X-Git-Url: https://hackdaworld.org/gitweb/?a=blobdiff_plain;f=posic%2Ftalks%2Fseminar_2010.tex;h=19a85785ea2318bffa0163102972107455962c2b;hb=0bfdf7eadfe8ca644895e758f5ba0bab4e04dba9;hp=58369fab1c5fee4dc78b2bd011e7b56cbddb7798;hpb=f9465130d3e796c6cf3a381b62285c281704b7ab;p=lectures%2Flatex.git

diff --git a/posic/talks/seminar_2010.tex b/posic/talks/seminar_2010.tex
index 58369fa..19a8578 100644
--- a/posic/talks/seminar_2010.tex
+++ b/posic/talks/seminar_2010.tex
@@ -1,5 +1,5 @@
 \pdfoutput=0
-\documentclass[landscape,semhelv]{seminar}
+\documentclass[landscape,semhelv,draft]{seminar}
 
 \usepackage{verbatim}
 \usepackage[greek,german]{babel}
@@ -71,6 +71,9 @@
 % itemize level ii
 \renewcommand\labelitemii{{\color{gray}$\bullet$}}
 
+% nice phi
+\renewcommand{\phi}{\varphi}
+
 % colors
 \newrgbcolor{si-yellow}{.6 .6 0}
 \newrgbcolor{hb}{0.75 0.77 0.89}
@@ -342,6 +345,7 @@ Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
   XTEM micrograph of single crystalline 3C-SiC in Si\hkl(1 0 0)
  }
  \end{minipage}
+\framebox{
  \begin{minipage}{6.3cm}
  \begin{center}
  {\color{blue}
@@ -356,6 +360,7 @@ Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
  \end{itemize}
  \end{center}
  \end{minipage}
+}
  
 \end{slide}
 
@@ -439,7 +444,7 @@ Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
 \begin{slide}
 
  {\large\bf
-  Basics of molecular dynamics (MD) simulations
+  Molecular dynamics (MD) simulations
  }
 
  \vspace{12pt}
@@ -465,7 +470,7 @@ Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
                $\tau_{\text{P}}=100\text{ fs}$,
                $\beta^{-1}=100\text{ GPa}$
         \end{itemize}
-  \item Potential: Tersoff-like bond order potential
+  \item Erhart/Albe potential: Tersoff-like bond order potential
   \vspace*{12pt}
         \[
         E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
@@ -482,33 +487,1000 @@ Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
 \begin{slide}
 
  {\large\bf
-  Basics of density functional theory (DFT) calculations
+  Density functional theory (DFT) calculations
  }
 
  \small
 
- Ingredients
+ Basic ingredients necessary for DFT
+
  \begin{itemize}
-  \item Hohenberg-Kohn (HK) theorem
+  \item \underline{Hohenberg-Kohn theorem} - ground state density $n_0(r)$ ...
+        \begin{itemize}
+         \item ... uniquely determines the ground state potential
+               / wavefunctions
+         \item ... minimizes the systems total energy
+        \end{itemize}
   \item \underline{Born-Oppenheimer}
-        - $N$ moving electrons in an external potential of static nuclei\\
+        - $N$ moving electrons in an external potential of static nuclei
 \[
 H\Psi = \left[-\sum_i^N \frac{\hbar^2}{2m}\nabla_i^2
               +\sum_i^N V_{\text{ext}}(r_i)
               +\sum_{i<j}^N V_{e-e}(r_i,r_j)\right]\Psi=E\Psi
 \]
   \item \underline{Effective potential}
-        - replace electrostatic potential by an average over e$^-$ positions\\
+        - averaged electrostatic potential \& exchange and correlation
 \[
-V_{\text{eff}}=...
