centered}
+ \begin{itemize}
+  \item $E_{\text{f}}=4.10\text{ eV}$
+ \end{itemize}
+ \includegraphics[width=3cm]{c_pd_vasp/bc_2333.eps}
+ \underline{\hkl<1 1 0> interstitial}
+ \begin{itemize}
+  \item $E_{\text{f}}=3.60\text{ eV}$
+ \end{itemize}
+ \includegraphics[width=3cm]{c_pd_vasp/110_2333.eps}
+ \end{minipage}
+ \begin{minipage}{4.5cm}
+ \begin{center}
+ \includegraphics[height=8cm]{c_pd_vasp/110_2333_ksl.ps}
+ {\scriptsize \hkl<1 1 0> interstitial}
+ \end{center}
+ \end{minipage}
+ \begin{minipage}{4.5cm}
+ \begin{center}
+ \includegraphics[height=8cm]{c_pd_vasp/bc_2333_ksl.ps}
+ {\scriptsize C bond centered}
+ \end{center}
+ \end{minipage}
+ 
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Carbon point defects in silicon
+ }
+
+ The hexagonal and tetrahedral C configurations both relax into the
+ \hkl<0 0 1> interstitial configuration!
+ 
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Combination of defects
+ }
+
+ \begin{itemize}
+  \item Supercell: $3\times 3\times 3$ Type 2
+  \item Starting configuration: \hkl<0 0 -1> C-Si interstitial
+        ($E_{\text{f}}=3.15\text{ eV}$)
+  \item Energies: $E_{\text{f}}$ of the interstitial combinations in eV
+ \end{itemize}
+
+ \underline{Along \hkl<1 1 0>:}
+
+ \begin{tabular}{|l|p{2.0cm}|p{1.8cm}|p{1.8cm}|p{1.8cm}|}
+ \hline
+  {\scriptsize
+  \backslashbox{2nd interstitial}{Distance $[\frac{a}{4}]$}
+  }
+  & \hkl<1 1 -1> & \hkl<2 2 0> & \hkl<3 3 -1> & \hkl<4 4 0>\\
+ \hline
+ \hkl<0 0 -1> & 6.23\newline {\color{blue}6.23514} 
+              & 4.65\newline {\color{blue}4.65014} 
+              & 5.97\newline {\color{blue}5.97314}
+              & 6.45\newline {\color{blue}6.45714} \\
+ \hline
+ \hkl<0 0 1> & 6.64\newline {\color{blue}6.65114} 
+             & 4.78\newline {\color{blue}4.78314} 
+             & 6.53\newline {\color{blue}6.53614}
+             & 6.18\newline {\color{blue}6.18914} \\
+ \hline
+ \hkl<1 0 0>, \hkl<0 1 0> & 4.06\newline alkmene
+                          & 4.93
+                          & 5.72
+                          & 6.00\\
+ \hline
+ \hkl<-1 0 0>, \hkl<0 -1 0> & 3.92 & 4.43 & 6.02 & 6.02 \\
+ \hline
+ Vacancy & 1.39 ($\rightarrow\text{ C}_{\text{S}}$)& 5.81 & 5.47 & 6.50 \\
+ \hline
+ \end{tabular}
+
+ Spin polarized and {\color{blue}non spin polarized} results
+ 
+\end{slide}
+
+\begin{slide}
+
+ \begin{minipage}{5cm}
+ {\large\bf\boldmath
+  Combination of defects
+ }
+
+ \scriptsize
+
+ Initial insterstital at: $\frac{1}{4}\hkl<1 1 1>$
+
+ Relative silicon neighbour positions:
+ \begin{enumerate}
+  \item The dumbbell Si
+  \item $\frac{1}{4}\hkl<1 1 -1>$, $\frac{1}{4}\hkl<-1 -1 -1>$
+  \item $\frac{1}{2}\hkl<1 0 -1>$, $\frac{1}{2}\hkl<0 1 -1>$,
+        $\frac{1}{2}\hkl<0 -1 -1>$, $\frac{1}{2}\hkl<-1 0 -1>$
+  \item $\frac{1}{4}\hkl<1 -1 1>$, $\frac{1}{4}\hkl<-1 1 1>$
+  \item $\frac{1}{4}\hkl<-1 1 -3>$, $\frac{1}{4}\hkl<1 -1 -3>$
+  \item $\frac{1}{2}\hkl<-1 -1 0>$, $\frac{1}{2}\hkl<1 1 0>$
+  \item $\frac{1}{2}\hkl<1 -1 0>$, $\frac{1}{2}\hkl<-1 1 0>$
+  \item $\frac{1}{4}\hkl<-1 3 -1>$, $\frac{1}{4}\hkl<1 -3 -1>$,
+        $\frac{1}{4}\hkl<3 -1 -1>$. $\frac{1}{4}\hkl<-3 1 -1>$
+  \item $\hkl<0 0 -1>$
+  \item $\frac{1}{2}\hkl<1 0 1>$, $\frac{1}{2}\hkl<0 1 1>$,
+        $\frac{1}{2}\hkl<0 -1 1>$, $\frac{1}{2}\hkl<-1 0 1>$
