commas (mainly Since)

[lectures/latex.git] / posic / thesis / basics.tex

diff --git a/posic/thesis/basics.tex b/posic/thesis/basics.tex
index c88c6c5..2123fa7 100644 (file)
--- a/posic/thesis/basics.tex
+++ b/posic/thesis/basics.tex
@@ -168,7 +168,7 @@ Details of the Tersoff potential derivative are presented in appendix~\ref{app:d
 \subsubsection{Improved analytical bond order potential}
 
 Although the Tersoff potential is one of the most widely used potentials, there are some shortcomings.
-Describing the Si-Si interaction Tersoff was unable to find a single parameter set to describe well both, bulk and surface properties.
+Describing the Si-Si interaction, Tersoff was unable to find a single parameter set to describe well both, bulk and surface properties.
 Due to this, and since the first approach labeled T1~\cite{tersoff_si1} turned out to be unstable~\cite{dodson87}, two further parametrizations exist, T2~\cite{tersoff_si2} and T3~\cite{tersoff_si3}.
 While T2 describes well surface properties, T3 yields improved elastic constants and should be used for describing bulk properties.
 However, T3, which is used in the Si/C potential, suffers from an underestimation of the dimer binding energy.
@@ -229,7 +229,7 @@ The so-called velocity Verlet algorithm is obtained by combining equation \eqref
 +\mathcal{O}(\delta t^3)
  \text{ .}
 \end{equation}
-Since the forces for the new positions are required to update the velocity the determination of the forces has to be carried out within the integration algorithm.
+Since the forces for the new positions are required to update the velocity, the determination of the forces has to be carried out within the integration algorithm.
 
 \subsection{Statistical ensembles}
 \label{subsection:statistical_ensembles}
@@ -624,7 +624,7 @@ If not by construction, the system should be fully relaxed.
 The substitutional or vacancy defect is realized by replacing or removing one atom contained in the supercell.
 Interstitial defects are created by adding an atom at positions located in the space between regular lattice sites.
 Once the intuitively created defect structure is generated structural relaxation methods will yield the respective local minimum configuration.
-Since the supercell approach applies periodic boundary conditions enough bulk material surrounding the defect is required to exclude possible interaction of the defect with its periodic image.
+Since the supercell approach applies periodic boundary conditions, enough bulk material surrounding the defect is required to exclude possible interaction of the defect with its periodic image.
 
 \begin{figure}[t]
 \begin{center}