basically finished point dfect chapter

[lectures/latex.git] / posic / talks / upb-ua-xc.tex

diff --git a/posic/talks/upb-ua-xc.tex b/posic/talks/upb-ua-xc.tex
index e95c0fb..7b953ff 100644 (file)
--- a/posic/talks/upb-ua-xc.tex
+++ b/posic/talks/upb-ua-xc.tex
@@ -20,6 +20,8 @@
 \usepackage{pstricks}
 \usepackage{pst-node}
 
 \usepackage{pstricks}
 \usepackage{pst-node}
 

+\usepackage{slashbox}
+

 %\usepackage{epic}
 %\usepackage{eepic}
 
 %\usepackage{epic}
 %\usepackage{eepic}
 


@@ -46,6 +48,8 @@
 
 \usepackage{upgreek}
 
 
 \usepackage{upgreek}
 

+\usepackage{miller}
+

 \begin{document}
 
 \extraslideheight{10in}
 \begin{document}
 
 \extraslideheight{10in}


@@ -218,8 +222,8 @@ POTIM = 0.1
  \begin{itemize}
   \item Calculation of cohesive energies for different lattice constants
   \item No ionic update
  \begin{itemize}
   \item Calculation of cohesive energies for different lattice constants
   \item No ionic update

-  \item tetrahedron method with Blöchl corrections for
-        the partial occupancies $f_{nk}$
+  \item Tetrahedron method with Blöchl corrections for
+        the partial occupancies $f(\{\epsilon_{n{\bf k}}\})$

   \item Supercell 3 (8 atoms, 4 primitive cells)
  \end{itemize}
  \vspace*{0.6cm}
   \item Supercell 3 (8 atoms, 4 primitive cells)
  \end{itemize}
  \vspace*{0.6cm}


@@ -269,8 +273,8 @@ POTIM = 0.1
  \begin{itemize}
   \item Calculation of cohesive energies for different lattice constants
   \item No ionic update
  \begin{itemize}
   \item Calculation of cohesive energies for different lattice constants
   \item No ionic update

-  \item tetrahedron method with Blöchl corrections for
-        the partial occupancies $f_{nk}$
+  \item Tetrahedron method with Blöchl corrections for
+        the partial occupancies $f(\{\epsilon_{n{\bf k}}\})$

  \end{itemize}
  \vspace*{0.6cm}
  \begin{minipage}{6.5cm}
  \end{itemize}
  \vspace*{0.6cm}
  \begin{minipage}{6.5cm}


@@ -283,7 +287,15 @@ POTIM = 0.1
  \begin{center}
  {\color{red}
   Non-continuous energies\\
  \begin{center}
  {\color{red}
   Non-continuous energies\\

-  for $E_{\textrm{cut-off}}<1050\,\textrm{eV}$!
+  for $E_{\textrm{cut-off}}<1050\,\textrm{eV}$!\\
+ }
+ \vspace*{0.5cm}
+ {\footnotesize
+ Does this matter in structural optimizaton simulations?
+ \begin{itemize}
+  \item Derivative might be continuous
+  \item Similar lattice constants where derivative equals zero
+ \end{itemize}

  }
  \end{center}
  \end{minipage}
  }
  \end{center}
  \end{minipage}


@@ -348,25 +360,30 @@ POTIM = 0.1
          \item Spin polarized calculation
          \item Interpolation formula according to Vosko Wilk and Nusair
                for the correlation part of the exchange correlation functional
          \item Spin polarized calculation
          \item Interpolation formula according to Vosko Wilk and Nusair
                for the correlation part of the exchange correlation functional

-         \item Gaussian smearing for the partial occupancies $f_{nk}$
+         \item Gaussian smearing for the partial occupancies
+               $f(\{\epsilon_{n{\bf k}}\})$

                ($\sigma=0.05$)
          \item Magnetic mixing: AMIX = 0.2, BMIX = 0.0001
          \item Supercell: one atom in cubic
                $10\times 10\times 10$ \AA$^3$ box
         \end{itemize}
         {\color{blue}
                ($\sigma=0.05$)
          \item Magnetic mixing: AMIX = 0.2, BMIX = 0.0001
          \item Supercell: one atom in cubic
                $10\times 10\times 10$ \AA$^3$ box
         \end{itemize}
         {\color{blue}

-        $E_{\textrm{free,sp}}(\textrm{Si},250\, \textrm{eV})=
+        $E_{\textrm{free,sp}}(\textrm{Si},{\color{green}250}\, \textrm{eV})=

          -0.70036911\,\textrm{eV}$
          -0.70036911\,\textrm{eV}$

+        }\\
+        {\color{blue}
+        $E_{\textrm{free,sp}}(\textrm{Si},{\color{red}650}\, \textrm{eV})=
+         -0.70021403\,\textrm{eV}$

