From: hackbard <hackbard@sage.physik.uni-augsburg.de>
Date: Wed, 8 Jul 2009 13:44:00 +0000 (+0200)
Subject: ome silicon point defects calculated
X-Git-Url: https://hackdaworld.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=fee777e5d2af71751eddd51826ede4945aea40e7;p=lectures%2Flatex.git

ome silicon point defects calculated
---

diff --git a/posic/talks/upb-ua-xc.tex b/posic/talks/upb-ua-xc.tex
index cb717df..e95c0fb 100644
--- a/posic/talks/upb-ua-xc.tex
+++ b/posic/talks/upb-ua-xc.tex
@@ -330,64 +330,83 @@ POTIM = 0.1
 \begin{slide}
 
  {\large\bf
-  Silicon point defects
+  Cohesive energies
  }
 
+ {\bf\color{red} From now on ...}
+
+ {\small Energies used: free energy without entropy ($\sigma \rightarrow 0$)}
+
  \small
- {\color{red}\bf\LARGE
- HIER NOCH NICHT LESEN! :)\\
- }
 
- \begin{minipage}{6.5cm}
- <110> Si interstitial
- \begin{itemize}
-  \item 2 pc's:
-        $E_{\textrm{f}}=-5.47342\,\textrm{eV}$ 
-  \item 4 pc's:
-        $E_{\textrm{f}}=-5.65098\,\textrm{eV}$
-  \item 32 pc's: running ...
-        $E_{\textrm{f}}=\,\textrm{eV}$
- \end{itemize}
- \end{minipage}
- \begin{minipage}{6.5cm}
- plain Si
  \begin{itemize}
-  \item 2 pc's:
-        $E_{\textrm{coh}}=-6.00846\,\textrm{eV}$
-  \item 4 pc's:
-        $E_{\textrm{coh}}=-5.97464\,\textrm{eV}$
-  \item 32 pc's:
-        $E_{\textrm{coh}}=-5.97633\,\textrm{eV}$
- \end{itemize}
- \end{minipage}\\[0.2cm]
- \begin{minipage}{6.5cm}
- hexagonal Si interstitial
- \begin{itemize}
-  \item 2 pc's:
-        $E_{\textrm{f}}=-5.60654\,\textrm{eV}$
-  \item 4 pc's:
-        $E_{\textrm{f}}=-5.60174\,\textrm{eV}$
-  \item 32 pc's: running ...
-        $E_{\textrm{f}}=\,\textrm{eV}$
- \end{itemize}
- tetrahedral Si interstitial
- \begin{itemize}
-  \item 2 pc's: $E_{\textrm{f}}=-5.53623\,\textrm{eV}$
-  \item 4 pc's: $E_{\textrm{f}}=-5.64704\,\textrm{eV}$
-  \item 32 pc's: $E_{\textrm{f}}=-5.92383\,\textrm{eV}$
+  \item $E_{\textrm{free,sp}}$:
+        energy of spin polarized free atom
+        \begin{itemize}
+         \item $k$-points: Monkhorst $1\times 1\times 1$
+         \item Symmetry switched off
+         \item Spin polarized calculation
+         \item Interpolation formula according to Vosko Wilk and Nusair
+               for the correlation part of the exchange correlation functional
+         \item Gaussian smearing for the partial occupancies $f_{nk}$
+               ($\sigma=0.05$)
+         \item Magnetic mixing: AMIX = 0.2, BMIX = 0.0001
+         \item Supercell: one atom in cubic
+               $10\times 10\times 10$ \AA$^3$ box
+        \end{itemize}
+        {\color{blue}
+        $E_{\textrm{free,sp}}(\textrm{Si},250\, \textrm{eV})=
+         -0.70036911\,\textrm{eV}$
+        },
+        {\color{gray}
+        $E_{\textrm{free,sp}}(\textrm{C},xxx\, \textrm{eV})=
+         yyy\,\textrm{eV}$
+        }
+  \item $E$:
+        energy (non-polarized) of system of interest composed of\\
+        n atoms of type N, m atoms of type M, \ldots
  \end{itemize}
- Si vacancy
+ \vspace*{0.3cm}
+ {\color{red}
+ \[
+ \Rightarrow
+ E_{\textrm{coh}}=\frac{
+ -\Big(E(N_nM_m\ldots)-nE_{\textrm{free,sp}}(N)-mE_{\textrm{free,sp}}(M)
+ -\ldots\Big)}
+ {n+m+\ldots}
+ \]
+ }
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Silicon point defects\\
+ }
+
+ \small
+
+ Calculation of formation energy $E_{\textrm{f}}$
  \begin{itemize}
-  \item 2 pc's: $E_{\textrm{f}}=-5.65965\,\textrm{eV}$
-  \item 4 pc's: $E_{\textrm{f}}=-5.56361\,\textrm{eV}$
-  \item 32 pc's:$E_{\textrm{f}}=-5.92053\,\textrm{eV}$
+  \item $E_{\textrm{coh}}^{\textrm{initial conf}}$:
+        cohesive energy per atom of the initial system
+  \item $E_{\textrm{coh}}^{\textrm{interstitial conf}}$:
+        cohesive energy per atom of the interstitial system
+  \item N: amount of atoms in the interstitial system
  \end{itemize}
- \end{minipage}
- \begin{minipage}{6.5cm}
+ \vspace*{0.2cm}
+ {\color{blue}
+ \[
+ \Rightarrow
+ E_{\textrm{f}}=\Big(E_{\textrm{coh}}^{\textrm{interstitial conf}}
+               -E_{\textrm{coh}}^{\textrm{initial conf}}\Big) N
+ \]
+ }
+
  \begin{center}
- \includegraphics[width=6.5cm]{si_self_int.ps}
+ \includegraphics[width=7.0cm]{si_self_int.ps}
  \end{center}
- \end{minipage}
 
 \end{slide}