From: hackbard Date: Mon, 7 Nov 2011 14:24:37 +0000 (+0100) Subject: started point defects X-Git-Url: https://hackdaworld.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=ab8104bce0b6ea93877f9a5102a9fa933c4bf17f;p=lectures%2Flatex.git started point defects --- diff --git a/posic/talks/mpi_app.tex b/posic/talks/mpi_app.tex index c05db6d..e4cdd48 100644 --- a/posic/talks/mpi_app.tex +++ b/posic/talks/mpi_app.tex @@ -991,9 +991,6 @@ r = \unit[2--4]{nm} \end{slide} -% continue here -\fi - \begin{slide} \headphd @@ -1001,21 +998,18 @@ r = \unit[2--4]{nm} Utilized computational methods } -\vspace{0.2cm} +\vspace{0.3cm} \small -{\bf Molecular dynamics (MD)}\\ +{\bf Molecular dynamics (MD)}\\[0.1cm] \scriptsize -\begin{tabular}{p{4.5cm} p{7.5cm}} -Basics & Details\\ +\begin{tabular}{| p{4.5cm} | p{7.5cm} |} \hline System of $N$ particles & $N=5832\pm 1$ (Defects), $N=238328+6000$ (Precipitation)\\ -\hline Phase space propagation & Velocity Verlet | timestep: \unit[1]{fs} \\ -\hline Analytical interaction potential & Tersoff-like {\color{red}short-range}, {\color{blue}bond order} potential (Erhart/Albe) @@ -1024,7 +1018,6 @@ E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad \pot_{ij} = {\color{red}f_C(r_{ij})} \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right] $\\ -\hline Observables: time/ensemble averages & NpT (isothermal-isobaric) | Berendsen thermostat/barostat\\ \hline @@ -1032,164 +1025,78 @@ NpT (isothermal-isobaric) | Berendsen thermostat/barostat\\ \small -\vspace{0.1cm} +\vspace{0.3cm} {\bf Density functional theory (DFT)} \scriptsize \begin{minipage}[t]{6cm} -\underline{Basics} \begin{itemize} - \item $\Psi_0(r_1,r_2,\ldots,r_N)=\Psi[n_0(r)]$, $E_0=E[n_0]$ - \item Single-particle effective theory -% \item Born-Oppenheimer approximation:\\ -% Decouple electronic \& ionic motion -% \item Hohenberg-Kohn theorem:\\ -% $n_0(r) \stackrel{\text{uniquely}}{\rightarrow}$ -% $V_0$ / $H$ / $\Phi_i$ / \underline{$E_0$} + \item Hohenberg-Kohn theorem:\\ + $\Psi_0(r_1,r_2,\ldots,r_N)=\Psi[n_0(r)]$, $E_0=E[n_0]$ + \item Kohn-Sham approach:\\ + Single-particle effective theory \end{itemize} -\underline{Details} +\hrule \begin{itemize} \item Code: \textsc{vasp} -\item Plane wave basis set $\{\phi_j\}$\\[0.1cm] -$\displaystyle -\Phi_i=\sum_{|G+k|}(3.5,-2.0){2.5}{130}{15} +\psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{230}{165} +\psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{345}{310} -\begin{pspicture}(0,0)(0,0) -\psellipse[linecolor=blue](1.5,6.75)(0.5,0.3) \end{pspicture} +\end{minipage} \end{slide} \begin{slide} +\headphd {\large\bf - C and Si self-interstitial point defects in silicon + Point defects \& defect migration } \small - \vspace*{0.3cm} + \vspace{0.2cm} -\begin{minipage}{8cm} -Procedure:\\[0.3cm] - \begin{pspicture}(0,0)(7,5) - \rput(3.5,4){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ +\begin{minipage}[b]{7.5cm} +{\bf Defect structure}\\ + \begin{pspicture}(0,0)(7,4.4) + \rput(3.5,3.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ \parbox{7cm}{ \begin{itemize} \item Creation of c-Si simulation volume @@ -1197,13 +1104,13 @@ Procedure:\\[0.3cm] \item $T=0\text{ K}$, $p=0\text{ bar}$ \end{itemize} }}}} -\rput(3.5,2.1){\rnode{insert}{\psframebox{ +\rput(3.5,1.3){\rnode{insert}{\psframebox{ \parbox{7cm}{ \begin{center} Insertion of interstitial C/Si atoms \end{center} }}}} - \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{ + \rput(3.5,0.2){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{ \parbox{7cm}{ \begin{center} Relaxation / structural energy minimization @@ -1213,49 +1120,83 @@ Procedure:\\[0.3cm] \ncline[]{->}{insert}{cool} \end{pspicture} \end{minipage} -\begin{minipage}{5cm} - \includegraphics[width=5cm]{unit_cell_e.eps}\\ +\begin{minipage}[b]{4.5cm} +\begin{center} +\includegraphics[width=3.8cm]{unit_cell_e.eps}\\ +\end{center} +\begin{minipage}{2.21cm} +{\scriptsize +{\color{red}$\bullet$} Tetrahedral\\[-0.1cm] +{\color{green}$\bullet$} Hexagonal\\[-0.1cm] +{\color{yellow}$\bullet$} \hkl<1 0 0> DB +} +\end{minipage} +\begin{minipage}{2.21cm} +{\scriptsize +{\color{magenta}$\bullet$} \hkl<1 1 0> DB\\[-0.1cm] +{\color{cyan}$\bullet$} Bond-centered\\[-0.1cm] +{\color{black}$\bullet$} Vac. / Sub. +} +\end{minipage} \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} +\vspace{0.2cm} + +\begin{minipage}[b]{6cm} +{\bf Defect formation energy}\\ +\framebox{ +$E_{\text{f}}=E-\sum_i N_i\mu_i$}\\[0.1cm] +Particle reservoir: Si \& SiC\\[0.2cm] +{\bf Binding energy}\\ +\framebox{ +$ +E_{\text{b}}= +E_{\text{f}}^{\text{comb}}- +E_{\text{f}}^{1^{\text{st}}}- +E_{\text{f}}^{2^{\text{nd}}} +$ +}\\[0.1cm] +\footnotesize +$E_{\text{b}}<0$: energetically favorable configuration\\ +$E_{\text{b}}\rightarrow 0$: non-interacting, isolated defects\\ \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 +\begin{minipage}[b]{6cm} +{\bf Migration barrier} +\footnotesize +\begin{itemize} + \item Displace diffusing atom + \item Constrain relaxation of (diffusing) atoms + \item Record configurational energy +\end{itemize} +\begin{picture}(0,0)(-60,-33) +\includegraphics[width=4.5cm]{crt_mod.eps} +\end{picture} \end{minipage} \end{slide} +% continue here +\fi + \begin{slide} \footnotesize \begin{minipage}{9.5cm} +\headphd {\large\bf - Si self-interstitial point defects in silicon\\ + Si self-interstitial point defects in silicon\\[0.1cm] } \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 \\ + \textsc{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] +\end{tabular}\\[0.3cm] \begin{minipage}{4.7cm} \includegraphics[width=4.7cm]{e_kin_si_hex.ps} @@ -1265,7 +1206,7 @@ Erhart/Albe & $9\times 9\times 9$ & $5832\pm 1$\\ {\tiny nearly T $\rightarrow$ T}\\ \end{center} \includegraphics[width=4.7cm]{nhex_tet.ps} -\end{minipage}\\ +\end{minipage}\\[0.1cm] \underline{Hexagonal} \hspace{2pt} \href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm] @@ -1292,9 +1233,10 @@ $E_{\text{f}}=3.96\text{ eV}$\\ \end{minipage} \end{minipage} -\begin{minipage}{3.5cm} +\begin{minipage}{2.5cm} \begin{flushright} +\vspace*{0.2cm} \underline{\hkl<1 1 0> dumbbell}\\ \includegraphics[width=3.0cm]{si_pd_albe/110.eps}\\ \underline{Tetrahedral}\\ @@ -1311,18 +1253,21 @@ $E_{\text{f}}=3.96\text{ eV}$\\ \footnotesize +\headphd {\large\bf C interstitial point defects in silicon\\[-0.1cm] } +{\scriptsize \begin{tabular}{l c c c c c c r} \hline $E_{\text{f}}$ & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B & \cs{} \& \si\\ \hline - VASP & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\ + \textsc{vasp} & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\ Erhart/Albe MD & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & {\color{red}0.75} & 5.59$^*$ & {\color{green}4.43} \\ \hline -\end{tabular}\\[0.1cm] +\end{tabular} +}\\[0.1cm] \framebox{ \begin{minipage}{2.7cm} @@ -1381,6 +1326,9 @@ $E_{\text{f}}=5.18\text{ eV}$\\ \end{slide} +\end{document} +\ifnum1=0 + \begin{slide} \footnotesize @@ -1614,25 +1562,6 @@ $\rightarrow$ \end{minipage} \end{minipage} \end{minipage} -\framebox{ -\begin{minipage}{4.2cm} - {\small Constrained relaxation\\ - technique (CRT) method}\\ -\includegraphics[width=4cm]{crt_orig.eps} -\begin{itemize} - \item Constrain diffusing atom - \item Static constraints -\end{itemize} -\vspace*{0.3cm} - {\small Modifications}\\ -\includegraphics[width=4cm]{crt_mod.eps} -\begin{itemize} - \item Constrain all atoms - \item Update individual\\ - constraints -\end{itemize} -\end{minipage} -} \end{slide}