X-Git-Url: https://hackdaworld.org/gitweb/?p=lectures%2Flatex.git;a=blobdiff_plain;f=posic%2Ftalks%2Fmpi_app.tex;h=2bf8383fd95ba5a487e0f7f27062a15681b7daf9;hp=67a4d40b15a25922447fbab4d6eb5581e4812e48;hb=1c838933fa76951ad4deb1164e8d2a950b6771cf;hpb=d0ff895e76b30891a3fcd4b9a037eada196e9f95

diff --git a/posic/talks/mpi_app.tex b/posic/talks/mpi_app.tex
index 67a4d40..2bf8383 100644
--- a/posic/talks/mpi_app.tex
+++ b/posic/talks/mpi_app.tex
@@ -991,9 +991,6 @@ r = \unit[2--4]{nm}
 
 \end{slide}
 
-% continue here
-\fi
-
 \begin{slide}
 
 \headphd
@@ -1001,21 +998,18 @@ r = \unit[2--4]{nm}
  Utilized computational methods
 }
 
-\vspace{0.2cm}
+\vspace{0.3cm}
 
 \small
 
-{\bf Molecular dynamics (MD)}\\
+{\bf Molecular dynamics (MD)}\\[0.1cm]
 \scriptsize
-\begin{tabular}{p{4.5cm} p{7.5cm}}
-Basics & Details\\
+\begin{tabular}{| p{4.5cm} | p{7.5cm} |}
 \hline
 System of $N$ particles &
 $N=5832\pm 1$ (Defects), $N=238328+6000$ (Precipitation)\\
-\hline
 Phase space propagation &
 Velocity Verlet | timestep: \unit[1]{fs} \\
-\hline
 Analytical interaction potential &
 Tersoff-like {\color{red}short-range}, {\color{blue}bond order} potential
 (Erhart/Albe)
@@ -1024,7 +1018,6 @@ E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
     \pot_{ij} = {\color{red}f_C(r_{ij})}
     \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
 $\\
-\hline
 Observables: time/ensemble averages &
 NpT (isothermal-isobaric) | Berendsen thermostat/barostat\\
 \hline
@@ -1032,161 +1025,78 @@ NpT (isothermal-isobaric) | Berendsen thermostat/barostat\\
 
 \small
 
-\vspace{0.1cm}
+\vspace{0.3cm}
 
 {\bf Density functional theory (DFT)}
 
 \scriptsize
 
 \begin{minipage}[t]{6cm}
-\underline{Basics}
 \begin{itemize}
- \item Born-Oppenheimer approximation:\\
-       Decouple electronic \& ionic motion
  \item Hohenberg-Kohn theorem:\\
-       $n_0(r) \stackrel{\text{uniquely}}{\rightarrow}$
-       $V_0$ / $H$ / $\Phi_i$ / \underline{$E_0$}
+       $\Psi_0(r_1,r_2,\ldots,r_N)=\Psi[n_0(r)]$, $E_0=E[n_0]$
+ \item Kohn-Sham approach:\\
+       Single-particle effective theory
 \end{itemize}
-\underline{Details}
+\hrule
 \begin{itemize}
 \item Code: \textsc{vasp}
-\item Plane wave basis set $\{\phi_j\}$\\[0.1cm]
-$\displaystyle
-\Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_j^i \phi_j(r)
-$\\
-$\displaystyle
-E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}=\unit[300]{eV}
-$
+\item Plane wave basis set
+%$\displaystyle
+%\Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_{i,k+G} \exp{\left(i(k+G)r\right)}
+%$\\
+%$\displaystyle
+%E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}=\unit[300]{eV}
+%$
 \item Ultrasoft pseudopotential
+\item Exchange \& correlation: GGA
 \item Brillouin zone sampling: $\Gamma$-point
+\item Supercell: $N=216\pm2$
 \end{itemize}
 \end{minipage}
-\begin{minipage}[t]{6cm}
-
-\[
+\begin{minipage}{6cm}
+\begin{pspicture}(0,0)(0,0)
+\pscircle[fillcolor=yellow,fillstyle=solid,linestyle=none](3.5,-2.0){2.5}
+\rput(2.7,-0.7){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
+$\displaystyle
 \left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) - \epsilon_i \right] \Phi_i(r) = 0
-\]
-\[
+$
+}}
+\rput(5.2,-2.0){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
+$\displaystyle
 n(r)=\sum_i^N|\Phi_i(r)|^2
-\]
-\[
-V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
-                 +V_{\text{XC}}[n(r)]
-\]
-
-\end{minipage}
-
-\end{slide}
-
-\end{document}
-\ifnum1=0
-
-\begin{slide}
-
- \small
- {\large\bf
-  Density functional theory (DFT) calculations
- }
-
- Basic ingredients necessary for DFT
-
- \begin{itemize}
-  \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
-\[
-H\Psi = \left[-\sum_i^N \frac{\hbar^2}{2m}\nabla_i^2
-              +\sum_i^N V_{\text{ext}}(r_i)
-              +\sum_{i<j}^N V_{e-e}(r_i,r_j)\right]\Psi=E\Psi
-\]
-  \item \underline{Effective potential}
-        - averaged electrostatic potential \& exchange and correlation
-\[
+$
+}}
+\rput(3.0,-4.5){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
+$\displaystyle
 V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
                  +V_{\text{XC}}[n(r)]
-\]
-  \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 depend 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 $\phi_j$
-  \item \underline{Brillouin zone sampling} -
-        {\color{blue}$\Gamma$-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}
+$
+}}
+\psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{130}{15}
+\psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{230}{165}
+\psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{345}{310}
 
