+\includegraphics[width=0.7\textwidth]{bc_00-1_albe_s.ps}
+%\includegraphics[width=13cm]{bc_00-1.ps}\\[5.6cm]
+%\begin{pspicture}(0,0)(0,0)
+%\psframe[linecolor=red,fillstyle=none](-7,2.7)(7.2,6)
+%\end{pspicture}
+%\begin{picture}(0,0)(140,-100)
+%\includegraphics[width=2.4cm]{albe_mig/bc_00-1_red_00.eps}
+%\end{picture}
+%\begin{picture}(0,0)(10,-100)
+%\includegraphics[width=2.4cm]{albe_mig/bc_00-1_red_01.eps}
+%\end{picture}
+%\begin{picture}(0,0)(-120,-100)
+%\includegraphics[width=2.4cm]{albe_mig/bc_00-1_red_02.eps}
+%\end{picture}
+%\begin{picture}(0,0)(25,-80)
+%\includegraphics[width=2.5cm]{110_arrow.eps}
+%\end{picture}
+%\begin{picture}(0,0)(215,-100)
+%\includegraphics[height=2.2cm]{001_arrow.eps}
+%\end{picture}\\
+%\begin{pspicture}(0,0)(0,0)
+%\psframe[linecolor=blue,fillstyle=none](-7,-0.5)(7.2,2.8)
+%\end{pspicture}
+%\begin{picture}(0,0)(160,-10)
+%\includegraphics[width=2.2cm]{albe_mig/bc_00-1_01.eps}
+%\end{picture}
+%\begin{picture}(0,0)(100,-10)
+%\includegraphics[width=2.2cm]{albe_mig/bc_00-1_02.eps}
+%\end{picture}
+%\begin{picture}(0,0)(10,-10)
+%\includegraphics[width=2.2cm]{albe_mig/bc_00-1_03.eps}
+%\end{picture}
+%\begin{picture}(0,0)(-120,-10)
+%\includegraphics[width=2.2cm]{albe_mig/bc_00-1_04.eps}
+%\end{picture}
+%\begin{picture}(0,0)(25,10)
+%\includegraphics[width=2.5cm]{100_arrow.eps}
+%\end{picture}
+%\begin{picture}(0,0)(215,-10)
+%\includegraphics[height=2.2cm]{010_arrow.eps}
+%\end{picture}
+\end{center}
+\caption[Migration barrier and structures of the \ci{} BC to {\hkl[0 0 -1]} DB transition using the classical EA potential.]{Migration barrier and structures of the \ci{} BC to \hkl[0 0 -1] DB transition using the classical EA potential. Two migration pathways are obtained for different time constants of the Berendsen thermostat. The lowest activation energy is \unit[2.2]{eV}.}
+\label{fig:defects:cp_bc_00-1_mig}
+% red: ./visualize -w 640 -h 480 -d saves/c_in_si_mig_bc_00-1_s20 -nll -0.56 -0.56 -0.7 -fur 0.2 0.2 0.0 -c 0.75 -1.25 -0.25 -L -0.25 -0.25 -0.25 -r 0.6 -B 0.1
+% blue: ./visualize -w 640 -h 480 -d saves/c_in_si_mig_bc_00-1_s20_tr100/ -nll -0.56 -0.56 -0.7 -fur 0.2 0.2 0.0 -c 0.0 -0.25 1.0 -L 0.0 -0.25 -0.25 -r 0.6 -B 0.1
+\end{figure}
+Fig.~\ref{fig:defects:cp_bc_00-1_mig} shows the evolution of structure and energy along the \ci{} BC to \hkl[0 0 -1] DB transition.
+Since the \ci{} BC configuration is unstable relaxing into the \hkl[1 1 0] DB configuration within this potential, the low kinetic energy state is used as a starting configuration.
+Two different pathways are obtained for different time constants of the Berendsen thermostat.
+With a time constant of \unit[1]{fs}, the C atom resides in the \hkl(-1 1 0) plane
+ resulting in a migration barrier of \unit[2.4]{eV}.
+However, weaker coupling to the heat bath realized by an increase of the time constant to \unit[100]{fs} enables the C atom to move out of the \hkl(-1 1 0) plane already at the beginning, which is accompanied by a reduction in energy, approaching the final configuration on a curved path.
+The energy barrier of this path is \unit[0.2]{eV} lower in energy than the direct migration within the \hkl(-1 1 0) plane.
+However, the investigated pathways cover an activation energy approximately twice as high as the one obtained by quantum-mechanical calculations.