+  \item $\frac{1}{4}\hkl<-1 -3 1>$, $\frac{1}{4}\hkl<-3 -1 1>$,
+        $\frac{1}{4}\hkl<1 3 1>$, $\frac{1}{4}\hkl<3 1 1>$
+  \item $\frac{1}{4}\hkl<1 3 -3>$, $\frac{1}{4}\hkl<3 1 -3>$,
+        $\frac{1}{4}\hkl<-1 -3 -3>$, $\frac{1}{4}\hkl<-3 -1 -3>$
+  \item $\hkl<1 0 0>$, $\hkl<0 1 0>$, $\hkl<-1 0 0>$, $\hkl<0 -1 0>$
+  \item $\frac{1}{4}\hkl<1 1 3>$, $\frac{1}{4}\hkl<-1 -1 3>$
+  \item $\frac{1}{4}\hkl<3 3 -1>$, $\frac{1}{4}\hkl<-3 -3 -1>$
+  \item $\frac{1}{2}\hkl<1 1 -2>$, $\frac{1}{2}\hkl<-1 -1 -2>$,
+  \item $\frac{1}{2}\hkl<1 -1 -2>$, $\frac{1}{2}\hkl<-1 1 -2>$
+ \end{enumerate}
+ One of a kind\\
+ {\color{red}Two of a kind}\\
+ {\color{blue}Four of a kind}
+ \end{minipage}
+ \begin{minipage}{6cm}
+ \includegraphics[width=8cm]{c_100_next_neighbours_02.eps}
+ \begin{center}
+ \includegraphics[width=5cm]{c_100_res_bonds_vasp.ps}
+ \end{center}
+ \end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Combination of defects
+ }
+
+ \small
+
+ Initial C \hkl<0 0 -1> insterstital at: $\frac{1}{4}\hkl<1 1 1>$
+
+ {\footnotesize
+ \begin{tabular}{|l|l|l|l|l|l|}
+ \hline
+ & 2 & 3 & 4 & 5 & 6 \\
+ \hline
+C \hkl<0 0 -1> & 6.23/-0.08 & 5.16/-1.15 & 6.23/-0.08 & 6.35/0.04 & 4.65/-1.66\\
+ \hline
+C \hkl<0 0 1> & 6.64/0.34 & 6.31/0.01 & 4.26/-2.05 & 6.57/0.26 & 4.78/-1.53 \\
+ \hline
+C \hkl<1 0 0> & 4.06/-2.25 & 6.13/-0.17 & 6.21/-0.10 & 6.03/-0.27 & 4.93/-1.38 \\
+ \hline
+C \hkl<-1 0 0> & \hkl<0 -1 0> & 4.41/-1.90 & 4.06/-2.25 & 6.19/-0.12 & 4.43/-1.88 \\
+ \hline
+C \hkl<0 1 0> & \hkl<1 0 0> & 5.95/-0.36 & \hkl<-1 0 0> & \hkl<-1 0 0> & \hkl<1 0 0> \\
+ \hline
+C \hkl<0 -1 0> & 3.92/-2.39 & 4.15/-2.16 & \hkl<1 0 0> & \hkl<1 0 0> & \hkl <-1 0 0> \\
+ \hline
+Vacancy & 1.39/-5.39 ($\rightarrow\text{ C}_{\text{S}}$) & 6.19/-0.59 & 3.65/-3.14 & 6.24/-0.54 & 6.50/-0.50 \\
+ \hline
+C$_{\text{sub}}$ & 4.80/0.26 & 4.03/-0.51 & 3.62/-0.93 & 4.39/-0.15 & 5.03/0.49 \\
+\hline
+ \end{tabular}\\[0.2cm]
+ }
+
+ \begin{minipage}{8cm}
+ Energies: $x/y$\\
+ $x$: Defect formation energy of the complex\\
+ $y$:
+  $E_{\text{f}}^{\text{defect combination}}-
+   E_{\text{f}}^{\text{isolated C \hkl<0 0 -1>}}-
+   E_{\text{f}}^{\text{isolated 2nd defect}}
+  $\\[0.3cm]
+  {\color{blue}
+  If $y<0$ $\rightarrow$ favored compared to far-off isolated defects
+  }
+ \end{minipage}
+ \begin{minipage}{4.5cm}
+ \includegraphics[width=5.0cm]{00-1dc/energy.ps}
+ \end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Combination of defects
+ }
+
+ \small
+
+ {\color{blue}
+ For defect position 3 and 5 (image 2 and 4) the unit cell is translated by
+ $\frac{a}{2} \hkl<0 -1 -1>$
+ }
+
+ Type of second defect: \hkl<0 0 -1>
+
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/00-1_1.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/00-1_3.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/00-1_4.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/00-1_5.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/00-1_6.eps}
+ \end{minipage}
+
+ \includegraphics[width=5.0cm]{00-1dc/energy_00x.ps}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Combination of defects
+ }
+
+ \small
+
+ {\color{blue}
+ For defect position 3 and 5 (image 2 and 4) the unit cell is translated by
+ $\frac{a}{2} \hkl<0 -1 -1>$
+ }
+
+ Type of second defect: \hkl<0 0 1>