-\begin{pspicture}(0,0)(0,0)
-\psellipse[linecolor=blue](1.5,6.75)(0.5,0.3)
 \end{pspicture}
+\end{minipage}
 
 \end{slide}
 
 \begin{slide}
 
+\headphd
  {\large\bf
-  C and Si self-interstitial point defects in silicon
+  Point defects \& defect migration
  }
 
  \small
 
- \vspace*{0.3cm}
+ \vspace{0.2cm}
 
-\begin{minipage}{8cm}
-Procedure:\\[0.3cm]
-  \begin{pspicture}(0,0)(7,5)
-  \rput(3.5,4){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
+\begin{minipage}[b]{7.5cm}
+{\bf Defect structure}\\
+  \begin{pspicture}(0,0)(7,4.4)
+  \rput(3.5,3.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
    \parbox{7cm}{
    \begin{itemize}
     \item Creation of c-Si simulation volume
@@ -1194,13 +1104,13 @@ Procedure:\\[0.3cm]
     \item $T=0\text{ K}$, $p=0\text{ bar}$
    \end{itemize}
   }}}}
-\rput(3.5,2.1){\rnode{insert}{\psframebox{
+\rput(3.5,1.3){\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]{
+  \rput(3.5,0.2){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
    \parbox{7cm}{
    \begin{center}
    Relaxation / structural energy minimization
@@ -1210,58 +1120,104 @@ Procedure:\\[0.3cm]
   \ncline[]{->}{insert}{cool}
  \end{pspicture}
 \end{minipage}
-\begin{minipage}{5cm}
-  \includegraphics[width=5cm]{unit_cell_e.eps}\\
+\begin{minipage}[b]{4.5cm}
+\begin{center}
+\includegraphics[width=3.8cm]{unit_cell_e.eps}\\
+\end{center}
+\begin{minipage}{2.21cm}
+{\scriptsize
+{\color{red}$\bullet$} Tetrahedral\\[-0.1cm]
+{\color{green}$\bullet$} Hexagonal\\[-0.1cm]
+{\color{yellow}$\bullet$} \hkl<1 0 0> DB
+}
+\end{minipage}
+\begin{minipage}{2.21cm}
+{\scriptsize
+{\color{magenta}$\bullet$} \hkl<1 1 0> DB\\[-0.1cm]
+{\color{cyan}$\bullet$} Bond-centered\\[-0.1cm]
+{\color{black}$\bullet$} Vac. / Sub.
+}
+\end{minipage}
 \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}
+\vspace{0.2cm}
+
+\begin{minipage}[b]{6cm}
+{\bf Defect formation energy}\\
+\framebox{
+$E_{\text{f}}=E-\sum_i N_i\mu_i$}\\[0.1cm]
+Particle reservoir: Si \& SiC\\[0.2cm]
+{\bf Binding energy}\\
+\framebox{
+$
+E_{\text{b}}=
+E_{\text{f}}^{\text{comb}}-
+E_{\text{f}}^{1^{\text{st}}}-
+E_{\text{f}}^{2^{\text{nd}}}
+$
+}\\[0.1cm]
+\footnotesize
+$E_{\text{b}}<0$: energetically favorable configuration\\
+$E_{\text{b}}\rightarrow 0$: non-interacting, isolated defects\\
 \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
+\begin{minipage}[b]{6cm}
+{\bf Migration barrier}
+\footnotesize
+\begin{itemize}
+ \item Displace diffusing atom
+ \item Constrain relaxation of (diffusing) atoms
+ \item Record configurational energy
+\end{itemize}
+\begin{picture}(0,0)(-60,-33)
+\includegraphics[width=4.5cm]{crt_mod.eps}
+\end{picture}
 \end{minipage}
 
 \end{slide}
 
 \begin{slide}
 
- \footnotesize
-
-\begin{minipage}{9.5cm}
+\footnotesize
 
- {\large\bf
-  Si self-interstitial point defects in silicon\\
- }
+\headphd
+{\large\bf
+ Si self-interstitial point defects in silicon\\[0.1cm]
+}
 
