bonds

diff --git a/posic/thesis/basics.tex b/posic/thesis/basics.tex
index 75dd18b..31d2d4e 100644 (file)
--- a/posic/thesis/basics.tex
+++ b/posic/thesis/basics.tex
@@ -165,6 +165,7 @@ f_C(r_{ij}) = \left\{
     \frac{1}{2} + \frac{1}{2} \cos \Big[ \pi (r_{ij} - R_{ij})/(S_{ij} - R_{ij}) \Big], & R_{ij} < r_{ij} < S_{ij} \\
     0, & r_{ij} > S_{ij}
   \end{array} \right.
+\label{eq:basics:fc}
 \end{equation}
 
 The function $b_{ij}$ represents a measure of the bond order, monotonically decreasing with the coordination of atoms $i$ and $j$.

diff --git a/posic/thesis/defects.tex b/posic/thesis/defects.tex
index 459b7f4..b4e0981 100644 (file)
--- a/posic/thesis/defects.tex
+++ b/posic/thesis/defects.tex
@@ -121,27 +121,27 @@ calculations\\
 \begin{flushleft}
 \begin{minipage}{5cm}
 \underline{\hkl<1 1 0> dumbbell}\\
-$E_{\text{f}}=3.39\text{ eV}$\\
+$E_{\text{f}}=4.39\text{ eV}$\\
 \includegraphics[width=4.0cm]{si_pd_albe/110.eps}
 \end{minipage}
 \begin{minipage}{5cm}
 \underline{Hexagonal}\\
-$E_{\text{f}}=3.42\text{ eV}$\\
+$E_{\text{f}}=3.96\text{ eV}$\\
 \includegraphics[width=4.0cm]{si_pd_albe/hex.eps}
 \end{minipage}
 \begin{minipage}{5cm}
 \underline{Tetrahedral}\\
-$E_{\text{f}}=3.77\text{ eV}$\\
+$E_{\text{f}}=3.40\text{ eV}$\\
 \includegraphics[width=4.0cm]{si_pd_albe/tet.eps}
 \end{minipage}\\[0.2cm]
 \begin{minipage}{5cm}
 \underline{\hkl<1 0 0> dumbbell}\\
-$E_{\text{f}}=4.41\text{ eV}$\\
+$E_{\text{f}}=5.42\text{ eV}$\\
 \includegraphics[width=4.0cm]{si_pd_albe/100.eps}
 \end{minipage}
 \begin{minipage}{5cm}
 \underline{Vacancy}\\
-$E_{\text{f}}=3.63\text{ eV}$\\
+$E_{\text{f}}=3.13\text{ eV}$\\
 \includegraphics[width=4.0cm]{si_pd_albe/vac.eps}
 \end{minipage}
 \begin{minipage}{5cm}
@@ -177,6 +177,13 @@ Hence these artefacts should have a negligent influence in finite temperature si
 
 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.
 
+In the case of the classical potential simulations bonds between atoms are displayed if there is an interaction according to the potential model, that is if the distance of two atoms is within the cut-off region $S_{ij}$ introduced in equation \eqref{eq:basics:fc}.
+For the tetrahedral and the slightly displaced configurations four bonds to the atoms located in the center of the planes of the unit cell exist in addition to the four tetrahedral bonds.
+The length of these bonds are, however, close to the cut-off range and thus are weak interactions not constituting actual chemical bonds.
+The same applies to the bonds between the interstitial and the upper two atoms in the \hkl<1 1 0> dumbbell configuration.
+
+A more detailed description of the chemical bonding is achieved by quantum-mechanical calculations by investigating the accumulation of negative charge between the nuclei.
+Todo: Plot the electron density for these types of defect to derive conclusions of existing bonds ...
 
 \section{Carbon related point defects}