From: hackbard Date: Mon, 14 Jun 2010 22:27:51 +0000 (+0200) Subject: finisched c 100 int X-Git-Url: https://hackdaworld.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=3e0cf069d29304120c01c063368bfa4d04365e57;p=lectures%2Flatex.git finisched c 100 int --- diff --git a/posic/talks/seminar_2010.tex b/posic/talks/seminar_2010.tex index 58369fa..5fe206d 100644 --- a/posic/talks/seminar_2010.tex +++ b/posic/talks/seminar_2010.tex @@ -439,7 +439,7 @@ Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\ \begin{slide} {\large\bf - Basics of molecular dynamics (MD) simulations + Molecular dynamics (MD) simulations } \vspace{12pt} @@ -465,7 +465,7 @@ Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\ $\tau_{\text{P}}=100\text{ fs}$, $\beta^{-1}=100\text{ GPa}$ \end{itemize} - \item Potential: Tersoff-like bond order potential + \item Erhart/Albe potential: Tersoff-like bond order potential \vspace*{12pt} \[ E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad @@ -482,33 +482,386 @@ Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\ \begin{slide} {\large\bf - Basics of density functional theory (DFT) calculations + Density functional theory (DFT) calculations } \small - Ingredients + Basic ingredients necessary for DFT + \begin{itemize} - \item Hohenberg-Kohn (HK) theorem + \item \underline{Hohenberg-Kohn theorem} - ground state density $n_0(r)$ ... + \begin{itemize} + \item ... uniquely determines the ground state potential + / wavefunctions + \item ... minimizes the systems total energy + \end{itemize} \item \underline{Born-Oppenheimer} - - $N$ moving electrons in an external potential of static nuclei\\ + - $N$ moving electrons in an external potential of static nuclei \[ H\Psi = \left[-\sum_i^N \frac{\hbar^2}{2m}\nabla_i^2 +\sum_i^N V_{\text{ext}}(r_i) +\sum_{i}{init}{insert} + \ncline[]{->}{insert}{cool} + \end{pspicture} +\end{minipage} +\begin{minipage}{5cm} + \includegraphics[width=5cm]{unit_cell_e.eps}\\ +\end{minipage} + +\begin{minipage}{9cm} + \begin{tabular}{l c c} + \hline + & size [unit cells] & \# atoms\\ +\hline +VASP & $3\times 3\times 3$ & $216\pm 1$ \\ +Erhart/Albe & $9\times 9\times 9$ & $5832\pm 1$\\ +\hline + \end{tabular} +\end{minipage} +\begin{minipage}{4cm} +{\color{red}$\bullet$} Tetrahedral\\ +{\color{green}$\bullet$} Hexagonal\\ +{\color{yellow}$\bullet$} \hkl<1 0 0> dumbbell\\ +{\color{magenta}$\bullet$} \hkl<1 1 0> dumbbell\\ +{\color{cyan}$\bullet$} Bond-centered\\ +{\color{black}$\bullet$} Vacancy / Substitutional +\end{minipage} + +\end{slide} + +\begin{slide} + + \footnotesize + +\begin{minipage}{9.5cm} + + {\large\bf + Si self-interstitial point defects in silicon\\ + } + +\begin{tabular}{l c c c c c} +\hline + $E_{\text{f}}$ [eV] & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\ +\hline + VASP & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\ + Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\ +\hline +\end{tabular}\\[0.2cm] + +\begin{minipage}{4.7cm} +\includegraphics[width=4.7cm]{e_kin_si_hex.ps} +\end{minipage} +\begin{minipage}{4.7cm} +\begin{center} +{\tiny nearly T $\rightarrow$ T}\\ +\end{center} +\includegraphics[width=4.7cm]{nhex_tet.ps} +\end{minipage}\\ + +\underline{Hexagonal} \hspace{2pt} +\href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm] +\framebox{ +\begin{minipage}{2.7cm} +$E_{\text{f}}^*=4.48\text{ eV}$\\ +\includegraphics[width=2.7cm]{si_pd_albe/hex_a.eps} +\end{minipage} +\begin{minipage}{0.4cm} +\begin{center} +$\Rightarrow$ +\end{center} +\end{minipage} +\begin{minipage}{2.7cm} +$E_{\text{f}}=3.96\text{ eV}$\\ +\includegraphics[width=2.8cm]{si_pd_albe/hex.eps} +\end{minipage} +} +\begin{minipage}{2.9cm} +\begin{flushright} +\underline{Vacancy}\\ +\includegraphics[width=3.0cm]{si_pd_albe/vac.eps} +\end{flushright} +\end{minipage} + +\end{minipage} +\begin{minipage}{3.5cm} + +\begin{flushright} +\underline{\hkl<1 