From: hackbard Date: Sun, 17 Aug 2008 17:03:29 +0000 (+0200) Subject: safety checkin - shopping ... X-Git-Url: https://hackdaworld.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=1771367c94e1b114a72343dabddd66412d9ca306;p=lectures%2Flatex.git safety checkin - shopping ... --- diff --git a/posic/talks/helsinki_2008.tex b/posic/talks/helsinki_2008.tex index 5a5ceda..8a3174e 100644 --- a/posic/talks/helsinki_2008.tex +++ b/posic/talks/helsinki_2008.tex @@ -170,6 +170,8 @@ Crystalline silicon and cubic silicon carbide } + \vspace{8pt} + {\bf Lattice types and unit cells:} \begin{itemize} \item Crystalline silicon (c-Si) has diamond structure\\ @@ -179,6 +181,7 @@ $\Rightarrow {\color{si-yellow}\bullet}$ are Si atoms, ${\color{gray}\bullet}$ are C atoms \end{itemize} + \vspace{8pt} \begin{minipage}{8cm} {\bf Lattice constants:} \[ @@ -237,11 +240,18 @@ \vspace{12pt} - Experimentally observed: + \begin{minipage}{7cm} + Experimentally observed [3]: \begin{itemize} \item Minimal diameter of precipitation: 4 - 5 nm \item Equal orientation of Si and SiC (hkl)-planes \end{itemize} + \end{minipage} + \begin{minipage}{6cm} + \vspace{32pt} + \hspace{16pt} + {\tiny [3] J. K. N. Lindner, Appl. Phys. A 77 (2003) 27.} + \end{minipage} \end{slide} @@ -251,32 +261,37 @@ Simulation details } - \vspace{12pt} + \small - MD basics: + {\bf MD basics:} \begin{itemize} \item Microscopic description of N particle system \item Analytical interaction potential \item Hamilton's equations of motion as propagation rule\\ in 6N-dimensional phase space - \item Observables obtained by time average + \item Observables obtained by time or ensemble averages \end{itemize} - - \vspace{12pt} - - Application details: + {\bf Application details:} \begin{itemize} - \item Integrator: Velocity Verlet, timestep: $1\, fs$ - \item Ensemble: NVT, Berendsen thermostat, $\tau=100.0$ - \item Potential: Tersoff-like bond order potential\\ + \item Integrator: Velocity Verlet, timestep: $1\text{ fs}$ + \item Ensemble: isothermal-isobaric NPT [4] + \begin{itemize} + \item Berendsen thermostat: + $\tau_{\text{T}}=100\text{ fs}$ + \item Brendsen barostat:\\ + $\tau_{\text{P}}=100\text{ fs}$, + $\beta^{-1}=100\text{ GPa}$ + \end{itemize} + \item Potential: Tersoff-like bond order potential [5] \[ E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad \pot_{ij} = f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right] \] - \begin{center} - {\scriptsize P. Erhart and K. Albe. Phys. Rev. B 71 (2005) 035211} - \end{center} \end{itemize} + {\tiny + [4] L. Verlet, Phys. Rev. 159 (1967) 98.}\\ + {\tiny + [5] P. Erhart and K. Albe, Phys. Rev. B 71 (2005) 35211.} \begin{picture}(0,0)(-240,-70) \includegraphics[width=5cm]{tersoff_angle.eps} @@ -287,22 +302,22 @@ \begin{slide} {\large\bf - Simulation details + Simulation sequence } \vspace{8pt} - Interstitial simulations: + Interstitial configurations: \vspace{8pt} \begin{pspicture}(0,0)(7,8) - \rput(3.5,7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=green]{ + \rput(3.5,7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ \parbox{7cm}{ \begin{itemize} \item Initial configuration: $9\times9\times9$ unit cells Si \item Periodic boundary conditions - \item $T=0 \, K$ + \item $T=0\text{ K}$, $p=0\text{ bar}$ \end{itemize} }}}} \rput(3.5,3.5){\rnode{insert}{\psframebox{ @@ -310,13 +325,16 @@ Insertion of C / Si atom: \begin{itemize} \item $(0,0,0)$ $\rightarrow$ {\color{red}tetrahedral} + (${\color{red}\triangleleft}$) \item $(-1/8,-1/8,1/8)$ $\rightarrow$ {\color{green}hexagonal} + (${\color{green}\triangleright}$) \item $(-1/8,-1/8,-1/4)$, $(-1/4,-1/4,-1/4)$\\ $\rightarrow$ {\color{magenta}110 dumbbell} + (${\color{magenta}\Box}$,$\circ$) \item random positions (critical distance check) \end{itemize} }}}} - \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=cyan]{ + \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{ \parbox{3.5cm}{ Relaxation time: $2\, ps$ }}}} @@ -325,7 +343,7 @@ \end{pspicture} \begin{picture}(0,0)(-210,-45) - \includegraphics[width=6cm]{unit_cell.eps} + \includegraphics[width=6cm]{unit_cell_s.eps} \end{picture} \end{slide} @@ -426,7 +444,7 @@ \begin{slide} {\large\bf - Simulation details + Simulation sequence } \small @@ -439,18 +457,18 @@ \begin{pspicture}(0,0)(12,8) % nodes - \rput(3.5,6.5){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=green]{ + \rput(3.5,6.5){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ \parbox{7cm}{ \begin{itemize} \item Initial configuration: $31\times31\times31$ unit cells Si \item Periodic boundary conditions - \item $T=450\, ^{\circ}C$ - \item Equilibration of $E_{kin}$ and $E_{pot}$ for $600\, fs$ + \item $T=450\, ^{\circ}\text{C}$, $p=0\text{ bar}$ + \item Equilibration of $E_{kin}$ and $E_{pot}$ \end{itemize} }}}} - \rput(3.5,3.2){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=red]{ + \rput(3.5,3.2){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{ \parbox{7cm}{ - Insertion of $6000$ carbon atoms at constant\\ + Insertion of 6000 carbon atoms at constant\\ temperature into: \begin{itemize} \item Total simulation volume {\pnode{in1}} @@ -458,7 +476,7 @@ \item Volume of necessary amount of Si {\pnode{in3}} \end{itemize} }}}} - \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=cyan]{ + \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{ \parbox{3.5cm}{ Cooling down to $20\, ^{\circ}C$ }}}} @@ -480,8 +498,8 @@ \begin{slide} {\large\bf - Very first results of the SiC precipitation runs - } + Results + } - SiC precipitation runs \footnotesize