+%\begin{figure}[!h]
+% \begin{center}
+% \includegraphics[width=12cm]{../plot/diff_dep.ps}
+% \caption{Diffusion coefficients of a single carbon atom for different amount of Si selft interstitials}
+% \end{center}
+%\end{figure}
+%The influence of Si self-interstitials on the diffusion of a single carbon atom is displayed in Fig. 3.
+%Diffusion coefficients for different amount of Si self-interstitials are shown.
+%A slight increase is first observed in the case of 30 interstitial atoms.
+%Further increasing the amount of interstitials leads to a tremendous decay of the diffusion coeeficient.
+%Generally there is no long range diffusion of the carbon atom for a temperature of $450\, ^{\circ} \textrm{C}$.
+%The maximal displacement of the carbon atom relativ to its insertion position is between 0.5 and 0.7 \AA.
+
+\begin{figure}[!h]
+ \begin{center}
+ \includegraphics[width=12cm]{pc_si-c_c-c.ps}
+ \caption{Pair correlation functions for Si-C and C-C bonds.
+ Carbon atoms are introduced into the whole simulation volume $V_1$, the region which corresponds to the size of a minimal SiC precipitate $V_2$ and the volume which contains the necessary amount of silicon for such a minimal precipitate $V_2$ respectively.}
+ \end{center}
+\end{figure}
+\begin{figure}[!h]
+ \begin{center}
+ \includegraphics[width=12cm]{pc_si-si.ps}
+ \caption{Si-Si pair correlation function for pure Si and Si with 3000 inserted C atoms.
+ The inset shows a magnified region between 0.28 and 0.36 nm.}
+ \end{center}
+\end{figure}
+Fig. 4 shows resulting pair correlation functions of the simulation runs targeting the observation of precipitation events.
+The contributions of Si-C and C-C pairs are presented separately each of them displaying the pair correlation for the three different volumes $V_1$, $V_2$ and $V_3$ (as explained above) exposed to carbon insertion.
+Results show no signigicant difference between $V_1$ and $V_2$.
+Si-Si pairs for the case of 3000 inserted C atoms inserted into $V_2$ and a reference function for pure Si are displayed in Fig. 5.
+
+The amount of C-C bonds for $V_1$ are much smaller than for $V_2$ and $V_3$ since carbon atoms are spread over the total simulation volume which means that there are only 0.2 carbon atoms per silicon unit cell on average.
+The first C-C peak appears at about 0.15 nm.
+This is comparable to the nearest neighbour distance for graphite or diamond.
+It is assumed that these carbon atoms form strong C-C bonds, which is supported by a decrease of the total energy during carbon insertion for the $V_2$ and $V_3$ in contrast to the $V_3$ simulation.
+
+The peak at 0.31 nm perfectly matches the distance of two carbon atoms in the SiC lattice which in SiC is also expected for the Si-Si bonds.
+After insertion of carbon atoms the Si-Si pair correlation function in fact shows non-zero values in the range of the C-C peak width while the amount of Si pairs at the regular distances at 0.24 and 0.38 nm decreases.
+However no clear peak is observed and random analyses of configurations in which distances around 0.3 nm appear, i.e. visualization of such atom pairs, identify <100> C-Si dumbbells to be responsible for stretching the Si-Si next neighbour distance for low concentrations of carbon, i.e. for the $V_1$ and early stages of $V_2$ and $V_3$ simulation runs.
+This excellently agrees with the calculation for a single <100> dumbbell ($r(13)$ in Fig. 4).
+For higher carbon concentrations the defect concentration is likewise increased and a considerable amount of damage is introduced into the inserted volume.
+Damage and superposition of defects generate new displacement arrangements which become hard to categorize and trace and obviously lead to a broader distribution of pair distances.
+The slightly higher amount and intense increase of Si-Si pairs at distances smaller 0.31 nm is probably due to the Si-Si cutoff radius of 0.296 nm.
+The cutoff function causes artificial forces pushing the Si atoms out of the cutoff region.
+By again visualizing the C-C atom pairs with distances of 0.31 nm concatenated, differently oriented <100> dumbbell interstitials are frequently observed.
+Since dumbbells of this type with different orientations are perpendicularly aligned the C atoms are displaced along the plane diagonal of the original lattice.
+One might now assume for the precipitation process, that C atoms are arrenged first and at a later point pull the Si atoms into the right configuration.
+In this way the hkl planes of the SiC in Si and the Si matrix would have equal orientations which is supported by experimental transmission electron microscopy data \cite{}.
+\\\\
+Ab hier weiter ...
+\\\\
+On the other hand the Si-C pair correlation function indicates formation of SiC bonds with an increased crystallinity for the simulation in which carbon is inserted into the whole simulation volume.
+There is more carbon forming Si-C bonds than C-C bonds.
+This gives suspect to the competition of Si-C and C-C bond formation in which the predominance of either of them depends on the method handling carbon insertion.
+
+\section*{Summary}
+The supposed conversion mechanism of heavily carbon doped silicon into silicon carbide is presented.
+Molecular dynamics simulation sequences to investigate interstitial configurations
+%, the influence of interstitials on the atomic diffusion
+and the precipitation of SiC are explained.
+The <100> C-Si dumbbel is reproduced and is the energetically most favorable configuration observed by simulation.
+%The influence of silicon self-interstitials on the diffusion of a single carbon atom is demonstrated.
+Two competing bond formations, either Si-C or C-C, seem to coexist, where the strength of either of them depends on the size of the region in which carbon is introduced.
+
+\bibliography{../../bibdb/bibdb}