\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.
-In order to find possible migration pathways that have an activation energy lower than the ones found up to now.
+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 dumbbell interstitial.
Figure \ref{fig:defects:110_mig_vasp} shows the migration barrier of the \hkl<1 1 0> C-Si dumbbell to the bond-centered, \hkl<0 0 -1> and \hkl<0 -1 0> (in place) transition.
Indeed less than 0.7 eV are necessary to turn a \hkl<0 -1 0>- to a \hkl<1 1 0>-type C-Si dumbbell interstitial.
-This transition is carried out in place, that is the Si dumbbell pair is not changed and both, the Si and C atom share the same lattice site.
+This transition is carried out in place, that is the Si dumbbell 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> interstitial configuration it can migrate into the bond-centered configuration by employing approximately 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 shown in figure \ref{fig:defects:00-1_0-10_mig}.
As already known from the migration of the \hkl<0 0 -1> to the bond-centered configuration as discussed in figure \ref{fig:defects:00-1_001_mig} another 0.25 eV are needed to turn back from the bond-centered to a \hkl<1 0 0>-type interstitial.
The same method for obtaining migration barriers and the same suggested pathways are applied to calculations employing the classical Erhard/Albe potential.
Since the evaluation of the classical potential and force is less computationally intensive higher amounts of steps can be used.
+The time constant $\tau$ for the Berendsen thermostat is set to 1 fs in order to have direct velocity scaling and with the temperature set to zero Kelvin perform a steepest descent minimazation to drive the system into a local minimum.
+However, in some cases a time constant of 100 fs resuls in lower barriers and, thus, is shown whenever appropriate.
\begin{figure}[th!]
\begin{center}
-\includegraphics[width=13cm]{bc_00-1.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 of the bond-centered to \hkl<0 0 -1> dumbbell transition using the classical Erhard/Albe potential.}
+\caption{Migration barrier and structures of the bond-centered to \hkl<0 0 -1> dumbbell transition using the classical Erhard/Albe potential.}
\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}
-Figure \ref{fig:defects:cp_bc_00-1_mig} shows the migration barrier of the bond-centered to \hkl<0 0 -1> dumbbell transition.
+Figure \ref{fig:defects:cp_bc_00-1_mig} shows the migration barrier and corresponding structures of the bond-centered to \hkl<0 0 -1> dumbbell transition.
Since the bond-centered configuration is unstable relaxing into the \hkl<1 1 0> C-Si dumbbell interstitial configuration within this potential the low kinetic energy state is used as a starting configuration.
-
+Depending on the time constant activation energies of 2.4 eV and 2.2 eV respectively are obtained.
+The migration path obtained by simulations with a time constant of 1 fs remains in the \hkl(1 1 0) plane.
+Using 100 fs as a time constant the C atom breaks out of the \hkl(1 0 0) plane already at the beginning of the migration accompanied by a reduction in energy.
+The energy barrier of this path is 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.
+For the entire transition of the \hkl<0 0 -1> into the \hkl<0 0 1> configuration by passing the bond-centered configuration an additional activation energy of 0.5 eV is necessary to escape from the bond-centered and reach the \hkl<0 0 1> configuration.
\begin{figure}[th!]
\begin{center}
-\includegraphics[width=13cm]{00-1_0-10.ps}
+\includegraphics[width=13cm]{00-1_0-10.ps}\\[2.4cm]
+\begin{pspicture}(0,0)(0,0)
+\psframe[linecolor=red,fillstyle=none](-6,-0.5)(7.2,2.8)
+\end{pspicture}
+\begin{picture}(0,0)(130,-10)
+\includegraphics[width=2.2cm]{albe_mig/00-1_0-10_red_00.eps}
+\end{picture}
+\begin{picture}(0,0)(0,-10)
+\includegraphics[width=2.2cm]{albe_mig/00-1_0-10_red_min.eps}
+\end{picture}
+\begin{picture}(0,0)(-120,-10)
+\includegraphics[width=2.2cm]{albe_mig/00-1_0-10_red_03.eps}
+\end{picture}
+\begin{picture}(0,0)(25,10)
+\includegraphics[width=2.5cm]{100_arrow.eps}
+\end{picture}
+\begin{picture}(0,0)(185,-10)
+\includegraphics[height=2.2cm]{001_arrow.eps}
+\end{picture}
\end{center}
-\caption{Migration barrier of the \hkl<0 0 -1> \hkl<0 -1 0> C-Si dumbbell transition using the classical Erhard/Albe potential.}
+\caption{Migration barrier and structures of the \hkl<0 0 -1> to \hkl<0 -1 0> C-Si dumbbell transition using the classical Erhard/Albe 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}
-Figure \ref{fig:defects:cp_00-1_0-10_mig} shows the migration barrier of the \hkl<0 0 -1> to \hkl<0 -1 0> C-Si dumbbell transition.
-After the first maximum the system relaxes to a configuration similar to the \hkl<1 1 0> C-Si dumbbell configuration.
