-This is also true for peaks located past distances of next neighbours indicating an increase for the long range order.
-However this change is rather small and no significant structural change is observeable.
-As for low temperatures order in the short range exist decreasing with increasing distance.
-The increase of the amount of Si-C pairs at 0.186 nm could pe 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 interconnect 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 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 said, there is clear evidence that this is amorphous SiC
-However there is no significant change in structure.
-But there is a decrease in the artifacts of the potential.
-So, first limitations might be condiered as
-Now, more temperature to increase infrequent events ...
-
-\subsection{Constructed 3C-SiC precipitate in crystalline silicon}
-
-{\color{red}Todo: We want to know where we want to go ...}
-
-In the following a spherical 3C-SiC precipitate enclosed in a c-Si surrounding is constructed as it is expected from IBS experiments and from simulations that finally succeed simulating the precipitation event.
-On the one hand this sheds light on characteristic values like the radial distribution function or the total amount of energy for configurations that are aimed to be reproduced by simulation possibly enabling the prediction of conditions necessary for the simulation of the precipitation process.
-On the other hand, assuming a correct alignment of the precipitate with the c-Si matrix, investigations of the behaviour of such precipitates and the surrounding can be made.
-
-To construct a spherical 3C-SiC precipitate in c-Si, the approach illustrated in the following is applied.
-A total simulation volume $V$ consisting of 21 unit cells of c-Si in each direction is used.
-To obtain a minimal and stable precipitate 5500 carbon atoms are considered necessary.
-The initial precipitate configuration is constructed in two steps.
-In the first step the surrounding silicon matrix is created.
-This is realized by just skipping the generation of silicon atoms inside a sphere of radius $x$, which is the first unknown variable.
-The silicon lattice constant $a_{\text{Si}}$ of the surrounding c-Si matrix is assumed to not alter dramatically and, thus, is used for the initial lattice creation.
-In a second step 3C-SiC is created inside the empty sphere of radius $x$.
-The lattice constant $y$, the second unknown variable, is chosen in such a way, that the necessary amount of carbon is generated.
-This is entirely described by the system of equations \eqref{eq:md:constr_sic_01}
-\begin{equation}
-\frac{8}{a_{\text{Si}}^3}(
-\underbrace{21^3 a_{\text{Si}}^3}_{=V}
--\frac{4}{3}\pi x^3)+
-\underbrace{\frac{4}{y^3}\frac{4}{3}\pi x^3}_{\stackrel{!}{=}5500}
-=21^3\cdot 8
-\label{eq:md:constr_sic_01}
-\text{ ,}
-\end{equation}
-which can be simplified to read
-\begin{equation}
-\frac{8}{a_{\text{Si}}^3}\frac{4}{3}\pi x^3=5500
-\Rightarrow x = \left(\frac{5500 \cdot 3}{32 \pi} \right)^{1/3}a_{\text{Si}}
-\label{eq:md:constr_sic_02}
-\end{equation}
-and
-\begin{equation}
-%x^3=\frac{16\pi}{5500 \cdot 3}y^3=
-%\frac{16\pi}{5500 \cdot 3}\frac{5500 \cdot 3}{32 \pi}a_{\text{Si}}^3
-%\Rightarrow
-y=\left(\frac{1}{2} \right)^{1/3}a_{\text{Si}}
-\text{ .}
-\label{eq:md:constr_sic_03}
-\end{equation}
-By this means values of 2.973 nm and 4.309 \AA{} are obtained for the initial precipitate radius and lattice constant of 3C-SiC.
-Since the generation of atoms is a discrete process with regard to the size of the volume the expected amounts of atoms are not obtained.
-However, by applying these values the final configuration varies only slightly from the expected one by five carbon and eleven silicon atoms, as can be seen in table \ref{table:md:sic_prec}.
-\begin{table}[!ht]
+This is also true for peaks located past distances of next neighbors indicating an increase in the long range order.
+However, this change is rather small and no significant structural change is observable.
+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 successively 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 separation.
+The increase of the amount of Si-C pairs at \distn{0.186} could be positively interpreted since this type of bond also exists in 3C-SiC.
