-with $E$ being the free energy of the precipitate configuration at zero temperature.
-An interfacial energy of 2267.28 eV is obtained.
-The amount of C atoms together with the observed lattice constant of the precipitate leads to a precipitate radius of 29.93 \AA.
-Thus, the interface tension, given by the energy of the interface devided by the surface area of the precipitate is $20.15\,\frac{\text{eV}}{\text{nm}^2}$ or $3.23\times 10^{-4}\,\frac{\text{J}}{\text{cm}^2}$.
-This is located inside the eperimentally estimated range of $2-8\times 10^{-4}\,\frac{\text{J}}{\text{cm}^2}$ \cite{taylor93}.
-
-Since the precipitate configuration is artificially constructed the resulting interface does not necessarily correspond to the energetically most favorable configuration or to the configuration that is expected for an actually grown precipitate.
-Thus annealing steps are appended to the gained structure in order to allow for a rearrangement of the atoms of the interface.
-The precipitate structure is rapidly heated up to $2050\,^{\circ}\mathrm{C}$ with a heating rate of approximately $75\,^{\circ}\mathrm{C}/\text{ps}$.
-From that point on the heating rate is reduced to $1\,^{\circ}\mathrm{C}/\text{ps}$ and heating is continued to 120 \% of the Si melting temperature, that is 2940 K.
-\begin{figure}[!ht]
-\begin{center}
-\includegraphics[width=12cm]{fe_and_t_sic.ps}
-\end{center}
-\caption{Free energy and temperature evolution of a constructed 3C-SiC precipitate embedded in c-Si at temperatures above the Si melting point.}
-\label{fig:md:fe_and_t_sic}
-\end{figure}
-Figure \ref{fig:md:fe_and_t_sic} shows the free energy and temperature evolution.
-The sudden increase of the free energy indicates possible melting occuring around 2840 K.
-\begin{figure}[!ht]
-\begin{center}
-\includegraphics[width=12cm]{pc_500-fin.ps}
-\end{center}
-\caption{Radial distribution of the constructed 3C-SiC precipitate embedded in c-Si at temperatures below and above the Si melting transition point.}
-\label{fig:md:pc_500-fin}
-\end{figure}
-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 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.
-% ./visualize -w 640 -h 480 -d saves/sic_prec_120Tm_cnt1 -nll -11.56 -0.56 -11.56 -fur 11.56 0.56 11.56 -c -0.2 -24.0 0.6 -L 0 0 0.2 -r 0.6 -B 0.1
-\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 $1\,^{\circ}\mathrm{C}/\text{ps}$.
-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.
+where $E$ is the total energy of the precipitate configuration at zero temperature.
+An interfacial energy of \unit[2267.28]{eV} is obtained.
+The amount of C atoms together with the observed lattice constant of the precipitate leads to a precipitate radius of \unit[29.93]{\AA}.
+Thus, the interface tension, given by the energy of the interface devided by the surface area of the precipitate is \unit[20.15]{eV/nm$^2$} or \unit[$3.23\times 10^{-4}$]{J/cm$^2$}.
+This value perfectly fits within the eperimentally estimated range of \unit[$2-8\times10^{-4}$]{J/cm$^2$} \cite{taylor93}.
+Thus, the EA potential is considered an appropriate choice for the current study properly describing the energetics of interfaces.
+
+% todo
+% nice to reproduce this value!
+
+%Since the precipitate configuration is artificially constructed, the resulting interface does not necessarily correspond to the energetically most favorable configuration or to the configuration that is expected for an actually grown precipitate.
+%Thus, annealing steps are appended to the gained structure in order to allow for a rearrangement of the atoms of the interface.
+%The precipitate structure is rapidly heated up to \unit[2050]{$^{\circ}$C} with a heating rate of approximately \unit[75]{$^{\circ}$C/ps}.
+%From that point on the heating rate is reduced to \unit[1]{$^{\circ}$C/ps} and heating is continued upto \unit[120]{\%} of the Si melting temperature of the potential, i.e. \unit[2940]{K}.
+%\begin{figure}[t]
+%\begin{center}
+%\includegraphics[width=0.7\textwidth]{fe_and_t_sic.ps}
+%\end{center}
+%\caption{Total energy and temperature evolution of a 3C-SiC precipitate embedded in c-Si at temperatures above the Si melting point.}
+%\label{fig:simulation:fe_and_t_sic}
+%\end{figure}
+%Figure \ref{fig:simulation:fe_and_t_sic} shows the total energy and temperature evolution.
+%The sudden increase of the total energy indicates possible melting occuring around \unit[2840]{K}.
+%\begin{figure}[ht]
+%\begin{center}
+%\includegraphics[width=0.7\textwidth]{pc_500-fin.ps}
+%\end{center}
+%\caption{Radial distribution of a 3C-SiC precipitate embedded in c-Si at temperatures below and above the Si melting transition point.}
+%%\label{fig:simulation:pc_500-fin}
+%\end{figure}
+%Investigating the radial distribution function shown in figure \ref{fig:simulation:pc_500-fin}, which shows configurations below and above the temperature of the estimated transition, indeed supports the assumption of melting gained by the total energy plot in Fig. \ref{fig:simulation:fe_and_t_sic}.
+%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 for the same heating conditions is expected at temperatures around \unit[3125]{K}, as will be discussed later 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.
+%% ./visualize -w 640 -h 480 -d saves/sic_prec_120Tm_cnt1 -nll -11.56 -0.56 -11.56 -fur 11.56 0.56 11.56 -c -0.2 -24.0 0.6 -L 0 0 0.2 -r 0.6 -B 0.1
+%\begin{figure}[t]
+%%\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 \unit[200]{ps} (top left), \unit[520]{ps} (top right) and \unit[720]{ps} (bottom).}
+%\label{fig:simulation:sic_melt}
+%\end{figure}
+%Fig. \ref{fig:simulation:sic_melt} shows cross section images of the atomic structures at different times and temperatures.
+%As can be seen from the image at \unit[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 \unit[720]{ps}.
+%As predicted from the radial distribution data the precipitate itself indeed 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 \unit[100]{\%} of the Si melting temperature is chosen and cooled down to \unit[20]{$^{\circ}$C} with a cooling rate of \unit[1]{$^{\circ}$C/ps}.
+%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.