+
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/001_1.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/001_3.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/001_4.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/001_5.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/001_6.eps}
+ \end{minipage}
+
+ \includegraphics[width=5.0cm]{00-1dc/energy_001.ps}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Combination of defects
+ }
+
+ \small
+
+ {\color{blue}
+ For defect position 3 and 5 (image 2 and 4) the unit cell is translated by
+ $\frac{a}{2} \hkl<0 -1 -1>$
+ }
+
+ Type of second defect: \hkl<1 0 0> or equivalent one
+
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/100_1.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/100_3.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/100_4.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/100_5.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/100_6.eps}
+ \end{minipage}
+
+ \includegraphics[width=5.0cm]{00-1dc/energy_100.ps}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Combination of defects
+ }
+
+ \small
+
+ {\color{blue}
+ For defect position 3 and 5 (image 2 and 4) the unit cell is translated by
+ $\frac{a}{2} \hkl<0 -1 -1>$
+ }
+
+
+ Type of second defect: \hkl<-1 0 0> or equivalent one
+
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/0-10_1.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/-100_3.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/-100_4.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/-100_5.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/0-10_6.eps}
+ \end{minipage}
+
+ \includegraphics[width=5.0cm]{00-1dc/energy_x00.ps}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Combination of defects
+ }
+
+ \small
+
+ {\color{blue}
+ For defect position 3 and 5 (image 2 and 4) the unit cell is translated by
+ $\frac{a}{2} \hkl<0 -1 -1>$
+ }
+
+ Type of second defect: \hkl<0 1 0> or equivalent one
+
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/100_1.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/010_3.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/-100_4.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/-100_5.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/100_6.eps}
+ \end{minipage}
+
+ \includegraphics[width=5.0cm]{00-1dc/energy_010.ps}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Combination of defects
+ }
+
+ \small
+
+ {\color{blue}
+ For defect position 3 and 5 (image 2 and 4) the unit cell is translated by
+ $\frac{a}{2} \hkl<0 -1 -1>$
+ }
+
+
+ Type of second defect: \hkl<0 -1 0> or equivalent one
+
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/0-10_1.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/0-10_3.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/100_4.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/100_5.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/0-10_6.eps}
+ \end{minipage}
+
+ \includegraphics[width=5.0cm]{00-1dc/energy_0x0.ps}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Combination of defects
+ }
+
+ \small
+
+ {\color{blue}
+ For defect position 3 and 5 (image 2 and 4) the unit cell is translated by
+ $\frac{a}{2} \hkl<0 -1 -1>$
+ }
+
+ Type of second defect: Vacancy