+On the other hand, the amount of next neighbored C atoms with a distance of approximately \distn{0.15}, which is the distance of C in graphite or diamond, is likewise increased.
+Thus, higher temperatures seem to additionally enhance a conflictive process, i.e.\ the formation of C agglomerates, obviously inconsistent with the desired process of 3C-SiC formation.
+This is supported by the C-C peak at \distn{0.252}, which corresponds to the second next neighbor 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 \distn{0.31}, which is slightly shifted to higher distances (\distn{0.317}) with increasing temperature still corresponds quite well to the next neighbor distance of C in 3C-SiC as well as a-SiC and, indeed, results from C-Si-C bonds.
+The Si-C peak at \distn{0.282}, 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 \distn{0.35}.
+In this case, the Si and the C atom are bound to a central Si atom.
+
+To summarize, the amorphous phase remains.
+Huge amounts of damage hamper identification.
+The alignment of the investigated structures to the c-Si host is lost in many cases, which suggests the necessity of much more time for structural evolution to maintain the topotactic orientation of the precipitate.
+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.
+
+\subsection{Conclusions concerning the usage of increased temperatures}
+
+Regarding the outcome of both, high and low C 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 distribution functions 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 C 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.
+As already pointed out in section~\ref{section:defects:noneq_process_01} and section~\ref{section:defects:noneq_process_02}, IBS is a non-equilibrium process, which might result in the formation of the thermodynamically less stable \cs{} and \si{} configuration.
+Indeed, 3C-SiC is metastable and if not fabricated by IBS requires strong deviation from equilibrium and low temperatures to stabilize the 3C polytype.
+In IBS, highly energetic C atoms are able to generate vacant sites, which in turn can be occupied by highly mobile \ci{} atoms.
+This is in fact found to be favorable in the absence of the \si{}, which turned out to have a low interaction capture radius with the \cs{} atom and very likely prevents the recombination into a thermodynamically stable \ci{} DB for appropriate separations of the defect pair.
+Results gained in this chapter show preferential occupation of Si lattice sites by \cs{} enabled by increased temperatures supporting the assumptions drawn from the defect studies of the last chapter.
+
+Moreover, the cut-off effect as detailed in section~\ref{section:md:limit} is particularly significant for configurations that are deviated to a great extent from their equilibrium structures.
+Thus, for instance, it is not surprising that short range potentials show overestimated melting temperatures while properties of structures that are only slightly deviated from equilibrium are well described.
+Due to this, increased temperatures are considered exceptionally necessary for modeling non-equilibrium processes and structures such as IBS and 3C-SiC.
+
+Thus, it is concluded that increased temperatures are not exclusively useful to accelerate the dynamics approximatively describing the structural evolution.
+Moreover, it can be considered a necessary condition to deviate the system out of equilibrium enabling the formation of 3C-SiC, which is obviously realized by a successive agglomeration of \cs{}.
+
+\ifnum1=0
+
+\section{Long time scale simulations at maximum temperature}
+
+As discussed in section~\ref{section:md:limit} and~\ref{section: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.
+Furthermore, these results indicate that increased temperatures are necessary to drive the system out of equilibrium enabling conditions needed for the formation of a metastable cubic polytype of SiC.
+
+A maximum temperature to avoid melting is determined in section~\ref{section: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 useful.
+This value is almost equal to the temperature of $2050\,^{\circ}\mathrm{C}$ already used in former simulations.
+Since the maximum temperature is reached, the approach is reduced to the application of longer time scales.
+This is considered useful since the estimated evolution of quality in the absence of the cooling down sequence in figure~\ref{fig:md:tot_si-c_q} predicts an increase in quality and, thus, structural evolution is likely to occur if the simulation is proceeded at maximum temperature.
+
+Next to the employment of longer time scales and a 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 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 \unit[100]{ps} sequence after C insertion intended for structural evolution is exchanged by a \unit[10]{ns} sequence, which is hoped to result in the occurrence of infrequent processes and a subsequent phase transition.
+The return to lower temperatures is considered separately.
+
+\begin{figure}[tp]