+A measure for the mobility of interstitial C is the activation energy necessary for the migration from one stable position to another.
+The stable defect geometries have been discussed in the previous subsection.
+In the following, the problem of interstitial C migration in Si is considered.
+Since the \ci{} \hkl<1 0 0> DB is the most probable, hence, most important configuration, the migration of this defect atom from one site of the Si host lattice to a neighboring site is in the focus of investigation.
+\begin{figure}[tp]
+\begin{center}
+%
+\begin{minipage}{15cm}
+\centering
+\framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 0 1]}\\
+\begin{minipage}{4.5cm}
+\includegraphics[width=4.5cm]{c_pd_vasp/100_2333.eps}
+\end{minipage}
+\begin{minipage}{0.5cm}
+$\rightarrow$
+\end{minipage}
+\begin{minipage}{4.5cm}
+\includegraphics[width=4.5cm]{c_pd_vasp/bc_2333.eps}
+\end{minipage}
+\begin{minipage}{0.5cm}
+$\rightarrow$
+\end{minipage}
+\begin{minipage}{4.5cm}
+\includegraphics[width=4.5cm]{c_pd_vasp/100_next_2333.eps}
+\end{minipage}
+\end{minipage}\\[0.5cm]
+%
+\begin{minipage}{15cm}
+\centering
+\framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 -1 0]}\\
+\begin{minipage}{4.5cm}
+\includegraphics[width=4.5cm]{c_pd_vasp/100_2333.eps}
+\end{minipage}
+\begin{minipage}{0.5cm}
+$\rightarrow$
+\end{minipage}
+\begin{minipage}{4.5cm}
+\includegraphics[width=4.5cm]{c_pd_vasp/00-1-0-10_2333.eps}
+\end{minipage}
+\begin{minipage}{0.5cm}
+$\rightarrow$
+\end{minipage}
+\begin{minipage}{4.5cm}
+\includegraphics[width=4.5cm]{c_pd_vasp/0-10_2333.eps}
+\end{minipage}
+\end{minipage}\\[0.5cm]
+%
+\begin{minipage}{15cm}
+\centering
+\framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 -1 0] (in place)}\\
+\begin{minipage}{4.5cm}
+\includegraphics[width=4.5cm]{c_pd_vasp/100_2333.eps}
+\end{minipage}
+\begin{minipage}{0.5cm}
+$\rightarrow$
+\end{minipage}
+\begin{minipage}{4.5cm}
+\includegraphics[width=4.5cm]{c_pd_vasp/00-1_ip0-10_2333.eps}
+\end{minipage}
+\begin{minipage}{0.5cm}
+$\rightarrow$
+\end{minipage}
+\begin{minipage}{4.5cm}
+\includegraphics[width=4.5cm]{c_pd_vasp/0-10_ip_2333.eps}
+\end{minipage}
+\end{minipage}
+\end{center}
+\caption{Conceivable migration pathways among two \ci{} \hkl<1 0 0> DB configurations.}
+\label{img:defects:c_mig_path}
+\end{figure}
+Three different migration paths are accounted in this work, which are displayed in Fig.~\ref{img:defects:c_mig_path}.
+The first investigated migration is a transition of a \hkl[0 0 -1] into a \hkl[0 0 1] DB interstitial configuration.
+During this migration the C atom is changing its Si DB partner.
+The new partner is the one located at $a_{\text{Si}}/4 \hkl[1 1 -1]$ relative to the initial one, where $a_{\text{Si}}$ is the Si lattice constant.
+Two of the three bonds to the next neighbored Si atoms are preserved while the breaking of the third bond and the accompanying formation of a new bond is observed.
+The C atom resides in the \hkl(-1 1 0) plane.
+This transition involves the intermediate BC configuration.
+However, results discussed in the previous section indicate that the BC configuration is a real local minimum.
+Thus, the \hkl[0 0 -1] to \hkl[0 0 1] migration can be thought of a two-step mechanism, in which the intermediate BC configuration constitutes a metastable configuration.
