X-Git-Url: https://hackdaworld.org/gitweb/?a=blobdiff_plain;f=posic%2Ftalks%2Fupb-ua-xc.tex;h=bc686f21d3899a62c4e391141f1f5910130a1af4;hb=e7b1460218a9d3da9c878e4f1294971d0178942d;hp=aa4c4bbc963cd5bd7ae8e481efdf11d84adde618;hpb=9a2910930de4342967ba79487ff72ff08711180d;p=lectures%2Flatex.git

diff --git a/posic/talks/upb-ua-xc.tex b/posic/talks/upb-ua-xc.tex
index aa4c4bb..bc686f2 100644
--- a/posic/talks/upb-ua-xc.tex
+++ b/posic/talks/upb-ua-xc.tex
@@ -20,6 +20,8 @@
 \usepackage{pstricks}
 \usepackage{pst-node}
 
+\usepackage{slashbox}
+
 %\usepackage{epic}
 %\usepackage{eepic}
 
@@ -1363,7 +1365,7 @@ POTIM = 0.1
  \begin{itemize}
   \item Start in fully relaxed (assumed) saddle point configuration
   \item Move towards \hkl<1 0 0> configuration using updated values
-        for $\Delta x$, $\Delta y$ and $\Delta z$
+        for $\Delta x$, $\Delta y$ and $\Delta z$ (CRT)
   \item \hkl<1 1 0> constraints applied, 1 Si atom fixed
   \item $4\times 4\times 3$ Type 1 supercell
  \end{itemize}
@@ -1487,6 +1489,104 @@ POTIM = 0.1
 
 \end{slide}
 
+\begin{slide}
+
+ {\large\bf\boldmath
+  Defect configurations in $4\times 4\times 3$ Type 1 supercells revisited
+ }
+
+ \footnotesize
+
+ \begin{tabular}{l|p{2.5cm}|p{2.5cm}|p{4cm}|}
+  & \hkl<0 0 -1> interstitial
+  & local minimum\newline
+    \hkl<1 1 0> C-Si split
+  & intermediate configuration\newline
+    (bond centered conf)\\
+ \hline
+ default & $E_{\text{f}}=3.3254\text{ eV}$\newline
+           {\tiny
+           386: 4.9458 - 2.00000\newline
+           387: 5.3358 - 0.00000}
+         & $E_{\text{f}}=4.1314\text{ eV}$\newline
+           {\tiny
+           386: 4.8797 - 1.99964\newline
+           387: 5.1321 - 0.00036}
+         & $E_{\text{f}}=4.2434\text{ eV}$\newline
+           {\tiny
+           386: 4.9879 - 1.92065\newline
+           387: 5.1120 - 0.07935} \\
+ \hline
+ No symmetry & $E_{\text{f}}=3.3154\text{ eV}$\newline
+               {\tiny
+               386: 4.9456 - 2.00000\newline
+               387: 5.3366 - 0.00000}
+             & $E_{\text{f}}=4.1314\text{ eV}$\newline
+               {\tiny
+               386: 4.8798 - 1.99961\newline
+               387: 5.1307 - 0.00039}
+             & $E_{\text{f}}=4.2454\text{ eV}$\newline
+               {\tiny
+               386: 4.9841 - 1.92147\newline
+               387: 5.1085 - 0.07853} \\
+ \hline
+ $+$ spin polarized & $E_{\text{f}}=3.3154\text{ eV}$\newline
+                      {\tiny
+                      {\color{blue}
+                      386: 4.9449 - 1.00000\newline
+                      387: 5.3365 - 0.00000\newline%
+                      }%
+                      {\color{green}%
+                      386: 4.9449 - 1.00000\newline
+                      387: 5.3365 - 0.00000}}
+                    & $E_{\text{f}}={\color{red}4.1314}\text{ eV}$\newline
+                      {\tiny
+                      {\color{blue}
+                      386: 4.8799 - 0.99980\newline
+                      387: 5.1307 - 0.00020\newline%
+                      }%
+                      {\color{green}%
+                      386: 4.8799 - 0.99980\newline
+                      387: 5.1306 - 0.00020}}
+                    & $E_{\text{f}}=4.0254\text{ eV}$\newline
+                      {\tiny
+                      {\color{blue}
+                      387: 4.8581 - 1.00000\newline
+                      388: 5.4662 - 0.00000\newline%
+                      }%
+                      {\color{green}%
+                      385: 4.8620 - 1.00000\newline
+                      386: 5.2951 - 0.00000}} \\
+ \hline
+ $+$ spin difference 2 & $E_{\text{f}}=3.6394\text{ eV}$\newline
+                         {\tiny
+                         {\color{blue}
+                         387: 5.2704 - 0.99891\newline
+                         388: 5.4886 - 0.00095\newline
+                         389: 5.5094 - 0.00011\newline
+                         390: 5.5206 - 0.00003\newline%
+                         }%
+                         {\color{green}%
+                         385: 4.8565 - 0.98603\newline
+                         386: 5.0119 - 0.01397}}
+                       & Relaxation into\newline
+                         bond centered\newline
+                         configuration\newline
+                         $\rightarrow$
+                       & $E_{\text{f}}=4.0254\text{ eV}$\newline
+                         {\tiny
+                         {\color{blue}
+                         387: 4.8578 - 1.00000\newline
+                         388: 5.4661 - 0.00000\newline%
+                         }%
+                         {\color{green}%
+                         385: 4.8618 - 1.00000\newline
+                         386: 5.2950 - 0.00000}} \\
+ \hline
+ \end{tabular}
+
+\end{slide}
+
 \begin{slide}
 