+V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
+                 +V_{\text{XC}}[n(r)]
 \]
-  \item Exchange correlation (EC) LDA / GGA
-  \item Self-consistent solution
-  \item Plane wave basis set
-  \item Pseudo potential
+  \item \underline{Kohn-Sham system}
+        - Schr\"odinger equation of N non-interacting particles
+\[
+\left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) \right] \Phi_i(r)
+=\epsilon_i\Phi_i(r)
+\quad
+\Rightarrow
+\quad
+n(r)=\sum_i^N|\Phi_i(r)|^2
+\]
+  \item \underline{Self-consistent solution}\\
+$n(r)$ depends on $\Phi_i$, which depends on $V_{\text{eff}}$,
+which in turn depends on $n(r)$
+  \item \underline{Variational principle}
+        - minimize total energy with respect to $n(r)$
  \end{itemize}
 
 \end{slide}
 
+\begin{slide}
+
+ {\large\bf
+  Density functional theory (DFT) calculations
+ }
+
+ \small
+
+ \vspace*{0.2cm}
+
+ Details of applied DFT calculations in this work
+
+ \begin{itemize}
+  \item \underline{Exchange correlation functional}
+        - approximations for the inhomogeneous electron gas
+        \begin{itemize}
+         \item LDA: $E_{\text{XC}}^{\text{LDA}}[n]=\int \epsilon_{\text{XC}}(n)n(r)d^3r$
+         \item GGA: $E_{\text{XC}}^{\text{GGA}}[n]=\int \epsilon_{\text{XC}}(n,\nabla n)n(r)d^3r$
+        \end{itemize}
+  \item \underline{Plane wave basis set}
+        - approximation of the wavefunction $\Phi_i$ by plane waves $\phi_j$
+\[
+\rightarrow
+\text{Fourier series: } \Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_j^i \phi_j(r), \quad E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}
+\]
+  \item \underline{$k$-point sampling} - $\Gamma$-point only calculations
+  \item \underline{Pseudo potential} 
+        - consider only the valence electrons
+  \item \underline{Code} - VASP 4.6
+ \end{itemize}
+
+ \vspace*{0.2cm}
+
+ MD and structural optimization
+
+ \begin{itemize}
+  \item MD integration: Gear predictor corrector algorithm
+  \item Pressure control: Parrinello-Rahman pressure control
+  \item Structural optimization: Conjugate gradient method
+ \end{itemize}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  C and Si self-interstitial point defects in silicon
+ }
+
+ \small
+
+ \vspace*{0.3cm}
+
+\begin{minipage}{8cm}
+Procedure:\\[0.3cm]
+  \begin{pspicture}(0,0)(7,5)
+  \rput(3.5,4){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
+   \parbox{7cm}{
+   \begin{itemize}
+    \item Creation of c-Si simulation volume
+    \item Periodic boundary conditions
+    \item $T=0\text{ K}$, $p=0\text{ bar}$
+   \end{itemize}
+  }}}}
+\rput(3.5,2.1){\rnode{insert}{\psframebox{
+ \parbox{7cm}{
+  \begin{center}
+  Insertion of interstitial C/Si atoms
+  \end{center}
+  }}}}
+  \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
+   \parbox{7cm}{
+   \begin{center}
+   Relaxation / structural energy minimization
+   \end{center}
+  }}}}
+  \ncline[]{->}{init}{insert}
+  \ncline[]{->}{insert}{cool}
+ \end{pspicture}
+\end{minipage}
+\begin{minipage}{5cm}
+  \includegraphics[width=5cm]{unit_cell_e.eps}\\
+\end{minipage}
+
+\begin{minipage}{9cm}
+ \begin{tabular}{l c c}
+ \hline
+ & size [unit cells] & \# atoms\\
+\hline
+VASP & $3\times 3\times 3$ & $216\pm 1$ \\
+Erhart/Albe & $9\times 9\times 9$ & $5832\pm 1$\\
+\hline
+ \end{tabular}
+\end{minipage}
+\begin{minipage}{4cm}
+{\color{red}$\bullet$} Tetrahedral\\