+Due to symmetry, it is enough to consider the transition from the BC to a \hkl<1 0 0> configuration or vice versa.
+In the second path, the C atom is changing its Si partner atom as in path one.
+However, the trajectory of the C atom is no longer proceeding in the \hkl(-1 1 0) plane.
+The orientation of the new DB configuration is transformed from \hkl[0 0 -1] to \hkl[0 -1 0].
+Again, one bond is broken while another one is formed.
+As a last migration path, the defect is only changing its orientation.
+Thus, this path is not responsible for long-range migration.
+The Si DB partner remains the same.
+The bond to the face-centered Si atom at the bottom of the unit cell breaks and a new one is formed to the face-centered atom at the forefront of the unit cell.
+
+\subsection{Migration paths obtained by first-principles calculations}
+
+\begin{figure}[tp]
+\begin{center}
+\includegraphics[width=0.7\textwidth]{im_00-1_nosym_sp_fullct_thesis_vasp_s.ps}
+\end{center}
+\caption[Migration barrier and structures of the {\hkl[0 0 -1]} DB to BC transition.]{Migration barrier and structures of the \hkl[0 0 -1] DB (left) to BC (right) transition. Bonds of the C atom are illustrated by blue lines.}
+\label{fig:defects:00-1_001_mig}
+\end{figure}
+In Fig.~\ref{fig:defects:00-1_001_mig} results of the \hkl[0 0 -1] to \hkl[0 0 1] migration fully described by the migration of the \hkl[0 0 -1] to the BC configuration is displayed.
+To reach the BC configuration, which is \unit[0.94]{eV} higher in energy than the \hkl[0 0 -1] DB configuration, an energy barrier of approximately \unit[1.2]{eV} given by the saddle point structure at a displacement of \unit[60]{\%} has to be passed.
+This amount of energy is needed to break the bond of the C atom to the Si atom at the bottom left.
+In a second process \unit[0.25]{eV} of energy are needed for the system to revert into a \hkl<1 0 0> configuration.
+
+\begin{figure}[tp]
+\begin{center}
+\includegraphics[width=0.7\textwidth]{00-1_0-10_vasp_s.ps}
+\end{center}
+\caption[Migration barrier and structures of the {\hkl[0 0 -1]} DB to the {\hkl[0 -1 0]} DB transition.]{Migration barrier and structures of the \hkl[0 0 -1] DB (left) to the \hkl[0 -1 0] DB (right) transition. Bonds of the C atom are illustrated by blue lines.}
+\label{fig:defects:00-1_0-10_mig}
+\end{figure}
+Fig.~\ref{fig:defects:00-1_0-10_mig} shows the migration barrier and structures of the \ci{} \hkl[0 0 -1] to \hkl[0 -1 0] DB transition.
+The resulting migration barrier of approximately \unit[0.9]{eV} is very close to the experimentally obtained values of \unit[0.70]{eV}~\cite{lindner06}, \unit[0.73]{eV}~\cite{song90} and \unit[0.87]{eV}~\cite{tipping87}.
+
+\begin{figure}[tp]
+\begin{center}
+\includegraphics[width=0.7\textwidth]{00-1_ip0-10_nosym_sp_fullct_vasp_s.ps}
+\end{center}
+\caption[Reorientation barrier and structures of the {\hkl[0 0 -1]} DB to the {\hkl[0 -1 0]} DB transition in place.]{Reorientation barrier and structures of the \hkl[0 0 -1] DB (left) to the \hkl[0 -1 0] DB (right) transition in place. Bonds of the carbon atoms are illustrated by blue lines.}
+\label{fig:defects:00-1_0-10_ip_mig}
+\end{figure}
+The third migration path, in which the DB is changing its orientation, is shown in Fig.~\ref{fig:defects:00-1_0-10_ip_mig}.
+An energy barrier of roughly \unit[1.2]{eV} is observed.
