+\caption[Si-C and C-C radial distribution for the high concentration simulations at different elevated temperatures.]{Si-C (top) and C-C (bottom) radial distribution for the high concentration simulations at different elevated temperatures. All structures are cooled down to $20\,^{\circ}\mathrm{C}$.}
+\label{fig:md:12_pc}
+\end{figure}
+Figure \ref{fig:md:12_pc} displays the radial distribution for Si-C and C-C pairs obtained from high C concentration simulations at different elevated temperatures.
+Again, in both cases, the cut-off artifact decreases with increasing temperature.
+Peaks that already exist for the low temperature simulations get slightly more distinct for elevated temperatures.
+This is also true for peaks located past distances of next neighbours indicating an increase in the long range order.
+However this change is rather small and no significant structural change is observeable.
+Due to the continuity of high amounts of damage atomic configurations remain hard to identify even for the highest temperature.
+Other than in the low concentration simulation analyzed defect structures are no longer necessarily aligned to the primarily existing but succesively disappearing c-Si host matrix inhibiting or at least hampering their identification and classification.
+As for low temperatures order in the short range exists decreasing with increasing distance.
+The increase of the amount of Si-C pairs at 0.186 nm could be positively interpreted since this type of bond also exists in 3C-SiC.
+On the other hand the amount of next neighboured C atoms with a distance of approximately 0.15 nm, which is the distance of C in graphite or diamond, is likewise increased.
+Thus, higher temperatures seem to additionally enhance a conflictive process, that is the formation of C agglomerates, instead of the desired process of 3C-SiC formation.
+This is supported by the C-C peak at 0.252 nm, which corresponds to the second next neighbour distance in the diamond structure of elemental C.
+Investigating the atomic data indeed reveals two C atoms which are bound to and interconnected by a third C atom to be responsible for this distance.
+The C-C peak at about 0.31 nm, wich is slightly shifted to higher distances (0.317 nm) with increasing temperature still corresponds quite well to the next neighbour distance of C in 3C-SiC as well as a-SiC and indeed results from C-Si-C bonds.
+The Si-C peak at 0.282 nm, which is pronounced with increasing temperature is constructed out of a Si atom and a C atom, which are both bound to another central C atom.
+This is similar for the Si-C peak at approximately 0.35 nm.
+In this case, the Si and the C atom are bound to a central Si atom.
+To summarize, the amorphous phase remains though sharper peaks in the radial distributions at distances expected for a-SiC are observed indicating a slight acceleration of the dynamics due to elevated temperatures.
+
+Regarding the outcome of both, high and low concentration simulations at increased temperatures, encouraging conclusions can be drawn.
+With the disappearance of the peaks at the respective cut-off radii one limitation of the short range potential seems to be accomplished.
+In addition, sharper peaks in the radial distributions lead to the assumption of expeditious structural formation.
+The increase in temperature leads to the occupation of new defect states, which is particularly evident but not limited to the low carbon concentration simulations.
+The question remains whether these states are only occupied due to the additional supply of kinetic energy and, thus, have to be considered unnatural for temperatures applied in IBS or whether the increase in temperature indeed enables infrequent transitions to occur faster, thus, leading to the intended acceleration of the dynamics and weakening of the unphysical quirks inherent to the potential.
+In the first case these occupied states would be expected to be higher in energy than the states occupied at low temperatures.
+Since substitutional C without the presence of a Si self-interstitial is energetically more favorable than the lowest defect structure obtained without removing a Si atom, that is the \hkl<1 0 0> dumbbell interstitial, and the migration of Si self-interstitials towards the sample surface can be assumed for real life experiments \cite{}, this approach is accepted as an accelerated way of approximatively describing the structural evolution.
+{\color{red}Todo: C sub and Si self-int is energetically less favorable! Maybe fast migration of Si (mentioned in another Todo)? If true, we have to care about Si removal in simulations? In any way these findings suggest a different prec model.}
+
+\subsection{Valuation of a practicable temperature limit}
+\label{subsection:md:tval}
+
+\begin{figure}[!ht]
+\begin{center}
+\includegraphics[width=12cm]{fe_and_t.ps}
+\end{center}
+\caption{Free energy and temperature evolution of plain silicon at temperatures in the region around the melting transition.}
+\label{fig:md:fe_and_t}
+\end{figure}
+The assumed applicability of increased temperature simulations as discussed above and the remaining absence of either agglomeration of substitutional C in low concentration simulations or amorphous to crystalline transition in high concentration simulations suggests to further increase the system temperature.