+\begin{center}
 \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 \\
+ \textsc{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]
+\end{tabular}\\[0.4cm]
+\end{center}
 
-\begin{minipage}{4.7cm}
-\includegraphics[width=4.7cm]{e_kin_si_hex.ps}
+\begin{minipage}{3cm}
+\begin{center}
+\underline{Vacancy}\\
+\includegraphics[width=2.8cm]{si_pd_albe/vac.eps}
+\end{center}
+\end{minipage}
+\begin{minipage}{3cm}
+\begin{center}
+\underline{\hkl<1 1 0> DB}\\
+\includegraphics[width=2.8cm]{si_pd_albe/110_bonds.eps}
+\end{center}
 \end{minipage}
-\begin{minipage}{4.7cm}
+\begin{minipage}{3cm}
 \begin{center}
-{\tiny nearly T $\rightarrow$ T}\\
+\underline{\hkl<1 0 0> DB}\\
+\includegraphics[width=2.8cm]{si_pd_albe/100_bonds.eps}
+\end{center}
+\end{minipage}
+\begin{minipage}{3cm}
+\begin{center}
+\underline{Tetrahedral}\\
+\includegraphics[width=2.8cm]{si_pd_albe/tet_bonds.eps}
 \end{center}
-\includegraphics[width=4.7cm]{nhex_tet.ps}
 \end{minipage}\\
 
 \underline{Hexagonal} \hspace{2pt}
@@ -1269,7 +1225,7 @@ Erhart/Albe & $9\times 9\times 9$ & $5832\pm 1$\\
 \framebox{
 \begin{minipage}{2.7cm}
 $E_{\text{f}}^*=4.48\text{ eV}$\\
-\includegraphics[width=2.7cm]{si_pd_albe/hex_a.eps}
+\includegraphics[width=2.7cm]{si_pd_albe/hex_a_bonds.eps}
 \end{minipage}
 \begin{minipage}{0.4cm}
 \begin{center}
@@ -1278,28 +1234,14 @@ $\Rightarrow$
 \end{minipage}
 \begin{minipage}{2.7cm}
 $E_{\text{f}}=3.96\text{ eV}$\\
-\includegraphics[width=2.8cm]{si_pd_albe/hex.eps}
+\includegraphics[width=2.8cm]{si_pd_albe/hex_bonds.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}
-
+\begin{minipage}{5.5cm}
+\begin{center}
+{\tiny nearly T $\rightarrow$ T}\\
+\end{center}
+\includegraphics[width=6.0cm]{nhex_tet.ps}
 \end{minipage}
 
 \end{slide}
@@ -1308,71 +1250,73 @@ $E_{\text{f}}=3.96\text{ eV}$\\
 
 \footnotesize
 
- {\large\bf
-  C interstitial point defects in silicon\\[-0.1cm]
- }
+\headphd
+{\large\bf
+ C interstitial point defects in silicon\\
+}
 
 \begin{tabular}{l c c c c c c r}
 \hline
- $E_{\text{f}}$ & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B & \cs{} \& \si\\
+ $E_{\text{f}}$ [eV] & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B &
+ {\color{black} \cs{} \& \si}\\
 \hline
- VASP & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\
- Erhart/Albe MD & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & {\color{red}0.75} & 5.59$^*$ & {\color{green}4.43} \\
+ \textsc{vasp} & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\
+ Erhart/Albe & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & {\color{red}0.75} & 5.59$^*$ & {\color{green}4.43} \\
 \hline
 \end{tabular}\\[0.1cm]
 
 \framebox{
-\begin{minipage}{2.7cm}
+\begin{minipage}{2.8cm}
 \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}
+\includegraphics[width=2.8cm]{c_pd_albe/hex_bonds.eps}
 \end{minipage}
 \begin{minipage}{0.4cm}
 \begin{center}
 $\Rightarrow$
 \end{center}
 \end{minipage}
-\begin{minipage}{2.7cm}
+\begin{minipage}{2.8cm}
 \underline{\hkl<1 0 0>}\\
 $E_{\text{f}}=3.88\text{ eV}$\\
-\includegraphics[width=2.7cm]{c_pd_albe/100.eps}
+\includegraphics[width=2.8cm]{c_pd_albe/100_bonds.eps}
 \end{minipage}
 }
-\begin{minipage}{2cm}
+\begin{minipage}{1.4cm}
 \hfill
 \end{minipage}
-\begin{minipage}{3cm}
+\begin{minipage}{3.0cm}
 \begin{flushright}
 \underline{Tetrahedral}\\
-\includegraphics[width=3.0cm]{c_pd_albe/tet.eps}
+\includegraphics[width=3.0cm]{c_pd_albe/tet_bonds.eps}
 \end{flushright}
 \end{minipage}
 