         },
         {\color{gray}
         },
         {\color{gray}

-        $E_{\textrm{free,sp}}(\textrm{C},xxx\, \textrm{eV})=
-         yyy\,\textrm{eV}$
+        $E_{\textrm{free,sp}}(\textrm{C},{\color{red}650}\, \textrm{eV})=
+         -1.3535731\,\textrm{eV}$

         }
   \item $E$:
         energy (non-polarized) of system of interest composed of\\
         n atoms of type N, m atoms of type M, \ldots
  \end{itemize}
         }
   \item $E$:
         energy (non-polarized) of system of interest composed of\\
         n atoms of type N, m atoms of type M, \ldots
  \end{itemize}

- \vspace*{0.3cm}
+ \vspace*{0.2cm}

  {\color{red}
  \[
  \Rightarrow
  {\color{red}
  \[
  \Rightarrow


@@ -382,12 +399,12 @@ POTIM = 0.1
 \begin{slide}
 
  {\large\bf
 \begin{slide}
 
  {\large\bf

-  Silicon point defects\\
+  Calculation of the defect formation energy\\

  }
 
  \small
  }
 
  \small

-
- Calculation of formation energy $E_{\textrm{f}}$
+ 
+ {\color{blue}Method 1} (single species)

  \begin{itemize}
   \item $E_{\textrm{coh}}^{\textrm{initial conf}}$:
         cohesive energy per atom of the initial system
  \begin{itemize}
   \item $E_{\textrm{coh}}^{\textrm{initial conf}}$:
         cohesive energy per atom of the initial system


@@ -402,13 +419,2528 @@ POTIM = 0.1
  E_{\textrm{f}}=\Big(E_{\textrm{coh}}^{\textrm{interstitial conf}}
                -E_{\textrm{coh}}^{\textrm{initial conf}}\Big) N
  \]
  E_{\textrm{f}}=\Big(E_{\textrm{coh}}^{\textrm{interstitial conf}}
                -E_{\textrm{coh}}^{\textrm{initial conf}}\Big) N
  \]

+ }\\[0.4cm]
+ {\color{magenta}Method 2} (two and more species)
+ \begin{itemize}
+  \item $E$: energy of the interstitial system
+        (with respect to the ground state of the free atoms!)
+  \item $N_{\text{Si}}$, $N_{\text{C}}$:
+        amount of Si and C atoms
+  \item $\mu_{\text{Si}}$, $\mu_{\text{C}}$:
+        chemical potential (cohesive energy) of Si and C
+ \end{itemize}
+ \vspace*{0.2cm}
+ {\color{magenta}
+ \[
+ \Rightarrow
+ E_{\textrm{f}}=E-N_{\text{Si}}\mu_{\text{Si}}-N_{\text{C}}\mu_{\text{C}}
+ \]

  }
 
  }
 

- \begin{center}
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Used types of supercells\\
+ }
+
+ \footnotesize
+
+ \begin{minipage}{4.3cm}
+  \includegraphics[width=4cm]{sc_type0.eps}\\[0.3cm]
+  \underline{Type 0}\\[0.2cm]
+  Basis: fcc\\
+  $x_1=(0.5,0.5,0)$\\
+  $x_2=(0,0.5,0.5)$\\
+  $x_3=(0.5,0,0.5)$\\
+  1 primitive cell / 2 atoms
+ \end{minipage}
+ \begin{minipage}{4.3cm}
+  \includegraphics[width=4cm]{sc_type1.eps}\\[0.3cm]
+  \underline{Type 1}\\[0.2cm]
+  Basis:\\
+  $x_1=(0.5,-0.5,0)$\\
+  $x_2=(0.5,0.5,0)$\\
+  $x_3=(0,0,1)$\\
+  2 primitive cells / 4 atoms
+ \end{minipage}
+ \begin{minipage}{4.3cm}
+  \includegraphics[width=4cm]{sc_type2.eps}\\[0.3cm]
+  \underline{Type 2}\\[0.2cm]
+  Basis: sc\\
+  $x_1=(1,0,0)$\\
+  $x_2=(0,1,0)$\\
+  $x_3=(0,0,1)$\\
+  4 primitive cells / 8 atoms
+ \end{minipage}\\[0.4cm]
+
+ {\bf\color{blue}
+ In the following these types of supercells are used and
+ are possibly scaled by integers in the different directions!
+ }
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Silicon point defects\\
+ }
+
+ \small
+
+ Influence of supercell size\\
+ \begin{minipage}{8cm}

  \includegraphics[width=7.0cm]{si_self_int.ps}
  \includegraphics[width=7.0cm]{si_self_int.ps}

