-Thus, in the following system temperatures of 100 \% and 120 \% of the silicon melting point are used.
-
-\subsection{Constructed 3C-SiC precipitate in crystalline silicon}
-
-{\color{red}Todo: We want to know where we want to go ...}
-
-In the following a spherical 3C-SiC precipitate enclosed in a c-Si surrounding is constructed as it is expected from IBS experiments and from simulations that finally succeed simulating the precipitation event.
-On the one hand this sheds light on characteristic values like the radial distribution function or the total amount of energy for configurations that are aimed to be reproduced by simulation possibly enabling the prediction of conditions necessary for the simulation of the precipitation process.
-On the other hand, assuming a correct alignment of the precipitate with the c-Si matrix, investigations of the behaviour of such precipitates and the surrounding can be made.
-
-To construct a spherical 3C-SiC precipitate in c-Si, the approach illustrated in the following is applied.
-A total simulation volume $V$ consisting of 21 unit cells of c-Si in each direction is used.
-To obtain a minimal and stable precipitate 5500 carbon atoms are considered necessary.
-The initial precipitate configuration is constructed in two steps.
-In the first step the surrounding silicon matrix is created.
-This is realized by just skipping the generation of silicon atoms inside a sphere of radius $x$, which is the first unknown variable.
-The silicon lattice constant $a_{\text{Si}}$ of the surrounding c-Si matrix is assumed to not alter dramatically and, thus, is used for the initial lattice creation.
-In a second step 3C-SiC is created inside the empty sphere of radius $x$.
-The lattice constant $y$, the second unknown variable, is chosen in such a way, that the necessary amount of carbon is generated.
-This is entirely described by the system of equations \eqref{eq:md:constr_sic_01}
-\begin{equation}
-\frac{8}{a_{\text{Si}}^3}(
-\underbrace{21^3 a_{\text{Si}}^3}_{=V}
--\frac{4}{3}\pi x^3)+
-\underbrace{\frac{4}{y^3}\frac{4}{3}\pi x^3}_{\stackrel{!}{=}5500}
-=21^3\cdot 8
-\label{eq:md:constr_sic_01}
-\text{ ,}
-\end{equation}
-which can be simplified to read
-\begin{equation}
-\frac{8}{a_{\text{Si}}^3}\frac{4}{3}\pi x^3=5500
-\Rightarrow x = \left(\frac{5500 \cdot 3}{32 \pi} \right)^{1/3}a_{\text{Si}}
-\label{eq:md:constr_sic_02}
-\end{equation}
-and
-\begin{equation}
-%x^3=\frac{16\pi}{5500 \cdot 3}y^3=
-%\frac{16\pi}{5500 \cdot 3}\frac{5500 \cdot 3}{32 \pi}a_{\text{Si}}^3
-%\Rightarrow
-y=\left(\frac{1}{2} \right)^{1/3}a_{\text{Si}}
-\text{ .}
-\label{eq:md:constr_sic_03}
-\end{equation}
-By this means values of 2.973 nm and 4.309 \AA{} are obtained for the initial precipitate radius and lattice constant of 3C-SiC.
-Since the generation of atoms is a discrete process with regard to the size of the volume the expected amounts of atoms are not obtained.
-However, by applying these values the final configuration varies only slightly from the expected one by five carbon and eleven silicon atoms, as can be seen in table \ref{table:md:sic_prec}.
-\begin{table}[!ht]
+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 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]