Another one is to use variable cut-off values scaled by the system volume, which properly describes thermomechanical properties of 3C-SiC \cite{tang95} but might be rather ineffective for the challange inherent to this study.
To conclude the obstacle needed to get passed is twofold.
-The sharp cut-off of the employed bond order model potential introduces overestimated high forces between next neighbored atoms enhancing the problem of slow phase space propagation immanent to MD simulations, termed {\em potential enhanced slow phase space propagation} in the following.
-Thus, pushing the time scale to the limits of computational ressources or applying one of the above mentioned accelerated dynamics methods exclusively will not be sufficient enough.
+The sharp cut-off of the employed bond order model potential introduces overestimated high forces between next neighbored atoms enhancing the problem of slow phase space propagation immanent to MD simulations.
+This obstacle could be referred to as {\em potential enhanced slow phase space propagation}.
+Due to this, pushing the time scale to the limits of computational ressources or applying one of the above mentioned accelerated dynamics methods exclusively will not be sufficient enough.
Instead, the approach followed in this study, is the use of higher temperatures as exploited in TAD to find transition pathways of one local energy minimum to another one more quickly.
Since merely increasing the temperature leads to different equilibrium kinetics than valid at low temperatures, TAD introduces basin-constrained MD allowing only those transitions that should occur at the original temperature and a properly advancing system clock \cite{sorensen2000}.
\label{section:md:inct}
Due to the limitations of short range potentials and conventional MD as discussed above, elevated temperatures are used in the following.
+Increased temperatures are expected to compensate the overestimated diffusion barriers.
+These are overestimated by a factor of 2.4 to 3.5.
+Scaling the absolute temperatures accordingly results in maximum temperatures of \unit[1460-2260]{$^{\circ}$C}.
+Since melting already occurs shortly below the melting point of the potential (\unit[2450]{K}) \cite{albe_sic_pot} due to the presence of defects, temperatures ranging from \unit[450-2050]{$^{\circ}$C} are used.
The simulation sequence and other parameters except for the system temperature remain unchanged as in section \ref{section:initial_sims}.
Since there is no significant difference among the $V_2$ and $V_3$ simulations only the $V_1$ and $V_2$ simulations are carried on and referred to as low C and high C concentration simulations.
-Temperatures ranging from \degc{450} up to \unit[2050]{$^{\circ}$C} are used.
A simple quality value $Q$ is introduced, which helps to estimate the progress of structural evolution.
In bulk 3C-SiC every C atom has four next neighbored Si atoms and every Si atom four next neighbored C atoms.
However, since the quality value does not account for bond lengthes, bond angles, crystallinity or the stacking sequence, high values of $Q$ not necessarily correspond to structures close to 3C-SiC.
Structures that look promising due to high quality values need to be further investigated by other means.
-\subsubsection{Low C concetration simulations}
+\subsection{Low C concetration simulations}
\begin{figure}[tp]
\begin{center}
Isolated structures of stretched SiC, which are adjusted to the c-Si host with respect to the lattice constant and alignement, are formed.
It would be conceivable that by agglomeration of further \cs{} atoms the interfacial energy could be overcome and a transition from a coherent and stretched SiC structure into an incoherent and partially strain-compensated SiC precipitate could occur.
-\subsubsection{High C concetration simulations}
+\subsection{High C concetration simulations}
\begin{figure}[tp]
\begin{center}
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.
-\subsubsection{Conclusions concerning the usage of increased 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.
Thus, it is concluded that increased temperatures is not exclusively usefull 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{}.
+
+\section{Conclusions concerning the SiC conversion mechanism}
+
+MD simulations at temperatures used in IBS result in structures that are dominated by the C$_{\text{i}}$ \hkl<1 0 0> DB and its combinations if C is inserted into the total volume.
+Incorporation into volumes $V_2$ and $V_3$ leads to an amorphous SiC-like structure within the respective volume.
+To compensate overestimated diffusion barriers, simulations at accordingly increased temperatures are performed.
+No significant change is observed for high C concentrations.
+The amorphous phase is maintained.
+Due to the incorporation of a huge amount of C into a small volume within a short period of time, damage is produced, which obviously decelerates structural evolution.
