+\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. 3 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. 4.
+
+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.
+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.
+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.
+
+Wieder durch visuelle untersuchungen -> c-c 0.31 paare durch aufeinandertreffen unterschiedlich orientierter 100 dumbbells bzw mit 110.
+C fuer sic schon besser arrangiert. Vorstellung, dass diese zuerst anordnen und spaeter dann evtl am Si ziehen ...
+Nevertheless this might indicate that carbon arranges first, then 'pulls' the Si ...
+\\\\