+If the entire transition of the \hkl[0 0 -1] into the \hkl[0 0 1] configuration is considered a two step process passing the intermediate BC configuration, an additional activation energy of \unit[0.5]{eV} is necessary to escape the BC towards the \hkl[0 0 1] configuration.
+Assuming equal preexponential factors for both diffusion steps, the total probability of diffusion is given by $\exp\left((2.2\,\text{eV}+0.5\,\text{eV})/k_{\text{B}}T\right)$.
+Thus, the activation energy should be located within the range of \unit[2.2--2.7]{eV}.
+
+\begin{figure}[tp]
+\begin{center}
+\includegraphics[width=0.7\textwidth]{00-1_0-10_albe_s.ps}
+\end{center}
+\caption{Migration barrier and structures of the \ci{} \hkl[0 0 -1] to \hkl[0 -1 0] DB transition using the classical EA potential.}
+% red: ./visualize -w 640 -h 480 -d saves/c_in_si_mig_00-1_0-10_s20 -nll -0.56 -0.56 -0.8 -fur 0.3 0.2 0 -c -0.125 -1.7 0.7 -L -0.125 -0.25 -0.25 -r 0.6 -B 0.1
+\label{fig:defects:cp_00-1_0-10_mig}
+\end{figure}
+\begin{figure}[tp]
+\begin{center}
+\includegraphics[width=0.7\textwidth]{00-1_ip0-10.ps}
+\end{center}
+\caption{Reorientation barrier of the \ci{} \hkl[0 0 -1] to \hkl[0 -1 0] DB transition in place using the classical EA potential.}
+\label{fig:defects:cp_00-1_ip0-10_mig}
+\end{figure}
+Figures~\ref{fig:defects:cp_00-1_0-10_mig} and~\ref{fig:defects:cp_00-1_ip0-10_mig} show the migration barriers of the \ci{} \hkl[0 0 -1] to \hkl[0 -1 0] DB transition.
+In the first case, the transition involves a change in the lattice site of the C atom whereas in the second case, a reorientation at the same lattice site takes place.
+In the first case, the pathways for the two different time constants look similar.
+A local minimum exists in between two peaks of the graph.
+The corresponding configuration, which is illustrated for the results obtained for a time constant of \unit[1]{fs}, looks similar to the \ci{} \hkl[1 1 0] configuration.
+Indeed, this configuration is obtained by relaxation simulations without constraints of configurations near the minimum.
+Activation energies of roughly \unit[2.8]{eV} and \unit[2.7]{eV} are needed for migration.
+
+The \ci{} \hkl[1 1 0] configuration seems to play a decisive role in all migration pathways in the classical potential calculations.
+As mentioned above, the starting configuration of the first migration path, i.e.\ the BC configuration, is fixed to be a transition point but in fact is unstable.
+Further relaxation of the BC configuration results in the \ci{} \hkl[1 1 0] configuration.
+Even the last two pathways show configurations almost identical to the \ci{} \hkl[1 1 0] configuration, which constitute local minima within the pathways.
+Thus, migration pathways involving the \ci{} \hkl[1 1 0] DB configuration as a starting or final configuration are further investigated.
+\begin{figure}[tp]
+\begin{center}
+\includegraphics[width=0.7\textwidth]{110_mig.ps}
+\end{center}
+\caption[{Migration barriers of the \ci{} \hkl[1 1 0] DB to BC, \hkl[0 0 -1] and \hkl[0 -1 0] (in place) transition.}]{Migration barriers of the \ci{} \hkl[1 1 0] DB to BC (blue), \hkl[0 0 -1] (green) and \hkl[0 -1 0] (in place, red) transition. Solid lines show results for a time constant of \unit[1]{fs} and dashed lines correspond to simulations employing a time constant of \unit[100]{fs}.}
+\label{fig:defects:110_mig}
+\end{figure}
+Fig.~\ref{fig:defects:110_mig} shows migration barriers of the \ci{} \hkl[1 1 0] DB to \hkl[0 0 -1], \hkl[0 -1 0] (in place) and BC configuration.
+As expected, there is no maximum for the transition into the BC configuration.
+As mentioned earlier, the BC configuration itself constitutes a saddle point configuration relaxing into the energetically more favorable \hkl[1 1 0] DB configuration.
+An activation energy of \unit[2.2]{eV} is necessary to reorientate the \hkl[0 0 -1] into the \hkl[1 1 0] DB configuration, which is \unit[1.3]{eV} higher in energy.
+Residing in this state another \unit[0.90]{eV} is enough to make the C atom form a \hkl[0 0 -1] DB configuration with the Si atom of the neighbored lattice site.