 \framebox{
-\begin{minipage}{2.7cm}
+\begin{minipage}{2.8cm}
 \underline{Bond-centered}\\
 $E_{\text{f}}^*=5.59\text{ eV}$\\
-\includegraphics[width=2.7cm]{c_pd_albe/bc.eps}
+\includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}
 \end{minipage}
 \begin{minipage}{0.4cm}
 \begin{center}
 $\Rightarrow$
 \end{center}
 \end{minipage}
-\begin{minipage}{2.7cm}
+\begin{minipage}{2.8cm}
 \underline{\hkl<1 1 0> dumbbell}\\
 $E_{\text{f}}=5.18\text{ eV}$\\
-\includegraphics[width=2.7cm]{c_pd_albe/110.eps}
+\includegraphics[width=2.8cm]{c_pd_albe/110_bonds.eps}
 \end{minipage}
 }
-\begin{minipage}{2cm}
+\begin{minipage}{1.4cm}
 \hfill
 \end{minipage}
-\begin{minipage}{3cm}
+\begin{minipage}{3.0cm}
 \begin{flushright}
 \underline{Substitutional}\\
-\includegraphics[width=3.0cm]{c_pd_albe/sub.eps}
+\includegraphics[width=3.0cm]{c_pd_albe/sub_bonds.eps}
 \end{flushright}
 \end{minipage}
 
@@ -1380,82 +1324,46 @@ $E_{\text{f}}=5.18\text{ eV}$\\
 
 \begin{slide}
 
-\footnotesize
+\headphd
+{\large\bf\boldmath
+ C-Si dimer \& bond-centered interstitial configuration
+}
 
- {\large\bf\boldmath
-  C \hkl<1 0 0> dumbbell interstitial configuration\\
- }
+\footnotesize
 
-{\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]
-}
+\vspace{0.1cm}
 
-\begin{minipage}{3.0cm}
+\begin{minipage}[t]{4.1cm}
+{\bf\boldmath C \hkl<1 0 0> DB interstitial}\\[0.1cm]
+\begin{minipage}{2.0cm}
 \begin{center}
 \underline{Erhart/Albe}
-\includegraphics[width=3.0cm]{c_pd_albe/100_cmp.eps}
+\includegraphics[width=2.0cm]{c_pd_albe/100_cmp.eps}
 \end{center}
 \end{minipage}
-\begin{minipage}{3.0cm}
+\begin{minipage}{2.0cm}
 \begin{center}
-\underline{VASP}
-\includegraphics[width=3.0cm]{c_pd_vasp/100_cmp.eps}
+\underline{\textsc{vasp}}
+\includegraphics[width=2.0cm]{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}\\[0.2cm]
+Si-C-Si bond angle $\rightarrow$ \unit[180]{$^{\circ}$}\\
+$\Rightarrow$ $sp$ hybridization\\[0.1cm]
+Si-Si-Si bond angle $\rightarrow$ \unit[120]{$^{\circ}$}\\
+$\Rightarrow$ $sp^2$ hybridization
+\begin{center}
+\includegraphics[width=3.4cm]{c_pd_vasp/eden.eps}\\[-0.1cm]
+{\tiny Charge density isosurface}
+\end{center}
+\end{minipage}
+\begin{minipage}{0.2cm}
+\hfill
 \end{minipage}
-\begin{minipage}{5.2cm}
+\begin{minipage}[t]{8.1cm}
+\begin{flushright}
+{\bf Bond-centered interstitial}\\[0.1cm]
+\begin{minipage}{4.4cm}
+%\scriptsize
 \begin{itemize}
  \item Linear Si-C-Si bond
  \item Si: one C \& 3 Si neighbours
@@ -1464,6 +1372,11 @@ VASP & 0.109 & -0.065 & 0.174 \\
        Real local minimum!
 \end{itemize}
 \end{minipage}
+\begin{minipage}{2.7cm}
+%\includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\
+\vspace{0.2cm}
+\includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}\\
+\end{minipage}
 
 \framebox{
  \tiny
@@ -1519,582 +1432,336 @@ VASP & 0.109 & -0.065 & 0.174 \\
   \end{flushright}
   \end{minipage}
  \end{minipage}
-}\\[0.1cm]
+}\\[0.4cm]
 
-\framebox{
-\begin{minipage}{4.5cm}
-\includegraphics[width=4cm]{c_100_mig_vasp/im_spin_diff.eps}
-\end{minipage}
-\begin{minipage}{3.5cm}
+%\framebox{
+\begin{minipage}{3.0cm}
+%\scriptsize
+\underline{Charge density}\\
 {\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}
-}
-
+\begin{minipage}{3.6cm}
+\includegraphics[width=3.8cm]{c_100_mig_vasp/im_spin_diff.eps}
 \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}
+\begin{pspicture}(0,0)(0,0)
+\psline[linecolor=gray,linewidth=0.05cm](-7.8,-8.7)(-7.8,0)
+\end{pspicture}
 
