X-Git-Url: https://hackdaworld.org/gitweb/?a=blobdiff_plain;f=posic%2Ftalks%2Fupb-ua-xc.tex;h=baa8758d498e4df49140316c7ce471e6b7643ccb;hb=3fd329819587d5b3b4d868d1b47e6c87fc47ec3e;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..baa8758 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}
@@ -1520,17 +1522,490 @@ Only works in direct mode!\\
 $z,x'$-axis rotation: $45.0^{\circ}$, $0.0^{\circ}$
  \end{minipage}
  \begin{minipage}{6.2cm}
- \includegraphics[width=6cm]{c_100_110sp-i_2333_vasp.ps}
- \includegraphics[width=6cm]{c_100_110sp-i_2333_rc_vasp.ps}
+ \includegraphics[width=5cm]{c_100_110sp-i_2333_vasp.ps}
+ \includegraphics[width=5cm]{c_100_110sp-i_2333_rc_vasp.ps}\\
+ {\color{red}One fixed Si atom not enough!}\\
+ Video: \href{../video/c_in_si_233_110mig_vasp.avi}{$\rhd_{\text{local}}$ } $|$
+ \href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/c_in_si_233_110mig_vasp.avi}{$\rhd_{\text{remote url}}$}\\
  \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
+  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
+  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 & $E_{\text{f}}=3.16107\text{ eV}$\newline
+                      {\tiny
+                      {\color{blue}
+                      434: 4.9033 - 1.00000\newline
+                      435: 5.2544 - 0.00000\newline%
+                      }%
+                      {\color{green}%
+                      434: 4.9035 - 1.00000\newline
+                      435: 5.2550 - 0.00000}}
+                    & $E_{\text{f}}=??\text{ eV}$\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}
+
+ \normalsize
+
+ \vspace*{0.3cm}
+
+ {\color{blue}Tracer:}\\
+ Smearing of electrons over two or more (degenerated) energy levels\\
+ $\Rightarrow$ use spin polarized calculations!
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  Bond centered configuration revisited ($3\times 3\times 3$ Type 2)
+ }
+
+ Spin polarized calculations
+
+ {\small
+ \begin{minipage}[t]{5.8cm}
+ \underline{Kohn-Sham eigenvalues}\\
+  \begin{minipage}{2.8cm}
+  Spin up:\\
+  430: 4.2639 - 1\newline
+  431: 4.7332 - 1\newline
+  432: 4.7354 - 1\newline
+  433: 4.7700 - 1\newline
+  434: 4.8116 - 1\newline
+  435: 4.8118 - 1\newline
+  436: 5.5360 - 0\newline
+  437: 5.5623 - 0
+  \end{minipage}
+  \begin{minipage}{2.8cm}
+  Spin down:\\
+  430: 4.2682 - 1\newline
+  431: 4.7738 - 1\newline
+  432: 4.8150 - 1\newline
+  433: 4.8151 - 1\newline
+  434: 5.3475 - 0\newline
+  435: 5.3476 - 0\newline
+  436: 5.5455 - 0\newline
+  437: 5.5652 - 0
+  \end{minipage}\\[0.3cm]
+ \begin{itemize}
+  \item linear Si-C-Si bond
+  \item Each Si has another 3 Si neighbours
+ \end{itemize}
+ \begin{center}
+ {\color{blue}Spin polarized calculations necessary!}\\[0.3cm]
+ \end{center}
+ {\scriptsize Charge density isosurface of
+              {\color{gray}spin up}, {\color{green}spin down} and
+              the {\color{blue}resulting spin up} electrons.\\
+              Two {\color{yellow} Si} atoms and one {\color{red}C}
+              atom are shown.
+ }
+ \end{minipage}
+ \begin{minipage}[t]{6.5cm}
+ \underline{MO diagram}\\
+  \begin{minipage}[t]{1.2cm}
+  {\color{red}Si}\\
+  {\tiny sp$^3$}\\[0.8cm]
+  \underline{${\color{red}\uparrow}$}
+  \underline{${\color{red}\uparrow}$}
+  \underline{${\color{red}\uparrow}$}
+  \underline{${\color{red}\uparrow}$}\\
+  sp$^3$
+  \end{minipage}
+  \begin{minipage}[t]{1.4cm}
+  \begin{center}
+  {\color{red}M}{\color{blue}O}\\[1.0cm]
+  \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
+  $\sigma_{\text{ab}}$\\[0.5cm]
+  \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
+  $\sigma_{\text{b}}$
+  \end{center}
+  \end{minipage}
+  \begin{minipage}[t]{1.0cm}
+  \begin{center}
+  {\color{blue}C}\\
+  {\tiny sp}\\[0.2cm]
+  \underline{${\color{white}\uparrow\uparrow}$}
+  \underline{${\color{white}\uparrow\uparrow}$}\\
+  2p\\[0.4cm]
+  \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
+  \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\
+  sp
+  \end{center}
+  \end{minipage}
+  \begin{minipage}[t]{1.4cm}
+  \begin{center}
+  {\color{blue}M}{\color{green}O}\\[1.0cm]
+  \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
+  $\sigma_{\text{ab}}$\\[0.5cm]
+  \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\
+  $\sigma_{\text{b}}$
+  \end{center}
+  \end{minipage}
