Fig.~\ref{fig:450} shows the radial distribution functions of simulations, in which C was inserted at \unit[450]{$^{\circ}$C}, an operative and efficient temperature in IBS\cite{lindner99}, for all three insertion volumes.
\begin{figure}
\begin{center}
-\includegraphics[width=\columnwidth]{../img/sic_prec_450_si-si_c-c.ps}\\
+\subfigure[]{\label{fig:450:a}
+\includegraphics[width=\columnwidth]{../img/sic_prec_450_si-si_c-c.ps}
+}
+\subfigure[]{\label{fig:450:b}
\includegraphics[width=\columnwidth]{../img/sic_prec_450_si-c.ps}
+}
\end{center}
-\caption{Radial distribution function for C-C and Si-Si (top) as well as Si-C (bottom) pairs for C inserted at \unit[450]{$^{\circ}$C}. In the latter case the resulting C-Si distances for a C$_{\text{i}}$ \hkl<1 0 0> DB are given additionally.}
+\caption{Radial distribution function for C-C and Si-Si (Fig.~\ref{fig:450:a}) as well as Si-C (Fig.~\ref{fig:450:b}) pairs for C inserted at \unit[450]{$^{\circ}$C}. In the latter case the resulting C-Si distances for a C$_{\text{i}}$ \hkl<1 0 0> DB are given additionally and the Si-C cut-off distance is marked by an arrow. Insets in Fig.~\ref{fig:450:a} show magnified regions of the respective distribution functions.}
\label{fig:450}
\end{figure}
There is no significant difference between C insertion into $V_2$ and $V_3$.
Thus, in the following, the focus is on low ($V_1$) and high ($V_2$, $V_3$) C concentration simulations only.
-In the low C concentration simulation the number of C-C bonds is small.
+In the low C concentration simulation the number of C-C bonds is small, as can be seen in the upper part of Fig.~\ref{fig:450:a}.
On average, there are only 0.2 C atoms per Si unit cell.
-By comparing the Si-C peaks of the low concentration simulation with the resulting Si-C distances of a C$_{\text{i}}$ \hkl<1 0 0> DB it becomes evident that the structure is clearly dominated by this kind of defect.
-One exceptional peak exists, which is due to the Si-C cut-off, at which the interaction is pushed to zero.
-Investigating the C-C peak at \unit[0.31]{nm}, which is also available for low C concentrations as can be seen in the inset, reveals a structure of two concatenated, differently oriented C$_{\text{i}}$ \hkl<1 0 0> DBs to be responsible for this distance.
-Additionally, the Si-Si radial distribution shows non-zero values at distances around \unit[0.3]{nm}, which, again, is due to the DB structure stretching two neighbored Si atoms.
+By comparing the Si-C peaks of the low concentration simulation with the resulting Si-C distances of a C$_{\text{i}}$ \hkl<1 0 0> DB in Fig.~\ref{fig:450:b} it becomes evident that the structure is clearly dominated by this kind of defect.
+One exceptional peak at \unit[0.26]{nm} exists, which is due to the Si-C cut-off, at which the interaction is pushed to zero.
+Investigating the C-C peak at \unit[0.31]{nm}, which is also available for low C concentrations as can be seen in the upper inset of Fig.~\ref{fig:450:a}, reveals a structure of two concatenated, differently oriented C$_{\text{i}}$ \hkl<1 0 0> DBs to be responsible for this distance.
+Additionally, in the inset of the bottom part of Fig.\ref{fig:450:a} the Si-Si radial distribution shows non-zero values at distances around \unit[0.3]{nm}, which, again, is due to the DB structure stretching two neighbored Si atoms.
This is accompanied by a reduction of the number of bonds at regular Si distances of c-Si.
A more detailed description of the resulting C-Si distances in the C$_{\text{i}}$ \hkl<1 0 0> DB configuration and the influence of the defect on the structure is available in a previous study\cite{zirkelbach09}.
