\end{minipage}
\begin{minipage}{6.0cm}
\underline{Positions given in $a_{\text{Si}}$}\\[0.3cm]
-Initial interstitial: $\frac{1}{4}\hkl<1 1 1>$\\
+Initial interstitial I: $\frac{1}{4}\hkl<1 1 1>$\\
Relative silicon neighbour positions:
\begin{enumerate}
\item $\frac{1}{4}\hkl<1 1 -1>$, $\frac{1}{4}\hkl<-1 -1 -1>$
\label{eq:defects:e_of_comb}
\end{equation}
with $E_{\text{f}}^{\text{defect combination}}$ being the formation energy of the defect combination, $E_{\text{f}}^{\text{C \hkl<0 0 -1> dumbbell}}$ being the formation energy of the C \hkl<0 0 -1> dumbbell interstitial defect and $E_{\text{f}}^{\text{2nd defect}}$ being the formation energy of the second defect.
-For defects far away from each other the formation energy of the defect combination should approximately become the sum of the formation energies of the individual defects.
-The interaction of such defects is low resulting in $E=0$.
-In fact, for another \hkl<0 0 -1> dumbbell interstitial created at position $\frac{a_{\text{Si}}}{2}\hkl<3 2 3>$ relative to the initial one an energy of \ldots eV is obtained.
+For defects far away from each other the formation energy of the defect combination should approximately become the sum of the formation energies of the individual defects with zero interaction resulting in $E=0$.
+In fact, for another \hkl<0 0 -1> dumbbell interstitial created at position $\frac{a_{\text{Si}}}{2}\hkl<3 2 3>$ ($\approx 10.2$ \AA) and $\frac{a_{\text{Si}}}{2}\hkl<2 3 2>$ ($\approx 12.8$ \AA, maximum distance due to periodic boundary conditions) relative to the initial one an energy of -0.19 eV and ... is obtained.
Configurations wih energies greater than zero are energetically unfavorable and expose a repulsive interaction.
These configurations are unlikely to arise or to persist for non-zero temperatures.
Energies below zero indicate configurations favored compared to configurations in which these point defects are separated far away from each other.
Investigating the first part of table \ref{tab:defects:e_of_comb}, namely the combinations with another \hkl<1 0 0>-type interstitial, most of the combinations result in energies below zero.
Surprisingly the most favorable configurations are the ones with the second defect created at the very next silicon neighbour and a change in orientation compared to the initial one.
+This leads to the conclusion that an agglomeration of C-Si dumbbell interstitials as proposed by the precipitation model introduced in section\ref{section:assumed_prec} is indeed an energetically favored configuration of the system.
+The reason for nearby interstitials being favored compared to isolated ones is most probably the reduction of strain energy enabled by combination in contrast to the strain energy created by two individual defects.
\begin{figure}[h]
-\caption{}
+\begin{center}
+\begin{minipage}[t]{7cm}
+a) \underline{$E=-2.25\text{ eV}$}
+\begin{center}
+\includegraphics[width=6cm]{00-1dc/2-25.eps}
+\end{center}
+\end{minipage}
+\begin{minipage}[t]{7cm}
+b) \underline{$E=-2.39\text{ eV}$}
+\begin{center}
+\includegraphics[width=6cm]{00-1dc/2-39.eps}
+\end{center}
+\end{minipage}
+\end{center}
+\caption{Relaxed structure of defect complexes consisting of two \hkl<1 0 0>-type dumbbell interstitial defects.}
\label{fig:defects:comb_db_01}
\end{figure}
-Figure \ref{} shows the structure of these two configurations.
+Figure \ref{fig:defects:comb_db_01} shows the structure of these two configurations.
+
+Structure b) is the energetically most favorable configuration.
+The two carbon atoms form a bond to each other.
+This suggests an unwanted C clustering in SiC production.
+However, for the second most favorable configuration, presented in figure a), the amount of possibilitie for this configuration is twice as high.
+Investigating C-Si and C-C bond lengths ...
+
+001 at pos 2 looks as if there is no interaction.
+There is an interaction but in the same time strain is reduced due to the opposing orientations of the defects, which leads to this low energy value.
+
+Explanation of results of defects created along <110>.
+-1.90 ...
+-2.16 ...
+the more far-off ones:
+-0.27 and -0.12 ...
+but better ...
+-1.88 and -1.38 ...
+Minimum E (reorientation) per distance
+Todo: Si int and C sub ...
+Todo: Model of kick-out and kick-in mechnism?
+Todo: Jahn-Teller distortion (vacancy) $\rightarrow$ actually three possibilities! :(
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