+ \end{minipage}
+ \begin{minipage}{5cm}
+ $E_{\textrm{f}}^{\hkl<1 1 0>,\,32\textrm{pc}}=3.38\textrm{ eV}$\\
+ $E_{\textrm{f}}^{\textrm{tet},\,32\textrm{pc}}=3.41\textrm{ eV}$\\
+ $E_{\textrm{f}}^{\textrm{hex},\,32\textrm{pc}}=3.42\textrm{ eV}$\\
+ $E_{\textrm{f}}^{\textrm{vac},\,32\textrm{pc}}=3.51\textrm{ eV}$\\\\
+ $E_{\textrm{f}}^{\textrm{hex},\,54\textrm{pc}}=3.42\textrm{ eV}$\\
+ $E_{\textrm{f}}^{\textrm{tet},\,54\textrm{pc}}=3.45\textrm{ eV}$\\
+ $E_{\textrm{f}}^{\textrm{vac},\,54\textrm{pc}}=3.47\textrm{ eV}$\\
+ $E_{\textrm{f}}^{\hkl<1 1 0>,\,54\textrm{pc}}=3.48\textrm{ eV}$
+ \end{minipage}
+
+ Comparison with literature (PRL 88 235501 (2002)):\\[0.2cm]
+ \begin{minipage}{8cm}
+ \begin{itemize}
+  \item GGA and LDA
+  \item $E_{\text{cut-off}}=35 / 25\text{ Ry}=476 / 340\text{ eV}$
+  \item 216 atom supercell
+  \item Gamma point only calculations
+ \end{itemize}
+ \end{minipage}
+ \begin{minipage}{5cm}
+ $E_{\textrm{f}}^{\hkl<1 1 0>}=3.31 / 2.88\textrm{ eV}$\\
+ $E_{\textrm{f}}^{\textrm{hex}}=3.31 / 2.87\textrm{ eV}$\\
+ $E_{\textrm{f}}^{\textrm{vac}}=3.17 / 3.56\textrm{ eV}$
+ \end{minipage}
+ 
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Questions so far ...\\
+ }
+
+ What configuration to chose for C in Si simulations?
+ \begin{itemize}
+  \item Switch to another method for the XC approximation (GGA, PAW)?
+  \item Reasonable cut-off energy
+  \item Switch off symmetry? (especially for defect simulations)
+  \item $k$-points
+        (Monkhorst? $\Gamma$-point only if cell is large enough?)
+  \item Switch to tetrahedron method or Gaussian smearing ($\sigma$?)
+  \item Size and type of supercell
+        \begin{itemize}
+         \item connected to choice of $k$-point mesh?
+         \item hence also connected to choice of smearing method?
+         \item constraints can only be applied to the lattice vectors!
+        \end{itemize}
+  \item Use of real space projection operators?
+  \item \ldots
+ \end{itemize}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Review (so far) ...\\
+ }
+
+ Smearing method for the partial occupancies $f(\{\epsilon_{n{\bf k}}\})$
+ and $k$-point mesh
+
+ \begin{minipage}{4.4cm}
+  \includegraphics[width=4.4cm]{sic_smear_k.ps}
+ \end{minipage}
+ \begin{minipage}{4.4cm}
+  \includegraphics[width=4.4cm]{c_smear_k.ps}
+ \end{minipage}
+ \begin{minipage}{4.3cm}
+  \includegraphics[width=4.4cm]{si_smear_k.ps}
+ \end{minipage}\\[0.3cm]
+ \begin{itemize}
+  \item Convergence reached at $6\times 6\times 6$ k-point mesh
+  \item No difference between Gauss ($\sigma=0.05$)
+        and tetrahedron smearing method!
+ \end{itemize}
+ \begin{center}
+ $\Downarrow$\\
+ {\color{blue}\bf
+   Gauss ($\sigma=0.05$) smearing
+   and $6\times 6\times 6$ Monkhorst $k$-point mesh used
+ }
+ \end{center}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Review (so far) ...\\
+ }
+
+ \underline{Symmetry (in defect simulations)}
+
+ \begin{center}
+ {\color{red}No}
+ difference in $1\times 1\times 1$ Type 2 defect calculations\\
+ $\Downarrow$\\
+ Symmetry precission (SYMPREC) small enough\\
+ $\Downarrow$\\
+ {\bf\color{blue}Symmetry switched on}\\