-
\begin{figure}[th!]
\begin{center}
\includegraphics[width=13cm]{00-1_ip0-10.ps}
\caption{Migration barrier of the \hkl<0 0 -1> to \hkl<0 -1 0> C-Si dumbbell transition in place using the classical Erhard/Albe potential.}
\label{fig:defects:cp_00-1_ip0-10_mig}
\end{figure}
-Figure \ref{fig:defects:cp_00-1_ip0-10_mig} shows the migration barrier of the \hkl<0 0 -1> to \hkl<0 -1 0> C-Si dumbbell transition in place.
+Figure \ref{fig:defects:cp_00-1_0-10_mig} and \ref{fig:defects:cp_00-1_ip0-10_mig} show the migration barriers of \hkl<0 0 -1> to \hkl<0 -1 0> C-Si dumbbell transition, with a transition of the C atom to the neighboured lattice site in the first case and a reorientation within the same lattice site in the latter case.
+Both pathways look similar.
+A local minimum exists inbetween two peaks of the graph.
+The corresponding configuration, which is illustrated for the migration simulation with a time constant of 1 fs, looks similar to the \hkl<1 1 0> configuration.
+Indeed, this configuration is obtained by relaxation simulations without constraints of configurations near the minimum.
+Activation energies of roughly 2.8 eV and 2.7 eV respectively are needed for migration.
+
+The \hkl<1 1 0> configuration seems to play a decisive role in all migration pathways.
+In the first migration path it is the configuration resulting from further relaxation of the rather unstable bond-centered configuration, which is fixed to be a transition point in the migration calculations.
+The last two pathways show configurations almost identical to the \hkl<1 1 0> configuration, which constitute a local minimum within the pathway.
+Thus, migration pathways with the \hkl<1 1 0> C-Si dumbbell interstitial configuration as a starting or final configuration are further investigated.
+\begin{figure}[ht!]
+\begin{center}
+\includegraphics[width=13cm]{110_mig.ps}
+\end{center}
+\caption[Migration barriers of the \hkl<1 1 0> dumbbell to bond-centered (blue), \hkl<0 0 -1> (green) and \hkl<0 -1 0> (in place, red) C-Si dumbbell transition.]{Migration barriers of the \hkl<1 1 0> dumbbell to bond-centered (blue), \hkl<0 0 -1> (green) and \hkl<0 -1 0> (in place, red) C-Si dumbbell transition. Solid lines show results for a time constant of 1 fs and dashed lines correspond to simulations employing a time constant of 100 fs.}
+\label{fig:defects:110_mig}
+\end{figure}
+Figure \ref{fig:defects:110_mig} shows migration barriers of the C-Si \hkl<1 1 0> dumbbell to \hkl<0 0 -1>, \hkl<0 -1 0> (in place) and bond-centered configuration.
+As expected there is no maximum for the transition into the bond-centered configuration.
+As mentioned earlier the bond-centered configuration itself constitutes a saddle point configuration relaxing into the energetically more favorable \hkl<1 1 0> configuration.
+An activation energy of 2.2 eV is necessary to reorientate the \hkl<0 0 -1> dumbbell configuration into the \hkl<1 1 0> configuration, which is 1.3 eV higher in energy.
+Residing in this state another 0.9 eV is enough to make the C atom form a \hkl<0 0 -1> dumbbell configuration with the Si atom of the neighboured 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 intermmediate migration steps is very unlikely to occur the just presented pathway is much more supposable in classical potential simulations, since the energetically most favorable transition found so far is also composed of two migration steps with activation energies of 2.2 eV and 0.5 eV.
+{\color{red}TODO: 00-1 to 001 transition, does it pass the bc conf?}
+
+Although classical potential simulations reproduce the order in energy of the \hkl<1 0 0> and \hkl<1 1 0> C-Si dumbbell 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.
+On the other hand the activation energies obtained by classical potential simulations are tremendously overestimated by a factor of almost 2.4.
+Thus, atomic diffusion is wrongly described in the classical potential approach.
+The probability of already rare diffusion events is further decreased for this reason.
+Since agglomeration of C and diffusion of Si self-interstitials are an important part of the proposed SiC precipitation mechanism a problem arises, which is formulated and discussed in more detail in section \ref{subsection:md:limit}.
\section{Combination of point defects}
The structural and energetic properties of combinations of point defects are examined in the following.
-Investigations are restricted to quantum-mechanical calculations.
+Investigations are restricted to quantum-mechanical calculations for two reasons.
+First of all, as mentioned in the last section, they are far more accurate.
+Secondly, the restrictions in size and simulation time for this type of calculation due to limited computational resources, necessitate to map the complex precipitation mechanism to a more compact and simplified modelling.
+The investigations of defect combinations approached in the following are still feasible within the available computational power and allow to draw conclusions on some important ongoing mechanisms during SiC precipitation.
\subsection[Combinations with a C-Si \hkl<1 0 0>-type interstitial]{\boldmath Combinations with a C-Si \hkl<1 0 0>-type interstitial}
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