well well ... security!

diff --git a/posic/thesis/ack.tex b/posic/thesis/ack.tex
index a3e5e01..bfe39bf 100644 (file)
--- a/posic/thesis/ack.tex
+++ b/posic/thesis/ack.tex
@@ -1,7 +1,33 @@
 \chapter*{Acknowledgment}
 \addcontentsline{toc}{chapter}{Acknowledgment}
 
 \chapter*{Acknowledgment}
 \addcontentsline{toc}{chapter}{Acknowledgment}
 

-First of all, I would like to thank Prof. Dr. Bernd Stritzker and Prof. Dr. Kai Nordlund for accepting me as a PhD student at their chairs at the University of Augsburg and Helsinki.
-Although Mr. Stritzker is doing experimental physics in Augsburg he gave me the opportunity to do this more or less theoretical work.
-During my stays in Finland Mr. Nordlund \ldots
+%First of all, I would like to thank Prof. Dr. Bernd Stritzker and Prof. Dr. Kai Nordlund for accepting me as a PhD student at their chairs at the University of Augsburg and Helsinki.
+%Although Mr. Stritzker is doing experimental physics in Augsburg he gave me the opportunity to do this more or less theoretical work.
+%During my stays in Finland Mr. Nordlund \ldots
+
+Thanks to \ldots
+
+ \underline{Augsburg}
+ \begin{itemize}
+  \item Prof. B. Stritzker (accomodation at EP \RM{4})
+  \item Ralf Utermann (EDV)
+ \end{itemize}
+ 
+ \underline{Helsinki}
+ \begin{itemize}
+  \item Prof. K. Nordlund (MD)
+ \end{itemize}
+ 
+ \underline{Munich}
+ \begin{itemize}
+  \item Bayerische Forschungsstiftung (financial support)
+ \end{itemize}
+ 
+ \underline{Paderborn}
+ \begin{itemize}
+  \item Prof. J. Lindner (SiC)
+  \item Prof. G. Schmidt (DFT + financial support)
+  \item Dr. E. Rauls (DFT + SiC)
+  \item Dr. S. Sanna (VASP)
+ \end{itemize}

 
 

diff --git a/posic/thesis/basics.tex b/posic/thesis/basics.tex
index f6a8eda..243d262 100644 (file)
--- a/posic/thesis/basics.tex
+++ b/posic/thesis/basics.tex
@@ -600,6 +600,22 @@ E_{\text{f}}=\left(E_{\text{coh}}^{\text{defect}}
 where $N$ and $E_{\text{coh}}^{\text{defect}}$ are the number of atoms and the cohesive energy per atom in the defect configuration and $E_{\text{coh}}^{\text{defect-free}}$ is the cohesive energy per atom of the defect-free structure.
 Clearly, for a single atom species equation \eqref{eq:basics:ef2} is equivalent to equation \eqref{eq:basics:ef1} since $NE_{\text{coh}}^{\text{defect}}$ is equal to the total energy of the defect structure and $NE_{\text{coh}}^{\text{defect-free}}$ corresponds to $N\mu$, provided the structure is fully relaxed at zero temperature.
 
 where $N$ and $E_{\text{coh}}^{\text{defect}}$ are the number of atoms and the cohesive energy per atom in the defect configuration and $E_{\text{coh}}^{\text{defect-free}}$ is the cohesive energy per atom of the defect-free structure.
 Clearly, for a single atom species equation \eqref{eq:basics:ef2} is equivalent to equation \eqref{eq:basics:ef1} since $NE_{\text{coh}}^{\text{defect}}$ is equal to the total energy of the defect structure and $NE_{\text{coh}}^{\text{defect-free}}$ corresponds to $N\mu$, provided the structure is fully relaxed at zero temperature.
 

+However, there is hardly ever only one defect in a crystal, not even only one kind of defect.
+Again, energetic considerations can be used to investigate the existing interaction of two defects.
+The binding energy $E_{\text{b}}$ of a defect pair is given by the difference of the formation energy of the defect combination $E_{\text{f}}^{\text{comb}} $ and the sum of the two separated defect configurations $E_{\text{f}}^{1^{\text{st}}}$ and $E_{\text{f}}^{2^{\text{nd}}}$.
+This can be expressed by
+\begin{equation}
+E_{\text{b}}=
+E_{\text{f}}^{\text{comb}}-
+E_{\text{f}}^{1^{\text{st}}}-
+E_{\text{f}}^{2^{\text{nd}}}
+\label{eq:basics:e_bind}
+\end{equation}
+where the formation energies $E_{\text{f}}^{\text{comb}}$, $E_{\text{f}}^{1^{\text{st}}}$ and $E_{\text{f}}^{2^{\text{nd}}}$ are determined as discussed above.
+Accordingly, energetically favorable configurations result in binding energies below zero while unfavorable configurations show positive values for the binding energy.
+The interaction strength, i.e. the absolute value of the binding energy, approaches zero for increasingly non-interacting isolated defects.
+Thus, $E_{\text{b}}$ indeed can be best thought of a binding energy, which is required to bring the defects to infinite separation.
+

 The methods presented in the last two chapters can be used to investigate defect structures and energetics.
 Therefore, a supercell containing the perfect crystal is generated in an initial process.
 If not by construction, the system should be fully relaxed.
 The methods presented in the last two chapters can be used to investigate defect structures and energetics.
 Therefore, a supercell containing the perfect crystal is generated in an initial process.
 If not by construction, the system should be fully relaxed.