+Experimentally measured activation energies for reorientation range from \unit[0.77]{eV} to \unit[0.88]{eV}~\cite{watkins76,song90}.
+Thus, this pathway is more likely to be composed of two consecutive steps of the second path.
+
+Since the activation energy of the first and last migration path is much greater than the experimental value, the second path is identified to be responsible as a migration path for the most likely C interstitial in Si explaining both, annealing and reorientation experiments.
+The activation energy of roughly \unit[0.9]{eV} nicely compares to experimental values reinforcing the correct identification of the C-Si DB diffusion mechanism.
+Slightly increased values compared to experiment might be due to the tightened constraints applied in the modified CRT approach.
+Nevertheless, the theoretical description performed in this work is improved compared to a former study~\cite{capaz94}, which underestimates the experimental value by \unit[35]{\%}.
+In addition, it is finally shown that the BC configuration, for which spin polarized calculations are necessary, constitutes a real local minimum instead of a saddle point configuration due to the presence of restoring forces for displacements in migration direction.
+
+\begin{figure}[tp]
+\begin{center}
+\includegraphics[width=0.7\textwidth]{vasp_mig/110_mig_vasp.ps}
+%\begin{picture}(0,0)(140,0)
+%\includegraphics[width=2.2cm]{vasp_mig/00-1_b.eps}
+%\end{picture}
+%\begin{picture}(0,0)(20,0)
+%\includegraphics[width=2.2cm]{vasp_mig/00-1_ip0-10_sp.eps}
+%\end{picture}
+%\begin{picture}(0,0)(-120,0)
+%\includegraphics[width=2.2cm]{vasp_mig/0-10_b.eps}
+%\end{picture}
+\end{center}
+\caption[{Migration barriers of the \hkl[1 1 0] DB to BC, \hkl[0 0 -1] and \hkl[0 -1 0] (in place) C-Si DB transition.}]{Migration barriers of the \hkl[1 1 0] DB to BC (blue), \hkl[0 0 -1] (green) and \hkl[0 -1 0] (in place, red) C-Si DB transition.}
+\label{fig:defects:110_mig_vasp}
+\end{figure}
+Further migration pathways, in particular those occupying other defect configurations than the \hkl<1 0 0>-type either as a transition state or a final or starting configuration, are totally conceivable.
+This is investigated in the following in order to find possible migration pathways that have an activation energy lower than the ones found up to now.
+The next energetically favorable defect configuration is the \hkl<1 1 0> C-Si DB interstitial.
+Fig.~\ref{fig:defects:110_mig_vasp} shows the migration barrier of the \hkl[1 1 0] C-Si DB to the BC, \hkl[0 0 -1] and \hkl[0 -1 0] (in place) transition.
+Indeed less than \unit[0.7]{eV} are necessary to turn the \hkl[0 -1 0] to the \hkl[1 1 0] C-Si DB interstitial.
+This transition is carried out in place, i.e.\ the Si DB pair is not changed and both, the Si and C atom share the initial lattice site.
+Thus, this transition does not contribute to long-range diffusion.
+Once the C atom resides in the \hkl[1 1 0] DB interstitial configuration, it can migrate into the BC configuration requiring approximately \unit[0.95]{eV} of activation energy, which is only slightly higher than the activation energy needed for the \hkl[0 0 -1] to \hkl[0 -1 0] pathway as shown in Fig.~\ref{fig:defects:00-1_0-10_mig}.
+As already known from the migration of the \hkl[0 0 -1] to the BC configuration discussed in Fig.~\ref{fig:defects:00-1_001_mig}, another \unit[0.25]{eV} are needed to turn back from the BC to a \hkl<1 0 0>-type interstitial.
+However, due to the fact that this migration consists of three single transitions with the second one having an activation energy slightly higher than observed for the direct transition, this sequence of paths is considered very unlikely to occur.
+The migration barrier of the \hkl[1 1 0] to \hkl[0 0 -1] transition, in which the C atom is changing its Si partner and, thus, moving to the neighbored lattice site, corresponds to approximately \unit[1.35]{eV}.