+{\color{green}$\bullet$} Hexagonal\\
+{\color{yellow}$\bullet$} \hkl<1 0 0> dumbbell\\
+{\color{magenta}$\bullet$} \hkl<1 1 0> dumbbell\\
+{\color{cyan}$\bullet$} Bond-centered\\
+{\color{black}$\bullet$} Vacancy / Substitutional
+\end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ \footnotesize
+
+\begin{minipage}{9.5cm}
+
+ {\large\bf
+  Si self-interstitial point defects in silicon\\
+ }
+
+\begin{tabular}{l c c c c c}
+\hline
+ $E_{\text{f}}$ [eV] & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\
+\hline
+ VASP & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\
+ Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\
+\hline
+\end{tabular}\\[0.2cm]
+
+\begin{minipage}{4.7cm}
+\includegraphics[width=4.7cm]{e_kin_si_hex.ps}
+\end{minipage}
+\begin{minipage}{4.7cm}
+\begin{center}
+{\tiny nearly T $\rightarrow$ T}\\
+\end{center}
+\includegraphics[width=4.7cm]{nhex_tet.ps}
+\end{minipage}\\
+
+\underline{Hexagonal} \hspace{2pt}
+\href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm]
+\framebox{
+\begin{minipage}{2.7cm}
+$E_{\text{f}}^*=4.48\text{ eV}$\\
+\includegraphics[width=2.7cm]{si_pd_albe/hex_a.eps}
+\end{minipage}
+\begin{minipage}{0.4cm}
+\begin{center}
+$\Rightarrow$
+\end{center}
+\end{minipage}
+\begin{minipage}{2.7cm}
+$E_{\text{f}}=3.96\text{ eV}$\\
+\includegraphics[width=2.8cm]{si_pd_albe/hex.eps}
+\end{minipage}
+}
+\begin{minipage}{2.9cm}
+\begin{flushright}
+\underline{Vacancy}\\
+\includegraphics[width=3.0cm]{si_pd_albe/vac.eps}
+\end{flushright}
+\end{minipage}
+
+\end{minipage}
+\begin{minipage}{3.5cm}
+
+\begin{flushright}
+\underline{\hkl<1 1 0> dumbbell}\\
+\includegraphics[width=3.0cm]{si_pd_albe/110.eps}\\
+\underline{Tetrahedral}\\
+\includegraphics[width=3.0cm]{si_pd_albe/tet.eps}\\
+\underline{\hkl<1 0 0> dumbbell}\\
+\includegraphics[width=3.0cm]{si_pd_albe/100.eps}
+\end{flushright}
+
+\end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+\footnotesize
+
+ {\large\bf
+  C interstitial point defects in silicon\\[-0.1cm]
+ }
+
+\begin{tabular}{l c c c c c c}
+\hline
+ $E_{\text{f}}$ & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B \\
+\hline
+ VASP & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 \\
+ Erhart/Albe MD & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & 0.75 & 5.59$^*$ \\
+\hline
+\end{tabular}\\[0.1cm]
+
+\framebox{
+\begin{minipage}{2.7cm}
+\underline{Hexagonal} \hspace{2pt}
+\href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
+$E_{\text{f}}^*=9.05\text{ eV}$\\
+\includegraphics[width=2.7cm]{c_pd_albe/hex.eps}
+\end{minipage}
+\begin{minipage}{0.4cm}
+\begin{center}
+$\Rightarrow$
+\end{center}
+\end{minipage}
+\begin{minipage}{2.7cm}
+\underline{\hkl<1 0 0>}\\
+$E_{\text{f}}=3.88\text{ eV}$\\
+\includegraphics[width=2.7cm]{c_pd_albe/100.eps}
+\end{minipage}
+}
+\begin{minipage}{2cm}
+\hfill
+\end{minipage}
+\begin{minipage}{3cm}
+\begin{flushright}
+\underline{Tetrahedral}\\
+\includegraphics[width=3.0cm]{c_pd_albe/tet.eps}
+\end{flushright}
+\end{minipage}
+
+\framebox{
+\begin{minipage}{2.7cm}
+\underline{Bond-centered}\\
+$E_{\text{f}}^*=5.59\text{ eV}$\\
+\includegraphics[width=2.7cm]{c_pd_albe/bc.eps}
+\end{minipage}
+\begin{minipage}{0.4cm}
+\begin{center}
+$\Rightarrow$
+\end{center}
+\end{minipage}
+\begin{minipage}{2.7cm}
+\underline{\hkl<1 1 0> dumbbell}\\
+$E_{\text{f}}=5.18\text{ eV}$\\
+\includegraphics[width=2.7cm]{c_pd_albe/110.eps}
