From: hackbard Date: Wed, 9 Sep 2009 15:28:29 +0000 (+0200) Subject: new migration stuff etc ... X-Git-Url: https://hackdaworld.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=49e043bbb553452f41f1d1b73d6f0d69273dbcf8;p=lectures%2Flatex.git new migration stuff etc ... --- diff --git a/posic/talks/upb-ua-xc.tex b/posic/talks/upb-ua-xc.tex index 2d7db85..c0e0aca 100644 --- a/posic/talks/upb-ua-xc.tex +++ b/posic/talks/upb-ua-xc.tex @@ -1000,6 +1000,9 @@ POTIM = 0.1 \item $4\times 4\times 3$ Type 1, $198+1$ atoms \item Atoms with $x=0$ or $y=0$ or $z=0$ fixed \end{itemize} + {\color{blue}Results:} + (Video \href{../video/c_in_si_smig_vasp.avi}{$\rhd_{\text{local}}$ } $|$ + \href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/c_in_si_smig_vasp.avi}{$\rhd_{\text{remote url}}$})\\ \includegraphics[width=7cm]{c_100_110mig_01_vasp.ps} \end{slide} @@ -1049,40 +1052,146 @@ POTIM = 0.1 \begin{slide} {\large\bf - Again: C 100 interstitial migration + Again: C 100 interstitial migration (Albe) + } + + Constraint applied by modyfing the Velocity Verlet algorithm + + {\color{blue}Results:} + (Video \href{../video/c_in_si_fmig_albe.avi}{$\rhd_{\text{local}}$ } $|$ + \href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/c_in_si_fmig_albe.avi}{$\rhd_{\text{remote url}}$})\\ + \begin{minipage}{6.3cm} + \includegraphics[width=6cm]{c_100_110fmig_01_albe.ps} + \end{minipage} + \begin{minipage}{6cm} + \begin{center} + Again there are jumps in energy corresponding to abrupt + structural changes as seen in the video + \end{center} + \end{minipage} + \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} + +\end{slide} + +\begin{slide} + + {\large\bf + Again: C 100 interstitial migration (VASP) } - Defining the transformation for the Type 1 supercell (VASP) + Transformation for the Type 2 supercell \small \begin{minipage}[t]{4.2cm} \underline{Starting configuration}\\ - \includegraphics[width=4cm]{c_100_mig_vasp/start.eps} + \includegraphics[width=3cm]{c_100_mig_vasp/start.eps} \end{minipage} \begin{minipage}[t]{4.0cm} - \vspace*{0.8cm} - $\Delta x=\frac{1}{4}a_{\text{Si}}=1.368\text{ \AA}$\\ - $\Delta y=\frac{1}{4}a_{\text{Si}}=1.368\text{ \AA}$\\ - $\Delta z=0.888\text{ \AA}$\\ + \vspace*{1.0cm} + $\Delta x=1.367\text{ \AA}$\\ + $\Delta y=1.367\text{ \AA}$\\ + $\Delta z=0.787\text{ \AA}$\\ \end{minipage} \begin{minipage}[t]{4.2cm} \underline{{\bf Expected} final configuration}\\ - \includegraphics[width=4cm]{c_100_mig_vasp/final.eps}\\ - \end{minipage}\\ - Angle of rotation about the 1-10 axis: + \includegraphics[width=3cm]{c_100_mig_vasp/final.eps}\\ + \end{minipage} + \begin{minipage}{6.2cm} + Rotation angles: \[ - \Theta=\arctan\frac{\Delta z}{\sqrt{2}\Delta x}=24.666^{\circ} + \alpha=45^{\circ} + \textrm{ , } + \beta=\arctan\frac{\Delta z}{\sqrt{2}\Delta x}=22.165^{\circ} \] + \end{minipage} + \begin{minipage}{6.2cm} + Length of migration path: + \[ + l=\sqrt{\Delta x^2+\Delta y^2+\Delta z^2}=2.087\text{ \AA} + \] + \end{minipage}\\[0.3cm] Transformation of basis: \[ - T(\Theta)=\left(\begin{array}{ccc} + T=ABA^{-1}A=AB \textrm{, mit } + A=\left(\begin{array}{ccc} + \cos\alpha & -\sin\alpha & 0\\ + \sin\alpha & \cos\alpha & 0\\ + 0 & 0 & 1 + \end{array}\right) + \textrm{, } + B=\left(\begin{array}{ccc} 1 & 0 & 0\\ - 0 & \cos\Theta & -\sin\Theta \\ - 0 & \sin\Theta & \cos\Theta + 0 & \cos\beta & \sin\beta \\ + 0 & -\sin\beta & \cos\beta \end{array}\right) \] - Transformation of atom coordinates: $T(-\Theta)$ + Atom coordinates transformed by: $T^{-1}=B^{-1}A^{-1}$ + +\end{slide} + +\begin{slide} + + {\large\bf + Again: C 100 interstitial migration\\ + } + + {\color{blue}Reminder:}\\ + Transformation needed since in VASP constraints can only be applied to + the basis vectors!\\ + {\color{red}Problem:} (stupid me!)\\ + Transformation of supercell 'destroys' the correct periodicity!\\ + {\color{green}Solution:}\\ + Find a supercell with one basis vector forming the correct constraint\\ + {\color{red}Problem:}\\ + Hard to find a supercell for the $22.165^{\circ}$ rotation\\ + + Another method to {\color{blue}\underline{estimate}} the migration energy: + \begin{itemize} + \item Assume an intermediate saddle point configuration during migration + \item Determine the energy of the saddle point configuration + \item Substract the saddle point configuration energy by + the energy of the initial (final) defect configuration + \end{itemize} + + +\end{slide} + +\begin{slide} + + {\large\bf + The C 100 defect configuration + } + + Needed so often for input configurations ...\\[0.8cm] + \begin{minipage}{7.7cm} + \includegraphics[width=7cm]{100-c-si-db_light.eps} + \hfill + \end{minipage} + \begin{minipage}{4.5cm} + \begin{tabular}{|l|l|l|} + \hline + & a & b \\ + \hline + \underline{VASP} & & \\ + fractional & 0.1969 & 0.1211 \\ + in \AA & 1.08 & 0.66 \\ + \hline + \underline{Albe} & & \\ + fractional & 0.1547 & 0.1676 \\ + in \AA & 0.84 & 0.91 \\ + \hline + \end{tabular} + \end{minipage} + + \begin{center} + Qualitative {\color{red}and} quantitative {\color{red}difference}! + \end{center} \end{slide}