+
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/vac_1.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/vac_3.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/vac_4.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/vac_5.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/vac_6.eps}
+ \end{minipage}
+
+ \includegraphics[width=5.0cm]{00-1dc/energy_vac.ps}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Combination of defects
+ }
+
+ \small
+
+ {\color{blue}
+ For defect position 3 and 5 (image 2 and 4) the unit cell is translated by
+ $\frac{a}{2} \hkl<0 -1 -1>$
+ }
+
+ Type of second defect: C$_{\text{sub}}$
+
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/csub_1.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/csub_3.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/csub_4.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/csub_5.eps}
+ \end{minipage}
+ \begin{minipage}{2.5cm}
+ \includegraphics[width=2.5cm]{00-1dc/csub_6.eps}
+ \end{minipage}
+
+ \includegraphics[width=5.0cm]{00-1dc/energy_csub.ps}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Brainstorming: Point defects in Si (as grown and as implanted)
+ }
+
+ \small
+
+ Supercell size: $2$ -- $2000 \cdot 10^{-21}\text{ cm}^3$
+
+ \underline{After crystal growth}
+ \begin{itemize}
+  \item Si point defects at $450\, ^{\circ}\text{C}$
+        \begin{itemize}
+         \item Interstitials:
+         \item Vacancies: 
+        \end{itemize}
+  \item C impurities: $10^{17}\text{ cm}^{-3}$\\
+        $\Rightarrow$ $10^{-4}$ -- $10^{-1}$ per sc
+        $\rightarrow$ neglected in simulations
+ \end{itemize}
+
+ \underline{After/during implantation}
+ \begin{itemize}
+  \item Si point defects\\
+        $E_{\text{d}}^{\text{av}}=35\text{ eV}$,
+        $D_{\text{imp}}=1\text{ -- }4 \cdot 10^{17}\text{ cm }^{-2}$,
+        $d_{\text{sc}}=3\text{ -- }30\cdot 4.38\text { \AA}$,
+        $A=(3\text{ -- }30\text{ \AA})^2$,\\
+        Amount of collisions with $\Delta E > E_{\text{d}}$
+        in depth region $[h,h+d_{\text{sc}}]$: $n=$ .. (SRIM)\\
+        $\Rightarrow N_{\text{FP}}=nAD$
+  \item C point defects
+        \begin{itemize}
+         \item Substitutional C: ...
+         \item Intesrtitial C: ...
+        \end{itemize}
+ \end{itemize}
+ 
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Reminder (just for me to keep in mind ...)
+ }
+
+ \small
+
+ \underline{Volume of the MD cell}
+ \begin{itemize}
+  \item $T=450, 900, 1400\text{ K}$ - (no melting, N\underline{V}T!)
+  \item $\alpha=2.0 \cdot 10^{-6}\text{ K}^{-1}$
+  \item $a = a_0(1+\alpha \Delta T)$
+  \item Plain Si$(T=0)$: $a_0=5.4575\text{ \AA}$
+        $\rightarrow a(900\text{ K})=5.4674\text{ \AA}$
+  \item C \hkl<1 0 0> in Si$(T=0)$: $a_0^{\text{avg}}=
+        \frac{1}{3}(a_0^x+a_0^y+a_0^z)=5.4605\text{ \AA}$
+        $\rightarrow a(900\text{ K})=5.4704{ \AA}$
+ \end{itemize}
+ Used in first 900 K simulations: 5.4705 \AA\\
+ BUT: Better use plain Si lattice constant! (only local distortions)\\
+ $\Rightarrow a(1400\text{ K})=5.4728\text{ \AA}$
+
+ \underline{Zero total momentum simulations}
+ \begin{itemize}
+  \item If C is randomly inserted there is a net total momentum
+  \item No correction in the temperature control routine of VASP?