+During this transition the C atom is escaping the \hkl(-1 1 0) plane approaching the final configuration on a curved path.
+This barrier is much higher than the ones found previously, which again make this transition very unlikely to occur.
+For this reason, the assumption that C diffusion and reorientation is achieved by transitions of the type presented in Fig.~\ref{fig:defects:00-1_0-10_mig} is reinforced.
+
+%As mentioned earlier the procedure to obtain the migration barriers differs from the usually applied procedure in two ways.
+%Firstly constraints to move along the displacement direction are applied on all atoms instead of solely constraining the diffusing atom.
+%Secondly the constrainted directions are not kept constant to the initial displacement direction.
+%Instead they are updated for every displacement step.
+%These modifications to the usual procedure are applied to avoid abrupt changes in structure and free energy on the one hand and to make sure the expected final configuration is reached on the other hand.
+%Due to applying updated constraints on all atoms the obtained migration barriers and pathes might be overestimated and misguided.
+%To reinforce the applicability of the employed technique the obtained activation energies and migration pathes for the \hkl<0 0 -1> to \hkl<0 -1 0> transition are compared to two further migration calculations, which do not update the constrainted direction and which only apply updated constraints on three selected atoms, that is the diffusing C atom and the Si dumbbell pair in the initial and final configuration.
+%Results are presented in figure~\ref{fig:defects:00-1_0-10_cmp}.
+%\begin{figure}[tp]
+%\begin{center}
+%\includegraphics[width=13cm]{vasp_mig/00-1_0-10_nosym_sp_cmp.ps}
+%\end{center}
+%\caption[Comparison of three different techniques for obtaining migration barriers and pathways applied to the \hkl<0 0 -1> to \hkl<0 -1 0> C-Si dumbbell transition.]{Comparison of three different techniques for obtaining migration barriers and pathways applied to the \hkl<0 0 -1> to \hkl<0 -1 0> C-Si dumbbell transition.}
+%\label{fig:defects:00-1_0-10_cmp}
+%\end{figure}
+%The method without updating the constraints but still applying them to all atoms shows a delayed crossing of the saddle point.
+%This is understandable since the update results in a more aggressive advance towards the final configuration.
+%In any case the barrier obtained is slightly higher, which means that it does not constitute an energetically more favorable pathway.
+%The method in which the constraints are only applied to the diffusing C atom and two Si atoms, ...
+
+% todo if there is plenty of time ... reinvestigate above stuff
+
+\subsection{Migration described by classical potential calculations}
+\label{subsection:defects:mig_classical}
+
+\begin{figure}[tp]
+\begin{center}
+\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 the 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 this local 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 involving the BC configuration.
+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]
+% ./visualize_contcar -w 640 -h 480 -d results/.../CONTCAR -nll -0.20 -0.20 -0.6 -fur 1.2 1.2 0.6 -c 0.5 -1.5 0.3 -L 0.5 0 0 -r 0.6 -m 3.0 0.0 0.0 0.0 3.0 0.0 0.0 0.0 3.0 -A -1 2.465
+\begin{center}
+\subfigure[]{\label{fig:defects:combos_ci}\includegraphics[width=0.3\textwidth]{combos_ci_col.eps}}
+\hspace{0.5cm}
+\subfigure[]{\label{fig:defects:combos_si}\includegraphics[width=0.3\textwidth]{combos.eps}}
+\end{center}
+\caption[Position of the initial \ci{} {\hkl[0 0 -1]} DB and of the lattice site chosen for the initial \si{} \hkl<1 1 0> DB.]{Position of the initial \ci{} \hkl[0 0 -1] DB (I) (a) and of the lattice site chosen for the initial \si{} \hkl<1 1 0> DB (\si) (b). Lattice sites for the second defect used for investigating defect pairs are numbered from 1 to 5. For black/red/blue numbers, one/two/four possible atom(s) exist for the second defect to create equivalent defect combinations.}
+\label{fig:defects:combos}
+\end{figure}
+Fig.~\ref{fig:defects:combos} schematically displays the initial \ci{} \hkl[0 0 -1] DB structure (Fig.~\ref{fig:defects:combos_ci}) as well as the lattice site chosen for the initial \si{} \hkl<1 1 0> DB (Fig.~\ref{fig:defects:combos_si}) and various positions for the second defect (1--5) that are used for investigating defect pairs.