+ \end{center}
+
+ \underline{Real space projection}
+
+ \begin{center}
+ Error in lattice constant of plain Si ($1\times 1\times 1$ Type 2):
+ $0.025\,\%$\\
+ Error in position of the \hkl<1 1 0> interstitital in Si
+ ($1\times 1\times 1$ Type 2):
+ $0.026\,\%$\\
+ $\Downarrow$\\
+ {\bf\color{blue}
+  Real space projection used for 'large supercell' simulations}
+ \end{center}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Review (so far) ...
+ }
+
+ Energy cut-off\\
+
+ \begin{center}
+
+ {\small
+ 3C-SiC equilibrium lattice constant and free energy\\ 
+ \includegraphics[width=7cm]{plain_sic_lc.ps}\\
+ $\rightarrow$ Convergence reached at 650 eV\\[0.2cm]
+ }
+
+ $\Downarrow$\\
+
+ {\bf\color{blue}
+  650 eV used as energy cut-off
+ }
+
+ \end{center}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Not answered (so far) ...\\
+ }
+
+\vspace{1.5cm}
+
+ \LARGE
+ \bf
+ \color{blue}
+
+ \begin{center}
+ Continue\\
+ with\\
+ US LDA?
+ \end{center}
+
+\vspace{1.5cm}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Final parameter choice
+ }
+
+ \footnotesize
+
+ \underline{Param 1}\\
+ My first choice. Used for more accurate calculations.
+ \begin{itemize}
+  \item $6\times 6 \times 6$ Monkhorst k-point mesh
+  \item $E_{\text{cut-off}}=650\text{ eV}$
+  \item Gaussian smearing ($\sigma=0.05$)
+  \item Use symmetry
+ \end{itemize}
+ \vspace*{0.2cm}
+ \underline{Param 2}\\
+ After talking to the pros!
+ \begin{itemize}
+  \item $\Gamma$-point only
+  \item $E_{\text{cut-off}}=xyz\text{ eV}$
+  \item Gaussian smearing ($\sigma=0.05$)
+  \item Use symmetry
+  \item Real space projection (Auto, Medium) for 'large' simulations
+ \end{itemize}
+ \vspace*{0.2cm}
+ {\color{blue}
+  In both parameter sets the ultra soft pseudo potential method
+  as well as the projector augmented wave method is used with both,
+  the LDA and GGA exchange correlation potential!
+ }
+\end{slide}
+
+\begin{slide}
+
+ \footnotesize
+
+ {\large\bf
+  Properties of Si, C and SiC using the new parameters\\
+ }
+
+ $2\times 2\times 2$ Type 2 supercell, Param 1, LDA, US PP\\[0.2cm]
+ \begin{tabular}{|l|l|l|l|}
+ \hline
+  & c-Si & c-C (diamond) & 3C-SiC \\
+ \hline
+ Lattice constant [\AA] & 5.389 & 3.527 & 4.319 \\
+ Expt. [\AA] & 5.429 & 3.567 & 4.359 \\
+ Error [\%] & {\color{green}0.7} & {\color{green}1.1} & {\color{green}0.9} \\
+ \hline
+ Cohesive energy [eV] & -5.277 & -8.812 & -7.318 \\
+ Expt. [eV] & -4.63 & -7.374 & -6.340 \\
+ Error [\%] & {\color{red}14.0} & {\color{red}19.5} & {\color{red}15.4} \\
+ \hline
+ \end{tabular}\\
+
+ \begin{minipage}{10cm}
+ $2\times 2\times 2$ Type 2 supercell, 3C-SiC, Param 1\\[0.2cm]
+ \begin{tabular}{|l|l|l|l|}
+ \hline
+  & {\color{magenta}US PP, GGA} & PAW, LDA & PAW, GGA \\
+ \hline
+ Lattice constant [\AA] & 4.370 & 4.330 & 4.379 \\
+ Error [\%] & {\color{green}0.3} & {\color{green}0.7} & {\color{green}0.5} \\
+ \hline
+ Cohesive energy [eV] & -6.426 & -7.371 & -6.491 \\
+ Error [\%] & {\color{green}1.4} & {\color{red}16.3} & {\color{green}2.4} \\
+ \hline
+ \end{tabular}
+ \end{minipage}
+ \begin{minipage}{3cm}
+ US PP, GGA\\[0.2cm]
