+\begin{figure}[!ht]
+\begin{center}
+ \includegraphics[width=12cm]{sic_prec_450_energy.ps}
+\end{center}
+\caption[Total energy per atom as a function of time for the whole simulation sequence and for all three types of insertion volumes.]{Total energy per atom as a function of time for the whole simulation sequence and for all three types of insertion volumes. Arrows mark the end of carbon insertion and the start of the cooling process respectively.}
+\label{fig:md:energy_450}
+\end{figure}
+It is easily and instantly visible that there is no significant difference among the two simulations of high carbon concentration.
+The first C-C peak appears at about 0.15 nm, which is compareable to the nearest neighbour distance of graphite or diamond.
+The number of C-C bonds is much smaller for $V_1$ than for $V_2$ and $V_3$ since carbon atoms are spread over the total simulation volume.
+These carbon atoms are assumed to form strong bonds.
+This is supported by figure \ref{fig:md:energy_450} displaying the total energy of all three simulations during the whole simulation sequence.
+A huge decrease of the total energy during carbon insertion is observed for the simulations with high carbon concentration in contrast to the $V_1$ simulation, which shows a slight increase.
+The difference in energy $\Delta$ growing within the carbon insertion process up to a value of roughly 0.06 eV per atom persists unchanged until the end of the simulation.
+Here is the problem.
+The excess amount of next neighboured strongly bounded C-C bonds in the high concentration simulations make these configurations energetically more favorable compared to the low concentration configuration.
+However, in the same way a lot of energy is needed to break these bonds to get out of the local energy minimum advancing towards the global minimum configuration.
+Thus, such conformational chamges are very unlikely to happen.
+This is in accordance with the constant total energy observed in the continuation step of 100 ps inbetween the end of carbon insertion and the cooling process.
+Obviously no energetically favorable relaxation is taking place at a system temperature of $450\,^{\circ}\mathrm{C}$.
+
+The C-C peak at about 0.31 nm perfectly matches the nearest neighbour distance of two carbon atoms in the 3C-SiC lattice.
+As can be seen from the inset this peak is also observed for the $V_1$ simulation.
+In 3C-SiC the same distance is also expected for nearest neighbour silicon atoms.
+The bottom of figure \ref{fig:md:pc_si-si_c-c} shows the radial distribution of Si-Si bonds together with a reference graph for pure c-Si.
+Indeed non-zero $g(r)$ values around 0.31 nm are observed while the amount of Si pairs at regular c-Si distances of 0.24 nm and 0.38 nm decreases.
+However, no clear peak is observed but the interval of enhanced $g(r)$ values corresponds to the width of the C-C $g(r)$ peak.
+In addition the abrupt increase of Si pairs at 0.29 nm can be attributed to the Si-Si cut-off radius of 0.296 nm as used in the present bond order potential.
+The cut-off function causes artificial forces pushing the Si atoms out of the cut-off region.
+Without the abrubt increase a maximum around 0.31 nm gets even more conceivable.
+For low concentrations of carbon, that is the $V_1$ simulation and early stages of the $V_2$ and $V_3$ simulations, analyses of configurations in which Si-Si distances around 0.3 nm appear and which are identifiable in regions of high disorder, which especially applies for the high concentration simulations, identify the \hkl<1 0 0> C-Si dumbbell to be responsible for stretching the Si-Si next neighbour distance.
+This excellently agrees with the calculated value $r(13)$ in table \ref{tab:defects:100db_cmp} for a resulting Si-Si distance in the \hkl<1 0 0> C-Si dumbbell configuration.
+
+\begin{figure}[!ht]
+\begin{center}
+ \includegraphics[width=12cm]{sic_prec_450_si-c.ps}
+\end{center}
+\caption{Radial distribution function of the Si-C distances for 6000 carbon atoms inserted into the three different volumes $V_1$, $V_2$ and $V_3$ at a temperature of $450\,^{\circ}\mathrm{C}$ and cooled down to room temperature together with Si-C bonds resulting in a C-Si \hkl<1 0 0> dumbbell configuration.}
+\label{fig:md:pc_si-c}
+\end{figure}
+Figure \ref{fig:md:pc_si-c} displays the Si-C radial distribution function for all three insertion volumes together with the Si-C bonds as observed in a C-Si \hkl<1 0 0> dumbbell configuration.
