X-Git-Url: https://hackdaworld.org/gitweb/?a=blobdiff_plain;f=posic%2Ftalks%2Fmpi_app.tex;h=167579f60aa89e20d0d477431f780e6474971dd3;hb=f0f8ad95bc74bee7fb7a01f50e67d7c83f932263;hp=4f0f76c74f97610289614585dcd702e04b5328fb;hpb=acc13142c245dde66027f86a444b652da7af3e00;p=lectures%2Flatex.git diff --git a/posic/talks/mpi_app.tex b/posic/talks/mpi_app.tex index 4f0f76c..167579f 100644 --- a/posic/talks/mpi_app.tex +++ b/posic/talks/mpi_app.tex @@ -7,6 +7,7 @@ \usepackage[latin1]{inputenc} \usepackage[T1]{fontenc} \usepackage{amsmath} +\usepackage{stmaryrd} \usepackage{latexsym} \usepackage{ae} @@ -20,6 +21,7 @@ \usepackage{pstricks} \usepackage{pst-node} +\usepackage{pst-grad} %\usepackage{epic} %\usepackage{eepic} @@ -54,6 +56,28 @@ \usepackage{upgreek} +\newcommand{\headdiplom}{ +\begin{pspicture}(0,0)(0,0) +\rput(6.0,0.2){\psframebox[fillstyle=gradient,gradbegin=red,gradend=white,gradlines=1000,gradmidpoint=1,linestyle=none]{ +\begin{minipage}{14cm} +\hfill +\vspace{0.7cm} +\end{minipage} +}} +\end{pspicture} +} + +\newcommand{\headphd}{ +\begin{pspicture}(0,0)(0,0) +\rput(6.0,0.2){\psframebox[fillstyle=gradient,gradbegin=blue,gradend=white,gradlines=1000,gradmidpoint=1,linestyle=none]{ +\begin{minipage}{14cm} +\hfill +\vspace{0.7cm} +\end{minipage} +}} +\end{pspicture} +} + \begin{document} \extraslideheight{10in} @@ -185,6 +209,8 @@ R. I. Scace and G. A. Slack, J. Chem. Phys. 30, 1551 (1959) \begin{slide} +\vspace*{1.8cm} + \small \begin{pspicture}(0,0)(13.5,5) @@ -401,18 +427,18 @@ Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0) \end{center} \begin{pspicture}(0,0)(0,0) -\rput(6.0,7.0){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{ +\rput(6.0,7.0){\rnode{init}{\psframebox[fillstyle=gradient,gradbegin=red,gradend=white,gradlines=1000,gradmidpoint=1.0,linestyle=none]{ \begin{minipage}{11cm} -{\color{red}Diploma thesis}\\ +{\color{black}Diploma thesis}\\ \underline{Monte Carlo} simulation modeling the selforganization process\\ leading to periodic arrays of nanometric amorphous SiC precipitates \end{minipage} }}} \end{pspicture} \begin{pspicture}(0,0)(0,0) -\rput(6.0,-0.5){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{ +\rput(6.0,-0.5){\rnode{init}{\psframebox[fillstyle=gradient,gradbegin=blue,gradend=white,gradmidpoint=1.0,gradlines=1000,linestyle=none]{ \begin{minipage}{11cm} -{\color{blue}Doctoral studies}\\ +{\color{black}Doctoral studies}\\ Classical potential \underline{molecular dynamics} simulations \ldots\\ \underline{Density functional theory} calculations \ldots\\[0.2cm] \ldots on defect formation and SiC precipitation in Si @@ -430,6 +456,7 @@ Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0) \begin{slide} +\headdiplom {\large\bf Selforganization of nanometric amorphous SiC lamellae } @@ -451,7 +478,8 @@ Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0) \begin{minipage}{12cm} \includegraphics[width=9cm]{../../nlsop/img/k393abild1_e_l.eps}\\ {\scriptsize -XTEM bright-field, \unit[180]{keV} C$^+ \rightarrow$ Si, \degc{150}, +XTEM bright-field, \unit[180]{keV} C$^+ \rightarrow$ Si, +{\color{red}\underline{\degc{150}}}, Dose: \unit[4.3 $\times 10^{17}$]{cm$^{-2}$} } \end{minipage} @@ -469,88 +497,304 @@ XTEM