 \end{slide}
 
 \begin{slide}
 
- {\large\bf\boldmath
-  Migration of the C \hkl<1 0 0> dumbbell interstitial
- }
+\headphd
+{\large\bf\boldmath
+ C interstitial migration --- ab initio
+}
 
 \scriptsize
 
- {\small Investigated pathways}
+\vspace{0.1cm}
 
-\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}
+\begin{minipage}{6.8cm}
+\framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 0 1]}\\
+\begin{minipage}{2.0cm}
+\includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps}
 \end{minipage}
-\begin{minipage}{0.4cm}
+\begin{minipage}{0.2cm}
 $\rightarrow$
 \end{minipage}
-\begin{minipage}{2.4cm}
-\includegraphics[width=2.4cm]{c_pd_vasp/00-1-0-10_2333.eps}
+\begin{minipage}{2.0cm}
+\includegraphics[width=2.0cm]{c_pd_vasp/bc_2333.eps}
 \end{minipage}
-\begin{minipage}{0.4cm}
+\begin{minipage}{0.2cm}
 $\rightarrow$
 \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}
+\begin{minipage}{2.0cm}
+\includegraphics[width=2.0cm]{c_pd_vasp/100_next_2333.eps}
+\end{minipage}\\[0.1cm]
+Spin polarization\\
+$\Rightarrow$ BC configuration constitutes local minimum\\
+$\Rightarrow$ Migration barrier to reach BC | $\Delta E=\unit[1.2]{eV}$
+\end{minipage}
+\begin{minipage}{5.4cm}
+\includegraphics[width=6.0cm]{im_00-1_nosym_sp_fullct_thesis_vasp_s.ps}
+\end{minipage}\\[0.2cm]
+%\hrule
+%
+\begin{minipage}{6.8cm}
+\framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 -1 0]}\\
+\begin{minipage}{2.0cm}
+\includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps}
 \end{minipage}
-\begin{minipage}{0.4cm}
+\begin{minipage}{0.2cm}
 $\rightarrow$
 \end{minipage}
-\begin{minipage}{2.4cm}
-\includegraphics[width=2.4cm]{c_pd_vasp/00-1_ip0-10_2333.eps}
+\begin{minipage}{2.0cm}
+\includegraphics[width=2.0cm]{c_pd_vasp/00-1-0-10_2333.eps}
 \end{minipage}
-\begin{minipage}{0.4cm}
+\begin{minipage}{0.2cm}
 $\rightarrow$
 \end{minipage}
-\begin{minipage}{2.4cm}
-\includegraphics[width=2.4cm]{c_pd_vasp/0-10_ip_2333.eps}
+\begin{minipage}{2.0cm}
+\includegraphics[width=2.0cm]{c_pd_vasp/0-10_2333.eps}
+\end{minipage}\\[0.1cm]
+$\Delta E=\unit[0.9]{eV}$ | Experimental values: \unit[0.70--0.87]{eV}\\
+$\Rightarrow$ {\color{red}Migration mechanism identified!}\\
+Note: Change in orientation
 \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{minipage}{5.4cm}
+\includegraphics[width=6.0cm]{00-1_0-10_vasp_s.ps}
+\end{minipage}\\[0.1cm]
+%
 \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}
+Reorientation pathway composed of two consecutive processes of the above type
 \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
- }
+\headphd
+{\large\bf\boldmath
+ C interstitial migration --- analytical potential
+}
 
 \scriptsize
 
- \vspace{0.1cm}
-
-\begin{minipage}{6.5cm}
-
-\framebox{
-\begin{minipage}[t]{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]
+\vspace{0.3cm}
 