+\end{minipage}
+}
+\begin{minipage}{2cm}
+\hfill
+\end{minipage}
+\begin{minipage}{3cm}
+\begin{flushright}
+\underline{Substitutional}\\
+\includegraphics[width=3.0cm]{c_pd_albe/sub.eps}
+\end{flushright}
+\end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+\footnotesize
+
+ {\large\bf\boldmath
+  C \hkl<1 0 0> dumbbell interstitial configuration\\
+ }
+
+{\tiny
+\begin{tabular}{l c c c c c c c c}
+\hline
+ Distances [nm] & $r(1C)$ & $r(2C)$ & $r(3C)$ & $r(12)$ & $r(13)$ & $r(34)$ & $r(23)$ & $r(25)$ \\
+\hline
+Erhart/Albe & 0.175 & 0.329 & 0.186 & 0.226 & 0.300 & 0.343 & 0.423 & 0.425 \\
+VASP & 0.174 & 0.341 & 0.182 & 0.229 & 0.286 & 0.347 & 0.422 & 0.417 \\
+\hline
+\end{tabular}\\[0.2cm]
+\begin{tabular}{l c c c c }
+\hline
+ Angles [$^{\circ}$] & $\theta_1$ & $\theta_2$ & $\theta_3$ & $\theta_4$ \\
+\hline
+Erhart/Albe & 140.2 & 109.9 & 134.4 & 112.8 \\
+VASP & 130.7 & 114.4 & 146.0 & 107.0 \\
+\hline
+\end{tabular}\\[0.2cm]
+\begin{tabular}{l c c c}
+\hline
+ Displacements [nm]& $a$ & $b$ & $|a|+|b|$ \\
+\hline
+Erhart/Albe & 0.084 & -0.091 & 0.175 \\
+VASP & 0.109 & -0.065 & 0.174 \\
+\hline
+\end{tabular}\\[0.6cm]
+}
+
+\begin{minipage}{3.0cm}
+\begin{center}
+\underline{Erhart/Albe}
+\includegraphics[width=3.0cm]{c_pd_albe/100_cmp.eps}
+\end{center}
+\end{minipage}
+\begin{minipage}{3.0cm}
+\begin{center}
+\underline{VASP}
+\includegraphics[width=3.0cm]{c_pd_vasp/100_cmp.eps}
+\end{center}
+\end{minipage}\\
+
+\begin{picture}(0,0)(-185,10)
+\includegraphics[width=6.8cm]{100-c-si-db_cmp.eps}
+\end{picture}
+\begin{picture}(0,0)(-280,-150)
+\includegraphics[width=3.3cm]{c_pd_vasp/eden.eps}
+\end{picture}
+
+\begin{pspicture}(0,0)(0,0)
+\psellipse[linecolor=green](5.18,5.92)(0.5,0.3)
+\psellipse[linecolor=red](3.45,5.92)(1.0,0.4)
+\psellipse[linecolor=blue](2.7,6.92)(0.9,0.2)
+\psellipse[linecolor=blue](4.65,6.92)(0.9,0.2)
+\end{pspicture}
+
+\end{slide}
+
+\begin{slide}
+
+\small
+
+\begin{minipage}{8.5cm}
+
+ {\large\bf
+  Bond-centered interstitial configuration\\[-0.1cm]
+ }
+
+\begin{minipage}{3.0cm}
+\includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\
+\end{minipage}
+\begin{minipage}{5.2cm}
+\begin{itemize}
+ \item Linear Si-C-Si bond
+ \item Si: one C \& 3 Si neighbours
+ \item Spin polarized calculations
+ \item No saddle point!\\
+       Real local minimum!
+\end{itemize}
+\end{minipage}
+
+\framebox{
+ \tiny
+ \begin{minipage}[t]{6.5cm}
+  \begin{minipage}[t]{1.2cm}
+  {\color{red}Si}\\
+  {\tiny sp$^3$}\\[0.8cm]
+  \underline{${\color{black}\uparrow}$}
+  \underline{${\color{black}\uparrow}$}
+  \underline{${\color{black}\uparrow}$}
+  \underline{${\color{red}\uparrow}$}\\
+  sp$^3$
+  \end{minipage}
+  \begin{minipage}[t]{1.4cm}
+  \begin{center}
+  {\color{red}M}{\color{blue}O}\\[0.8cm]
+  \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}\\[0.8cm]
+  \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{${\color{black}\uparrow}$}
+  \underline{${\color{black}\uparrow}$}
+  \underline{${\color{black}\uparrow}$}\\
+  sp$^3$
+  \end{flushright}
+  \end{minipage}
+ \end{minipage}
+}\\[0.1cm]
+
+\framebox{
+\begin{minipage}{4.5cm}
+\includegraphics[width=4cm]{c_100_mig_vasp/im_spin_diff.eps}
+\end{minipage}
+\begin{minipage}{3.5cm}
+{\color{gray}$\bullet$} Spin up\\
+{\color{green}$\bullet$} Spin down\\
+{\color{blue}$\bullet$} Resulting spin up\\
+{\color{yellow}$\bullet$} Si atoms\\