bright-field and respective EFTEM C map \end{slide} -% continue here -\fi - \begin{slide} +\headdiplom {\large\bf Model displaying the formation of ordered lamellae } +\vspace{0.1cm} + +\begin{center} + \includegraphics[width=8.0cm]{../../nlsop/img/modell_ng_e.eps} +\end{center} + +\footnotesize + +\begin{itemize} +\item Supersaturation of C in c-Si\\ + $\rightarrow$ {\bf Carbon induced} nucleation of spherical + SiC$_x$-precipitates +\item High interfacial energy between 3C-SiC and c-Si\\ + $\rightarrow$ {\bf Amorphous} precipitates +\item \unit[20-- 30]{\%} lower silicon density of a-SiC$_x$ compared to c-Si\\ + $\rightarrow$ {\bf Lateral strain} (black arrows) +\item Implantation range near surface\\ + $\rightarrow$ {\bf Relaxation} of {\bf vertical strain component} +\item Reduction of the carbon supersaturation in c-Si\\ + $\rightarrow$ {\bf Carbon diffusion} into amorphous volumina + (white arrows) +\item Remaining lateral strain\\ + $\rightarrow$ {\bf Strain enhanced} lateral amorphisation +\item Absence of crystalline neighbours (structural information)\\ + $\rightarrow$ {\bf Stabilization} of amorphous inclusions + {\bf against recrystallization} +\end{itemize} + \end{slide} -\end{document} -\ifnum1=0 +\begin{slide} + +\headdiplom +{\large\bf + Implementation of the Monte Carlo code +} + +\small + +\begin{enumerate} + \item \underline{Amorphization / Recrystallization}\\ + Ion collision in discretized target determined by random numbers + distributed according to nuclear energy loss. + Amorphization/recrystallization probability: +\[ +p_{c \rightarrow a}(\vec{r}) = {\color{green} p_b} + {\color{blue} p_c c_C(\vec{r})} + {\color{red} \sum_{\textrm{amorphous neighbours}} \frac{p_s c_C(\vec{r'})}{(r-r')^2}} +\] +\begin{itemize} + \item {\color{green} $p_b$} normal `ballistic' amorphization + \item {\color{blue} $p_c$} carbon induced amorphization + \item {\color{red} $p_s$} stress enhanced amorphization +\end{itemize} +\[ +p_{a \rightarrow c}(\vec r) = (1 - p_{c \rightarrow a}(\vec r)) \Big(1 - \frac{\sum_{direct \, neighbours} \delta (\vec{r'})}{6} \Big) \, \textrm{,} +\] +\[ +\delta (\vec r) = \left\{ +\begin{array}{ll} + 1 & \textrm{if volume at position $\vec r$ is amorphous} \\ + 0 & \textrm{otherwise} \\ +\end{array} +\right. +\] + \item \underline{Carbon incorporation}\\ + Incorporation volume determined according to implantation profile + \item \underline{Diffusion / Sputtering} + \begin{itemize} + \item Transfer fraction of C atoms + of crystalline into neighbored amorphous volumes + \item Remove surface layer + \end{itemize} +\end{enumerate} + +\end{slide} \begin{slide} +\begin{minipage}{3.7cm} +\begin{pspicture}(0,0)(0,0) +\rput(1.7,0.2){\psframebox[fillstyle=gradient,gradbegin=red,gradend=white,gradlines=1000,gradangle=10,gradmidpoint=1,linestyle=none]{ +\begin{minipage}{3.7cm} +\hfill +\vspace{0.7cm} +\end{minipage} +}} +\end{pspicture} {\large\bf - Model displaying the formation of ordered lamellae + Results } +\footnotesize + +\vspace{1.2cm} + +Evolution of the \ldots +\begin{itemize} + \item continuous\\ + amorphous layer + \item a/c interface + \item lamellar precipitates +\end{itemize} +\ldots reproduced!