In the following, the simulation methods used within the scope of this study are introduced.
Enabling the investigation of the evolution of structure on the atomic scale, molecular dynamics (MD) simulations are chosen for modeling the behavior and precipitation of C introduced into an initially crystalline Si environment.
-To be able to model systems with a large amount of atoms computational efficient classical potentials to describe the interaction of the atoms are most often used in MD studies.
+To be able to model systems with a large amount of atoms, computational efficient classical potentials to describe the interaction of the atoms are most often used in MD studies.
For reasons of flexibility in executing this non-standard task and in order to be able to use a novel interaction potential~\cite{albe_sic_pot}, an appropriate MD code called \textsc{posic}\footnote{\textsc{posic} is an abbreviation for {\bf p}recipitation {\bf o}f {\bf SiC}} including a library collecting respective MD subroutines was developed from scratch\footnote{Source code: http://www.physik.uni-augsburg.de/\~{}zirkelfr/posic}.
-The basic ideas of MD in general and the adopted techniques as implemented in \textsc{posic} in particular are outlined in section~\ref{section:md}, while the functional form and derivative of the employed classical potential is presented in appendix~\ref{app:d_tersoff}.
+The basic ideas of MD in general and the adopted techniques as implemented in \textsc{posic} in particular are outlined in section~\ref{section:md} while the functional form and derivative of the employed classical potential is presented in appendix~\ref{app:d_tersoff}.
An overview of the most important tools within the MD package is given in appendix~\ref{app:code}.
Although classical potentials are often most successful and at the same time computationally efficient in calculating some physical properties of a particular system, not all of its properties might be described correctly due to the lack of quantum-mechanical effects.
Thus, in order to obtain more accurate results quantum-mechanical calculations from first principles based on density functional theory (DFT) were performed.
\subsection{Structural relaxation and Hellmann-Feynman theorem}
-Up to this point, the system is in the ground state with respect to the electronic subsystem, while the positions of the ions as well as size and shape of the supercell are fixed.
+Up to this point, the system is in the ground state with respect to the electronic subsystem while the positions of the ions as well as size and shape of the supercell are fixed.
To investigate equilibrium structures, however, the ionic subsystem must also be allowed to relax into a minimum energy configuration.
Local minimum configurations can be easily obtained in a MD-like way by moving the nuclei over small distances along the directions of the forces, as discussed in the MD chapter above.
Clearly, the conjugate gradient method constitutes a more sophisticated scheme, which will locate the equilibrium positions of the ions more rapidly.
The C atom is slightly displaced in \hkl[0 1 -1] direction.
A binding energy of \unit[-0.59]{eV} indicates the occurrence of much less strain reduction compared to that in the latter configuration.
Evidently this is due to a smaller displacement of Si atom 1, which would be directly bound to the replaced Si atom at position 2.
-In the case of a vacancy created at position 4, even a slightly higher binding energy of \unit[-0.54]{eV} is observed, while the Si atom at the bottom left, which is bound to the \ci{} DB atom, is vastly displaced along \hkl[1 0 -1].
+In the case of a vacancy created at position 4, even a slightly higher binding energy of \unit[-0.54]{eV} is observed while the Si atom at the bottom left, which is bound to the \ci{} DB atom, is vastly displaced along \hkl[1 0 -1].
However the displacement of the C atom along \hkl[0 0 -1] is less compared to the one in the previous configuration.
Although expected due to the symmetric initial configuration, Si atom number 1 is not displaced correspondingly and also the \si DB atom is displaced to a greater extent in \hkl[-1 0 0] than in \hkl[0 -1 0] direction.
The symmetric configuration is, thus, assumed to constitute a local maximum, which is driven into the present state by the conjugate gradient method used for relaxation.
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