more 100 db

diff --git a/posic/thesis/defects.tex b/posic/thesis/defects.tex
index 2a4dcb2..c286426 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}.
 
 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}
 \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}
 %
 \label{fig:defects:100db_cmp}
 \end{figure}
 %


@@ -344,7 +345,7 @@ Displacements\\
 \hline
 \hline
  & & & & \multicolumn{3}{c}{Atom 2} & \multicolumn{3}{c}{Atom 3} \\
 \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 \\
 \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
 \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}
 \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}
 \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.
 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.
 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.
 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}
 
 \subsection{Bond-centered interstitial configuration}
 \label{subsection:bc}