+  \begin{minipage}[t]{1.2cm}
+  \begin{flushright}
+  {\color{green}Si}\\
+  {\tiny sp$^3$}\\[0.8cm]
+  \underline{${\color{green}\uparrow}$}
+  \underline{${\color{green}\uparrow}$}
+  \underline{${\color{green}\uparrow}$}
+  \underline{${\color{green}\uparrow}$}\\
+  sp$^3$
+  \end{flushright}
+  \end{minipage}\\[0.4cm]
+ \begin{flushright}
+ \includegraphics[width=6cm]{c_100_mig_vasp/im_spin_diff.eps}
+ \end{flushright}
+ \end{minipage}
+ }
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  \hkl<0 0 -1> configuration revisited ($3\times 3\times 3$ Type 2)
+ }
+
+ Spin polarized calculations
+
+ {\small
+ \begin{minipage}[t]{5.8cm}
+ \underline{Kohn-Sham eigenvalues}\\
+  \begin{minipage}{2.8cm}
+  Spin up:\\
+  430: 4.3317 - 1\newline
+  431: 4.7418 - 1\newline
+  432: 4.8014 - 1\newline
+  433: 4.8060 - 1\newline
+  434: 4.9033 - 1\newline
+  435: 5.2544 - 0\newline
+  436: 5.5723 - 0\newline
+  437: 5.5848 - 0
+  \end{minipage}
+  \begin{minipage}{2.8cm}
+  Spin down:\\
+  430: 4.3317 - 1\newline
+  431: 4.7420 - 1\newline
+  432: 4.8013 - 1\newline
+  433: 4.8059 - 1\newline
+  434: 4.9035 - 1\newline
+  435: 5.2550 - 0\newline
+  436: 5.5724 - 0\newline
+  437: 5.5846 - 0
+  \end{minipage}
+ \end{minipage}
+ \begin{minipage}[t]{6.5cm}
+ \underline{MO diagram}\\
+  \begin{minipage}[t]{1.2cm}
+  {\color{red}Si}\\
+  {\tiny sp$^2$}\\[0.1cm]
+  \underline{${\color{white}\uparrow}$}\\
+  p\\[0.4cm]
+  \underline{${\color{red}\uparrow\downarrow}$}
+  \underline{${\color{red}\uparrow}{\color{white}\downarrow}$}
+  \underline{${\color{red}\uparrow}{\color{white}\downarrow}$}\\
+  sp$^2$
+  \end{minipage}
+  \begin{minipage}[t]{1.2cm}
+  \begin{flushright}
+  {\color{red}M}\\[1.0cm]
+  \underline{${\color{white}\uparrow}{\color{white}\downarrow}$}\\
+  $\sigma_{\text{ab}}$\\[0.5cm]
+  \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
+  $\sigma_{\text{b}}$
+  \end{flushright}
+  \end{minipage}
+  \begin{minipage}[t]{1.2cm}
+  \begin{flushleft}
+  {\color{blue}O}\\[0.4cm]
+  \underline{${\color{white}\uparrow}{\color{white}\downarrow}$}\\
+  $\pi_{\text{ab}}$\\[0.5cm]
+  \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
+  $\pi_{\text{b}}$
+  \end{flushleft}
+  \end{minipage}
+  \begin{minipage}[t]{2.0cm}
+  \begin{center}
+  {\color{blue}C}\\
+  {\tiny sp$^2$}\\[0.5cm]
+  \underline{${\color{white}\uparrow\uparrow}$}\\
+  p\\[0.4cm]
+  \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
+  \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}
+  \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
+  sp$^2$
+  \end{center}
+  \end{minipage}
+ \end{minipage}
+ }
+
+ \vspace*{0.4cm}
+
+ \begin{itemize}
+  \item Si-C double bond
+  \item Si and C atom have another 2 Si neighbours
+ \end{itemize}
+ 
+ \begin{center}
+ {\color{blue}Spin polarized calculations {\color{red}not} necessary!}
+ \end{center}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+  New default parameter set\\[1cm]
+ }
+
+ Since some defect configurations need spin polarized calculations ...\\[1cm]
+
+ from now on the default parameter set\\
+ {\bf\color{blue}
+ $+$ no symmetry\\
+ $+$ spin polarized\\
+ }
+ \ldots is used!\\[1cm]
+
+\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
+  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|p{1.8cm}|p{1.8cm}|p{1.8cm}|p{1.8cm}|}
+ \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\newline {\color{blue}6.23514} 
+              & 4.65214\newline {\color{blue}4.65014} 
+              & 5.97314\newline {\color{blue}5.97314}
+              & 6.45514\newline {\color{blue}6.45714} \\
+ \hline
+ \hkl<0 0 1> & 6.65114\newline {\color{blue}6.65114} 
+             & 4.78514\newline {\color{blue}4.78314} 
+             & 6.53614\newline {\color{blue}6.53614}
+             & 6.18914\newline {\color{blue}6.18914} \\
+ \hline
+ \hkl<1 0 0>, \hkl<0 1 0> & 4.07014\newline alkmene
+                          & 4.93814
+                          & 5.72914
+                          & 6.00214\\
+ \hline
+ \hkl<-1 0 0>, \hkl<0 -1 0> & TODO & TODO & TODO & TODO\\
+ \hline
+ \end{tabular}
+
+ Spin polarized and {\color{blue}non spin polarized} results
+ 
+\end{slide}
+
 \begin{slide}
 
  {\large\bf
@@ -1590,6 +2065,30 @@ $z,x'$-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 +2098,24 @@ $z,x'$-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}