  {\large\bf\boldmath
@@ -1525,12 +1625,161 @@ $z,x'$-axis rotation: $45.0^{\circ}$, $0.0^{\circ}$
  \end{minipage}
 
  {\color{blue}
-  Next: Migration calculation in 2333 using 'correct' constraints
+  Next: Migration calculation in 2333 using CRT
   (\hkl<0 0 -1> $\rightarrow$ \hkl<0 0 1> and \hkl<0 -1 0>)
  }
 
 \end{slide}
 
+\begin{slide}
+
+ {\large\bf\boldmath
+  \hkl<0 0 -1> to \hkl <0 0 1> migration
+   in the $3\times 3\times 3$ Type 2 supercell
+ }
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  \hkl<0 0 -1> to \hkl <0 -1 0> migration
+  in the $3\times 3\times 3$ Type 2 supercell
+ }
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Defect configurations in $3\times 3\times 3$ Type 2 supercells revisited
+ }
+
+ \footnotesize
+
+ \begin{tabular}{l|p{2.5cm}|p{2.5cm}|p{4cm}|}
+  & \hkl<0 0 -1> interstitial
+  & local minimum\newline
+    \hkl<1 1 0> C-Si split
+  & intermediate configuration\newline
+    (bond centered conf)\\
+ \hline
+ default & $E_{\text{f}}=3.15407\text{ eV}$\newline
+           {\tiny
+           434: 4.9027 - 2.00000\newline
+           435: 5.2543 - 0.00000}
+         & $E_{\text{f}}=??\text{ eV}$\newline
+           {\tiny
+           ??\newline
+           ??}
+         & $E_{\text{f}}=4.40907\text{ eV}$\newline
+           {\tiny
+           434: 5.0109 - 1.00264\newline
+           435: 5.0111 - 0.99736}\\
+ \hline
+ No symmetry & $E_{\text{f}}=3.16107\text{ eV}$\newline
+               {\tiny
+               434: 4.9032 - 2.00000\newline
+               435: 5.2547 - 0.00000}
+             & $E_{\text{f}}=??\text{ eV}$\newline
+               {\tiny
+               ??\newline
+               ??}
+             & $E_{\text{f}}=4.41507\text{ eV}$\newline
+               {\tiny
+               434: 5.0113 - 1.00140\newline
+               435: 5.0114 - 0.99860} \\
+ \hline
+ $+$ spin polarized & $E_{\text{f}}=??\text{ eV}$\newline
+                      {\tiny
+                      {\color{blue}
+                      ??\newline
+                      ??\newline%
+                      }%
+                      {\color{green}%
+                      ??\newline
+                      ??}}
+                    & $E_{\text{f}}={\color{red}??}\text{ eV}$\newline
+                      {\tiny
+                      {\color{blue}
+                      ??\newline
+                      ??\newline%
+                      }%
+                      {\color{green}%
+                      ??\newline
+                      ??}}