+ \begin{tabular}{|l|l|}
+ \hline
+ c-Si & c-C \\
+ \hline
+ 5.455 & 3.567 \\
+ {\color{green}0.5} & {\color{green}0.01} \\
+ \hline
+ -4.591 & -7.703 \\
+ {\color{green}0.8} & {\color{orange}4.5} \\
+ \hline
+ \end{tabular}
+ \end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Energy cut-off for $\Gamma$-point only caclulations
+ }
+
+ $2\times 2\times 2$ Type 2 supercell, Param 2, US PP, LDA, 3C-SiC\\[0.2cm]
+ \includegraphics[width=5.5cm]{sic_32pc_gamma_cutoff.ps}
+ \includegraphics[width=5.5cm]{sic_32pc_gamma_cutoff_lc.ps}\\
+ $\Rightarrow$ Use 300 eV as energy cut-off?\\[0.2cm]
+ $2\times 2\times 2$ Type 2 supercell, Param 2, 300 eV, US PP, GGA\\[0.2cm]
+ \small
+ \begin{minipage}{10cm}
+ \begin{tabular}{|l|l|l|l|}
+ \hline
+  & c-Si & c-C (diamond) & 3C-SiC \\
+ \hline
+ Lattice constant [\AA] & 5.470 & 3.569 & 4.364 \\
+ Error [\%] & {\color{green}0.8} & {\color{green}0.1} & {\color{green}0.1} \\
+ \hline
+ Cohesive energy [eV] & -4.488 & -7.612 & -6.359 \\
+ Error [\%] & {\color{orange}3.1} & {\color{orange}3.2} & {\color{green}0.3} \\
+ \hline
+ \end{tabular}
+ \end{minipage}
+ \begin{minipage}{2cm}
+ {\LARGE
+  ${\color{green}\surd}$
+ }
+ \end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  C \hkl<1 0 0> interstitial migration along \hkl<1 1 0>
+  in c-Si (Albe)
+ }
+
+ \small
+
+ \begin{minipage}[t]{4.2cm}
+ \underline{Starting configuration}\\
+ \includegraphics[width=4cm]{c_100_mig/start.eps}
+ \end{minipage}
+ \begin{minipage}[t]{4.0cm}
+ \vspace*{0.8cm}
+ $\Delta x=\frac{1}{4}a_{\text{Si}}=1.357\text{ \AA}$\\
+ $\Delta y=\frac{1}{4}a_{\text{Si}}=1.357\text{ \AA}$\\
+ $\Delta z=0.325\text{ \AA}$\\
+ \end{minipage}
+ \begin{minipage}[t]{4.2cm}
+ \underline{{\bf Expected} final configuration}\\
+ \includegraphics[width=4cm]{c_100_mig/final.eps}\\
+ \end{minipage}
+ \begin{minipage}{6cm}
+ \begin{itemize}
+  \item Fix border atoms of the simulation cell
+  \item Constraints and displacement of the C atom:
+        \begin{itemize}
+         \item along {\color{green}\hkl<1 1 0> direction}\\
+               displaced by {\color{green} $\frac{1}{10}(\Delta x,\Delta y)$}
+         \item C atom {\color{red}entirely fixed in position}\\
+               displaced by
+               {\color{red}$\frac{1}{10}(\Delta x,\Delta y,\Delta z)$}
+        \end{itemize}
+  \item Berendsen thermostat applied
+ \end{itemize}
+ {\bf\color{blue}Expected configuration not obtained!}
+ \end{minipage}
+ \begin{minipage}{0.5cm}
+ \hfill
+ \end{minipage}
+ \begin{minipage}{6cm}
+ \includegraphics[width=6.0cm]{c_100_110mig_01_albe.ps}
+ \end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  C \hkl<1 0 0> interstitial migration along \hkl<1 1 0>
+  in c-Si (Albe)
+ }
+
+ \footnotesize
+
+ \begin{minipage}{3.2cm}
+ \includegraphics[width=3cm]{c_100_mig/fixmig_50.eps}
+ \begin{center}
+ 50 \% 
+ \end{center}
+ \end{minipage}
+ \begin{minipage}{3.2cm}
+ \includegraphics[width=3cm]{c_100_mig/fixmig_80.eps}
+ \begin{center}
+ 80 \% 
+ \end{center}
+ \end{minipage}
+ \begin{minipage}{3.2cm}
+ \includegraphics[width=3cm]{c_100_mig/fixmig_90.eps}
+ \begin{center}
+ 90 \% 

