X-Git-Url: https://hackdaworld.org/cgi-bin/gitweb.cgi?a=blobdiff_plain;f=posic%2Ftalks%2Fupb-ua-xc.tex;h=b1483e68751a54f3ca6d0a078eaaf58af853b0b9;hb=e8c736106da8aa48a4e3794d3e2384358f08d8d6;hp=04192521224a543fbf628c5741fdbf4d2ac86d69;hpb=162206abf206f18e6d23e452b95a903bd2aafae1;p=lectures%2Flatex.git

diff --git a/posic/talks/upb-ua-xc.tex b/posic/talks/upb-ua-xc.tex
index 0419252..b1483e6 100644
--- a/posic/talks/upb-ua-xc.tex
+++ b/posic/talks/upb-ua-xc.tex
@@ -675,52 +675,298 @@ POTIM = 0.1
  \end{itemize}
  \vspace*{0.2cm}
  \underline{Param 2}\\
- After talking to the pros! Used for 'large' simulations.
+ After talking to the pros!
  \begin{itemize}
   \item $\Gamma$-point only
   \item $E_{\text{cut-off}}=xyz\text{ eV}$
   \item Gaussian smearing ($\sigma=0.05$)
   \item Use symmetry
-  \item Real space projection (Auto, Medium)
+  \item Real space projection (Auto, Medium) for 'large' simulations
  \end{itemize}
  \vspace*{0.2cm}
  {\color{blue}
   In both parameter sets the ultra soft pseudo potential method
-  as well as the projector augmented wave method is used!
+  as well as the projector augmented wave method is used with both,
+  the LDA and GGA exchange correlation potential!
  }
 \end{slide}
 
 \begin{slide}
 
+ \footnotesize
+
  {\large\bf
   Properties of Si, C and SiC using the new parameters\\
  }
 
- $2\times 2\times 2$ Type 2 supercell, Param 1\\[0.2cm]
+ $2\times 2\times 2$ Type 2 supercell, Param 1, LDA, US PP\\[0.2cm]
  \begin{tabular}{|l|l|l|l|}
  \hline
   & c-Si & c-C (diamond) & 3C-SiC \\
  \hline
- Lattice constant [\AA] & 5.389 & 3.527 &  \\
- Expt. [\AA] & 5.429 & 3.567 & \\
- Error [\%] & {\color{green}0.7} & 1.1 & \\
+ Lattice constant [\AA] & 5.389 & 3.527 & 4.319 \\
+ Expt. [\AA] & 5.429 & 3.567 & 4.359 \\
+ Error [\%] & {\color{green}0.7} & {\color{green}1.1} & {\color{green}0.9} \\
  \hline
- Cohesive energy [eV] & -4.674 & -8.812 &  \\
- Expt. [eV] & -4.63 & -7.374 & \\
- Error [\%] & {\color{green}1.0} & {\color{red}19.5} &  \\
+ Cohesive energy [eV] & -5.277 & -8.812 & -7.318 \\
+ Expt. [eV] & -4.63 & -7.374 & -6.340 \\
+ Error [\%] & {\color{red}14.0} & {\color{red}19.5} & {\color{red}15.4} \\
  \hline
  \end{tabular}\\
 
