From: hackbard <hackbard@sage.physik.uni-augsburg.de>
Date: Tue, 24 May 2011 23:29:45 +0000 (+0200)
Subject: well well ... security!
X-Git-Url: https://hackdaworld.org/gitweb/?a=commitdiff_plain;h=cbed3c8589a70f445c4f2c7ae6532261afb65351;p=lectures%2Flatex.git

well well ... security!
---

diff --git a/posic/thesis/ack.tex b/posic/thesis/ack.tex
index a3e5e01..bfe39bf 100644
--- a/posic/thesis/ack.tex
+++ b/posic/thesis/ack.tex
@@ -1,7 +1,33 @@
 \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
--- 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.
 
+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.