Fig.~\ref{fig:tot} shows the resulting radial distribution functions for various temperatures.
\begin{figure}
\begin{center}
-\includegraphics[width=\columnwidth]{../img/tot_pc_thesis.ps}\\
-\includegraphics[width=\columnwidth]{../img/tot_pc3_thesis.ps}\\
+\subfigure[]{\label{fig:tot:si-c}
+\includegraphics[width=\columnwidth]{../img/tot_pc_thesis.ps}
+}
+\subfigure[]{\label{fig:tot:si-si}
+\includegraphics[width=\columnwidth]{../img/tot_pc3_thesis.ps}
+}
+\subfigure[]{\label{fig:tot:c-c}
\includegraphics[width=\columnwidth]{../img/tot_pc2_thesis.ps}
+}
\end{center}
-\caption{Radial distribution function for Si-C (top), Si-Si (center) and C-C (bottom) pairs for the C insertion into $V_1$ at elevated temperatures. For the Si-C distribution resulting Si-C distances of a C$_{\text{s}}$ configuration are plotted. In the C-C distribution dashed arrows mark C-C distances occurring from C$_{\text{i}}$ \hkl<1 0 0> DB combinations, solid arrows mark C-C distances of pure C$_{\text{s}}$ combinations and the dashed line marks C-C distances of a C$_{\text{i}}$ and C$_{\text{s}}$ combination.}
+\caption{Radial distribution function for Si-C (Fig.~\ref{fig:tot:si-c}), Si-Si (Fig.~\ref{fig:tot:si-si}) and C-C (Fig.~\ref{fig:tot:c-c}) pairs for the C insertion into $V_1$ at elevated temperatures. For the Si-C distribution resulting Si-C distances of a C$_{\text{s}}$ configuration are plotted. In the C-C distribution dashed arrows mark C-C distances occurring from C$_{\text{i}}$ \hkl<1 0 0> DB combinations, solid arrows mark C-C distances of pure C$_{\text{s}}$ combinations and the dashed line marks C-C distances of a C$_{\text{i}}$ and C$_{\text{s}}$ combination.}
\label{fig:tot}
\end{figure}
-The first noticeable and promising change observed for the Si-C bonds is the successive decline of the artificial peak at the cut-off distance with increasing temperature.
+In Fig.~\ref{fig:tot:si-c}, the first noticeable and promising change observed for the Si-C bonds is the successive decline of the artificial peak at the cut-off distance with increasing temperature.
Obviously, sufficient kinetic energy is provided to affected atoms that are enabled to escape the cut-off region.
-Additionally, a more important structural change was observed, which is illustrated in the two shaded areas of the graph.
+Additionally, a more important structural change was observed, which is illustrated in the two shaded areas in Fig.~\ref{fig:tot:si-c}.
Obviously, the structure obtained at \unit[450]{$^{\circ}$C}, which was found to be dominated by C$_{\text{i}}$, transforms into a C$_{\text{s}}$ dominated structure with increasing temperature.
Comparing the radial distribution at \unit[2050]{$^{\circ}$C} to the resulting bonds of C$_{\text{s}}$ in c-Si excludes all possibility of doubt.
-The phase transformation is accompanied by an arising Si-Si peak at \unit[0.325]{nm}, which corresponds to the distance of next neighbored Si atoms along the \hkl<1 1 0> bond chain with C$_{\text{s}}$ in between.
+The phase transformation is accompanied by an arising Si-Si peak at \unit[0.325]{nm} in Fig.~\ref{fig:tot:si-si}, which corresponds to the distance of next neighbored Si atoms along the \hkl<1 1 0> bond chain with C$_{\text{s}}$ in between.
Since the expected distance of these Si pairs in 3C-SiC is \unit[0.308]{nm} the existing SiC structures embedded in the c-Si host are stretched.
-According to the C-C radial distribution, agglomeration of C fails to appear even for elevated temperatures, as can be seen on the total amount of C pairs within the investigated separation range, which does not change significantly.
+According to the C-C radial distribution displayed in Fig.~\ref{fig:tot:c-c}, agglomeration of C fails to appear even for elevated temperatures, as can be seen on the total amount of C pairs within the investigated separation range, which does not change significantly.