+{\color{red}$\bullet$} C atom
+\end{minipage}
+}
+
+\end{minipage}
+\begin{minipage}{4.2cm}
+\begin{flushright}
+\includegraphics[width=4.3cm]{c_pd_vasp/bc_2333_ksl.ps}\\
+{\color{green}$\Box$} {\tiny unoccupied}\\
+{\color{red}$\bullet$} {\tiny occupied}
+\end{flushright}
+\end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Migration of the C \hkl<1 0 0> dumbbell interstitial
+ }
+
+\scriptsize
+
+ {\small Investigated pathways}
+
+\begin{minipage}{8.5cm}
+\begin{minipage}{8.3cm}
+\underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 0 1>}\\
+\begin{minipage}{2.4cm}
+\includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
+\end{minipage}
+\begin{minipage}{0.4cm}
+$\rightarrow$
+\end{minipage}
+\begin{minipage}{2.4cm}
+\includegraphics[width=2.4cm]{c_pd_vasp/bc_2333.eps}
+\end{minipage}
+\begin{minipage}{0.4cm}
+$\rightarrow$
+\end{minipage}
+\begin{minipage}{2.4cm}
+\includegraphics[width=2.4cm]{c_pd_vasp/100_next_2333.eps}
+\end{minipage}
+\end{minipage}\\
+\begin{minipage}{8.3cm}
+\underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0>}\\
+\begin{minipage}{2.4cm}
+\includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
+\end{minipage}
+\begin{minipage}{0.4cm}
+$\rightarrow$
+\end{minipage}
+\begin{minipage}{2.4cm}
+\includegraphics[width=2.4cm]{c_pd_vasp/00-1-0-10_2333.eps}
+\end{minipage}
+\begin{minipage}{0.4cm}
+$\rightarrow$
+\end{minipage}
+\begin{minipage}{2.4cm}
+\includegraphics[width=2.4cm]{c_pd_vasp/0-10_2333.eps}
+\end{minipage}
+\end{minipage}\\
+\begin{minipage}{8.3cm}
+\underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0> (in place)}\\
+\begin{minipage}{2.4cm}
+\includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
+\end{minipage}
+\begin{minipage}{0.4cm}
+$\rightarrow$
+\end{minipage}
+\begin{minipage}{2.4cm}
+\includegraphics[width=2.4cm]{c_pd_vasp/00-1_ip0-10_2333.eps}
+\end{minipage}
+\begin{minipage}{0.4cm}
+$\rightarrow$
+\end{minipage}
+\begin{minipage}{2.4cm}
+\includegraphics[width=2.4cm]{c_pd_vasp/0-10_ip_2333.eps}
+\end{minipage}
+\end{minipage}
+\end{minipage}
+\framebox{
+\begin{minipage}{4.2cm}
+ {\small Constrained relaxation\\
+         technique (CRT) method}\\
+\includegraphics[width=4cm]{crt_orig.eps}
+\begin{itemize}
+ \item Constrain diffusing atom
+ \item Static constraints 
+\end{itemize}
+\vspace*{0.3cm}
+ {\small Modifications}\\
+\includegraphics[width=4cm]{crt_mod.eps}
+\begin{itemize}
+ \item Constrain all atoms
+ \item Update individual\\
+       constraints
+\end{itemize}
+\end{minipage}
+}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Migration of the C \hkl<1 0 0> dumbbell interstitial
+ }
+
+\scriptsize
+
+\framebox{
+\begin{minipage}{5.9cm}
+\begin{flushleft}
+\includegraphics[width=5.8cm]{im_00-1_nosym_sp_fullct_thesis.ps}\\[0.45cm]
+\end{flushleft}
+\begin{center}
+\begin{picture}(0,0)(60,0)
+\includegraphics[width=1cm]{vasp_mig/00-1.eps}
+\end{picture}
+\begin{picture}(0,0)(-5,0)
+\includegraphics[width=1cm]{vasp_mig/bc_00-1_sp.eps}
+\end{picture}
+\begin{picture}(0,0)(-55,0)
+\includegraphics[width=1cm]{vasp_mig/bc.eps}
+\end{picture}
+\begin{picture}(0,0)(12.5,10)
+\includegraphics[width=1cm]{110_arrow.eps}
+\end{picture}
+\begin{picture}(0,0)(90,0)
+\includegraphics[height=0.9cm]{001_arrow.eps}
+\end{picture}
+\end{center}
+\vspace*{0.35cm}
+\end{minipage}
+}
+\begin{minipage}{0.3cm}
+\hfill
+\end{minipage}