  \end{center}
  \end{center}

+ \end{minipage}
+ \begin{minipage}{3.2cm}
+ \includegraphics[width=3cm]{c_100_mig/fixmig_99.eps}
+ \begin{center}
+ 100 \% 
+ \end{center}
+ \end{minipage}
+
+ Open questions ...
+ \begin{enumerate}
+  \item Why is the expected configuration not obtained?
+  \item How to find a migration path preceding to the expected configuration?
+ \end{enumerate}
+
+ Answers ...
+ \begin{enumerate}
+  \item Simple: it is not the right migration path!
+        \begin{itemize}
+         \item (Surrounding) atoms settle into a local minimum configuration
+         \item A possibly existing more favorable configuration is not achieved
+        \end{itemize}
+  \item \begin{itemize}
+         \item Search global minimum in each step (by simulated annealing)\\
+               {\color{red}But:}
+               Loss of the correct energy needed for migration
+         \item Smaller displacements\\
+               A more favorable configuration might be achieved
+               possibly preceding to the expected configuration
+        \end{itemize}
+ \end{enumerate}
+ 
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  C \hkl<1 0 0> interstitial migration along \hkl<1 1 0>
+  in c-Si (Albe)\\
+ }
+
+ Displacement step size decreased to
+ $\frac{1}{100} (\Delta x,\Delta y)$\\[0.2cm]
+
+ \begin{minipage}{7.5cm}
+ Result: (Video \href{../video/c_in_si_smig_albe.avi}{$\rhd_{\text{local}}$ } $|$
+ \href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/c_in_si_smig_albe.avi}{$\rhd_{\text{remote url}}$})
+ \begin{itemize}
+  \item Expected final configuration not obtained
+  \item Bonds to neighboured silicon atoms persist
+  \item C and neighboured Si atoms move along the direction of displacement
+  \item Even the bond to the lower left silicon atom persists
+ \end{itemize}
+ {\color{red}
+  Obviously: overestimated bond strength
+ }
+ \end{minipage}
+ \begin{minipage}{5cm}
+  \includegraphics[width=6cm]{c_100_110smig_01_albe.ps}
+ \end{minipage}\\[0.4cm]
+ New approach to find the migration path:\\
+ {\color{blue}
+ Place interstitial carbon atom at the respective coordinates
+ into a perfect c-Si matrix!
+ }
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  C \hkl<1 0 0> interstitial migration along \hkl<1 1 0>
+  in c-Si (Albe)
+ }
+
+ {\color{blue}New approach:}\\
+ Place interstitial carbon atom at the respective coordinates
+ into a perfect c-Si matrix!\\
+ {\color{blue}Problem:}\\
+ Too high forces due to the small distance of the C atom to the Si
+ atom sharing the lattice site.\\
+ {\color{blue}Solution:}
+ \begin{itemize}
+  \item {\color{red}Slightly displace the Si atom}
+  (Video \href{../video/c_in_si_pmig_albe.avi}{$\rhd_{\text{local}}$ } $|$
+  \href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/c_in_si_pmig_albe.avi}{$\rhd_{\text{remote url}}$})
+  \item {\color{green}Immediately quench the system}
+  (Video \href{../video/c_in_si_pqmig_albe.avi}{$\rhd_{\text{local}}$ } $|$
+  \href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/c_in_si_pqmig_albe.avi}{$\rhd_{\text{remote url}}$})
+ \end{itemize}
+
+ \begin{minipage}{6.5cm}
+ \includegraphics[width=6cm]{c_100_110pqmig_01_albe.ps}
+ \end{minipage}
+ \begin{minipage}{6cm}
+ \begin{itemize}
+  \item Jump in energy corresponds to the abrupt
+        structural change (as seen in the videos)
+  \item Due to the abrupt changes in structure and energy
+        this is {\color{red}not} the correct migration path and energy!?!
+ \end{itemize}
+ \end{minipage}

