In particular, molecular dynamics (MD) constitutes a suitable technique to investigate the dynamical and structural properties of some material.
Modelling the processes mentioned above requires the simulation of a large amount of atoms ($\approx 10^5-10^6$), which inevitably dictates the atomic interaction to be described by computationally efficient classical potentials.
These are, however, less accurate compared to quantum-mechanical methods and their applicability for the description of the physical problem has to be verified first.
-The most common empirical potentials for covalent systems are the Stillinger-Weber\cite{stillinger85} (SW), Brenner\cite{brenner90}, Tersoff\cite{tersoff_si3} and environment-dependent interatomic potential (EDIP)\cite{bazant96,bazant97,justo98}.
+The most common empirical potentials for covalent systems are the Stillinger-Weber\cite{stillinger85}, Brenner\cite{brenner90}, Tersoff\cite{tersoff_si3} and environment-dependent interatomic potential\cite{bazant96,bazant97,justo98}.
These potentials are assumed to be reliable for large-scale simulations\cite{balamane92,huang95,godet03} on specific problems under investigation providing insight into phenomena that are otherwise not accessible by experimental or first-principles methods.
Until recently\cite{lucas10}, a parametrization to describe the C-Si multicomponent system within the mentioned interaction models did only exist for the Tersoff\cite{tersoff_m} and related potentials, e.g. the one by Gao and Weber\cite{gao02} as well as the one by Erhart and Albe\cite{albe_sic_pot}.
All these potentials are short range potentials employing a cut-off function, which drops the atomic interaction to zero in between the first and second next neighbor distance.
A proper description of C diffusion, however, is crucial for the problem under study.
In this work, a combined ab initio and empirical potential simulation study on the initially mentioned SiC precipitation mechanism has been performed.
-High accurate quantum-mechanical results have been used to identify shortcomings of the classical potentials, which are then taken into account in these type of simulations.
+Highly accurate quantum-mechanical results have been used to identify shortcomings of the classical potentials, which are then taken into account in these type of simulations.
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\section{Methodology}
The potential was used as is, i.e. without any repulsive potential extension at short interatomic distances.
Constant pressure simulations are realized by the Berendsen barostat\cite{berendsen84} using a time constant of \unit[100]{fs} and a bulk modulus of \unit[100]{GPa} for Si.
The temperature is kept constant by the Berendsen thermostat\cite{berendsen84} with a time constant of \unit[100]{fs}.
-Integration of equations of motion is realized by the velocity Verlet algorithm\cite{verlet67} and a fixed time step of \unit[1]{fs}.
+Integration of the equations of motion is realized by the velocity Verlet algorithm\cite{verlet67} and a fixed time step of \unit[1]{fs}.
For structural relaxation of defect structures the same algorithm is used with the temperature set to 0 K.
The formation energy $E-N_{\text{Si}}\mu_{\text{Si}}-N_{\text{C}}\mu_{\text{C}}$ of a defect configuration is defined by choosing SiC as a particle reservoir for the C impurity, i.e. the chemical potentials are determined by the cohesive energies of a perfect Si and SiC supercell after ionic relaxation.
This is particularly important since the energy of formation of C$_{\text{s}}$ is drastically underestimated by the EA potential.
A possible occurrence of C$_{\text{s}}$ could then be attributed to a lower energy of formation of the C$_{\text{s}}$-Si$_{\text{i}}$ combination due to the low formation energy of C$_{\text{s}}$, which obviously is wrong.
-Since quantum-mechanical calculation reveal the Si$_{\text{i}}$ \hkl<1 1 0> DB as the ground state configuration of Si$_{\text{i}}$ in Si it is assumed to provide the energetically most favorable configuration in combination with C$_{\text{s}}$.
+Since quantum-mechanical calculations reveal the Si$_{\text{i}}$ \hkl<1 1 0> DB as the ground state configuration of Si$_{\text{i}}$ in Si it is assumed to provide the energetically most favorable configuration in combination with C$_{\text{s}}$.
Empirical potentials, however, predict Si$_{\text{i}}$ T to be the energetically most favorable configuration.
Thus, investigations of the relative energies of formation of defect pairs need to include combinations of C$_{\text{s}}$ with Si$_{\text{i}}$ T.
Results of VASP and EA calculations are summarized in Table~\ref{tab:defect_combos}.
\subsection{Molecular dynamics simulations}
-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, for all three insertion volumes.
+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}\\
On closer inspection two reasons for describing this obstacle become evident.
First of all there is the time scale problem inherent to MD in general.
-To minimize the integration error the discretized time step must be chosen smaller than the reciprocal of the fastest vibrational mode resulting in a time step of \unit[1]{fs} for the current problem under study.
+To minimize the integration error the discretized time step must be chosen smaller than the reciprocal of the fastest vibrational mode resulting in a time step of \unit[1]{fs} for the investigated materials system.
Limitations in computer power result in a slow propagation in phase space.
Several local minima exist, which are separated by large energy barriers.
Due to the low probability of escaping such a local minimum a single transition event corresponds to a multiple of vibrational periods.
The cut-off function of the short range potential limits the interaction to next neighbors, which results in overestimated and unphysical high forces between next neighbor atoms.
This behavior, as observed and discussed for the Tersoff potential\cite{tang95,mattoni2007}, is supported by the overestimated activation energies necessary for C diffusion as investigated in section \ref{subsection:cmob}.
Indeed it is not only the strong C-C bond which is hard to break inhibiting C diffusion and further rearrangements in the case of the high C concentration simulations.
-This is also true for the low concentration simulations dominated by the occurrence of C$_{\text{i}}$ \hkl<1 1 0> DBs spread over the whole simulation volume, which are unable to agglomerate due to the high migration barrier.
+This is also true for the low concentration simulations dominated by the occurrence of C$_{\text{i}}$ \hkl<1 0 0> DBs spread over the whole simulation volume, which are unable to agglomerate due to the high migration barrier.
\subsection{Increased temperature simulations}
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