+                    & $E_{\text{f}}=4.10307\text{ eV}$\newline
+                      {\tiny
+                      {\color{blue}
+                      435: 4.8118 - 1.00000\newline
+                      436: 5.5360 - 0.00000\newline%
+                      }%
+                      {\color{green}%
+                      433: 4.8151 - 1.00000\newline
+                      434: 5.3475 - 0.00000}} \\
+ \hline
+ \end{tabular}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Bond centered configuration revisited ($3\times 3\times 3$ Type 2)
+ }
+
+ \begin{minipage}{6cm}
+ Besetzungen hier rein ... Netto Spin 2 ...
+ \end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Combination of defects
+ }
+
+ TODO: introduce some Si self-interstitials and C interstitials before\\
+ BUT: Concentrate on 100 C interstitial combinations and 100 C + vacancy\\
+ 
+ Agglomeration of 100 defects energetically favorable?
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Combination of defects
+ }
+
+ \begin{itemize}
+  \item Supercell: $3\times 3\times 3$ Type 2
+  \item Starting configuration: \hkl<0 0 -1> C-Si interstitial
+  \item Energies: $E_{\text{f}}$ of the interstitial combinations in eV
+ \end{itemize}
+
+ \underline{Along \hkl<1 1 0>:}
+
+ \begin{tabular}{|l|l|l|l|l|}
+ \hline
+  {\scriptsize
+  \backslashbox{2nd interstitial}{Distance $[\frac{a}{4}]$}
+  }
+  & \hkl<1 1 -1> & \hkl<2 2 0> & \hkl<3 3 -1> & \hkl<4 4 0>\\
+ \hline
+ \hkl<0 0 -1> & 6.23514 & 4.65014 & - & -\\
+ \hline
+ \hkl<0 0 1> & - & - & 6.53614 & - \\
+ \hline
+ \hkl<1 0 0>, \hkl<0 1 0> & & & &\\
+ \hline
+ \hkl<-1 0 0>, \hkl<0 -1 0> & & & &\\
+ \hline
+ \end{tabular}
+ 
+\end{slide}
+
 \begin{slide}
 
  {\large\bf
@@ -1590,6 +1839,30 @@ $z,x'$-axis rotation: $45.0^{\circ}$, $0.0^{\circ}$
 
 \end{slide}
 
+\begin{slide}
+
+ {\large\bf
+  Molecular dynamics simulations (VASP)
+ }
+
+ 1 C atom in $3\times 3\times 3$ Type 2 supercell at $900\,^{\circ}\text{C}$
+
+ in progress ...
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Molecular dynamics simulations (VASP)
+ }
+
+ 10 C atoms in $3\times 3\times 3$ Type 2 supercell at $900\,^{\circ}\text{C}$
+
+ in progress ...
+
+\end{slide}
+
 \begin{slide}
 
  {\large\bf
@@ -1599,9 +1872,24 @@ $z,x'$-axis rotation: $45.0^{\circ}$, $0.0^{\circ}$
  Hohenberg-Kohn theorem
 
  \small
- 
 
 \end{slide}
 
+\begin{slide}
+
+ {\large\bf
+  More theory ...
+ }
+
+ Transition state theory\\
+ ART,NEB ...
+
+ Group theory
+
+ \small
+
+\end{slide}
+
+\end{document}
 \end{document}