+ \begin{minipage}{10cm}
+ $2\times 2\times 2$ Type 2 supercell, 3C-SiC, Param 1\\[0.2cm]
+ \begin{tabular}{|l|l|l|l|}
+ \hline
+  & {\color{magenta}US PP, GGA} & PAW, LDA & PAW, GGA \\
+ \hline
+ Lattice constant [\AA] & 4.370 & 4.330 & 4.379 \\
+ Error [\%] & {\color{green}0.3} & {\color{green}0.7} & {\color{green}0.5} \\
+ \hline
+ Cohesive energy [eV] & -6.426 & -7.371 & -6.491 \\
+ Error [\%] & {\color{green}1.4} & {\color{red}16.3} & {\color{green}2.4} \\
+ \hline
+ \end{tabular}
+ \end{minipage}
+ \begin{minipage}{3cm}
+ US PP, GGA\\[0.2cm]
+ \begin{tabular}{|l|l|}
+ \hline
+ c-Si & c-C \\
+ \hline
+ 5.455 & 3.567 \\
+ {\color{green}0.5} & {\color{green}0.01} \\
+ \hline
+ -4.591 & -7.703 \\
+ {\color{green}0.8} & {\color{orange}4.5} \\
+ \hline
+ \end{tabular}
+ \end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Energy cut-off for $\Gamma$-point only caclulations
+ }
+
+ $2\times 2\times 2$ Type 2 supercell, Param 2, US PP, LDA, 3C-SiC\\[0.2cm]
+ \includegraphics[width=5.5cm]{sic_32pc_gamma_cutoff.ps}
+ \includegraphics[width=5.5cm]{sic_32pc_gamma_cutoff_lc.ps}\\
+ $\Rightarrow$ Use 300 eV as energy cut-off?\\[0.2cm]
+ $2\times 2\times 2$ Type 2 supercell, Param 2, 300 eV, US PP, GGA\\[0.2cm]
+ \small
+ \begin{minipage}{10cm}
+ \begin{tabular}{|l|l|l|l|}
+ \hline
+  & c-Si & c-C (diamond) & 3C-SiC \\
+ \hline
+ Lattice constant [\AA] & 5.470 & 3.569 & 4.364 \\
+ Error [\%] & {\color{green}0.8} & {\color{green}0.1} & {\color{green}0.1} \\
+ \hline
+ Cohesive energy [eV] & -4.488 & -7.612 & -6.359 \\
+ Error [\%] & {\color{orange}3.1} & {\color{orange}3.2} & {\color{green}0.3} \\
+ \hline
+ \end{tabular}
+ \end{minipage}
+ \begin{minipage}{2cm}
+ {\LARGE
+  ${\color{green}\surd}$
+ }
+ \end{minipage}
+
 \end{slide}
 
 \begin{slide}
 
  {\large\bf
-  C interstitial in c-Si
+  C 100 interstitial migration along 110 in c-Si (Albe potential)
  }
 
+ \small
+
+ \begin{minipage}[t]{4.2cm}
+ \underline{Starting configuration}\\
+ \includegraphics[width=4cm]{c_100_mig/start.eps}
+ \end{minipage}
+ \begin{minipage}[t]{4.0cm}
+ \vspace*{0.8cm}
+ $\Delta x=\frac{1}{4}a_{\text{Si}}=1.357\text{ \AA}$\\
+ $\Delta y=\frac{1}{4}a_{\text{Si}}=1.357\text{ \AA}$\\
+ $\Delta z=0.325\text{ \AA}$\\
+ \end{minipage}
+ \begin{minipage}[t]{4.2cm}
+ \underline{{\bf Expected} final configuration}\\
+ \includegraphics[width=4cm]{c_100_mig/final.eps}\\
+ \end{minipage}
+ \begin{minipage}{6cm}
+ \begin{itemize}
+  \item Fix border atoms of the simulation cell
+  \item Constraints and displacement of the C atom:
+        \begin{itemize}
+         \item along {\color{green}110 direction}\\
+               displaced by {\color{green} $\frac{1}{10}(\Delta x,\Delta y)$}
+         \item C atom {\color{red}entirely fixed in position}\\
+               displaced by
+               {\color{red}$\frac{1}{10}(\Delta x,\Delta y,\Delta z)$}
+        \end{itemize}
+  \item Berendsen thermostat applied
+ \end{itemize}
+ {\bf\color{blue}Expected configuration not obtained!}
+ \end{minipage}
+ \begin{minipage}{0.5cm}
+ \hfill
+ \end{minipage}
+ \begin{minipage}{6cm}
+ \includegraphics[width=6.0cm]{c_100_110mig_01_albe.ps}
+ \end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  C 100 interstitial migration along 110 in c-Si (Albe potential)
+ }
+
+ \footnotesize
+
+ \begin{minipage}{3.2cm}
+ \includegraphics[width=3cm]{c_100_mig/fixmig_50.eps}
+ \begin{center}
+ 50 \% 
+ \end{center}
+ \end{minipage}
+ \begin{minipage}{3.2cm}
+ \includegraphics[width=3cm]{c_100_mig/fixmig_80.eps}
+ \begin{center}
+ 80 \% 
+ \end{center}
+ \end{minipage}
+ \begin{minipage}{3.2cm}
+ \includegraphics[width=3cm]{c_100_mig/fixmig_90.eps}
+ \begin{center}
+ 90 \% 
+ \end{center}
+ \end{minipage}
+ \begin{minipage}{3.2cm}
+ \includegraphics[width=3cm]{c_100_mig/fixmig_99.eps}
+ \begin{center}
+ 100 \% 
+ \end{center}
+ \end{minipage}
+
+ Open questions ...
+ \begin{enumerate}
+  \item Why is the expected configuration not obtained?
+  \item How to find a migration path preceding to the expected configuration?
+ \end{enumerate}
+
+ Answers ...
+ \begin{enumerate}
+  \item Simple: it is not the right migration path!
+        \begin{itemize}
+         \item (Surrounding) atoms settle into a local minimum configuration
+         \item A possibly existing more favorable configuration is not achieved
+        \end{itemize}
+  \item \begin{itemize}
+         \item Search global minimum in each step (by simulated annealing)\\
+               {\color{red}But:}
+               Loss of the correct energy needed for migration
+         \item Smaller displacements\\
+               A more favorable configuration might be achieved
+               possibly preceding to the expected configuration
+        \end{itemize}
+ \end{enumerate}
  
