In contrast to the quantum-mechanical MD simulations the developed classical potential MD code is able to do constant pressure simulations using the Berendsen barostat.
The system pressure is set to zero pressure.
-Due to promising advantages over the Tersoff potential the bond order potential of Erhard and Albe is used.
+Due to promising advantages over the Tersoff potential the bond order potential of Erhart and Albe is used.
A time step of one fs is set.
\subsection{Simulations at temperatures used in ion beam synthesis}
The insertion is realized in a way to keep the system temperature constant.
In each of 600 insertion steps 10 carbon atoms are inserted at random positions within the respective region, which involves an increase in kinetic energy.
Thus, the simulation is continued without adding more carbon atoms until the system temperature is equal to the chosen temperature again, which is realized by the thermostat decoupling excessive energy.
-Every inserted carbon atom must exhibit a distance greater or equal than 1.5 \AA{} to present neighboured atoms to prevent too high temperatures.
+Every inserted carbon atom must exhibit a distance greater or equal than 1.5 \AA{} to present neighboured atoms to prevent too high forces to occur.
Once the total amount of carbon is inserted the simulation is continued for 100 ps followed by a cooling-down process until room temperature, that is $20\, ^{\circ}\mathrm{C}$ is reached.
Figure \ref{fig:md:prec_fc} displays a flow chart of the applied steps involved in the simulation sequence.
\begin{figure}[!ht]
This is supported by figure \ref{fig:md:energy_450} displaying the total energy of all three simulations during the whole simulation sequence.
A huge decrease of the total energy during carbon insertion is observed for the simulations with high carbon concentration in contrast to the $V_1$ simulation, which shows a slight increase.
The difference in energy $\Delta$ growing within the carbon insertion process up to a value of roughly 0.06 eV per atom persists unchanged until the end of the simulation.
-Here is the problem.
The excess amount of next neighboured strongly bounded C-C bonds in the high concentration simulations make these configurations energetically more favorable compared to the low concentration configuration.
However, in the same way a lot of energy is needed to break these bonds to get out of the local energy minimum advancing towards the global minimum configuration.
-Thus, such conformational chamges are very unlikely to happen.
+Thus, such conformational changes are very unlikely to happen.
This is in accordance with the constant total energy observed in the continuation step of 100 ps inbetween the end of carbon insertion and the cooling process.
Obviously no energetically favorable relaxation is taking place at a system temperature of $450\,^{\circ}\mathrm{C}$.
The C-C peak at about 0.31 nm perfectly matches the nearest neighbour distance of two carbon atoms in the 3C-SiC lattice.
-{\color{red}Todo: Mention somewhere(!) that the distance is due to neighboured differently oriented C-Si \hkl<1 0 0> dumbbells!}
As can be seen from the inset this peak is also observed for the $V_1$ simulation.
+Investigating the corresponding coordinates of the atoms it turns out that concatenated and differently oriented C-Si \hkl<1 0 0> dumbbell interstitials constitute configurations yielding separations of C atoms by this distance.
In 3C-SiC the same distance is also expected for nearest neighbour silicon atoms.
The bottom of figure \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 0.31 nm are observed while the amount of Si pairs at regular c-Si distances of 0.24 nm and 0.38 nm decreases.
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 carbon concetration simulations}
+
\begin{figure}[!ht]
\begin{center}
\includegraphics[width=12cm]{tot_pc_thesis.ps}\\
Similarly the peaks at 0.335 nm and 0.386 nm shrink in contrast to a new peak forming at 0.372 nm as can be seen in the yellow shaded region.
Obviously the structure obtained from the $450\,^{\circ}\mathrm{C}$ simulations, which is dominated by the existence of \hkl<1 0 0> C-Si dumbbells transforms into a different structure with increasing simulation temperature.
Investigations of the atomic data reveal substitutional carbon to be responsible for the new Si-C bonds.
-The peak at 0.197 nm corresponds to the distance of a substitutional carbon to the next neighboured silicon atoms.
-The one at 0.372 is the distance of the substitutional carbon atom to the second next silicon neighbour along the \hkl<1 1 0> direction.
