+ Limitations of molecular dynamics and short range potentials
+ }
+
+\footnotesize
+
+\vspace{0.2cm}
+
+\underline{Time scale problem of MD}\\[0.2cm]
+Minimize integration error\\
+$\Rightarrow$ discretization considerably smaller than
+ reciprocal of fastest vibrational mode\\[0.1cm]
+Order of fastest vibrational mode: $10^{13} - 10^{14}\text{ Hz}$\\
+$\Rightarrow$ suitable choice of time step:
+ $\tau=1\text{ fs}=10^{-15}\text{ s}$\\
+$\Rightarrow$ {\color{red}\underline{slow}} phase space propagation\\[0.1cm]
+Several local minima in energy surface separated by large energy barriers\\
+$\Rightarrow$ transition event corresponds to a multiple
+ of vibrational periods\\
+$\Rightarrow$ phase transition made up of {\color{red}\underline{many}}
+ infrequent transition events\\[0.1cm]
+{\color{blue}Accelerated methods:}
+\underline{Temperature accelerated} MD (TAD), self-guided MD \ldots
+
+\vspace{0.3cm}
+
+\underline{Limitations related to the short range potential}\\[0.2cm]
+Cut-off function pushing forces and energies to zero between 1$^{\text{st}}$
+and 2$^{\text{nd}}$ next neighbours\\
+$\Rightarrow$ overestimated unphysical high forces of next neighbours
+
+\vspace{0.3cm}
+
+\framebox{
+\color{red}
+Potential enhanced problem of slow phase space propagation
+}
+
+\vspace{0.3cm}
+
+\underline{Approach to the (twofold) problem}\\[0.2cm]
+Increased temperature simulations without TAD corrections\\
+(accelerated methods or higher time scales exclusively not sufficient)
+
+\begin{picture}(0,0)(-260,-30)
+\framebox{
+\begin{minipage}{4.2cm}
+\tiny
+\begin{center}
+\vspace{0.03cm}
+\underline{IBS}
+\end{center}
+\begin{itemize}
+\item 3C-SiC also observed for higher T
+\item higher T inside sample
+\item structural evolution vs.\\
+ equilibrium properties
+\end{itemize}
+\end{minipage}
+}
+\end{picture}
+
+\begin{picture}(0,0)(-305,-155)
+\framebox{
+\begin{minipage}{2.5cm}
+\tiny
+\begin{center}
+retain proper\\
+thermodynmic sampling
+\end{center}
+\end{minipage}
+}
+\end{picture}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Increased temperature simulations at low C concentration
+ }
+
+\small
+
+\begin{minipage}{6.5cm}
+\includegraphics[width=6.4cm]{tot_pc_thesis.ps}
+\end{minipage}
+\begin{minipage}{6.5cm}
+\includegraphics[width=6.4cm]{tot_pc3_thesis.ps}
+\end{minipage}
+
+\begin{minipage}{6.5cm}
+\includegraphics[width=6.4cm]{tot_pc2_thesis.ps}
+\end{minipage}
+\begin{minipage}{6.5cm}
+\scriptsize
+ \underline{Si-C bonds:}
+ \begin{itemize}
+ \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
+ \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
+ \end{itemize}
+ \underline{Si-Si bonds:}
+ {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
+ ($\rightarrow$ 0.325 nm)\\[0.1cm]
+ \underline{C-C bonds:}
+ \begin{itemize}
+ \item C-C next neighbour pairs reduced (mandatory)
+ \item Peak at 0.3 nm slightly shifted
+ \begin{itemize}
+ \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
+ $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
+ combinations (|)\\
+ $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
+ ($\downarrow$)
+ \item Range [|-$\downarrow$]:
+ {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
+ with nearby Si$_{\text{I}}$}
+ \end{itemize}
+ \end{itemize}
+\end{minipage}
+
+\begin{picture}(0,0)(-330,-74)
+\color{blue}
+\framebox{
+\begin{minipage}{1.6cm}
+\tiny
+\begin{center}
+stretched SiC\\[-0.1cm]
+in c-Si
+\end{center}
+\end{minipage}
+}
+\end{picture}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Increased temperature simulations at high C concentration
+ }
+
+\footnotesize
+
+\begin{minipage}{6.5cm}
+\includegraphics[width=6.4cm]{12_pc_thesis.ps}
+\end{minipage}
+\begin{minipage}{6.5cm}
+\includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
+\end{minipage}
+
+\begin{center}
+Decreasing cut-off artifact\\
+High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
+$\Rightarrow$ hard to categorize
+\end{center}
+
+\vspace{0.1cm}
+
+\framebox{
+\begin{minipage}[t]{6.0cm}
+0.186 nm: Si-C pairs $\uparrow$\\
+(as expected in 3C-SiC)\\[0.2cm]
+0.282 nm: Si-C-C\\[0.2cm]
+$\approx$0.35 nm: C-Si-Si
+\end{minipage}
+}
+\begin{minipage}{0.2cm}
+\hfill
+\end{minipage}
+\framebox{
+\begin{minipage}[t]{6.0cm}
+0.15 nm: C-C pairs $\uparrow$\\
+(as expected in graphite/diamond)\\[0.2cm]
+0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm]
+0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C
+\end{minipage}
+}
+
+\vspace{0.1cm}
+
+\begin{center}
+{\color{red}Amorphous} SiC-like phase remains\\
+Slightly sharper peaks
+$\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics}
+due to temperature\\[0.1cm]
+\framebox{
+\bf
+Continue with higher temperatures and longer time scales
+}
+\end{center}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Valuation of a practicable temperature limit