+For the low C concentrations, time scales are still too low to observe C agglomeration sufficient for SiC precipitation, which is attributed to the slow phase space propagation inherent to MD in general.
+However, a phase transition of the C$_{\text{i}}$-dominated into a clearly C$_{\text{s}}$-dominated structure is observed.
+The amount of substitutionally occupied C atoms increases with increasing temperature.
+Isolated structures of stretched SiC adjusted to the c-Si host with respect to the lattice constant and alignement are formed.
+Entropic contributions are assumed to be responsible for these structures at elevated temperatures that deviate from the ground state at 0 K.
+
+Results of the MD simulations at different temperatures and C concentrations can be correlated to experimental findings.
+IBS studies revealed increased implantation temperatures to be more efficient than postannealing methods for the formation of topotactically aligned precipitates \cite{kimura82,eichhorn02}.
+In particular, restructuring of strong C-C bonds is affected \cite{deguchi92}, which preferentially arise if additional kinetic energy provided by an increase of the implantation temperature is missing to accelerate or even enable atomic rearrangements.
+This is assumed to be related to the problem of slow structural evolution encountered in the high C concentration simulations.
+The insertion of high amounts of C into a small volume within a short period of time resulting in essentially no time for the system to rearrange.
+% rt implantation + annealing
+Furthermore, C implanted at room temperature was found to be able to migrate towards the surface and form C-rich clusters in contrast to implantations at elevated temperatures, which form stable epitaxially aligned 3C-SiC precipitates \cite{serre95}.
+In simulation, low temperatures result in configurations of highly mobile \ci{} \hkl<1 0 0> DBs whereas elevated temperatures show configurations of \cs{}, which constitute an extremely stable configuration that is unlikely to migrate.
+Indeed, in the optimized recipe to form 3C-SiC by IBS \cite{lindner99}, elevated temperatures are used to improve the epitaxial orientation together with a low temperature implant to destroy stable SiC nanocrystals at the interface, which are unable to migrate during thermal annealing resulting in a rough surface.
+Furtermore, the improvement of the epitaxial orientation of the precipitate with increasing temperature in experiment perfectly conforms to the increasing occurrence of \cs{} in simulation.
+At elevated temperatures, implanted C is therefore expected to occupy substitutionally usual Si lattice sites right from the start.
+
+Thus, elevated temperatures are considered to constitute a necessary condition to deviate the system from equilibrium, as it is the case in IBS.
+It is concluded that precipitation occurs by successive agglomeration of C$_{\text{s}}$ as already proposed by Nejim et~al.~\cite{nejim95}.
+This agrees well with a previous results of the {\em ab initio} study on defects in C implanted Si, which show C$_{\text{s}}$ to occur in all probability.
+However, agglomeration and rearrangement is enabled by mobile C$_{\text{i}}$, which has to be present at the same time and is formed by recombination of C$_{\text{s}}$ and Si$_{\text{i}}$.
+In contrast to assumptions of an abrupt precipitation of an agglomerate of C$_{\text{i}}$ \cite{werner96,werner97,eichhorn99,lindner99_2,koegler03}, however, structural evolution is believed to occur by a successive occupation of usual Si lattice sites with substitutional C.
+This mechanism satisfies the experimentally observed alignment of the \hkl(h k l) planes of the precipitate and the substrate, whereas there is no obvious reason for the topotactic orientation of an agglomerate consisting exclusively of C-Si dimers, which would necessarily involve a much more profound change in structure for the transition into SiC.
+
\ifnum1=0
\section{Valuation of a practicable temperature limit}
For both, high and low concentration simulations the radial distribution converges as can be seen by the nearly identical graphs of the two most advanced configurations.
Changes exist ... bridge to results after cooling down to 20 degree C.
-{\color{red}Todo: Cooling down to $20\,^{\circ}\mathrm{C}$ by $1\,^{\circ}\mathrm{C/s}$ in progress.}
-% todo evtl in ausblick
-
-%\subsection{Further accelerated dynamics approaches}
-%{\color{red}Todo: self-guided MD?}
-%{\color{red}Todo: ART MD?\\
-%How about forcing a migration of a $V_2$ configuration to a constructed prec configuration, determine the saddle point configuration and continue the simulation from this configuration?
-%}
-
\fi
-\section{Conclusions concerning the SiC conversion mechanism}
-
-
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