+\framebox{
+\begin{minipage}{5.9cm}
+\begin{flushright}
+\includegraphics[width=5.9cm]{vasp_mig/00-1_0-10_nosym_sp_fullct.ps}\\[0.5cm]
+\end{flushright}
+\begin{center}
+\begin{picture}(0,0)(60,0)
+\includegraphics[width=1cm]{vasp_mig/00-1_a.eps}
+\end{picture}
+\begin{picture}(0,0)(5,0)
+\includegraphics[width=1cm]{vasp_mig/00-1_0-10_sp.eps}
+\end{picture}
+\begin{picture}(0,0)(-55,0)
+\includegraphics[width=1cm]{vasp_mig/0-10.eps}
+\end{picture}
+\begin{picture}(0,0)(12.5,10)
+\includegraphics[width=1cm]{100_arrow.eps}
+\end{picture}
+\begin{picture}(0,0)(90,0)
+\includegraphics[height=0.9cm]{001_arrow.eps}
+\end{picture}
+\end{center}
+\vspace*{0.3cm}
+\end{minipage}\\
+}
+
+\vspace*{0.05cm}
+
+\framebox{
+\begin{minipage}{5.9cm}
+\begin{flushleft}
+\includegraphics[width=5.9cm]{vasp_mig/00-1_ip0-10_nosym_sp_fullct.ps}\\[0.6cm]
+\end{flushleft}
+\begin{center}
+\begin{picture}(0,0)(60,0)
+\includegraphics[width=0.9cm]{vasp_mig/00-1_b.eps}
+\end{picture}
+\begin{picture}(0,0)(10,0)
+\includegraphics[width=0.9cm]{vasp_mig/00-1_ip0-10_sp.eps}
+\end{picture}
+\begin{picture}(0,0)(-60,0)
+\includegraphics[width=0.9cm]{vasp_mig/0-10_b.eps}
+\end{picture}
+\begin{picture}(0,0)(12.5,10)
+\includegraphics[width=1cm]{100_arrow.eps}
+\end{picture}
+\begin{picture}(0,0)(90,0)
+\includegraphics[height=0.9cm]{001_arrow.eps}
+\end{picture}
+\end{center}
+\vspace*{0.3cm}
+\end{minipage}
+}
+\begin{minipage}{0.3cm}
+\hfill
+\end{minipage}
+\begin{minipage}{6.5cm}
+VASP results
+\begin{itemize}
+ \item Energetically most favorable path
+       \begin{itemize}
+        \item Path 2
+        \item Activation energy: $\approx$ 0.9 eV 
+        \item Experimental values: 0.73 ... 0.87 eV
+       \end{itemize}
+       $\Rightarrow$ {\color{blue}Diffusion} path identified!
+ \item Reorientation (path 3)
+       \begin{itemize}
+        \item More likely composed of two consecutive steps of type 2
+        \item Experimental values: 0.77 ... 0.88 eV
+       \end{itemize}
+       $\Rightarrow$ {\color{blue}Reorientation} transition identified!
+\end{itemize}
+\end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Migration of the C \hkl<1 0 0> dumbbell interstitial
+ }
+
+\scriptsize
+
+\begin{minipage}{6.5cm}
+
+\framebox{
+\begin{minipage}{5.9cm}
+\begin{flushleft}
+\includegraphics[width=5.9cm]{bc_00-1.ps}\\[2.35cm]
+\end{flushleft}
+\begin{center}
+\begin{pspicture}(0,0)(0,0)
+\psframe[linecolor=red,fillstyle=none](-2.8,1.35)(3.3,2.7)
+\end{pspicture}
+\begin{picture}(0,0)(60,-50)
+\includegraphics[width=1cm]{albe_mig/bc_00-1_red_00.eps}
+\end{picture}
+\begin{picture}(0,0)(5,-50)
+\includegraphics[width=1cm]{albe_mig/bc_00-1_red_01.eps}
+\end{picture}
+\begin{picture}(0,0)(-55,-50)
+\includegraphics[width=1cm]{albe_mig/bc_00-1_red_02.eps}
+\end{picture}
+\begin{picture}(0,0)(12.5,-40)
+\includegraphics[width=1cm]{110_arrow.eps}
+\end{picture}
+\begin{picture}(0,0)(90,-45)
+\includegraphics[height=0.9cm]{001_arrow.eps}
+\end{picture}\\
+\begin{pspicture}(0,0)(0,0)
+\psframe[linecolor=blue,fillstyle=none](-2.8,0)(3.3,1.6)
+\end{pspicture}
+\begin{picture}(0,0)(60,-15)
+\includegraphics[width=0.9cm]{albe_mig/bc_00-1_01.eps}
+\end{picture}
+\begin{picture}(0,0)(35,-15)
+\includegraphics[width=0.9cm]{albe_mig/bc_00-1_02.eps}
+\end{picture}
+\begin{picture}(0,0)(-5,-15)
+\includegraphics[width=0.9cm]{albe_mig/bc_00-1_03.eps}
+\end{picture}