+The first peak observed for all insertion volumes is at approximately 0.186 nm.
+This corresponds quite well to the expected next neighbour distance of 0.189 nm for Si and C atoms in 3C-SiC.
+By comparing the resulting Si-C bonds of a C-Si \hkl<1 0 0> dumbbell with the C-Si distances of the low concentration simulation it is evident that the resulting structure of the $V_1$ simulation is dominated by this type of defects.
+This is not surpsising, since the \hkl<1 0 0> dumbbell is found to be the ground state defect of a C interstitial in c-Si and for the low concentration simulations a carbon interstitial is expected in every fifth silicon unit cell only, thus, excluding defect superposition phenomena.
+The peak distance at 0.186 nm and the bump at 0.175 nm corresponds to the distance $r(3C)$ and $r(1C)$ as listed in table \ref{tab:defects:100db_cmp} and visualized in figure \ref{fig:defects:100db_cmp}.
+In addition it can be easily identified that the \hkl<1 0 0> dumbbell configuration contributes to the peaks at about 0.335 nm, 0.386 nm, 0.434 nm, 0.469 nm and 0.546 nm observed in the $V_1$ simulation.
+Not only the peak locations but also the peak widths and heights become comprehensible.
+The distinct peak at 0.26 nm, which exactly matches the cut-off radius of the Si-C interaction, is again a potential artifact.
+
+For high carbon concentrations, that is the $V_2$ and $V_3$ simulation, the defect concentration is likewiese increased and a considerable amount of damage is introduced in the insertion volume.
+The consequential superposition of these defects and the high amounts of damage generate new displacement arrangements for the C-C as well as for the Si-C pair distances, which become hard to categorize and trace and obviously lead to a broader distribution.
+Short range order indeed is observed but only hardly visible is the long range order.
+This indicates the formation of an amorphous SiC-like phase.
+In fact the resulting Si-C and C-C radial distribution functions compare quite well with these obtained by cascade amorphized and melt-quenched amorphous SiC using a modified Tersoff potential \cite{gao02}.
+
+\subsection{Limitations of conventional MD and short order potentials}
+
+{\color{blue}
+Alternatively: Explain general problem of the slow propagation through phase space using conventional molecular dynamics and the accompanying difficulties for conformational search.
+Explain the methods available to overcome this limitation.
+Point out, that in this work, the sharp cut-off introduces unphysical and overestimated high forces between next neighboured atoms enhancing the problem of slow phase space propagation.
+}
+
+The formation of an amoprhous SiC-like phase although experiments show crystalline 3C-SiC precipitates at prevailing temperatures remains unexplained.
+The answer is found in the short range and sharp cut-off of the employed bond order potential.
+The cut-off funtion, which limits the interacting ions to the next neighboured atoms by gradually pushing the interaction force and energy to zero betwenn the first and second next neighbour distance, is responsible for overestimated and unphysical high forces of next neighboured atoms \cite{mattoni2007}.
+Indeed it is not only the strong C-C bond which is hard to break inhibiting carbon diffusion and further conformational changes.
+This is also true for the low concentration simulations dominated by C-Si dumbbells spread over the whole simulation volume.
+The bonds of these C-Si pairs are also affected by the cut-off artifact preventing carbon diffusion and agglomeration of the dumbbells.
+This can be seen from the almost horizontal progress of the total energy graph in the continuation step, even for the low concentration simulation.
+Thus, applying longer time scales in order to enable the system to undergo diffusion events, which become very unlikely to happen due to the overestimated bond strengthes, and in the end observe the agglomeration and precipitation might not be sufficient.
+On the other hand longer time scales are not accessible to simulation due to limited computational ressources.
+Alternatively the approach of using higher temperatures to speed up or actually make possible the steps involved in the precipitation mechanism is applied.