-\begin{minipage}{5.9cm}
-Erhart/Albe results
+\begin{minipage}[t]{6.0cm}
+{\bf\boldmath BC to \hkl[0 0 -1] transition}\\[0.2cm]
+\includegraphics[width=6.0cm]{bc_00-1_albe_s.ps}\\
 \begin{itemize}
- \item Lowest activation energy: $\approx$ 2.2 eV
- \item 2.4 times higher than VASP
+ \item Lowermost migration barrier
+ \item $\Delta E \approx \unit[2.2]{eV}$
+ \item 2.4 times higher than ab initio result
  \item Different pathway
 \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_110_0-10_mig_albe.ps}
+\begin{minipage}[t]{0.2cm}
+\hfill
 \end{minipage}
-}\\[0.1cm]
-
-\begin{minipage}{5.9cm}
-Transition involving \ci{} \hkl<1 1 0>
+\begin{minipage}[t]{6.0cm}
+{\bf\boldmath Transition involving a \hkl<1 1 0> configuration}
+\vspace{0.1cm}
 \begin{itemize}
  \item Bond-centered configuration unstable\\
        $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
- \item Transition minima of path 2 \& 3\\
-       $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
- \item Activation energy: $\approx$ 2.2 eV \& 0.9 eV
- \item 2.4 - 3.4 times higher than VASP
- \item Rotation of dumbbell orientation
+ \item Minima of the \hkl[0 0 -1] to \hkl[0 -1 0] transition\\
+       $\rightarrow$ \ci{} \hkl<1 1 0> DB
 \end{itemize}
 \vspace{0.1cm}
+\includegraphics[width=6.0cm]{00-1_110_0-10_mig_albe.ps}
+\begin{itemize}
+ \item $\Delta E \approx \unit[2.2]{eV} \text{ \& } \unit[0.9]{eV}$
+ \item 2.4 -- 3.4 times higher than ab initio result
+ \item After all: Change of the DB orientation
+\end{itemize}
+\end{minipage}
+
+\vspace{0.5cm}
 \begin{center}
-{\color{blue}Overestimated diffusion barrier}
+{\color{red}\bf Drastically overestimated diffusion barrier}
 \end{center}
-\end{minipage}
 
-\end{minipage}
+\begin{pspicture}(0,0)(0,0)
+\psline[linewidth=0.05cm,linecolor=gray](6.1,1.0)(6.1,9.3)
+\end{pspicture}
 
 \end{slide}
 
 \begin{slide}
 
- {\large\bf\boldmath
-  Combinations with a C-Si \hkl<1 0 0>-type interstitial
- }
-
-\small
-
-\vspace*{0.1cm}
+\headphd
+{\large\bf\boldmath
+ Defect combinations
+}
 
-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}}
-$
+\footnotesize
 
-\vspace*{0.1cm}
+\vspace{0.3cm}
 
+\begin{minipage}{9cm}
+{\bf
+ Summary of combinations}\\[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}\\
+ \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\\
+ C$_{\text{sub}}$ & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
+ Vacancy & -5.39 ($\rightarrow$ C$_{\text{sub}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
 \hline
 \end{tabular}
 }
+\vspace{0.2cm}
+\begin{center}
+{\color{blue}
+ $E_{\text{b}}$ explainable by stress compensation / increase
+}
+\end{center}
+\end{minipage}
+\begin{minipage}{3cm}
+\includegraphics[width=3.5cm]{comb_pos.eps}
+\end{minipage}
 
-\vspace*{0.3cm}
-
-\footnotesize
+\vspace{0.2cm}
 
-\begin{minipage}[t]{3.8cm}
-\underline{\hkl<1 0 0> at position 1}\\[0.1cm]
-\includegraphics[width=3.5cm]{00-1dc/2-25.eps}
+{\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm]
+\begin{minipage}[t]{3.2cm}
+\underline{\hkl[1 0 0] at position 1}\\[0.1cm]
+\includegraphics[width=2.8cm]{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}
+\begin{minipage}[t]{3.0cm}
+\underline{\hkl[0 -1 0] at position 1}\\[0.1cm]
+\includegraphics[width=2.8cm]{00-1dc/2-39.eps}
 \end{minipage}
-\begin{minipage}[t]{5.5cm}
+\begin{minipage}[t]{6.1cm}
+\vspace{0.7cm}
 \begin{itemize}
- \item $E_{\text{b}}=0$ $\Leftrightarrow$ non-interacting defects\\
-       $E_{\text{b}} \rightarrow 0$ for increasing distance (R)
- \item Stress compensation / increase
- \item Unfavored: antiparallel orientations
- \item Indication of energetically favored\\
-       agglomeration
- \item Most favorable: C clustering
- \item However: High barrier ($>4\,\text{eV}$)
- \item $4\times{\color{cyan}-2.25}$ versus $2\times{\color{orange}-2.39}$
-       (Entropy)
+ \item \ci{} agglomeration energetically favorable
+ \item Most favorable: C clustering\\
+       {\color{red}However \ldots}\\
+        \ldots high migration barrier ($>4\,\text{eV}$)\\
+        \ldots entropy:
+        $4\times{\color{cyan}[-2.25]}$ versus
+        $2\times{\color{orange}[-2.39]}$
 \end{itemize}
+\begin{center}
+{\color{blue}\ci{} agglomeration / no C clustering}
+\end{center}
 \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}
+\headphd
+{\large\bf\boldmath
+ Defect combinations
+}
 