+\begin{picture}(0,0)(-55,-15)
+\includegraphics[width=0.9cm]{albe_mig/bc_00-1_04.eps}
+\end{picture}
+\begin{picture}(0,0)(12.5,-5)
+\includegraphics[width=1cm]{100_arrow.eps}
+\end{picture}
+\begin{picture}(0,0)(90,-15)
+\includegraphics[height=0.9cm]{010_arrow.eps}
+\end{picture}
+\end{center}
+\end{minipage}
+}\\[0.1cm]
+
+\begin{minipage}{5.9cm}
+Erhart/Albe results
+\begin{itemize}
+ \item Lowest activation energy: $\approx$ 2.2 eV
+ \item 2.4 times higher than VASP
+ \item Different pathway
+ \item Transition minima ($\rightarrow$ \hkl<1 1 0> dumbbell)
+\end{itemize}
+\end{minipage}
+
+\end{minipage}
+\begin{minipage}{6.5cm}
+
+\framebox{
+\begin{minipage}{5.9cm}
+\begin{flushright}
+\includegraphics[width=5.9cm]{00-1_0-10.ps}\\[0.75cm]
+\end{flushright}
+\begin{center}
+\begin{pspicture}(0,0)(0,0)
+\psframe[linecolor=red,fillstyle=none](-2.8,-0.25)(3.3,1.1)
+\end{pspicture}
+\begin{picture}(0,0)(60,-5)
+\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_00.eps}
+\end{picture}
+\begin{picture}(0,0)(0,-5)
+\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_min.eps}
+\end{picture}
+\begin{picture}(0,0)(-55,-5)
+\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_03.eps}
+\end{picture}
+\begin{picture}(0,0)(12.5,5)
+\includegraphics[width=1cm]{100_arrow.eps}
+\end{picture}
+\begin{picture}(0,0)(90,0)
+\includegraphics[height=0.9cm]{001_arrow.eps}
+\end{picture}
+\end{center}
+\vspace{0.2cm}
+\end{minipage}
+}\\[0.2cm]
+
+\framebox{
+\begin{minipage}{5.9cm}
+\includegraphics[width=5.9cm]{00-1_ip0-10.ps}
+\end{minipage}
+}
+
+\end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Migrations involving the C \hkl<1 1 0> dumbbell interstitial
+ }
+
+\small
+
+\vspace*{0.1cm}
+
+VASP
+
+\begin{minipage}{6.0cm}
+\includegraphics[width=6cm]{vasp_mig/110_mig_vasp.ps}
+\end{minipage}
+\begin{minipage}{7cm}
+\underline{Alternative pathway and energies [eV]}\\[0.1cm]
+\hkl<0 -1 0> $\stackrel{0.7}{{\color{red}\longrightarrow}}$
+\hkl<1 1 0> $\stackrel{0.95}{{\color{blue}\longrightarrow}}$
+BC $\stackrel{0.25}{\longrightarrow}$ \hkl<0 0 -1>\\[0.3cm]
+Composed of three single transitions\\[0.3cm]
+Activation energy of second transition slightly\\
+higher than direct transition (path 2)\\[0.3cm]
+$\Rightarrow$ very unlikely to happen
+\end{minipage}\\[0.2cm]
+
+Erhart/Albe
+
+\begin{minipage}{6.0cm}
+\includegraphics[width=6cm]{110_mig.ps}
+\end{minipage}
+\begin{minipage}{7cm}
+\underline{Alternative pathway and energies [eV]}\\[0.1cm]
+\hkl<0 0 -1> $\stackrel{2.2}{{\color{green}\longrightarrow}}$
+\hkl<1 1 0> $\stackrel{0.9}{{\color{red}\longrightarrow}}$
+\hkl<0 0 -1>\\[0.3cm]
+Composed of two single transitions\\[0.3cm]
+Compared to direct transition: (2.2 eV \& 0.5 eV)\\[0.3cm]
+$\Rightarrow$ more readily constituting a probable transition
+\end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Combinations with a C-Si \hkl<1 0 0>-type interstitial
+ }
+
+\small
+
+\vspace*{0.1cm}
+
+Binding energy: 
+$
+E_{\text{b}}=
+E_{\text{f}}^{\text{defect combination}}-
+E_{\text{f}}^{\text{C \hkl<0 0 -1> dumbbell}}-
+E_{\text{f}}^{\text{2nd defect}}
+$
+
+\vspace*{0.1cm}
+
+{\scriptsize
+\begin{tabular}{l c c c c c c}
+\hline
+ $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
+ \hline
+ \hkl<0 0 -1> & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
+ \hkl<0 0 1> & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
