However, this fact could not be reproduced by spin polarized \textsc{vasp} calculations performed in this work.
Present results suggest this configuration to correspond to a real local minimum.
In fact, an additional barrier has to be passed to reach this configuration starting from the \ci{} \hkl<1 0 0> interstitial configuration, which is investigated in section~\ref{subsection:100mig}.
-After slightly displacing the C atom along the \hkl[1 0 0] (equivalent to a displacement along \hkl[0 1 0]), \hkl[0 0 1], \hkl[0 0 -1] and \hkl[1 -1 0] direction the distorted structures relax back into the BC configuration.
+After slightly displacing the C atom along the \hkl[1 0 0] (equivalent to a displacement along \hkl[0 1 0]), \hkl[0 0 1], \hkl[0 0 -1] and \hkl[1 -1 0] direction, the distorted structures relax back into the BC configuration.
As will be shown in subsequent migration simulations, the same would happen to structures where the C atom is displaced along the migration direction, which approximately is the \hkl[1 1 0] direction.
These relaxations indicate that the BC configuration is a real local minimum instead of an assumed saddle point configuration.
Fig.~\ref{img:defects:bc_conf} shows the structure, charge density isosurface and Kohn-Sham levels of the BC configuration.
\label{fig:059-539}
\end{figure}
Activation energies as low as \unit[0.1]{eV} and \unit[0.6]{eV} are observed.
-In the first case the Si and C atom of the DB move towards the vacant and initial DB lattice site respectively.
+In the first case, the Si and C atom of the DB move towards the vacant and initial DB lattice site respectively.
In total three Si-Si and one more Si-C bond is formed during transition.
The activation energy of \unit[0.1]{eV} is needed to tilt the DB structure.
Once this barrier is overcome, the C atom forms a bond to the top left Si atom and the \si{} atom capturing the vacant site is forming new tetrahedral bonds to its neighbored Si atoms.
To further improve the interface quality and crystallinity, a two-temperature implantation technique was developed~\cite{lindner99}.
To form a narrow, box-like density profile of oriented SiC nanocrystals, \unit[93]{\%} of the total dose of \unit[$8.5\cdot 10^{17}$]{cm$^{-2}$} is implanted at \unit[500]{$^{\circ}$C}.
The remaining dose is implanted at \unit[250]{$^{\circ}$C}, which leads to the formation of amorphous zones above and below the SiC precipitate layer and the destruction of SiC nanocrystals within these zones.
-After annealing for \unit[10]{h} at \unit[1250]{$^{\circ}$C} a homogeneous, stoichiometric SiC layer with sharp interfaces is formed.
+After annealing for \unit[10]{h} at \unit[1250]{$^{\circ}$C}, a homogeneous, stoichiometric SiC layer with sharp interfaces is formed.
Fig.~\ref{fig:sic:hrem_sharp} shows the respective high resolution transmission electron microscopy micrographs.
\begin{figure}[t]
\begin{center}
To obtain a minimal and stable precipitate, 5500 carbon atoms are considered necessary according to experimental results as discussed in section~\ref{subsection:ibs} and~\ref{section:assumed_prec}.
This corresponds to a spherical 3C-SiC precipitate with a radius of approximately \unit[3]{nm}.
The initial precipitate configuration is constructed in two steps.
-In the first step the surrounding Si matrix is created.
+In the first step, the surrounding Si matrix is created.
This is realized by just skipping the generation of Si atoms inside a sphere of radius $x$, which is the first unknown variable.
The Si 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 $x$.
\text{ .}
\label{eq:simulation:constr_sic_03}
\end{equation}
-By this means values of \unit[2.973]{nm} and \unit[4.309]{\AA} are obtained for the initial precipitate radius and lattice constant of 3C-SiC.
+By this means, values of \unit[2.973]{nm} and \unit[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:simulation:sic_prec}.
+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:simulation:sic_prec}.
\begin{table}[t]
\begin{center}
\begin{tabular}{l c c c c}
\end{center}
\end{table}
-After the initial configuration is constructed some of the atoms located at the 3C-SiC/c-Si interface show small distances, which results in high repulsive forces acting on the atoms.
+After the initial configuration is constructed, some of the atoms located at the 3C-SiC/c-Si interface show small distances, which results in high repulsive forces acting on the atoms.
Thus, the system is equilibrated using strong coupling to the heat bath, which is set to be \unit[20]{$^{\circ}$C}.
Once the main part of the excess energy is carried out previous settings for the Berendsen thermostat are restored and the system is relaxed for another \unit[10]{ps}.
A lattice constant of \unit[4.34]{\AA} compared to \unit[4.36]{\AA} for bulk 3C-SiC is obtained.
This is in accordance with the peak of Si-C pairs at a distance of \unit[0.188]{nm}.
Thus, the precipitate structure is slightly compressed compared to the bulk phase.
-This is a quite surprising result since due to the finite size of the c-Si surrounding a non-negligible impact of the precipitate on the materializing c-Si lattice constant especially near the precipitate could be assumed.
+This is a quite surprising result since due to the finite size of the c-Si surrounding, a non-negligible impact of the precipitate on the materializing c-Si lattice constant especially near the precipitate could be assumed.
However, it seems that the size of the c-Si host matrix is chosen large enough to even find the precipitate in a compressed state.
The absence of a compression of the c-Si surrounding is due to the possibility of the system to change its volume.
Since the c-Si surrounding resides in an uncompressed state, the excess increase must be attributed to relaxation of strain with the strain resulting from either the compressed precipitate or the 3C-SiC/c-Si interface region.
This also explains the possibly identified slight increase of the c-Si lattice constant in the surrounding as mentioned earlier.
As the pressure is set to zero, the free energy is minimized with respect to the volume enabled by the Berendsen barostat algorithm.
-Apparently the minimized structure with respect to the volume is a configuration of a small compressively stressed precipitate and a large amount of slightly stretched c-Si in the surrounding.
+Apparently, the minimized structure with respect to the volume is a configuration of a small compressively stressed precipitate and a large amount of slightly stretched c-Si in the surrounding.
To finally draw some conclusions concerning the capabilities of the potential, the 3C-SiC/c-Si interface is now addressed.
One important size analyzing the interface is the interfacial energy.
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