-Energetically most favorable combinations along \hkl<1 1 0>
+\footnotesize
 
-\vspace*{0.1cm}
+\vspace{0.3cm}
 
+\begin{minipage}{9cm}
+{\bf
+ Summary of combinations}\\[0.1cm]
 {\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>\\
+ $E_{\text{b}}$ [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$_{\text{sub}}$ & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
+ Vacancy & -5.39 ($\rightarrow$ C$_{\text{sub}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
 \hline
 \end{tabular}
 }
-
-\vspace*{0.3cm}
-
-\begin{minipage}{7.0cm}
-\includegraphics[width=7cm]{db_along_110_cc.ps}
-\end{minipage}
-\begin{minipage}{6.0cm}
-\begin{itemize}
- \item Interaction proportional to reciprocal cube of C-C distance
- \item Saturation in the immediate vicinity
- \renewcommand\labelitemi{$\Rightarrow$}
- \item Agglomeration of \ci{} expected
- \item Absence of C clustering
-\end{itemize}
+\vspace{0.2cm}
 \begin{center}
 {\color{blue}
- Consisten with initial precipitation model
+ $E_{\text{b}}$ explainable by stress compensation / increase
 }
 \end{center}
 \end{minipage}
+\begin{minipage}{3cm}
+\includegraphics[width=3.5cm]{comb_pos.eps}
+\end{minipage}
 
 \vspace{0.2cm}
 
-\end{slide}
-
-\begin{slide}
-
- {\large\bf\boldmath
-  Combinations of substitutional C and \hkl<1 1 0> Si self-interstitials
- }
-
- \scriptsize
-
-%\begin{center}
-%\begin{minipage}{3.2cm}
-%\includegraphics[width=3cm]{sub_110_combo.eps}
-%\end{minipage}
-%\begin{minipage}{7.8cm}
-%\begin{tabular}{l c c c c c c}
-%\hline
-%C$_{\text{sub}}$ & \hkl<1 1 0> & \hkl<-1 1 0> & \hkl<0 1 1> & \hkl<0 -1 1> &
-%                   \hkl<1 0 1> & \hkl<-1 0 1> \\
-%\hline
-%1 & \RM{1} & \RM{3} & \RM{3} & \RM{1} & \RM{3} & \RM{1} \\
-%2 & \RM{2} & A & A & \RM{2} & C & \RM{5} \\
-%3 & \RM{3} & \RM{1} & \RM{3} & \RM{1} & \RM{1} & \RM{3} \\
-%4 & \RM{4} & B & D & E & E & D \\
-%5 & \RM{5} & C & A & \RM{2} & A & \RM{2} \\
-%\hline
-%\end{tabular}
-%\end{minipage}
-%\end{center}
-
-%\begin{center}
-%\begin{tabular}{l c c c c c c c c c c}
-%\hline
-%Conf & \RM{1} & \RM{2} & \RM{3} & \RM{4} & \RM{5} & A & B & C & D & E \\
-%\hline
-%$E_{\text{f}}$ [eV]& 4.37 & 5.26 & 5.57 & 5.37 & 5.12 & 5.10 & 5.32 & 5.28 & 5.39 & 5.32 \\
-%$E_{\text{b}}$ [eV] & -0.97 & -0.08 & 0.22 & -0.02 & -0.23 & -0.25 & -0.02 & -0.06 & 0.05 & -0.03 \\
-%$r$ [nm] & 0.292 & 0.394 & 0.241 & 0.453 & 0.407 & 0.408 & 0.452 & 0.392 & 0.456 & 0.453\\
-%\hline
-%\end{tabular}
-%\end{center}
-
-\begin{minipage}{6.0cm}
-\includegraphics[width=5.8cm]{c_sub_si110.ps}
+{\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm]
+\begin{minipage}[t]{3.2cm}
+\underline{\hkl[1 0 0] at position 1}\\[0.1cm]
+\includegraphics[width=2.8cm]{00-1dc/2-25.eps}
 \end{minipage}
-\begin{minipage}{7cm}
-\scriptsize
+\begin{minipage}[t]{3.0cm}
+\underline{\hkl[0 -1 0] at position 1}\\[0.1cm]
+\includegraphics[width=2.8cm]{00-1dc/2-39.eps}
+\end{minipage}
+\begin{minipage}[t]{6.1cm}
+\vspace{0.7cm}
 \begin{itemize}
- \item IBS: C may displace Si\\
-       $\Rightarrow$ C$_{\text{sub}}$ + \hkl<1 1 0> Si self-interstitial
- \item Assumption:\\
-       \hkl<1 1 0>-type $\rightarrow$ favored combination
- \renewcommand\labelitemi{$\Rightarrow$}
- \item Most favorable: \cs{} along \hkl<1 1 0> chain \si{}
- \item Less favorable than C-Si \hkl<1 0 0> dumbbell
- \item Interaction drops quickly to zero\\
-       $\rightarrow$ low capture radius
+ \item \ci{} agglomeration energetically favorable
+ \item Most favorable: C clustering\\
+       {\color{red}However \ldots}\\
+        \ldots high migration barrier ($>4\,\text{eV}$)\\
+        \ldots entropy:
+        $4\times{\color{cyan}[-2.25]}$ versus
+        $2\times{\color{orange}[-2.39]}$
 \end{itemize}
 \begin{center}
- {\color{blue}
- IBS process far from equilibrium\\
- \cs{} \& \si{} instead of thermodynamic ground state
- }
+{\color{blue}\ci{} agglomeration / no C clustering}
 \end{center}
 \end{minipage}
 