+The color of the number denotes the amount of possible atoms for the second defect resulting in equivalent configurations.
+Binding energies of the defect pair are determined by equation~\ref{eq:basics:e_bind}.
+Next to formation and binding energies, migration barriers are investigated, which allow to draw conclusions on the probability of the formation of such defect complexes by thermally activated diffusion processes.
+
+\subsection[Pairs of \ci{} \hkl<1 0 0>-type interstitials]{\boldmath Pairs of \ci{} \hkl<1 0 0>-type interstitials}
+\label{subsection:defects:c-si_comb}
+
+\ci{} pairs of the \hkl<1 0 0>-type are investigated in the first part.
+\begin{table}[tp]
+\begin{center}
+\begin{tabular}{l c c c c c c}
+\hline
+\hline
+ & 1 & 2 & 3 & 4 & 5 & R\\
+ \hline
+ \hkl[0 0 -1] & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
+ \hkl[0 0 1] & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
+ \hkl[0 -1 0] & {\color{orange}-2.39} & -0.17 & {\color{green}-0.10} & {\color{blue}-0.27} & {\color{magenta}-1.88} & {\color{gray}-0.05}\\
+ \hkl[0 1 0] & {\color{cyan}-2.25} & -1.90 & {\color{cyan}-2.25} & {\color{purple}-0.12} & {\color{violet}-1.38} & {\color{yellow}-0.06}\\
+ \hkl[-1 0 0] & {\color{orange}-2.39} & -0.36 & {\color{cyan}-2.25} & {\color{purple}-0.12} & {\color{magenta}-1.88} & {\color{gray}-0.05}\\
+ \hkl[1 0 0] & {\color{cyan}-2.25} & -2.16 & {\color{green}-0.10} & {\color{blue}-0.27} & {\color{violet}-1.38} & {\color{yellow}-0.06}\\
+% \hline
+% C substitutional (C$_{\text{S}}$) & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
+% Vacancy & -5.39 ($\rightarrow$ C$_{\text{S}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
+\hline
+\hline
+\end{tabular}
+\end{center}
+\caption[Binding energies in eV of \ci{} \hkl<1 0 0>-type defect pairs.]{Binding energies in eV of \ci{} \hkl<1 0 0>-type defect pairs. The given energies in eV are defined by equation \eqref{eq:basics:e_bind}. Equivalent configurations are marked by identical colors. The first column lists the types of the second defect combined with the initial \ci \hkl[0 0 -1] DB interstitial. The position index of the second defect is given in the first row according to Fig.~\ref{fig:defects:combos_ci}. R is the position located at $\frac{a_{\text{Si}}}{2}\hkl[3 2 3]$ relative to the initial defect, which is the maximum realizable distance due to periodic boundary conditions.}
+\label{tab:defects:e_of_comb}
+\end{table}
+Table~\ref{tab:defects:e_of_comb} summarizes resulting binding energies for the combination with a second \ci{} \hkl<1 0 0> DB obtained for different orientations at positions 1 to 5 after structural relaxation.
+Most of the obtained configurations result in binding energies well below zero indicating a preferable agglomeration of this type of defects.
+For increasing distances of the defect pair, the binding energy approaches to zero as it is expected for non-interacting isolated defects.
+%
+In fact, a \ci{} \hkl[0 0 -1] DB interstitial created at position R separated by a distance of $\frac{a_{\text{Si}}}{2}\hkl<3 2 3>$ ($\approx$\unit[12.8]{\AA}) from the initial one results in an energy as low as \unit[-0.19]{eV}.
