+\begin{figure}[t!h!]
+\begin{center}
+\includegraphics[width=12.5cm]{db_along_110.ps}\\
+\includegraphics[width=12.5cm]{db_along_110_cc.ps}
+\end{center}
+\caption{Minimum binding energy of dumbbell combinations with respect to the separation distance in bonds along \hkl<1 1 0> and C-C distance.}
+\label{fig:defects:comb_db110}
+\end{figure}
+Figure \ref{fig:defects:comb_db110} shows the corresponding plot of the data including a cubic spline interplation and a suitable fitting curve.
+The funtion found most suitable for curve fitting is $f(x)=a/x^3$ comprising the single fit parameter $a$.
+Thus, far-off located dumbbells show an interaction proportional to the reciprocal cube of the distance and the amount of bonds along \hkl<1 1 0> respectively.
+This behavior is no longer valid for the immediate vicinity revealed by the saturating binding energy of a second dumbbell at position 1, which is ignored in the fitting procedure.
+{\color{red}Todo: DB mig along 110?}
+
+\begin{figure}[t!h!]
+\begin{center}
+\begin{minipage}[t]{5cm}
+a) \underline{Pos: 1, $E_{\text{b}}=0.26\text{ eV}$}
+\begin{center}
+\includegraphics[width=4.8cm]{00-1dc/0-26.eps}
+\end{center}
+\end{minipage}
+\begin{minipage}[t]{5cm}
+b) \underline{Pos: 3, $E_{\text{b}}=-0.93\text{ eV}$}
+\begin{center}
+\includegraphics[width=4.8cm]{00-1dc/0-93.eps}
+\end{center}
+\end{minipage}
+\begin{minipage}[t]{5cm}
+c) \underline{Pos: 5, $E_{\text{b}}=0.49\text{ eV}$}
+\begin{center}
+\includegraphics[width=4.8cm]{00-1dc/0-49.eps}
+\end{center}
+\end{minipage}
+\end{center}
+\caption{Relaxed structures of defect complexes obtained by creating a carbon substitutional at position 1 (a)), 3 (b)) and 5 (c)).}
+\label{fig:defects:comb_db_04}
+\end{figure}
+\begin{figure}[t!h!]
+\begin{center}
+\begin{minipage}[t]{7cm}
+a) \underline{Pos: 2, $E_{\text{b}}=-0.51\text{ eV}$}
+\begin{center}
+\includegraphics[width=6cm]{00-1dc/0-51.eps}
+\end{center}
+\end{minipage}
+\begin{minipage}[t]{7cm}
+b) \underline{Pos: 4, $E_{\text{b}}=-0.15\text{ eV}$}
+\begin{center}
+\includegraphics[width=6cm]{00-1dc/0-15.eps}
+\end{center}
+\end{minipage}
+\end{center}
+\caption{Relaxed structures of defect complexes obtained by creating a carbon substitutional at position 2 (a)) and 4 (b)).}
+\label{fig:defects:comb_db_05}
+\end{figure}
+The second part of table \ref{tab:defects:e_of_comb} lists the energetic results of substitutional carbon and vacancy combinations with the initial \hkl<0 0 -1> dumbbell.
+Figures \ref{fig:defects:comb_db_04} and \ref{fig:defects:comb_db_05} show relaxed structures of substitutional carbon in combination with the \hkl<0 0 -1> dumbbell for several positions.
+In figure \ref{fig:defects:comb_db_04} positions 1 (a)), 3 (b)) and 5 (c)) are displayed.
+A substituted carbon atom at position 5 results in an energetically extremely unfavorable configuration.
+Both carbon atoms, the substitutional and the dumbbell atom, pull silicon atom number 1 towards their own location regarding the \hkl<1 1 0> direction.
+Due to this a large amount of tensile strain energy is needed, which explains the high positive value of 0.49 eV.
+The lowest binding energy is observed for a substitutional carbon atom inserted at position 3.
+The substitutional carbon atom is located above the dumbbell substituting a silicon atom which would usually be bound to and displaced along \hkl<0 0 1> and \hkl<1 1 0> by the silicon dumbbell atom.
+In contrast to the previous configuration strain compensation occurs resulting in a binding energy as low as -0.93 eV.
+Substitutional carbon at position 2 and 4, visualized in figure \ref{fig:defects:comb_db_05}, is located below the initial dumbbell.
+Silicon atom number 1, which is bound to the interstitial carbon atom is displaced along \hkl<0 0 -1> and \hkl<-1 -1 0>.
+In case a) only the first displacement is compensated by the substitutional carbon atom.
+This results in a somewhat higher binding energy of -0.51 eV.
