The bottom of Fig.~\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 \unit[0.31]{nm} are observed while the amount of Si pairs at regular c-Si distances of \unit[0.24]{nm} and \unit[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 \unit[0.29]{nm} can be attributed to the Si-Si cut-off radius of \unit[0.296]{nm} as used in the present bond order potential.
+In addition, the abrupt increase of Si pairs at \unit[0.29]{nm} can be attributed to the Si-Si cut-off radius of \unit[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 abrupt increase, a maximum around \unit[0.31]{nm} gets even more conceivable.
Analyses of randomly chosen configurations, in which distances around \unit[0.3]{nm} appear, identify \ci{} \hkl<1 0 0> DBs to be responsible for stretching the Si-Si next neighbor distance for low C concentrations, i.e.\ for the $V_1$ and early stages of $V_2$ and $V_3$ simulation runs.
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, i.e.\ the large amount of strong neighbored C-C bonds at \unit[0.15]{nm} as expected in graphite or diamond and Si-C bonds at \unit[0.19]{nm} as expected in SiC, 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}.
+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}.
In both cases, i.e.\ low and high C concentrations, the formation of 3C-SiC fails to appear.
With respect to the precipitation model, the formation of C$_{\text{i}}$ \hkl<1 0 0> DBs indeed occurs for low C concentrations.
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.
+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.
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