+There is still a low interaction remaining, which is due to the equal orientation of the defects.
+By changing the orientation of the second DB interstitial to the \hkl[0 -1 0]-type, the interaction is even more reduced resulting in an energy of \unit[-0.05]{eV} for a distance, which is the maximum that can be realized due to periodic boundary conditions.
+Energetically favorable and unfavorable configurations can be explained by stress compensation and increase respectively based on the resulting net strain of the respective configuration of the defect combination.
+Antiparallel orientations of the second defect, i.e.\ \hkl[0 0 1] for positions located below the \hkl(0 0 1) plane with respect to the initial one (positions 1, 2 and 4) form the energetically most unfavorable configurations.
+In contrast, the parallel and particularly the twisted orientations constitute energetically favorable configurations, in which a vast reduction of strain is enabled by combination of these defects.
+
+\begin{figure}[tp]
+\begin{center}
+\subfigure[\underline{$E_{\text{b}}=-2.25\,\text{eV}$}]{\label{fig:defects:225}\includegraphics[width=0.3\textwidth]{00-1dc/2-25.eps}}
+\hspace{0.5cm}
+\subfigure[\underline{$E_{\text{b}}=-2.39\,\text{eV}$}]{\label{fig:defects:239}\includegraphics[width=0.3\textwidth]{00-1dc/2-39.eps}}
+\end{center}
+\caption[Relaxed structures of defect combinations obtained by creating {\hkl[1 0 0]} and {\hkl[0 -1 0]} DBs at position 1.]{Relaxed structures of defect combinations obtained by creating \hkl[1 0 0] (a) and \hkl[0 -1 0] (b) DBs at position 1.}
+\label{fig:defects:comb_db_01}
+\end{figure}
+Mattoni~et~al.~\cite{mattoni2002} predict the ground-state configuration of \ci{} \hkl<1 0 0>-type defect pairs for a \hkl[1 0 0] or equivalently a \hkl[0 1 0] defect created at position 1 with both defects basically maintaining the as-isolated DB structure resulting in a binding energy of \unit[-2.1]{eV}.
+In the present study, a further relaxation of this defect structure is observed.
+The C atom of the second and the Si atom of the initial DB move towards each other forming a bond, which results in a somewhat lower binding energy of \unit[-2.25]{eV}.
+The corresponding defect structure is displayed in Fig.~\ref{fig:defects:225}.
+In this configuration the initial Si and C DB atoms are displaced along \hkl[1 0 0] and \hkl[-1 0 0] in such a way that the Si atom is forming tetrahedral bonds with two Si and two C atoms.
+The C and Si atom constituting the second defect are as well displaced in such a way that the C atom forms tetrahedral bonds with four Si neighbors, a configuration expected in SiC.
+The two carbon atoms, which are spaced by \unit[2.70]{\AA}, do not form a bond but anyhow reside in a shorter distance than expected in SiC.
+Si atom number 2 is pushed towards the C atom, which results in the breaking of the bond to Si atom number 4.
+Breaking of the $\sigma$ bond is indeed confirmed by investigating the charge density isosurface of this configuration.
+
+Apart from that, a more favorable configuration is found for the combination with a \hkl[0 -1 0] and \hkl[-1 0 0] DB respectively, which is assumed to constitute the actual ground-state configuration of two \ci{} DBs in Si.
+The atomic arrangement is shown in Fig.~\ref{fig:defects:239}.
+The initial configuration is still evident in the relaxed configuration.
+The two \ci{} atoms form a strong C-C bond, which is responsible for the large gain in energy resulting in a binding energy of \unit[-2.39]{eV}.
+This bond has a length of \unit[1.38]{\AA} close to the next neighbor distance in diamond or graphite, which is approximately \unit[1.54]{\AA}.
+The minimum of the binding energy observed for this configuration suggests preferred C clustering as a competing mechanism to the \ci{} DB interstitial agglomeration inevitable for the SiC precipitation.
