\chapter{Basic principles of utilized simulation techniques}
\label{chapter:basics}
-In the following the simulation methods used within the scope of this study are introduced.
+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.
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}.
Approximations that consider a truncated Hilbert space of single-particle orbitals yield promising results, however, with increasing complexity and demand for high accuracy the amount of Slater determinants to be evaluated massively increases.
In contrast, instead of using the description by the many-body wave function, the key point in density functional theory (DFT) is to recast the problem to a description utilizing the charge density $n(\vec{r})$, which constitutes a quantity in real space depending only on the three spatial coordinates.
-In the following sections the basic idea of DFT will be outlined.
+In the following sections, the basic idea of DFT will be outlined.
As will be shown, DFT can formally be regarded as an exactification of the Thomas Fermi theory~\cite{thomas27,fermi27} and the self-consistent Hartree equations~\cite{hartree28}.
A nice review is given in the Nobel lecture of Kohn~\cite{kohn99}, one of the inventors of DFT.
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