\usepackage{upgreek}
+\usepackage{miller}
+
\begin{document}
\extraslideheight{10in}
\includegraphics[width=7.0cm]{si_self_int.ps}
\end{minipage}
\begin{minipage}{5cm}
- $E_{\textrm{f}}^{\textrm{110},\,32\textrm{pc}}=3.38\textrm{ eV}$\\
+ $E_{\textrm{f}}^{\hkl<1 1 0>,\,32\textrm{pc}}=3.38\textrm{ eV}$\\
$E_{\textrm{f}}^{\textrm{tet},\,32\textrm{pc}}=3.41\textrm{ eV}$\\
$E_{\textrm{f}}^{\textrm{hex},\,32\textrm{pc}}=3.42\textrm{ eV}$\\
$E_{\textrm{f}}^{\textrm{vac},\,32\textrm{pc}}=3.51\textrm{ eV}$\\\\
$E_{\textrm{f}}^{\textrm{hex},\,54\textrm{pc}}=3.42\textrm{ eV}$\\
$E_{\textrm{f}}^{\textrm{tet},\,54\textrm{pc}}=3.45\textrm{ eV}$\\
$E_{\textrm{f}}^{\textrm{vac},\,54\textrm{pc}}=3.47\textrm{ eV}$\\
- $E_{\textrm{f}}^{\textrm{110},\,54\textrm{pc}}=3.48\textrm{ eV}$
+ $E_{\textrm{f}}^{\hkl<1 1 0>,\,54\textrm{pc}}=3.48\textrm{ eV}$
\end{minipage}
Comparison with literature (PRL 88 235501 (2002)):\\[0.2cm]
\end{itemize}
\end{minipage}
\begin{minipage}{5cm}
- $E_{\textrm{f}}^{\textrm{110}}=3.31 / 2.88\textrm{ eV}$\\
+ $E_{\textrm{f}}^{\hkl<1 1 0>}=3.31 / 2.88\textrm{ eV}$\\
$E_{\textrm{f}}^{\textrm{hex}}=3.31 / 2.87\textrm{ eV}$\\
$E_{\textrm{f}}^{\textrm{vac}}=3.17 / 3.56\textrm{ eV}$
\end{minipage}
\begin{center}
Error in lattice constant of plain Si ($1\times 1\times 1$ Type 2):
$0.025\,\%$\\
- Error in position of the 110 interstitital in Si ($1\times 1\times 1$ Type 2):
+ 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}
\begin{slide}
- {\large\bf
+ {\large\bf\boldmath
Energy cut-off for $\Gamma$-point only caclulations
}
\begin{slide}
- {\large\bf
- C 100 interstitial migration along 110 in c-Si (Albe potential)
+ {\large\bf\boldmath
+ C \hkl<1 0 0> interstitial migration along \hkl<1 1 0>
+ in c-Si (Albe)
}
\small
\item Fix border atoms of the simulation cell
\item Constraints and displacement of the C atom:
\begin{itemize}
- \item along {\color{green}110 direction}\\
+ \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
\begin{slide}
- {\large\bf
- C 100 interstitial migration along 110 in c-Si (Albe potential)
+ {\large\bf\boldmath
+ C \hkl<1 0 0> interstitial migration along \hkl<1 1 0>
+ in c-Si (Albe)
}
\footnotesize
\begin{slide}
- {\large\bf
- C 100 interstitial migration along 110 in c-Si (Albe potential)\\
+ {\large\bf\boldmath
+ C \hkl<1 0 0> interstitial migration along \hkl<1 1 0>
+ in c-Si (Albe)\\
}
Displacement step size decreased to
\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}
+
+\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
- C 100 interstitial migration along 110 in c-Si (VASP)
+ 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
- \vspace*{1cm}
- \ldots simulations running!
- \vspace*{1cm}
- \begin{minipage}{5cm}
+ \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 $\Delta z$
+ \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}{7cm}
+ \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
+ \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
+ 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
+ Density Functional Theory
+ }
+
+ Hohenberg-Kohn theorem
+
+ \small
+
\end{slide}
projects / lectures / latex.git / blobdiff