 
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  C 100 interstitial migration along 110 in c-Si (Albe potential)\\
+ }
+
+ Displacement step size decreased to
+ $\frac{1}{100} (\Delta x,\Delta y)$\\[0.2cm]
+
+ \begin{minipage}{7.5cm}
+ Result: (Video \href{../video/c_in_si_smig_albe.avi}{$\rhd_{\text{local}}$ } $|$
+ \href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/c_in_si_smig_albe.avi}{$\rhd_{\text{remote url}}$})
+ \begin{itemize}
+  \item Expected final configuration not obtained
+  \item Bonds to neighboured silicon atoms persist
+  \item C and neighboured Si atoms move along the direction of displacement
+  \item Even the bond to the lower left silicon atom persists
+ \end{itemize}
+ {\color{red}
+  Obviously: overestimated bond strength
+ }
+ \end{minipage}
+ \begin{minipage}{5cm}
+  \includegraphics[width=6cm]{c_100_110smig_01_albe.ps}
+ \end{minipage}\\[0.4cm]
+ New approach to find the migration path:\\
+ {\color{blue}
+ Place interstitial carbon atom at the respective coordinates
+ into a perfect c-Si matrix!
+ }
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  C 100 interstitial migration along 110 in c-Si (Albe potential)\\
+ }
+
+ {\color{blue}New approach:}\\
+ Place interstitial carbon atom at the respective coordinates
+ into a perfect c-Si matrix!\\
+ {\color{red}Problem:}\\
+ Too high forces due to the small distance of the C atom to the Si
+ atom sharing the lattice site.\\
+ {\color{green}Solution:}
+ Slightly displace the Si atom\\
+
+ \begin{minipage}{6.5cm}
+ Result:
+ (Video \href{../video/c_in_si_pmig_albe.avi}{$\rhd_{\text{local}}$ } $|$
+ \href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/c_in_si_pmig_albe.avi}{$\rhd_{\text{remote url}}$})\\
+ \includegraphics[width=6cm]{c_100_110pmig_01_albe.ps}
+ \end{minipage}
+ \begin{minipage}{6cm}
+ \begin{itemize}
+  \item Jump in energy (25 and 75 \%) corresponds to the abrupt
+        structural change (as seen in the video)
+  \item Due to the abrupt changes in structure and energy
+        this is {\color{red}not} the correct migration path and energy!?!
+ \end{itemize}
+ \end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  C 100 interstitial migration along 110 in c-Si (VASP)
+ }
+
+ \small
+ \vspace*{1cm}
+ \ldots simulations running!
+ \vspace*{1cm}
+
+ \begin{minipage}{5cm}
+
+ \end{minipage}
+ \begin{minipage}{7cm}
+
+ \end{minipage}
+
+
 \end{slide}
 
 \end{document}