 
 \end{slide}
 
 
 \end{slide}
 

+\begin{slide}
+
+ {\large\bf\boldmath
+  C \hkl<1 0 0> interstitial migration along \hkl<1 1 0> in c-Si (VASP)
+ }
+
+ \small
+
+ {\color{blue}Method:}
+ \begin{itemize}
+  \item Place interstitial carbon atom at the respective coordinates
+        into perfect c-Si
+  \item \hkl<1 1 0> direction fixed for the C atom
+  \item $4\times 4\times 3$ Type 1, $198+1$ atoms
+  \item Atoms with $x=0$ or $y=0$ or $z=0$ fixed
+ \end{itemize}
+ {\color{blue}Results:}
+ (Video \href{../video/c_in_si_pmig_vasp.avi}{$\rhd_{\text{local}}$ } $|$
+ \href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/c_in_si_pmig_vasp.avi}{$\rhd_{\text{remote url}}$})\\
+ \begin{minipage}{7cm}
+ \includegraphics[width=7cm]{c_100_110pmig_01_vasp.ps} 
+ \end{minipage}
+ \begin{minipage}{5.5cm}
+ \begin{itemize}
+  \item Characteristics nearly equal to classical calulations
+  \item Approximately half of the classical energy
+        needed for migration
+ \end{itemize}
+ \end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  C \hkl<1 0 0> interstitial migration along \hkl<1 1 0> in c-Si (VASP)
+ }
+
+ \small
+
+ {\color{blue}Method:}
+ \begin{itemize}
+  \item Continue with atomic positions of the last run
+  \item Displace the C atom in \hkl<1 1 0> direction
+  \item \hkl<1 1 0> direction fixed for the C atom
+  \item $4\times 4\times 3$ Type 1, $198+1$ atoms
+  \item Atoms with $x=0$ or $y=0$ or $z=0$ fixed
+ \end{itemize}
+ {\color{blue}Results:}
+ (Video \href{../video/c_in_si_smig_vasp.avi}{$\rhd_{\text{local}}$ } $|$
+ \href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/c_in_si_smig_vasp.avi}{$\rhd_{\text{remote url}}$})\\
+ \includegraphics[width=7cm]{c_100_110mig_01_vasp.ps} 
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Again: C \hkl<1 0 0> interstitial migration
+ }
+
+ \small
+
+ {\color{blue}The applied methods:}
+ \begin{enumerate}
+  \item Method
+        \begin{itemize}
+          \item Start in relaxed \hkl<1 0 0> interstitial configuration
+          \item Displace C atom along \hkl<1 1 0> direction
+          \item Relaxation (Berendsen thermostat)
+          \item Continue with configuration of the last run
+        \end{itemize} 
+  \item Method
+        \begin{itemize}
+          \item Place interstitial carbon at the respective coordinates
+                into the perfect Si matrix
+          \item Quench the system
+        \end{itemize} 
+ \end{enumerate}
+ {\color{blue}In both methods:}
+ \begin{itemize} 
+  \item Fixed border atoms
+  \item Applied \hkl<1 1 0> constraint for the C atom
+ \end{itemize}
+ {\color{red}Pitfalls} and {\color{green}refinements}:
+ \begin{itemize}
+  \item {\color{red}Fixed border atoms} $\rightarrow$
+        Relaxation of stress not possible\\
+        $\Rightarrow$
+        {\color{green}Fix only one Si atom} (the one furthermost to the defect)
+  \item {\color{red}\hkl<1 1 0> constraint not sufficient}\\
+        $\Rightarrow$ {\color{green}Apply 11x constraint}
+        (connecting line of initial and final C positions)
+ \end{itemize}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Again: C \hkl<1 0 0> interstitial migration (Albe)
+ }
+
+ Constraint applied by modifying the Velocity Verlet algorithm
+
+ {\color{blue}Results:}
+ (Video \href{../video/c_in_si_fmig_albe.avi}{$\rhd_{\text{local}}$ } $|$
+ \href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/c_in_si_fmig_albe.avi}{$\rhd_{\text{remote url}}$})\\
+ \begin{minipage}{6.3cm}
+ \includegraphics[width=6cm]{c_100_110fmig_01_albe.ps}
+ \end{minipage}
+ \begin{minipage}{6cm}
+ \begin{center}
+  Again there are jumps in energy corresponding to abrupt
+  structural changes as seen in the video
+ \end{center}
+ \end{minipage}
+ \begin{itemize}
+  \item Expected final configuration not obtained
+  \item Bonds to neighboured silicon atoms persist
+  \item C and neighboured Si atoms move along the direction of displacement
+  \item Even the bond to the lower left silicon atom persists
+ \end{itemize}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Again: C \hkl<1 0 0> interstitial migration (VASP)
+ }
+
+ Transformation for the Type 2 supercell
+
+ \small
+
+ \begin{minipage}[t]{4.2cm}
+ \underline{Starting configuration}\\
+ \includegraphics[width=3cm]{c_100_mig_vasp/start.eps}
+ \end{minipage}
+ \begin{minipage}[t]{4.0cm}
+ \vspace*{1.0cm}
+ $\Delta x=1.367\text{ \AA}$\\
+ $\Delta y=1.367\text{ \AA}$\\
+ $\Delta z=0.787\text{ \AA}$\\
+ \end{minipage}
+ \begin{minipage}[t]{4.2cm}
+ \underline{{\bf Expected} final configuration}\\
+ \includegraphics[width=3cm]{c_100_mig_vasp/final.eps}\\