+So far, the highest temperature applied corresponds to 95 \% of the absolute silicon melting temperature, which is 2450 K and specific to the Erhart/Albe potential.
+However, melting is not predicted to occur instantly after exceeding the melting point due to additionally required transition enthalpy and hysteresis behaviour.
+To check for the possibly highest temperature at which a transition fails to appear plain silicon is heated up using a heating rate of $1\,^{\circ}\mathrm{C}/\text{ps}$.
+Figure \ref{fig:md:fe_and_t} shows the free energy and temperature evolution in the region around the transition temperature.
+Indeed a transition and the accompanying critical behaviour of the free energy is first observed at approximately 3125 K, which corresponds to 128 \% of the silicon melting temperature.
+The difference in free energy is 0.58 eV per atom corresponding to $55.7 \text{ kJ/mole}$, which compares quite well to the silicon enthalpy of melting of $50.2 \text{ kJ/mole}$.
+The late transition probably occurs due to the high heating rate and, thus, a large hysteresis behaviour extending the temperature of transition.
+To avoid melting transitions in further simulations system temperatures well below the transition point are considered safe.
+According to this study temperatures of 100 \% and 120 \% of the silicon melting point could be used.
+However, defects, which are introduced due to the insertion of C atoms are known to lower the transition point.
+Indeed simulations show melting transitions already at the melting point whenever C is inserted.
+Thus, a system temperature of 95 \% of the silicon melting point is used in the following.
+
+\subsection{Long time scale simulations at maximum temperature}
+
+HERE: Quality evolution showed that without cooling it could have increased ... mention that, while at temperatures already simulated, the time time scale is extended! ...
+
+As discussed in section \ref{subsection:md:limit} and \ref{subsection:md:inct} a further increase of the system temperature might help to overcome limitations of the short range potential and accelerate the dynamics involved in structural evolution.
+A maximum temperature to avoid melting is determined in section \ref{subsection:md:tval} to be 120 \% of the Si melting point but due to defects lowering the transition point a maximum temperature of 95 \% of the Si melting temperature is considered usefull.
+This value is almost equal to the temperature of $2050\,^{\circ}\mathrm{C}$ already used in former simulations.
+Thus, this approach reduces to the application of longer time scales.
+Super!
+
+Next to a longer time scale of simulating at maximum temperature a few more changes are applied.
+In the following simulations the system volume, the amount of C atoms inserted and the shape of the insertion volume are modified from the values used in the first MD simulations.
+To speed up the simulation the initial simulation volume is reduced to 21 Si unit cells in each direction and 5500 inserted C atoms in either the whole volume or in a sphere with a radius of 3 nm corresponding to the size of a precipitate consisting of 5500 C atoms.
+The 100 ps sequence after C insertion intended for structural evolution is exchanged by a 10 ns sequence, which is hoped to result in the occurence of infrequent processes.
+The return to lower temperatures is considered seperately.
+
+\begin{figure}[!ht]
+\begin{center}
+\includegraphics[width=12cm]{fe_100.ps}
+\includegraphics[width=12cm]{q_100.ps}
+\end{center}
+\caption[Evolution of the free energy and quality of a simulation at 100 \% of the Si melting temperature.]{Evolution of the free energy and quality of a simulation at 100 \% of the Si melting temperature. Matt colored parts of the graphs represent the C insertion sequence.}
+\label{fig:md:exceed100}
+\end{figure}
+\begin{figure}[!ht]
+\begin{center}
+\includegraphics[width=12cm]{fe_120.ps}
+\includegraphics[width=12cm]{q_120.ps}
+\end{center}
+\caption[Evolution of the free energy and quality of a simulation at 120 \% of the Si melting temperature.]{Evolution of the free energy and quality of a simulation at 120 \% of the Si melting temperature. Matt colored parts of the graphs represent the C insertion sequence.}
+\label{fig:md:exceed120}
+\end{figure}
+Figure \ref{fig:md:exceed100} and \ref{fig:md:exceed120} show the evolution of the free energy per atom and the quality at 100 \% and 120 \% of the Si melting temperature.
+
+{\color{red}Todo: Melting occurs, show and explain it and that it's due to the defects created.}
+
+{\color{red}Todo: Due to melting, after insertion, simulation is continued NVE, so melting hopefully will not occur, before it will be cooled down later on.}