more 100 db

diff --git a/posic/thesis/defects.tex b/posic/thesis/defects.tex
index 2a4dcb240d9082b91894a517826e5fc4707797b4..c286426133078b5fe4127486a2a5b76b83958211 100644 (file)
--- a/posic/thesis/defects.tex
+++ b/posic/thesis/defects.tex
@@ -328,12 +328,13 @@ In calculations performed in this work the bond-centered configuration in fact i
 As the \hkl<1 0 0> dumbbell interstitial is the lowest configuration in energy it is the most probable hence important interstitial configuration of carbon in silicon.
 It was first identified by infra-red (IR) spectroscopy \cite{bean70} and later on by electron paramagnetic resonance (EPR) spectroscopy \cite{watkins76}.
 
-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.
+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 the atomic displacements, distances and bond angles obtained by analytical potential and quantum-mechanical calculations.
+For comparison, the obtained structures for both methods visualized out of the atomic position data are presented in figure \ref{fig:defects:100db_vis_cmp}.
 \begin{figure}[h]
 \begin{center}
 \includegraphics[width=12cm]{100-c-si-db_cmp.eps}
 \end{center}
-\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}.}
+\caption[Sketch of the \hkl<1 0 0> dumbbell structure.]{Sketch of the \hkl<1 0 0> dumbbell structure. Atomic displacements, distances and bond angles are listed in table \ref{tab:defects:100db_cmp}.}
 \label{fig:defects:100db_cmp}
 \end{figure}
 %
@@ -344,7 +345,7 @@ Displacements\\
 \hline
 \hline
  & & & & \multicolumn{3}{c}{Atom 2} & \multicolumn{3}{c}{Atom 3} \\
- & $a$ & $b$ & $|a|+|b|$ & $\Delta x$ & $\Delta y$ & $\Delta z$ & $\Delta x$ & $\Delta y$ & $\Delta z$ \\
+and bond angles  & $a$ & $b$ & $|a|+|b|$ & $\Delta x$ & $\Delta y$ & $\Delta z$ & $\Delta x$ & $\Delta y$ & $\Delta z$ \\
 \hline
 Erhard/Albe & 0.084 & -0.091 & 0.175 & -0.015 & -0.015 & -0.031 & -0.014 & 0.014 & 0.020 \\
 VASP & 0.109 & -0.065 & 0.174 & -0.011 & -0.011 & -0.024 & -0.014 & 0.014 & 0.025 \\
@@ -372,23 +373,44 @@ Angles\\
 \hline
  & $\theta_1$ & $\theta_2$ & $\theta_3$ & $\theta_4$ \\
 \hline
-Erhard/Albe & 0.175 & 0.329 & 0.186 & 0.226 \\
-VASP & 0.174 & 0.341 & 0.182 & 0.229 \\
+Erhard/Albe & 140.2 & 109.9 & 134.4 & 112.8 \\
+VASP & 130.7 & 114.4 & 146.0 & 107.0 \\
 \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.}
+\caption[Atomic displacements, distances and bond angles of the \hkl<1 0 0> dumbbell structure obtained by the Erhard/Albe potential and VASP calculations.]{Atomic displacements, distances and bond angles 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 the angles are given in degrees. Displacements, distances and angles are 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}
 \end{table}
+\begin{figure}[h]
+\begin{center}
+\begin{minipage}{6cm}
+\begin{center}
+\underline{Erhard/Albe}
+\includegraphics[width=5cm]{c_pd_albe/100_cmp.eps}
+\end{center}
+\end{minipage}
+\begin{minipage}{6cm}
+\begin{center}
+\underline{VASP}
+\includegraphics[width=5cm]{c_pd_vasp/100_cmp.eps}
+\end{center}
+\end{minipage}
+\end{center}
+\caption{Comparison of the visualized \hkl<1 0 0> dumbbel structures obtained by Erhard/Albe potential and VASP calculations.}
+\label{fig:defects:100db_vis_cmp}
+\end{figure}
 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.
+Instead, each of the dumbbell atoms forms threefold coordinated bonds, which 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.
+However, in the case of the VASP calculation, the dumbbell structure is pushed upwards compared to the Erhard/Albe results.
+Thus, the angles of bonds of the silicon dumbbell atom are clos to $120^{\circ}$ signifying the predominance of $sp^2$ hybridization.
+On the other hand, the carbon atom forms an almost colinear bond with the two silicon edge atoms implying the predominance of $p$ and $sp$ bonding.
+This is   in figure \ref{fig:defects:100db_vis_cmp} as well as by the ...
 
 \subsection{Bond-centered interstitial configuration}
 \label{subsection:bc}