+  \item Relax a Si:C configuration first
+        (at T=0, no volume relaxation, scaled volume)
+  \item Use this configuration as the MD initial configuration
+ \end{itemize}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Molecular dynamics simulations (VASP)
+ }
+
+ 2 C atoms in $2\times 2\times 2$ Type 2 supercell at $450\,^{\circ}\text{C}$
+
+ \small
+
+ \begin{minipage}{7.6cm}
+ Radial distribution\\
+ \includegraphics[width=7.6cm]{md_02c_2222si_pc.ps}
+ \end{minipage}
+ \begin{minipage}{5.0cm}
+ \begin{center}
+ PC average from\\
+ $t_1=50$ ps to $t_2=50.93$ ps
+ \end{center}
+ \end{minipage}
+ Diffusion:
+ \begin{itemize}
+  \item $<(x(t)-x(0))^2>$ hard to determine due to missing info of
+        boundary crossings
+  \item No jumps recognized in the
+ Video \href{../video/md_02c_2222si_vasp.avi}{$\rhd_{\text{local}}$ } $|$
+ \href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/md_02c_2222si_vasp.avi}{$\rhd_{\text{remote url}}$}
+ \end{itemize}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Molecular dynamics simulations (VASP)
+ }
+
+ 10 C atoms in $3\times 3\times 3$ Type 2 supercell at $450\,^{\circ}\text{C}$
+
+ \small
+
+ \begin{minipage}{7.2cm}
+ Radial distribution (PC averaged over 1 ps)\\
+ \includegraphics[width=7.0cm]{md_10c_2333si_pc_vasp.ps}
+ \end{minipage}
+ \begin{minipage}{5.0cm}
+ \includegraphics[width=6.0cm]{md_10c_2333si_pcc_vasp.ps}
+ \end{minipage}
+ Diffusion:
+ (Video \href{../video/md_10c_2333si_vasp.avi}{$\rhd_{\text{local}}$ } $|$
+ \href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/md_10c_2333si_vasp.avi}{$\rhd_{\text{remote url}}$})
+ \begin{itemize}
+  \item $<(x(t)-x(0))^2>$ hard to determine due to missing info of
+        boundary crossings
+  \item Agglomeration of C? (Video)
+ \end{itemize}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Molecular dynamics simulations (VASP)
+ }
+
+ 1 C atom in $3\times 3\times 3$ Type 2 supercell at $900\,^{\circ}\text{C}$\\\\
+
+ Video \href{../video/md_01c_2333si_900_vasp.avi}{$\rhd_{\text{local}}$ } $|$
+ \href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/md_01c_2333si_900_vasp.avi}{$\rhd_{\text{remote url}}$}\\\\
+
+ \begin{itemize}
+ \item Inserted C becomes a \hkl<0 0 1> interstitial after a few femto-seconds
+ \item  {\color{red}There is a non-zero total momentum!}
+ \item Migration of the C atom not observed
+ \item C \hkl<0 0 1> configuration persists
+ \end{itemize}
+
+ Problem: Thermostat doesn't do momentum correction
+
+ TODO: Start MD using relaxed (at zero temperature) initial configuration
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Molecular dynamics simulations (VASP)
+ }
+
+ 10 C atoms in $3\times 3\times 3$ Type 2 supercell at $900\,^{\circ}\text{C}$
+
+ in progress ...
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Density Functional Theory
+ }
+
+ Hohenberg-Kohn theorem
+
+ \small
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  More theory ...
+ }
+
+ Transition state theory\\
+ ART,NEB ...
+
+ Group theory
+
+ \small
+
+\end{slide}
+
+\end{document}
 \end{document}