+The binding energy gets even higher in case b) ($E_{\text{b}}=-0.15\text{ eV}$), in which the substitutional carbon is located further away from the initial dumbbell.
+In both cases, silicon atom number 1 is displaced in such a way, that the bond to silicon atom number 5 vanishes.
+In case of \ref{fig:defects:comb_db_04} a) the carbon atoms form a bond with a distance of 1.5 \AA, which is close to the C-C distance expected in diamond or graphit.
+Both carbon atoms are highly attracted by each other resulting in large displacements and high strain energy in the surrounding.
+A binding energy of 0.26 eV is observed.
+Substitutional carbon at positions 2, 3 and 5 are the energetically most favorable configurations and constitute promising starting points for SiC precipitation.
+On the one hand, C-C distances around 3.1 \AA{} exist for substitution positions 2 and 3, which are close to the C-C distance expected in silicon carbide.
+On the other hand stretched silicon carbide is obtained by the transition of the silicon dumbbell atom into a silicon self-interstitial located somewhere in the silicon host matrix and th etransition of the carbon dumbbell atom into another substitutional atom occupying the dumbbell lattice site.
+
+\begin{figure}[t!h!]
+\begin{center}
+\begin{minipage}[t]{7cm}
+a) \underline{$E_{\text{b}}=-1.53\text{ eV}$}
+\begin{center}
+\includegraphics[width=6.0cm]{00-1dc/1-53.eps}
+\end{center}
+\end{minipage}
+\begin{minipage}[t]{7cm}
+b) \underline{$E_{\text{b}}=-1.66\text{ eV}$}
+\begin{center}
+\includegraphics[width=6.0cm]{00-1dc/1-66.eps}
+\end{center}
+\end{minipage}\\[0.2cm]
+\begin{minipage}[t]{7cm}
+c) \underline{$E_{\text{b}}=-1.88\text{ eV}$}
+\begin{center}
+\includegraphics[width=6.0cm]{00-1dc/1-88.eps}
+\end{center}
+\end{minipage}
+\begin{minipage}[t]{7cm}
+d) \underline{$E_{\text{b}}=-1.38\text{ eV}$}
+\begin{center}
+\includegraphics[width=6.0cm]{00-1dc/1-38.eps}
+\end{center}
+\end{minipage}
+\end{center}
+\caption{Relaxed structures of defect complexes obtained by creating vacancies at positions 2 (a)), 3 (b)), 4 (c)) and 5 (d)).}
+\label{fig:defects:comb_db_03}
+\end{figure}
+The creation of the vacancy at position 1 ... c interstitital moves to acancy position ending up in a configuration of a substitutional carbon which explains the highbinding energy.
+At position 3 a great amount of strain energy is reduced, since the the vacancy replaces a silicon atom usually bond to and thus starined by the silicon dumbbell atom.
+db moves towards the vacancy in \hkl<1 -1 0> direction.
+Vac at position 2 and 4 have similar results.
+Less strain is reduced, since the displacement of the bottom silicon atom, whcih would be directly bond to the silicon atom replaced by the vacancy, is less.
+In the second case, there is even less strain reduction since the second next neighbour is replaced by the vacancy.
+A symmetric configuration is expected, but it is not!
+jahn-Teller distortion ... check this!
+In both cases the db is tilted in such a way, that the carbon atom moves towards the vacancy.
+At position 5 the silicon dumbbell atom moves in \hkl<1 1 0> direction, the same direction where the vacancy is located.
+Strain reducde by this is partialy absorbed by strain originating from the fact that si atom bound to and pulled by the carbon atom is also pulled by the vacancy.
+
+CHECK C-C DIST AND SI-C DIST !!! of all!!!
+
+{\color{red}Todo: Jahn-Teller distortion (vacancy) $\rightarrow$ actually three possibilities? Due to the initial defect symmetries are broken. It should have relaxed into the minumum energy configuration!?}
+Once a vacancy exists the minimal e conf is the c sub conf and ofcourse necessary for formation of SiC.
+The question is whether the migration into this conf is possible.
+Fig shows the migration of the 2 and 3 conf into the c sub conf.
+Low migration barriers, which means that SiC will modt probably form ... and so on ...
+
+{\color{red}Todo: Si int and C sub ...}
+The existance of a vacancy is most often accompanied by an interstitial.
+The silicon interstitital might diffuse to the surface or recombine with other vacancy defects and tus is out of the interested simulation region.
+However, investigation of near by vacancy, Si and C interstititla is necessary, too.
+As for the ground state of the single Si self-int a 110 this is also assumed as the lowest possibility in combination with other defects, which is a cruel assumption!!!