Investigating the radial distribution function shown in figure \ref{fig:md:pc_500-fin}, which shows configurations below and above the temperature of the estimated transition, indeed supports the assumption of melting gained by the free energy plot.
However the precipitate itself is not involved, as can be seen from the Si-C and C-C distribution, which essentially stays the same for both temperatures.
Thus, it is only the c-Si surrounding undergoing a structural phase transition, which is very well reflected by the difference observed for the two Si-Si distributions.
-This is surprising since the melting transition of plain c-Si is expected at temperatures around 3125 K, as discussed in the last section.
+This is surprising since the melting transition of plain c-Si is expected at temperatures around 3125 K, as discussed in section \ref{subsection:md:tval}.
Obviously the precipitate lowers the transition point of the surrounding c-Si matrix.
+This is indeed verified by visualizing the atomic data.
+\begin{figure}[!ht]
+\begin{center}
+\begin{minipage}{7cm}
+\includegraphics[width=7cm,draft=false]{sic_prec/melt_01.eps}
+\end{minipage}
+\begin{minipage}{7cm}
+\includegraphics[width=7cm,draft=false]{sic_prec/melt_02.eps}
+\end{minipage}
+\begin{minipage}{7cm}
+\includegraphics[width=7cm,draft=false]{sic_prec/melt_03.eps}
+\end{minipage}
+\end{center}
+\caption{Cross section image of atomic data gained by annealing simulations of the constructed 3C-SiC precipitate in c-Si at 200 ps (top left), 520 ps (top right) and 720 ps (bottom).}
+\label{fig:md:sic_melt}
+\end{figure}
+Figure \ref{fig:md:sic_melt} shows cross section images of the atomic structures at different times and temperatures.
+As can be seen from the image at 520 ps melting of the Si surrounding in fact starts in the defective interface region of the 3C-SiC precipitate and the c-Si surrounding propagating outwards until the whole Si matrix is affected at 720 ps.
+As predicted from the radial distribution data the precipitate itself remains stable.
+
For the rearrangement simulations temperatures well below the transition point should be used since it is very unlikely to recrystallize the molten Si surrounding properly when cooling down.
To play safe the precipitate configuration at 100 \% of the Si melting temperature is chosen and cooled down to $20\,^{\circ}\mathrm{C}$ with a cooling rate of $1\,^{\circ}\mathrm{C}/\text{ps}$.
-{\color{blue}Todo: Wait for results and then compare structure (PC) and interface energy, maybe a energetically more favorable configuration arises.}
-{\color{red}Todo: Mention the fact, that the precipitate is stable for eleveated temperatures, even for temperatures where the Si matrix is melting.}
-{\color{red}Todo: Si starts to melt at the interface, show pictures and explain, it is due to the defective interface region.}
+However, an energetically more favorable interface is not obtained by quenching this structure to zero Kelvin.
+Obviously the increased temperature run enables structural changes that are energetically less favorable but can not be exploited to form more favorable configurations by an apparently yet too fast cooling down process.
\section{Coherent to incoherent transition of 3C-SiC precipitates in crystalline silicon}
-Results of the defect ... indicate the very likely possibility of another precipitation mechanism.
+As already pointed out, some of the previous results indicate the very likely possibility of another precipitation mechanism.
This mechanism is based on the successive formation of substitutional C sites, which might result in coherent 3C-SiC structures within the c-Si matrix assuming that Si self-interstitials might diffuse out of the affected region easily.
-Reaching a critical size these coherent precipitates release the alignement on the c-Si lattice spacing by contracting to an incoherent SiC precipitate with lower lattice constant.
+Reaching a critical size these coherent SiC structures release the alignement on the c-Si lattice spacing by contracting to an incoherent SiC precipitate with lower lattice constant.
Precipitation -> contraction ... free 'space' might be compensated by volume changes due to the barostat ...
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.
-Thus, in the following system temperatures of 100 \% and 120 \% of the silicon melting point are used.
+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}
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 was determined in section \ref{subsection:md:tval}, which is 120 \% of the Si melting point.
-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 now match the conditions given in the simulations of the self-constructed precipitate configuration for reasons of comparability.
-To quantify, the initial simulation volume now consists of 21 Si unit cells in each direction and 5500 C atoms are inserted in either the whole volume or in a sphere with a radius of 3 nm.
-Since the investigated temperatures exceed the Si melting point the initial Si bulk material is heated up slowly by $1\,^{\circ}\mathrm{C}/\text{ps}$ starting from $1650\,^{\circ}\mathrm{C}$ before the C insertion sequence is started.
-The 100 ps sequence at the respective temperature intended for the structural evolution is exchanged by a 10 ns sequence, which will hopefully result in the occurence of infrequent processes.
+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]
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