$U_2$ is a two body pair potential which only depends on the distance $r_{ij}$ between the two atoms $i$ and $j$.
If not only pair potentials are considered, three body potentials $U_3$ or many body potentials $U_n$ can be included.
Usually these higher order terms are avoided since they are not easy to model and it is rather time consuming to evaluate potentials and forces originating from these many body terms.
-Ordinary pair potentials have a close-packed structure like face-centered cubic (FCC) or hexagonal close-packed (HCP) as a ground state.
-A pair potential is, thus, unable to describe properly elements with other structures than FCC or HCP.
+Ordinary pair potentials have a close-packed structure like face-centered cubic (fcc) or hexagonal close-packed (hcp) as a ground state.
+A pair potential is, thus, unable to describe properly elements with other structures than fcc or hcp.
Silicon and carbon for instance, have a diamond and zincblende structure with four covalently bonded neighbors, which is far from a close-packed structure.
A three body potential has to be included for these types of elements.
\paragraph{calc\_delta\_e}
determines defect formation energies using SiC as a particle reservoir.
\paragraph{pair\_correlation\_calc.c}
-computes the radial dsitribution function.
+computes the radial distribution function.
\paragraph{display\_atom\_data.c}
displays atom specific information.
\paragraph{bond\_analyze.c}
\paragraph{search\_bonds.c}
prints out pairs of atoms featuring specific bond properties.
\paragraph{visual\_atoms.c}
-creates a detailed atomic datafile.
+creates a detailed atomic data file.
\paragraph{visualize}
creates images of atomic configurations.
\paragraph{parcasconv}
\subsection[Operating {\normalfont\textsc{vasp}}]{Operating VASP}
\paragraph{create\_lattice.c}
-create the lattice in \textsc{vasp} POSCAR fomat.
+create the lattice in \textsc{vasp} POSCAR format.
\paragraph{runvasp\_rx200}
executing \textsc{vasp} on the Augsburg Linux Compute Cluster.
\paragraph{sd\_rot\_all-atoms.patch}
This is nicely reproduced by the DFT calculations performed in this work.
It has turned out to be very difficult to capture the results of quantum-mechanical calculations in analytical potential models.
-Among the established analytical potentials only the EDIP \cite{bazant97,justo98} and Stillinger-Weber \cite{stillinger85} potential reproduce the correct order in energy of the defects.
+Among the established analytical potentials only the environment-dependent interatomic potential (EDIP) \cite{bazant97,justo98} and Stillinger-Weber \cite{stillinger85} potential reproduce the correct order in energy of the defects.
However, these potentials show shortcomings concerning the description of other physical properties and are unable to describe the C-C and C-Si interaction.
In fact the EA potential calculations favor the tetrahedral defect configuration.
This limitation is assumed to arise due to the cut-off.
\label{fig:sic:unit_cell}
\end{figure}
Its unit cell is shown in Fig.~\ref{fig:sic:unit_cell}.
-3C-SiC grows in zincblende structure, i.e. it is composed of two fcc lattices, which are displaced by one quarter of the volume diagonal as in Si.
+3C-SiC grows in zincblende structure, i.e. it is composed of two face-centered cubic (fcc) lattices, which are displaced by one quarter of the volume diagonal as in Si.
However, in 3C-SiC, one of the fcc lattices is occupied by Si atoms while the other one is occupied by C atoms.
Its lattice constant of \unit[0.436]{nm} compared to \unit[0.543]{nm} from that of Si results in a lattice mismatch of almost \unit[20]{\%}, i.e. four lattice constants of Si approximately match five SiC lattice constants.
Thus, the Si density of SiC is only slightly lower, i.e. \unit[97]{\%} of plain Si.
Estimates of the SiC/Si interfacial energy \cite{taylor93} and the consequent critical size correspond well with the experimentally observed precipitate radii within these studies.
This different mechanism of precipitation might be attributed to the respective method of fabrication.
-While in CVD and MBE surface effects need to be taken into account, SiC formation during IBS takes place in the bulk of the Si crystal.
+While in CVD and MBE, surface effects need to be taken into account, SiC formation during IBS takes place in the bulk of the Si crystal.
However, in another IBS study Nejim et~al. \cite{nejim95} propose a topotactic transformation that is likewise based on substitutional C, which replaces four of the eight Si atoms in the Si unit cell accompanied by the generation of four Si interstitials.
Since the emerging strain due to the expected volume reduction of \unit[48]{\%} would result in the formation of dislocations, which, however, are not observed, the interstitial Si is assumed to react with further implanted C atoms in the released volume.
The resulting strain due to the slightly lower Si density of SiC compared to Si of about \unit[3]{\%} is sufficiently small to legitimate the absence of dislocations.
\label{fig:simulation:sc}
\end{figure}
Type 1 (Fig. \ref{fig:simulation:sc1}) constitutes the primitive cell.
-The basis is face-centered cubic (fcc) and is given by $x_1=(0.5,0.5,0)$, $x_2=(0,0.5,0.5)$ and $x_3=(0.5,0,0.5)$.
+The basis is face-centered cubic and is given by $x_1=(0.5,0.5,0)$, $x_2=(0,0.5,0.5)$ and $x_3=(0.5,0,0.5)$.
Two atoms, one at $(0,0,0)$ and the other at $(0.25,0.25,0.25)$ with respect to the basis, generate the Si diamond primitive cell.
Type 2 (Fig. \ref{fig:simulation:sc2}) covers two primitive cells with 4 atoms.
The basis is given by $x_1=(0.5,-0.5,0)$, $x_2=(0.5,0.5,0)$ and $x_3=(0,0,1)$.
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