1 0> dumbbell}\\ +\includegraphics[width=3.0cm]{si_pd_albe/110.eps}\\ +\underline{Tetrahedral}\\ +\includegraphics[width=3.0cm]{si_pd_albe/tet.eps}\\ +\underline{\hkl<1 0 0> dumbbell}\\ +\includegraphics[width=3.0cm]{si_pd_albe/100.eps} +\end{flushright} + +\end{minipage} + +\end{slide} + +\begin{slide} + +\footnotesize + + {\large\bf + C interstitial point defects in silicon\\[-0.1cm] + } + +\begin{tabular}{l c c c c c c} +\hline + $E_{\text{f}}$ & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B \\ +\hline + VASP & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 \\ + Erhart/Albe MD & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & 0.75 & 5.59$^*$ \\ +\hline +\end{tabular}\\[0.1cm] + +\framebox{ +\begin{minipage}{2.7cm} +\underline{Hexagonal} \hspace{2pt} +\href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\ +$E_{\text{f}}^*=9.05\text{ eV}$\\ +\includegraphics[width=2.7cm]{c_pd_albe/hex.eps} +\end{minipage} +\begin{minipage}{0.4cm} +\begin{center} +$\Rightarrow$ +\end{center} +\end{minipage} +\begin{minipage}{2.7cm} +\underline{\hkl<1 0 0>}\\ +$E_{\text{f}}=3.88\text{ eV}$\\ +\includegraphics[width=2.7cm]{c_pd_albe/100.eps} +\end{minipage} +} +\begin{minipage}{2cm} +\hfill +\end{minipage} +\begin{minipage}{3cm} +\begin{flushright} +\underline{Tetrahedral}\\ +\includegraphics[width=3.0cm]{c_pd_albe/tet.eps} +\end{flushright} +\end{minipage} + +\framebox{ +\begin{minipage}{2.7cm} +\underline{Bond-centered}\\ +$E_{\text{f}}^*=5.59\text{ eV}$\\ +\includegraphics[width=2.7cm]{c_pd_albe/bc.eps} +\end{minipage} +\begin{minipage}{0.4cm} +\begin{center} +$\Rightarrow$ +\end{center} +\end{minipage} +\begin{minipage}{2.7cm} +\underline{\hkl<1 1 0> dumbbell}\\ +$E_{\text{f}}=5.18\text{ eV}$\\ +\includegraphics[width=2.7cm]{c_pd_albe/110.eps} +\end{minipage} +} +\begin{minipage}{2cm} +\hfill +\end{minipage} +\begin{minipage}{3cm} +\begin{flushright} +\underline{Substitutional}\\ +\includegraphics[width=3.0cm]{c_pd_albe/sub.eps} +\end{flushright} +\end{minipage} + +\end{slide} + +\begin{slide} + +\footnotesize + + {\large\bf\boldmath + C \hkl<1 0 0> dumbbell interstitial configuration\\ + } + +{\tiny +\begin{tabular}{l c c c c c c c c} +\hline + Distances & $r(1C)$ & $r(2C)$ & $r(3C)$ & $r(12)$ & $r(13)$ & $r(34)$ & $r(23)$ & $r(25)$ \\ +\hline +Erhart/Albe & 0.175 & 0.329 & 0.186 & 0.226 & 0.300 & 0.343 & 0.423 & 0.425 \\ +VASP & 0.174 & 0.341 & 0.182 & 0.229 & 0.286 & 0.347 & 0.422 & 0.417 \\ +\hline +\end{tabular}\\[0.2cm] +\begin{tabular}{l c c c c } +\hline + Angles & $\theta_1$ & $\theta_2$ & $\theta_3$ & $\theta_4$ \\ +\hline +Erhart/Albe & 140.2 & 109.9 & 134.4 & 112.8 \\ +VASP & 130.7 & 114.4 & 146.0 & 107.0 \\ +\hline +\end{tabular}\\[0.2cm] +\begin{tabular}{l c c c} +\hline + Displacements & $a$ & $b$ & $|a|+|b|$ \\ +\hline +Erhart/Albe & 0.084 & -0.091 & 0.175 \\ +VASP & 0.109 & -0.065 & 0.174 \\ +\hline +\end{tabular}\\[0.6cm] +} + +\begin{minipage}{3.0cm} +\begin{center} +\underline{Erhart/Albe} +\includegraphics[width=3.0cm]{c_pd_albe/100_cmp.eps} +\end{center} +\end{minipage} +\begin{minipage}{3.0cm} +\begin{center} +\underline{VASP} +\includegraphics[width=3.0cm]{c_pd_vasp/100_cmp.eps} +\end{center} +\end{minipage}\\ + +\begin{picture}(0,0)(-185,10) +\includegraphics[width=6.8cm]{100-c-si-db_cmp.eps} +\end{picture} +\begin{picture}(0,0)(-280,-150) +\includegraphics[width=3.3cm]{c_pd_vasp/eden.eps} +\end{picture} + +\end{slide} + +\begin{slide} + +\footnotesize + + {\large\bf + Bond-centered interstitial configuration\\ + } + + +\end{slide} + +\begin{slide} + + {\large\bf + Silicon carbide precipitation simulations + } + + \small + +\end{slide} + +\begin{slide} + + {\large\bf + Investigation of a silicon carbide precipitate in silicon + } + + \small + +\end{slide} \end{document}