\\[1.4cm] + +{\color{blue} +\begin{center} +Experiment \& simulation\\ +in good agreement\\[1.0cm] + +Simulation is able to model the whole depth region\\[1.2cm] +\end{center} +} + +\end{minipage} +\begin{minipage}{0.5cm} +\vfill +\end{minipage} +\begin{minipage}{8.0cm} + \vspace{-0.3cm} + \includegraphics[width=9cm]{../../nlsop/img/dosis_entwicklung_ng_e_1-2.eps}\\ + \includegraphics[width=9cm]{../../nlsop/img/dosis_entwicklung_ng_e2_2-2.eps} +\end{minipage} + +\end{slide} + +\begin{slide} + +\headdiplom +{\large\bf + Structural \& compositional details +} + +\begin{minipage}[t]{7.5cm} +\includegraphics[height=6.5cm]{../../nlsop/img/ac_cconc_ver2_e.eps}\\ +\end{minipage} +\begin{minipage}[t]{5.0cm} +\includegraphics[height=6.5cm]{../../nlsop/img/97_98_e.eps} +\end{minipage} + +\footnotesize + +\vspace{-0.1cm} + +\begin{itemize} + \item Fluctuation of C concentration in lamellae region + \item \unit[8--10]{at.\%} C saturation limit + within the respective conditions + \item Complementarily arranged and alternating sequence of layers\\ + with a high and low amount of amorphous regions + \item C accumulation in the amorphous phase / Origin of stress +\end{itemize} + +\begin{picture}(0,0)(-260,-50) \framebox{ - \begin{minipage}{6.3cm} +\begin{minipage}{3cm} +\begin{center} +{\color{blue} +Precipitation process\\ +gets traceable\\ +by simulation! +} +\end{center} +\end{minipage} +} +\end{picture} + +\end{slide} + +\begin{slide} + +\headphd +{\large\bf + Formation of epitaxial single crystalline 3C-SiC +} + +\footnotesize + +\vspace{0.2cm} + +\begin{center} +\begin{itemize} + \item \underline{Implantation step 1}\\[0.1cm] + Almost stoichiometric dose | \unit[180]{keV} | \degc{500}\\ + $\Rightarrow$ Epitaxial {\color{blue}3C-SiC} layer \& + {\color{blue}precipitates} + \item \underline{Implantation step 2}\\[0.1cm] + Little remaining dose | \unit[180]{keV} | \degc{250}\\ + $\Rightarrow$ + Destruction/Amorphization of precipitates at layer interface + \item \underline{Annealing}\\[0.1cm] + \unit[10]{h} at \degc{1250}\\ + $\Rightarrow$ Homogeneous 3C-SiC layer with sharp interfaces +\end{itemize} +\end{center} + +\begin{minipage}{7cm} +\includegraphics[width=7cm]{ibs_3c-sic.eps} +\end{minipage} +\begin{minipage}{5cm} +\begin{pspicture}(0,0)(0,0) +\rnode{box}{ +\psframebox[fillstyle=solid,fillcolor=white,linecolor=blue,linestyle=solid]{ +\begin{minipage}{5.3cm} \begin{center} {\color{blue} - Precipitation mechanism not yet fully understood! + 3C-SiC precipitation\\ + not yet fully understood } + \end{center} + \vspace*{0.1cm} \renewcommand\labelitemi{$\Rightarrow$} - \small - \underline{Understanding the SiC precipitation} + Details of the SiC precipitation \begin{itemize} - \item significant technological progress in SiC thin film formation - \item perspectives for processes relying upon prevention of SiC precipitation + \item significant technological progress\\ + in SiC thin film formation + \item perspectives for processes relying\\ + upon prevention of SiC precipitation \end{itemize} - \end{center} - \end{minipage} -} +\end{minipage} +}} +\rput(-6.8,5.4){\pnode{h0}} +\rput(-3.0,5.4){\pnode{h1}} +\ncline[linecolor=blue]{-}{h0}{h1} +\ncline[linecolor=blue]{->}{h1}{box} +\end{pspicture} +\end{minipage} \end{slide} \begin{slide} - {\large\bf +\headphd +{\large\bf Supposed precipitation mechanism of SiC in Si - } +} \scriptsize \vspace{0.1cm} - \begin{minipage}{3.8cm} - Si \& SiC lattice structure\\[0.2cm] - \includegraphics[width=3.5cm]{sic_unit_cell.eps}\\[-0.3cm] - \hrule + \framebox{ + \begin{minipage}{3.6cm} + \begin{center} + Si \& SiC lattice structure\\[0.1cm] + \includegraphics[width=2.3cm]{sic_unit_cell.eps} + \end{center} +{\tiny + \begin{minipage}{1.7cm} +\underline{Silicon}\\ +{\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\ +$a=\unit[5.429]{\\A}$\\ +$\rho^*_{\text{Si}}=\unit[100]{\%}$ + \end{minipage} + \begin{minipage}{1.7cm} +\underline{Silicon carbide}\\ +{\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\ +$a=\unit[4.359]{\\A}$\\ +$\rho^*_{\text{Si}}=\unit[97]{\%}$ \end{minipage} - \hspace{0.6cm} - \begin{minipage}{3.8cm} +} + \end{minipage} + } + \hspace{0.1cm} + \begin{minipage}{4.1cm} \begin{center} \includegraphics[width=3.3cm]{tem_c-si-db.eps} \end{center} \end{minipage} - \hspace{0.6cm} - \begin{minipage}{3.8cm} + \hspace{0.1cm} + \begin{minipage}{4.0cm} \begin{center} \includegraphics[width=3.3cm]{tem_3c-sic.eps} \end{center} \end{minipage} - \begin{minipage}{4cm} + \vspace{0.1cm} + + \begin{minipage}{4.0cm} \begin{center} C-Si dimers (dumbbells)\\[-0.1cm] on Si interstitial sites \end{center} \end{minipage} - \hspace{0.2cm} - \begin{minipage}{4.2cm} + \hspace{0.1cm} + \begin{minipage}{4.1cm} \begin{center} Agglomeration of C-Si dumbbells\\[-0.1cm] $\Rightarrow$ dark contrasts \end{center} \end{minipage} - \hspace{0.2cm} - \begin{minipage}{4cm} + \hspace{0.1cm} + \begin{minipage}{4.0cm} \begin{center} Precipitation of 3C-SiC in Si\\[-0.1cm] $\Rightarrow$ Moir\'e fringes\\[-0.1cm] @@ -558,37 +802,39 @@ XTEM bright-field and respective EFTEM C map \end{center} \end{minipage} - \begin{minipage}{3.8cm} + \vspace{0.1cm} + + \begin{minipage}{4.0cm} \begin{center} \includegraphics[width=3.3cm]{sic_prec_seq_01.eps} \end{center} \end{minipage} - \hspace{0.6cm} - \begin{minipage}{3.8cm} + \hspace{0.1cm} + \begin{minipage}{4.1cm} \begin{center} \includegraphics[width=3.3cm]{sic_prec_seq_02.eps} \end{center} \end{minipage} - \hspace{0.6cm} - \begin{minipage}{3.8cm} + \hspace{0.1cm} + \begin{minipage}{4.0cm} \begin{center} \includegraphics[width=3.3cm]{sic_prec_seq_03.eps} \end{center} \end{minipage} \begin{pspicture}(0,0)(0,0) -\psline[linewidth=4pt]{->}(8.5,2)(9.0,2) -\psellipse[linecolor=blue](11.5,5.8)(0.3,0.5) -\rput{-20}{\psellipse[linecolor=blue](3.3,8.1)(0.3,0.5)} -\psline[linewidth=4pt]{->}(4.0,2)(4.5,2) -\rput(12.7,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ +\psline[linewidth=2pt]{->}(8.3,2)(8.8,2) +\psellipse[linecolor=blue](11.1,6.0)(0.3,0.5) +\rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)} +\psline[linewidth=2pt]{->}(3.9,2)(4.4,2) +\rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ $4a_{\text{Si}}=5a_{\text{SiC}}$ }}} -\rput(12.2,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ +\rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ \hkl(h k l) planes match }}} -\rput(9.7,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ -r = 2 - 4 nm +\rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ +r = \unit[2--4]{nm} }}} \end{pspicture} @@ -596,47 +842,67 @@ r = 2 - 4 nm \begin{slide} - {\large\bf - Supposed precipitation mechanism of SiC in Si - } +\headphd +{\large\bf + Supposed precipitation mechanism of SiC in Si +} \scriptsize \vspace{0.1cm} - \begin{minipage}{3.8cm} - Si \& SiC lattice structure\\[0.2cm] - \includegraphics[width=3.5cm]{sic_unit_cell.eps}\\[-0.3cm] - \hrule + \framebox{ + \begin{minipage}{3.6cm} + \begin{center} + Si \& SiC lattice structure\\[0.1cm] + \includegraphics[width=2.3cm]{sic_unit_cell.eps} + \end{center} +{\tiny + \begin{minipage}{1.7cm} +\underline{Silicon}\\ +{\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\ +$a=\unit[5.429]{\\A}$\\ +$\rho^*_{\text{Si}}=\unit[100]{\%}$ + \end{minipage} + \begin{minipage}{1.7cm} +\underline{Silicon carbide}\\ +{\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\ +$a=\unit[4.359]{\\A}$\\ +$\rho^*_{\text{Si}}=\unit[97]{\%}$ \end{minipage} - \hspace{0.6cm} - \begin{minipage}{3.8cm} +} + \end{minipage} + } + \hspace{0.1cm} + \begin{minipage}{4.1cm} \begin{center} \includegraphics[width=3.3cm]{tem_c-si-db.eps} \end{center} \end{minipage} - \hspace{0.6cm} - \begin{minipage}{3.8cm} + \hspace{0.1cm} + \begin{minipage}{4.0cm} \begin{center} \includegraphics[width=3.3cm]{tem_3c-sic.eps} \end{center} \end{minipage} - \begin{minipage}{4cm} + \vspace{0.1cm} + + \begin{minipage}{4.0cm} \begin{center} C-Si dimers (dumbbells)\\[-0.1cm] on Si interstitial sites \end{center} \end{minipage} - \hspace{0.2cm} - \begin{minipage}{4.2cm} + \hspace{0.1cm} + \begin{minipage}{4.1cm} \begin{center} Agglomeration of C-Si dumbbells\\[-0.1cm] $\Rightarrow$ dark contrasts \end{center} \end{minipage} - \hspace{0.2cm} - \begin{minipage}{4cm} + \hspace{0.1cm} + \begin{minipage}{4.0cm} \begin{center} Precipitation of 3C-SiC in Si\\[-0.1cm] $\Rightarrow$ Moir\'e fringes\\[-0.1cm] @@ -644,77 +910,121 @@ r = 2 - 4 nm \end{center} \end{minipage} - \begin{minipage}{3.8cm} + \vspace{0.1cm} + + \begin{minipage}{4.0cm} \begin{center} \includegraphics[width=3.3cm]{sic_prec_seq_01.eps} \end{center} \end{minipage} - \hspace{0.6cm} - \begin{minipage}{3.8cm} + \hspace{0.1cm} + \begin{minipage}{4.1cm} \begin{center} \includegraphics[width=3.3cm]{sic_prec_seq_02.eps} \end{center} \end{minipage} - \hspace{0.6cm} - \begin{minipage}{3.8cm} + \hspace{0.1cm} + \begin{minipage}{4.0cm} \begin{center} \includegraphics[width=3.3cm]{sic_prec_seq_03.eps} \end{center} \end{minipage} \begin{pspicture}(0,0)(0,0) -\psline[linewidth=4pt]{->}(8.5,2)(9.0,2) -\psellipse[linecolor=blue](11.5,5.8)(0.3,0.5) -\rput{-20}{\psellipse[linecolor=blue](3.3,8.1)(0.3,0.5)} -\psline[linewidth=4pt]{->}(4.0,2)(4.5,2) -\rput(12.7,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ +\psline[linewidth=2pt]{->}(8.3,2)(8.8,2) +\psellipse[linecolor=blue](11.1,6.0)(0.3,0.5) +\rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)} +\psline[linewidth=2pt]{->}(3.9,2)(4.4,2) +\rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ $4a_{\text{Si}}=5a_{\text{SiC}}$ }}} -\rput(12.2,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ +\rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ \hkl(h k l) planes match }}} -\rput(9.7,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ -r = 2 - 4 nm +\rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{ +r = \unit[2--4]{nm} }}} -\rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{ +% controversial view! +\rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{ +\begin{minipage}{14cm} +\hfill +\vspace{12cm} +\end{minipage} +}} +\rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{ \begin{minipage}{10cm} \small -{\color{red}\bf Controversial views} +\vspace*{0.2cm} +\begin{center} +{\color{gray}\bf Controversial findings} +\end{center} \begin{itemize} -\item Implantations at high T (Nejim et al.) +\item High-temperature implantation {\tiny\color{gray}/Nejim~et~al./} \begin{itemize} - \item Topotactic transformation based on \cs - \item \si{} as supply reacting with further C in cleared volume + \item C incorporated {\color{blue}substitutionally} on regular Si lattice sites + \item \si{} reacting with further C in cleared volume \end{itemize} -\item Annealing behavior (Serre et al.) +\item Annealing behavior {\tiny\color{gray}/Serre~et~al./} \begin{itemize} - \item Room temperature implants $\rightarrow$ highly mobile C - \item Elevated T implants $\rightarrow$ no/low C redistribution/migration\\ - (indicate stable \cs{} configurations) + \item Room temperature implantation $\rightarrow$ high C diffusion + \item Elevated temperature implantation $\rightarrow$ no C redistribution \end{itemize} + $\Rightarrow$ mobile {\color{red}\ci} opposed to + stable {\color{blue}\cs{}} configurations \item Strained silicon \& Si/SiC heterostructures + {\tiny\color{gray}/Strane~et~al./Guedj~et~al./} \begin{itemize} - \item Coherent SiC precipitates (tensile strain) + \item {\color{blue}Coherent} SiC precipitates (tensile strain) \item Incoherent SiC (strain relaxation) \end{itemize} \end{itemize} +\vspace{0.1cm} +\begin{center} +{\Huge${\lightning}$} \hspace{0.3cm} +{\color{blue}\cs{}} --- vs --- {\color{red}\ci} \hspace{0.3cm} +{\Huge${\lightning}$} +\end{center} +\vspace{0.2cm} \end{minipage} }}} \end{pspicture} \end{slide} +% continue here +\fi + \begin{slide} - {\large\bf - Molecular dynamics (MD) simulations - } +\headphd +{\large\bf + Utilized computational methods +} - \vspace{12pt} + \vspace{0.1cm} \small - {\bf MD basics:} +{\bf Molecular dynamics (MD):}\\ +\scriptsize +\begin{tabular}{l r} +\hline +Basics & Details\\ +\hline +Microscopic description of N particle system & \\ +Analytical interaction potential & Tersoff-like bond order potential (Erhart/Albe) \\ +Numerical integration using Newtons equation of motion as a propagation rule in 6N-dimensional phase space & Velocity Verlet | timestep: \unit[1]{fs} \\ +Observables obtained by time and/or ensemble averages & NpT (isothermal-isobaric)\\ +%\begin{itemize} +%\item Berendsen thermostat: +% $\tau_{\text{T}}=100\text{ fs}$ +%\item Berendsen barostat:\\ +% $\tau_{\text{P}}=100\text{ fs}$, +% $\beta^{-1}=100\text{ GPa}$ +%\end{itemize}\\ +\hline +\end{tabular} + \begin{itemize} \item Microscopic description of N particle system \item Analytical interaction potential @@ -748,6 +1058,9 @@ r = 2 - 4 nm \end{slide} +\end{document} +\ifnum1=0 + \begin{slide} {\large\bf