+However, the second most favorable configuration ($E_{\text{f}}=-2.25\,\text{eV}$) is represented four times, i.e.\ two times more often than the ground-state configuration, within the systematically investigated configuration space.
+Thus, particularly at high temperatures that cause an increase of the entropic contribution, this structure constitutes a serious opponent to the ground state.
+In fact, following results on migration simulations will reinforce the assumption of a low probability for C clustering by thermally activated processes.
+
+\begin{figure}[tp]
+\begin{center}
+\subfigure[\underline{$E_{\text{b}}=-2.16\,\text{eV}$}]{\label{fig:defects:216}\includegraphics[width=0.25\textwidth]{00-1dc/2-16.eps}}
+\hspace{0.2cm}
+\subfigure[\underline{$E_{\text{b}}=-1.90\,\text{eV}$}]{\label{fig:defects:190}\includegraphics[width=0.25\textwidth]{00-1dc/1-90.eps}}
+\hspace{0.2cm}
+\subfigure[\underline{$E_{\text{b}}=-2.05\,\text{eV}$}]{\label{fig:defects:205}\includegraphics[width=0.25\textwidth]{00-1dc/2-05.eps}}
+\end{center}
+\caption[Relaxed structures of defect combinations obtained by creating {\hkl[1 0 0]} and {\hkl[0 1 0]} DBs at position 2 and a {\hkl[0 0 1]} DB at position 3.]{Relaxed structures of defect combinations obtained by creating \hkl[1 0 0] (a) and \hkl[0 1 0] (b) DBs at position 2 and a \hkl[0 0 1] (c) DB at position 3.}
+\label{fig:defects:comb_db_02}
+\end{figure}
+Fig.~\ref{fig:defects:comb_db_02} shows the next three energetically favorable configurations.
+The relaxed configuration obtained by creating a \hkl[1 0 0] DB at position 2 is shown in Fig.~\ref{fig:defects:216}.
+A binding energy of \unit[-2.16]{eV} is observed.
+After relaxation, the second DB is aligned along \hkl[1 1 0].
+The bond of Si atoms 1 and 2 does not persist.
+Instead, the Si atom forms a bond with the initial \ci{} and the second C atom forms a bond with Si atom 1 forming four bonds in total.
+The C atoms are spaced by \unit[3.14]{\AA}, which is very close to the expected C-C next neighbor distance of \unit[3.08]{\AA} in SiC.
+Figure~\ref{fig:defects:205} displays the results of a \hkl[0 0 1] DB inserted at position 3.
+The binding energy is \unit[-2.05]{eV}.
+Both DBs are tilted along the same direction remaining aligned in parallel and the second DB is pushed downwards in such a way that the four DB atoms form a rhomboid.
+Both C atoms form tetrahedral bonds to four Si atoms.
+However, Si atom number 1 and number 3, which are bound to the second \ci{} atom are also bound to the initial C atom.
+These four atoms of the rhomboid reside in a plane and, thus, do not match the situation in SiC.
+The C atoms have a distance of \unit[2.75]{\AA}.
+In Fig.~\ref{fig:defects:190} the relaxed structure of a \hkl[0 1 0] DB constructed at position 2 is displayed.
+An energy of \unit[-1.90]{eV} is observed.
+The initial DB and especially the C atom is pushed towards the Si atom of the second DB forming an additional fourth bond.
+Si atom number 1 is pulled towards the C atoms of the DBs accompanied by the disappearance of its bond to Si number 5 as well as the bond of Si number 5 to its neighbored Si atom in \hkl[1 1 -1] direction.
+The C atom of the second DB forms threefold coordinated bonds to its Si neighbors.
+A distance of \unit[2.80]{\AA} is observed for the two C atoms.
+Again, the two C atoms and its two interconnecting Si atoms form a rhomboid.
+C-C distances of \unit[2.70--2.80]{\AA} seem to be characteristic for such configurations, in which the C atoms and the two interconnecting Si atoms reside in a plane.