+ \end{minipage}
+ \begin{minipage}{6.2cm}
+ Rotation angles:
+ \[
+ \alpha=45^{\circ}
+ \textrm{ , }
+ \beta=\arctan\frac{\Delta z}{\sqrt{2}\Delta x}=22.165^{\circ}
+ \]
+ \end{minipage}
+ \begin{minipage}{6.2cm}
+ Length of migration path:
+ \[
+ l=\sqrt{\Delta x^2+\Delta y^2+\Delta z^2}=2.087\text{ \AA}
+ \]
+ \end{minipage}\\[0.3cm]
+ Transformation of basis:
+ \[
+ T=ABA^{-1}A=AB \textrm{, mit }
+ A=\left(\begin{array}{ccc}
+ \cos\alpha & -\sin\alpha & 0\\
+ \sin\alpha & \cos\alpha & 0\\
+ 0 & 0 & 1
+ \end{array}\right)
+ \textrm{, }
+ B=\left(\begin{array}{ccc}
+ 1 & 0 & 0\\
+ 0 & \cos\beta & \sin\beta \\
+ 0 & -\sin\beta & \cos\beta
+ \end{array}\right)
+ \]
+ Atom coordinates transformed by: $T^{-1}=B^{-1}A^{-1}$
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Again: C \hkl<1 0 0> interstitial migration\\
+ }
+
+ {\color{blue}Reminder:}\\
+ Transformation needed since in VASP constraints can only be applied to
+ the basis vectors!\\
+ {\color{red}Problem:} (stupid me!)\\
+ Transformation of supercell 'destroys' the correct periodicity!\\
+ {\color{green}Solution:}\\
+ Find a supercell with one basis vector forming the correct constraint\\
+ {\color{red}Problem:}\\
+ Hard to find a supercell for the $22.165^{\circ}$ rotation\\
+
+ Another method to {\color{blue}\underline{estimate}} the migration energy:
+ \begin{itemize}
+  \item Assume an intermediate saddle point configuration during migration
+  \item Determine the energy of the saddle point configuration
+  \item Substract the saddle point configuration energy by
+        the energy of the initial (final) defect configuration
+ \end{itemize}
+ 
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  The C \hkl<1 0 0> defect configuration
+ }
+
+ Needed so often for input configurations ...\\[0.8cm]
+ \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}{5.5cm}
+ \scriptsize
+ \begin{center}
+ \begin{tabular}{|l|l|l|}
+ \hline
+  & a & b \\
+ \hline
+ \underline{VASP} & & \\
+ fractional & 0.1969 & 0.1211 \\
+ in \AA & 1.08 & 0.66 \\
+ \hline
+ \underline{Albe} & & \\
+ fractional & 0.1547 & 0.1676 \\
+ in \AA & 0.84 & 0.91 \\
+ \hline
+ \end{tabular}\\[0.2cm]
+ {\scriptsize\underline{PC (Vasp)}}
+ \includegraphics[width=6.1cm]{c_100_pc_vasp.ps}
+ \end{center}
+ \end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Again: C \hkl<1 0 0> interstitial migration (VASP)
+ }
+
+ $\hkl<0 0 -1> \rightarrow \hkl<0 0 1>$ migration
+ ($3\times 3\times 3$ Type 2):
+
+ \small
+
+ \begin{minipage}[t]{4.1cm}
+ \underline{Starting configuration}\\
+ \includegraphics[height=3.2cm]{c_100_mig_vasp/start.eps}
+ \begin{center}
+ $E_{\text{f}}=3.15 \text{ eV}$
+ \end{center}
+ \end{minipage}
+ \begin{minipage}[t]{4.1cm}
+ \underline{Intermediate configuration}\\
+ \includegraphics[height=3.2cm]{c_100_mig_vasp/00-1_001_im.eps}
+ \begin{center}
+ $E_{\text{f}}=4.41 \text{ eV}$
+ \end{center}
+ \end{minipage}
+ \begin{minipage}[t]{4.1cm}
+ \underline{Final configuration}\\
+ \includegraphics[height=3.2cm]{c_100_mig_vasp/final.eps}
+ \begin{center}
+ $E_{\text{f}}=3.17 \text{ eV}$
+ \end{center}
+ \end{minipage}\\[0.4cm]
+ \[
+ \Rightarrow \Delta E_{\text{f}} = E_{\text{mig}} = 1.26 \text{ eV}
+ \]
+
+ Unexpected \& ({\color{red}more} or {\color{orange}less}) fatal:
+ \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}$\bullet$}}
+ \end{itemize}
+ 
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Again: C \hkl<1 0 0> interstitial migration (VASP)
+ }
+
+ $\hkl<0 0 -1> \rightarrow \hkl<0 -1 0>$ migration
+ ($3\times 3\times 3$ Type 2):
+
+ \small
+
+ \begin{minipage}[t]{4.1cm}
+ \underline{Starting configuration}\\
+ \includegraphics[height=3.2cm]{c_100_mig_vasp/start.eps}
+ \begin{center}
+ $E_{\text{f}}=3.154 \text{ eV}$
+ \end{center}
+ \end{minipage}
+ \begin{minipage}[t]{4.1cm}
+ \underline{Intermediate configuration}\\
+ in progress ...
+ \begin{center}
+ $E_{\text{f}}=?.?? \text{ eV}$
+ \end{center}
+ \end{minipage}
+ \begin{minipage}[t]{4.1cm}
+ \underline{Final configuration}\\
+ \includegraphics[height=3.2cm]{c_100_mig_vasp/0-10.eps}
+ \begin{center}
+ $E_{\text{f}}=3.157 \text{ eV}$
+ \end{center}
+ \end{minipage}\\[0.4cm]
+ \[
+ \Rightarrow \Delta E_{\text{f}} = E_{\text{mig}} = ?.?? \text{ eV}
+ \]
+
+ \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}
+  \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\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\boldmath
+  Displacing the \hkl<1 1 0> Si-C split along \hkl<1 -1 0> (VASP)
+ }
+
+ \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}
 
 \end{document}