+ \hkl<0 -1 0> & {\color{orange}-2.39} & -0.17 & {\color{green}-0.10} & {\color{blue}-0.27} & {\color{magenta}-1.88} & {\color{gray}-0.05}\\
+ \hkl<0 1 0> & {\color{cyan}-2.25} & -1.90 & {\color{cyan}-2.25} & {\color{purple}-0.12} & {\color{violet}-1.38} & {\color{yellow}-0.06}\\
+ \hkl<-1 0 0> & {\color{orange}-2.39} & -0.36 & {\color{cyan}-2.25} & {\color{purple}-0.12} & {\color{magenta}-1.88} & {\color{gray}-0.05}\\
+ \hkl<1 0 0> & {\color{cyan}-2.25} & -2.16 & {\color{green}-0.10} & {\color{blue}-0.27} & {\color{violet}-1.38} & {\color{yellow}-0.06}\\
+ \hline
+ C substitutional (C$_{\text{S}}$) & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
+ Vacancy & -5.39 ($\rightarrow$ C$_{\text{S}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
+\hline
+\end{tabular}
+}
+
+\vspace*{0.3cm}
+
+\footnotesize
+
+\begin{minipage}[t]{3.8cm}
+\underline{\hkl<1 0 0> at position 1}\\[0.1cm]
+\includegraphics[width=3.5cm]{00-1dc/2-25.eps}
+\end{minipage}
+\begin{minipage}[t]{3.5cm}
+\underline{\hkl<0 -1 0> at position 1}\\[0.1cm]
+\includegraphics[width=3.2cm]{00-1dc/2-39.eps}
+\end{minipage}
+\begin{minipage}[t]{5.5cm}
+\begin{itemize}
+ \item Restricted to VASP simulations
+ \item $E_{\text{b}}=0$ for isolated non-interacting defects
+ \item $E_{\text{b}} \rightarrow 0$ for increasing distance (R)
+ \item Stress compensation / increase
+ \item Most favorable: C clustering
+ \item Unfavored: antiparallel orientations
+ \item Indication of energetically favored\\
+       agglomeration
+\end{itemize}
+\end{minipage}
+
+\begin{picture}(0,0)(-295,-130)
+\includegraphics[width=3.5cm]{comb_pos.eps}
+\end{picture}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Combinations of C-Si \hkl<1 0 0>-type interstitials
+ }
+
+\small
+
+\vspace*{0.1cm}
+
+Energetically most favorable combinations along \hkl<1 1 0>
+
+{\scriptsize
+\begin{tabular}{l c c c c c c}
+\hline
+ & 1 & 2 & 3 & 4 & 5 & 6\\
+\hline
+$E_{\text{b}}$ [eV] & -2.39 & -1.88 & -0.59 & -0.31 & -0.24 & -0.21 \\
+C-C distance [\AA] & 1.4 & 4.6 & 6.5 & 8.6 & 10.5 & 10.8 \\
+Type & \hkl<-1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0>, \hkl<0 -1 0>\\
+\hline
+\end{tabular}
+}
+
+\vspace*{0.1cm}
+
+\begin{minipage}{7.0cm}
+\includegraphics[width=7cm,draft=false]{db_along_110_cc.ps}
+\end{minipage}
+\begin{minipage}{6.0cm}
+\begin{itemize}
+ \item Interaction proportional to reciprocal cube of C-C distance
+ \item 
+ \item 
+\end{itemize}
+\end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Combinations of substitutional C and \hkl<1 1 0> Si self-interstitials
+ }
+
+ \small
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Migration of combined defects
+ }
+
+ \small
+
+ present (describe) two starting confs, i.e. vac in c-Si
+
+ present migration results $\rightarrow$ SiC
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Silicon carbide precipitation simulations
+ }
+
+ \small
+ 
+ restricted to classical MD
+
+ explain procedure
+
+ then there is:
+
+ 1. temperature as in exps
+
+ 2. exkurs: limitations of conv...
+
+ 3. increased temp ... high and low
+
+ 4. temperature limit
+
+ 5. final TODO
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Silicon carbide precipitation simulations
+ }
+
+ \small
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Investigation of a silicon carbide precipitate in silicon
+ }
+
+ \small
+
+ 
+
+\end{slide}
 
 \end{document}