+In contrast to quantum-mechanical calculations, in which the direct transition is the energetically most favorable transition and the transition composed of the intermediate migration steps is very unlikely to occur, the just presented pathway is much more conceivable in classical potential simulations since the energetically most favorable transition found so far is likewise composed of two migration steps with activation energies of \unit[2.2]{eV} and \unit[0.5]{eV}, for which the intermediate state is the BC configuration, which is unstable.
+Thus, the just proposed migration path, which involves the \hkl[1 1 0] interstitial configuration, becomes even more probable than the initially proposed path, which involves the BC configuration that is, in fact, unstable.
+Due to these findings, the respective path is proposed to constitute the diffusion-describing path.
+The evolution of structure and configurational energy is displayed again in Fig.~\ref{fig:defects:involve110}.
+\begin{figure}[tp]
+\begin{center}
+\includegraphics[width=0.7\textwidth]{00-1_110_0-10_mig_albe.ps}
+\end{center}
+\caption[Migration barrier and structures of the \ci{} {\hkl[0 0 -1]} to the {\hkl[0 -1 0]} DB transition involving the {\hkl[1 1 0]} DB configuration.]{Migration barrier and structures of the \ci{} \hkl[0 0 -1] (left) to the \hkl[0 -1 0] DB (right) transition involving the \hkl[1 1 0] DB (center) configuration. Migration simulations are performed utilizing time constants of \unit[1]{fs} (solid line) and \unit[100]{fs} (dashed line) for the Berendsen thermostat.}
+\label{fig:defects:involve110}
+\end{figure}
+Approximately \unit[2.2]{eV} are needed to turn the \ci{} \hkl[0 0 -1] into the \hkl[1 1 0] DB located at the neighbored lattice site in \hkl[1 1 -1] direction.
+Another barrier of \unit[0.90]{eV} exists for the rotation into the \ci{} \hkl[0 -1 0] DB configuration for the path obtained with a time constant of \unit[100]{fs} for the Berendsen thermostat.
+Roughly the same amount would be necessary to excite the C$_{\text{i}}$ \hkl[1 1 0] DB to the BC configuration (\unit[0.40]{eV}) and a successive migration into the \hkl[0 0 1] DB configuration (\unit[0.50]{eV}) as displayed in Fig.~\ref{fig:defects:110_mig} and Fig.~\ref{fig:defects:cp_bc_00-1_mig}.
+The former diffusion process, however, would more nicely agree with the {\em ab initio} path since the migration is accompanied by a rotation of the DB orientation.
+By considering a two step process and assuming equal preexponential factors for both diffusion steps, the probability of the total diffusion event is given by $\exp(\frac{\unit[2.24]{eV}+\unit[0.90]{eV}}{k_{\text{B}}T})$, which corresponds to a single diffusion barrier that is 3.5 times higher than the barrier obtained by {\em ab initio} calculations.
+
+\subsection{Conclusions}
+
+Although classical potential simulations reproduce the same order in energy of the \ci{} \hkl<1 0 0> and \hkl<1 1 0> DB interstitial configurations as obtained by more accurate quantum-mechanical calculations, the obtained migration pathways and resulting activation energies differ to a great extent.
+On the one hand, the most favorable pathways differ.
+However, the pathway, which is considered most probable in the classical potential treatment, exhibits the same starting and final configuration of the DB structure as well as the change in orientation during migration as obtained by quantum-mechanical calculations.
+On the other hand, the activation energy obtained by classical potential simulations is tremendously overestimated by a factor of 2.4 to 3.5.
+The overestimated barrier is due to the short range character of the potential, which drops the interaction to zero within the first and next neighbor distance.
+Since the total binding energy is accommodated within a short distance, which according to the universal energy relation would usually correspond to a much larger distance, unphysical high forces between two neighbored atoms arise.
+This is explained in more detail in a previous study~\cite{mattoni2007}.
+Thus, atomic diffusion is wrongly described in the classical potential approach.
+The probability of already rare diffusion events is further decreased for this reason.
+However, agglomeration of C and diffusion of Si self-interstitials are an important part of the proposed SiC precipitation mechanism.
+Thus, a serious limitation that has to be taken into account for appropriately modeling the C/Si system using the otherwise quite promising EA potential is revealed.
+Possible workarounds are discussed in more detail in section~\ref{section:md:limit}.
+
+\section{Combination of point defects and related diffusion processes}
+
+The study proceeds with a structural and energetic investigation of pairs of the ground-state and, thus, most probable defect configurations that are believed to be fundamental in the Si to SiC conversion.
+Investigations are restricted to quantum-mechanical calculations.
+\begin{figure}[tp]