However, a small decrease in the amount of neighbored C pairs can be observed with increasing temperature.
This high temperature behavior is promising since breaking of these diamond- and graphite-like bonds is mandatory for the formation of 3C-SiC.
Obviously, acceleration of the dynamics occurred by supplying additional kinetic energy.
Fig.~\ref{fig:v2} displays the radial distribution for high C concentrations.
\begin{figure}
\begin{center}
-\includegraphics[width=\columnwidth]{../img/12_pc_thesis.ps}\\
+\subfigure[]{\label{fig:v2:si-c}
+\includegraphics[width=\columnwidth]{../img/12_pc_thesis.ps}
+}
+\subfigure[]{\label{fig:v2:c-c}
\includegraphics[width=\columnwidth]{../img/12_pc_c_thesis.ps}
+}
\end{center}
-\caption{Radial distribution function for Si-C (top) and C-C (bottom) pairs for the C insertion into $V_2$ at elevated temperatures.}
+\caption{Radial distribution function for Si-C (Fig.~\ref{fig:v2:si-c}) and C-C (Fig.~\ref{fig:v2:c-c}) pairs for the C insertion into $V_2$ at elevated temperatures. Arrows mark the respective cut-off distances.}
\label{fig:v2}
\end{figure}
The amorphous SiC-like phase remains.
However, the decrease of the cut-off artifact and slightly sharper peaks observed with increasing temperature, in turn, indicate a slight acceleration of the dynamics realized by the supply of kinetic energy.
However, it is not sufficient to enable the amorphous to crystalline transition.
In contrast, even though bonds of neighbored C atoms could be partially dissolved in the system exhibiting low C concentrations, the amount of neighbored C pairs even increased in the latter case.
-Moreover, the C-C peak at \unit[0.252]{nm}, which gets slightly more distinct, equals the second nearest neighbor distance in diamond and indeed is made up by a structure of two C atoms interconnected by a third C atom.
+Moreover, the C-C peak at \unit[0.252]{nm} in Fig.~\ref{fig:v2:c-c}, which gets slightly more distinct, equals the second nearest neighbor distance in diamond and indeed is made up by a structure of two C atoms interconnected by a third C atom.
Obviously, processes that appear to be non-conducive are likewise accelerated in a system, in which high amounts of C are incorporated within a short period of time, which is accompanied by a concurrent introduction of accumulating, for the reason of time non-degradable damage.
% non-degradable, non-regenerative, non-recoverable
Thus, for these systems even larger time scales, which are not accessible within traditional MD, must be assumed for an amorphous to crystalline transition or structural evolution in general.
% maybe put description of bonds in here ...
Nevertheless, some results likewise indicate the acceleration of other processes that, again, involve C$_{\text{s}}$.
-The increasingly pronounced Si-C peak at \unit[0.35]{nm} corresponds to the distance of a C and a Si atom interconnected by another Si atom.
-Additionally, the C-C peak at \unit[0.31]{nm} corresponds to the distance of two C atoms bound to a central Si atom.
+The increasingly pronounced Si-C peak at \unit[0.35]{nm} in Fig.~\ref{fig:v2:si-c} corresponds to the distance of a C and a Si atom interconnected by another Si atom.
+Additionally, the C-C peak at \unit[0.31]{nm} in Fig.~\ref{fig:v2:c-c} corresponds to the distance of two C atoms bound to a central Si atom.
For both structures the C atom appears to reside on a substitutional rather than an interstitial lattice site.
However, 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.
-\section{Summary and discussion}
+\section{Discussion and Summary}
Investigations are targeted at the initially stated controversy of SiC precipitation, i.e. whether precipitation occurs abruptly after enough C$_{\text{i}}$ agglomerated or after a successive agglomeration of C$_{\text{s}}$ on usual Si lattice sites (and Si$_{\text{i}}$) followed by a contraction into incoherent SiC.
Results of a previous ab initio study on defects and defect combinations in C implanted Si\cite{zirkelbach10b} suggest C$_{\text{s}}$ to play a decisive role in the precipitation of SiC in Si.
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