doenser ...

diff --git a/posic/thesis/defects.tex b/posic/thesis/defects.tex
index b914a9c..2a4dcb2 100644 (file)
--- a/posic/thesis/defects.tex
+++ b/posic/thesis/defects.tex
@@ -52,7 +52,7 @@ E_{\text{f}}=E-\sum_i N_i\mu_i
 \end{equation}
 where $E$ is the free energy of the interstitial system and $N_i$ and $\mu_i$ are the amount of atoms and the chemical potential of species $i$.
 The chemical potential is determined by the cohesive energy of the structure of the specific type in equilibrium at zero Kelvin.
-For a defect configuration of a single atom species equation \ref{eq:defects:ef2} is equivalent to equation \ref{eq:defects:ef1}.
+For a defect configuration of a single atom species equation \eqref{eq:defects:ef2} is equivalent to equation \eqref{eq:defects:ef1}.
 
 \section{Silicon self-interstitials}
 
@@ -186,9 +186,9 @@ In figure \ref{fig:defects:kin_si_hex} the relaxation process is shown on the ba
 To exclude failures in the implementation of the potential or the MD code itself the hexagonal defect structure was double-checked with the PARCAS MD code \cite{}.
 The same type of interstitial arises using random insertions.
 In addition, variations exist in which the displacement is only along two \hkl<1 0 0> axes ($E_\text{f}=3.8\text{ eV}$) or along a single \hkl<1 0 0> axes ($E_\text{f}=3.6\text{ eV}$) successively approximating the tetdrahedral configuration and formation energy.
-The existence of these local minima located near the tetrahedral configuration seems to be an artefact of the analytical potential without physical authenticity revealing basic problems of analytical potential models for describing defect structures.
+The existence of these local minima located near the tetrahedral configuration seems to be an artifact of the analytical potential without physical authenticity revealing basic problems of analytical potential models for describing defect structures.
 However, the energy barrier is small (DAS MAL DURCHRECHNEN).
-Hence these artefacts should have a negligent influence in finite temperature simulations.
+Hence these artifacts should have a negligent influence in finite temperature simulations.
 
 The bond-centered configuration is unstable and the \hkl<1 0 0> dumbbell interstitial is the most unfavorable configuration for both, the Erhard/Albe and VASP calculations.
 
@@ -331,14 +331,15 @@ It was first identified by infra-red (IR) spectroscopy \cite{bean70} and later o
 Figure \ref{fig:defects:100db_cmp} schematically shows the \hkl<1 0 0> dumbbell structure and table \ref{tab:defects:100db_cmp} lists the details of displacements obtained by analytical potential and quantum-mechanical calculations.
 \begin{figure}[h]
 \begin{center}
-\includegraphics[width=10cm]{100-c-si-db_cmp.eps}
+\includegraphics[width=12cm]{100-c-si-db_cmp.eps}
 \end{center}
-\label{fig:defects:100db_cmp}
 \caption[Sketch of the \hkl<1 0 0> dumbbell structure.]{Sketch of the \hkl<1 0 0> dumbbell structure. Atomic displacements and distances are listed in table \ref{tab:defects:100db_cmp}.}
+\label{fig:defects:100db_cmp}
 \end{figure}
 %
 \begin{table}[h]
 \begin{center}
+Displacements\\
 \begin{tabular}{l c c c c c c c c c}
 \hline
 \hline
@@ -346,26 +347,48 @@ Figure \ref{fig:defects:100db_cmp} schematically shows the \hkl<1 0 0> dumbbell
  & $a$ & $b$ & $|a|+|b|$ & $\Delta x$ & $\Delta y$ & $\Delta z$ & $\Delta x$ & $\Delta y$ & $\Delta z$ \\
 \hline
 Erhard/Albe & 0.084 & -0.091 & 0.175 & -0.015 & -0.015 & -0.031 & -0.014 & 0.014 & 0.020 \\
-VASP & & & & & & & & & \\
+VASP & 0.109 & -0.065 & 0.174 & -0.011 & -0.011 & -0.024 & -0.014 & 0.014 & 0.025 \\
 \hline
 \hline
-\end{tabular}
+\end{tabular}\\[0.5cm]
+\end{center}
+\begin{center}
+Distances\\
+\begin{tabular}{l c c c c c c c c r}
+\hline
+\hline
+ & $r(1C)$ & $r(2C)$ & $r(3C)$ & $r(12)$ & $r(13)$ & $r(34)$ & $r(23)$ & $r(25)$ & $a_{\text{Si}}^{\text{equi}}$\\
+\hline
+Erhard/Albe & 0.175 & 0.329 & 0.186 & 0.226 & 0.300 & 0.343 & 0.423 & 0.425 & 0.543 \\
+VASP & 0.174 & 0.341 & 0.182 & 0.229 & 0.286 & 0.347 & 0.422 & 0.417 & 0.548 \\
+\hline
+\hline
+\end{tabular}\\[0.5cm]
 \end{center}
 \begin{center}
-\begin{tabular}{l c c c c c c c c}
+Angles\\
+\begin{tabular}{l c c c c }
 \hline
 \hline
- & $r(1C)$ & $r(2C)$ & $r(3C)$ & $r(12)$ & $r(13)$ & $r(34)$ & $r(23)$ & $r(25)$\\
+ & $\theta_1$ & $\theta_2$ & $\theta_3$ & $\theta_4$ \\
 \hline
-Erhard/Albe & & & & & & & \\
-VASP & & & & & & & \\
+Erhard/Albe & 0.175 & 0.329 & 0.186 & 0.226 \\
+VASP & 0.174 & 0.341 & 0.182 & 0.229 \\
 \hline
 \hline
 \end{tabular}\\[0.5cm]
 \end{center}
+\caption[Atomic displacements and distances of the \hkl<1 0 0> dumbbell structure obtained by the Erhard/Albe potential and VASP calculations.]{Atomic displacements and distances of the \hkl<1 0 0> dumbbell structure obtained by the Erhard/Albe potential and VASP calculations. The displacements and distances are given in nm and schematically displayed in figure \ref{fig:defects:100db_cmp}. In addition, the equilibrium lattice constant for crystalline silicon is listed.}
 \label{tab:defects:100db_cmp}
-\caption[Atomic displacements and distances of the \hkl<1 0 0> dumbbell structure obtained by the Erhard/Albe potential and VASP calculations.]{Atomic displacements and distances of the \hkl<1 0 0> dumbbell structure obtained by the Erhard/Albe potential and VASP calculations. The displacements and distances are given in nm and schematically displayed in figure \ref{fig:defects:100db_cmp}.}
 \end{table}
+The silicon atom numbered '1' and the C atom compose the dumbbell structure.
+They share the lattice site which is indicated by the dashed red circle and which they are displaced from by length $a$ and $b$ respectively.
+The atoms no longer have four tetrahedral bonds to the silicon atoms located on the alternating opposite edges of the cube.
+Instead, each of the dumbbell atoms forms threefold coordinated bonds, whcih are located in a plane.
+One bond is formed to the other dumbbell atom.
+The other two bonds are bonds to the two silicon edge atoms located in the opposite direction of the dumbbell atom.
+Angles ...
+The distance of the two dumbbell atoms is almost the same for both types of calculations.
 
 \subsection{Bond-centered interstitial configuration}
 \label{subsection:bc}