-\begin{minipage}{6.5cm}
-\includegraphics[width=6.0cm]{162-097.ps}
-\begin{itemize}
- \item Low migration barrier
-\end{itemize}
+% insert graph ...
+\begin{pspicture}(0,0)(0,0)
+\rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
+\begin{minipage}{14cm}
+\hfill
+\vspace{12cm}
 \end{minipage}
-\begin{minipage}{6.5cm}
+}}
+\rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
+\begin{minipage}{8cm}
 \begin{center}
-Ab initio MD at \degc{900}\\
-\includegraphics[width=3.3cm]{md_vasp_01.eps}
-$t=\unit[2230]{fs}$\\
-\includegraphics[width=3.3cm]{md_vasp_02.eps}
-$t=\unit[2900]{fs}$
+\vspace{0.2cm}
+\scriptsize
+Interaction along \hkl[1 1 0]
+\includegraphics[width=7cm]{db_along_110_cc.ps}
 \end{center}
-{\color{blue}
-Contribution of entropy to structural formation
-}
 \end{minipage}
+}}}
+\end{pspicture}
 
 \end{slide}
 
+% continue here
+\fi
+
 \begin{slide}
 
- {\large\bf\boldmath
-  Migration in C-Si \hkl<1 0 0> and vacancy combinations
- }
+{\large\bf
+ Defect combinations
+}
 
- \footnotesize
+\footnotesize
 
 \vspace{0.1cm}
 
+{\bf Combinations of \ci{} \hkl[0 0 -1] and a vacancy}\\
 \begin{minipage}[t]{3cm}
 \underline{Pos 2, $E_{\text{b}}=-0.59\text{ eV}$}\\
 \includegraphics[width=2.8cm]{00-1dc/0-59.eps}
 \end{minipage}
+
+
+
 \begin{minipage}[t]{7cm}
 \vspace{0.2cm}
 \begin{center}
@@ -2108,9 +1775,10 @@ Contribution of entropy to structural formation
  Without nearby \hkl<1 1 0> Si self-interstitial (IBS)\\
  $\Downarrow$\\
  {\color{blue}Formation of SiC by successive substitution by C}
-
 \end{center}
 \end{minipage}
+
+
 \begin{minipage}[t]{3cm}
 \underline{Pos 3, $E_{\text{b}}=-3.14\text{ eV}$}\\
 \includegraphics[width=2.8cm]{00-1dc/3-14.eps}
@@ -2175,6 +1843,62 @@ Contribution of entropy to structural formation
 
 \end{slide}
 
+\end{document}
+\ifnum1=0
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Combinations of substitutional C and \hkl<1 1 0> Si self-interstitials
+ }
+
+ \scriptsize
+
+\begin{minipage}{6.0cm}
+\includegraphics[width=5.8cm]{c_sub_si110.ps}
+\end{minipage}
+\begin{minipage}{7cm}
+\scriptsize
+\begin{itemize}
+ \item IBS: C may displace Si\\
+       $\Rightarrow$ C$_{\text{sub}}$ + \hkl<1 1 0> Si self-interstitial
+ \item Assumption:\\
+       \hkl<1 1 0>-type $\rightarrow$ favored combination
+ \renewcommand\labelitemi{$\Rightarrow$}
+ \item Most favorable: \cs{} along \hkl<1 1 0> chain \si{}
+ \item Less favorable than C-Si \hkl<1 0 0> dumbbell
+ \item Interaction drops quickly to zero\\
+       $\rightarrow$ low capture radius
+\end{itemize}
+\begin{center}
+ {\color{blue}
+ IBS process far from equilibrium\\
+ \cs{} \& \si{} instead of thermodynamic ground state
+ }
+\end{center}
+\end{minipage}
+
+\begin{minipage}{6.5cm}
+\includegraphics[width=6.0cm]{162-097.ps}
+\begin{itemize}
+ \item Low migration barrier
+\end{itemize}
+\end{minipage}
+\begin{minipage}{6.5cm}
+\begin{center}
+Ab initio MD at \degc{900}\\
+\includegraphics[width=3.3cm]{md_vasp_01.eps}
+$t=\unit[2230]{fs}$\\
+\includegraphics[width=3.3cm]{md_vasp_02.eps}
+$t=\unit[2900]{fs}$
+\end{center}
+{\color{blue}
+Contribution of entropy to structural formation
+}
+\end{minipage}
+
+\end{slide}
+
 \begin{slide}
 
  {\large\bf