+The peak at 0.197 nm corresponds to the distance of a substitutional carbon atom to the next neighboured silicon atoms.
+The one at 0.372 nm is the distance of a substitutional carbon atom to the second next silicon neighbour along a \hkl<1 1 0> direction.
Comparing the radial distribution for the Si-C bonds at $2050\,^{\circ}\mathrm{C}$ to the resulting Si-C bonds in a configuration of a substitutional carbon atom in crystalline silicon excludes all possibility of doubt.
The resulting bonds perfectly match and, thus, explain the peaks observed for the increased temperature simulations.
To conclude, by increasing the simulation temperature, the \hkl<1 0 0> C-Si dumbbell characterized structure transforms into a structure dominated by substitutional C.
Since the expected distance of these Si pairs in 3C-SiC is 0.308 nm the existing SiC structures embedded in the c-Si host are stretched.
In the upper part of figure \ref{fig:md:tot_c-c_si-si} the C-C radial distribution is shown.
-With increasing temperature a decrease of the amount of next neighboured C pairs can be observed.
+The total amount of C-C bonds with a distance inside the displayed separation range does not change significantly.
+Thus, even for elevated temperatures agglomeration of C atoms neccessary to form a SiC precipitate does not take place within the simulated time scale.
+However, with increasing temperature a decrease of the amount of next neighboured C pairs can be observed.
This is a promising result gained by the high temperature simulations since the breaking of these diomand and graphite like bonds is mandatory for the formation of 3C-SiC.
A slight shift towards higher distances can be observed for the maximum above 0.3 nm.
Arrows with dashed lines mark C-C distances resulting from \hkl<1 0 0> dumbbell combinations while the arrows with solid lines mark distances arising from combinations of substitutional C.
Again, this is a quite promising result, since the C atoms are taking the appropriate coordination as expected in 3C-SiC.
However, this is contrary to the initial precipitation model proposed in section \ref{section:assumed_prec}, which assumes that the transformation into 3C-SiC takes place in a very last step once enough C-Si dumbbells agglomerated.
-{\color{red}Todo: Summarize again! Mention, that the agglomeration necessary in order to form 3C-SiC is missing.}
+To summarize, results of low concentration simulations show a phase transition in conjunction with an increase in temperature.
+The C-Si \hkl<1 0 0> dumbbell dominated struture turns into a structure characterized by the occurence of an increasing amount of substitutional C with respect to temperature.
+Although diamond and graphite like bonds are reduced no agglomeration of C is observed within the simulated time resulting in the formation of isolated structures of stretched SiC, which are adjusted to the c-Si host with respect to the lattice constant and alignement.
+It would be conceivable that by agglomeration of further substitutional C atoms the interfacial energy could be overcome and a transition into an incoherent SiC precipitate could occur.
+
+{\color{red}Todo: Results reinforce the assumption of an alternative precipitation model as already pointed out in the defects chapter.}
+
+\subsubsection{High carbon concetration simulations}
\begin{figure}[!ht]
\begin{center}
\label{fig:md:fe_and_t}
\end{figure}
The assumed applicability of increased temperature simulations as discussed above and the remaining absence of either agglomeration of substitutional C in low concentration simulations or amorphous to crystalline transition in high concentration simulations suggests to further increase the system temperature.
-So far, the highest temperature applied corresponds to 95 \% of the absolute silicon melting temperature, which is 2450 K and specific to the Erhard/Albe potential.
+So far, the highest temperature applied corresponds to 95 \% of the absolute silicon melting temperature, which is 2450 K and specific to the Erhart/Albe potential.
However, melting is not predicted to occur instantly after exceeding the melting point due to additionally required transition enthalpy and hysteresis behaviour.
To check for the possibly highest temperature at which a transition fails to appear plain silicon is heated up using a heating rate of $1\,^{\circ}\mathrm{C}/\text{ps}$.
Figure \ref{fig:md:fe_and_t} shows the free energy and temperature evolution in the region around the transition temperature.
\subsection{Long time scale simulations at maximum temperature}
+HERE: Quality evolution showed that without cooling it could have increased ... mention that, while at temperatures already simulated, the time time scale is extended! ...
+
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 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.
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