From 3a603fd2c4a898cb84fce07564a372f93e57935b Mon Sep 17 00:00:00 2001 From: hackbard Date: Wed, 24 May 2006 14:40:36 +0000 Subject: [PATCH 01/16] some updates --- nlsop/poster/nlsop_ibmm2006.tex | 112 ++++++++++++++++++++------------ 1 file changed, 70 insertions(+), 42 deletions(-) diff --git a/nlsop/poster/nlsop_ibmm2006.tex b/nlsop/poster/nlsop_ibmm2006.tex index 324c6b5..2d00cb9 100644 --- a/nlsop/poster/nlsop_ibmm2006.tex +++ b/nlsop/poster/nlsop_ibmm2006.tex @@ -167,25 +167,28 @@ \vspace*{0.2cm} \hfill % first column +%\begin{spalte} +% \begin{kasten} +% \begin{center} +% {\large{\color{blue}\underline{ABSTRACT}}} +% \end{center} +% +% abstract ... skip it +%High-dose ion implantation into solids usually leads to a disordered distribution of defects or precipitates with variable sizes. +%However materials exist for which high-dose ion irradiation at certain conditions results in periodically arranged, self-organized, nanometric amorphous inclusions. +%This has been observed for a number of ion/target combinations \cite{ommen,specht,ishimaru} which all have in common a largely reduced density of host atoms of the amorphous phase compared to the crystalline host lattice. +%A simple model explaining the phenomenon is introduced and realized in a Monte Carlo simulation code, which focuses on high dose carbon implantation into silicon. +%The simulation is able to reproduce the depth distribution observed by TEM and RBS. +%While first versions of the simulation \cite{me1,me2} just covered a limited depth region of the target in which the selforganization is observed, the new version of this simulation code presented here is able to model the whole depth region affected by the irradiation process, as can be seen in chapter 4. +%Based on simulation results a recipe is proposed for producing broad distributions of lamellar, ordered structures which, according to recent studies \cite{wong}, are the starting point for materials with high photoluminescence. +% \end{kasten} +% \begin{spalte} - \begin{kasten} - \begin{center} - {\large{\color{blue}\underline{ABSTRACT}}} - \end{center} -High-dose ion implantation into solids usually leads to a disordered distribution of defects or precipitates with variable sizes. -However materials exist for which high-dose ion irradiation at certain conditions results in periodically arranged, self-organized, nanometric amorphous inclusions. -This has been observed for a number of ion/target combinations \cite{ommen,specht,ishimaru} which all have in common a largely reduced density of host atoms of the amorphous phase compared to the crystalline host lattice. -A simple model explaining the phenomenon is introduced and realized in a Monte Carlo simulation code, which focuses on high dose carbon implantation into silicon. -The simulation is able to reproduce the depth distribution observed by TEM and RBS. -While first versions of the simulation \cite{me1,me2} just covered a limited depth region of the target in which the selforganization is observed, the new version of this simulation code presented here is able to model the whole depth region affected by the irradiation process, as can be seen in chapter 4. -Based on simulation results a recipe is proposed for producing broad distributions of lamellar, ordered structures which, according to recent studies \cite{wong}, are the starting point for materials with high photoluminescence. - \end{kasten} - \begin{kasten} - \section*{1\hspace{0.1cm}{\color{blue}Experimental observations}} + \section*{1 \hspace{0.1cm} {\color{blue}Experimental observations}} - \subsection*{1.1{\color{blue} Amorphous inclusions}} + \subsection*{1.1 {\color{blue} Amorphous inclusions}} \begin{center} \includegraphics[width=11cm]{k393abild1_e.eps} \end{center} @@ -196,7 +199,7 @@ Based on simulation results a recipe is proposed for producing broad distributio black/white: crystalline/amorphous material\\ L: amorphous lamellae, S: spherical amorphous inclusions - \subsection*{1.2{\color{blue} Carbon distribution}} + \subsection*{1.2 {\color{blue} Carbon distribution}} \begin{center} \includegraphics[width=11cm]{eftem.eps} \end{center} @@ -207,11 +210,9 @@ Based on simulation results a recipe is proposed for producing broad distributio yellow/blue: high/low concentrations of carbon \end{kasten} -\end{spalte} -% second column -\begin{spalte} + \begin{kasten} - \section*{2\hspace{0.1cm}{\color{blue}Model}} + \section*{2 \hspace{0.1cm} {\color{blue}Model}} \begin{center} \includegraphics[width=11cm]{modell_ng_e.eps} @@ -231,13 +232,14 @@ Based on simulation results a recipe is proposed for producing broad distributio $\rightarrow$ {\bf strain induced} lateral amorphization \end{itemize} \end{kasten} - +\end{spalte} +\begin{spalte} \begin{kasten} - \section*{3\hspace{0.1cm}{\color{blue}Simulation}} + \section*{3 \hspace{0.1cm} {\color{blue}Simulation}} - \subsection*{3.1{\color{blue} Discretization of the target}} + \subsection*{3.1 {\color{blue} Discretization of the target}} \begin{center} - \includegraphics[width=10cm]{gitter_e.eps} + \includegraphics[width=6cm]{gitter_e.eps} \end{center} \subsection*{3.2 {\color{blue} Simulation algorithm}} @@ -273,11 +275,7 @@ Three contributions to the amorphization process controlled by: \item {\color{blue} $p_c$} carbon induced amorphization \item {\color{red} $p_s$} stress enhanced amorphization \end{itemize} - \end{kasten} -\end{spalte} -% third column -\begin{spalte} - \begin{kasten} + \subsubsection*{3.2.2 Carbon incorporation} \begin{itemize} \item random numbers according to the @@ -287,27 +285,57 @@ Three contributions to the amorphization process controlled by: that volume \end{itemize} \subsubsection*{3.2.3 Diffusion/Sputtering} + \begin{itemize} + \item every $d_v$ steps transfer $d_r$ of the + carbon atoms of crystalline volumina to + an amorphous neighbour volume + \item do the sputter routine after $n$ steps + corresponding to $3 \, nm$ of substrat + removal + \end{itemize} \end{kasten} - +\end{spalte} +\begin{spalte} \begin{kasten} \section*{4 \hspace{0.1cm} {\color{blue}Simulation results}} + + \subsection*{4.1 {\color{blue} Comparison with experiments}} + \begin{center} + \includegraphics[width=11cm]{dosis_entwicklung_ng_e_1-2.eps} + \end{center} + \begin{center} + \includegraphics[width=11cm]{dosis_entwicklung_ng_e_2-2.eps} + \end{center} + + \subsection*{4.1 {\color{blue} Carbon distribution}} \begin{center} - foo + \includegraphics[width=11cm]{ac_cconc_ver2_e.eps} \end{center} + \end{kasten} - bar - \vspace{0.5cm} - foobar \end{spalte} % fourth column -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - \begin{spalte} - \begin{kasten} - \section*{5 \hspace{0.1cm} {\color{red}Fifth Section}} - \begin{center} - \includegraphics[width=10cm]{blank.ps} - \end{center} - \end{kasten} +\begin{spalte} + \begin{kasten} + \section*{5 \hspace{0.1cm} {\color{blue}Broad distribution of + lamellar structure}} + \begin{mbox} + \begin{itemize} + \item $10 \, at.\%$ constant carbon plateau + by multiple implantation steps at + energies between $180$ and $10 \, keV$ + \end{itemize} + \begin{center} + \includegraphics[width=6cm]{multiple_impl_cp.eps} + \end{center} + \begin{itemize} + \item foloowed by $2 \, MeV$ $C^+$ implantation + \end{itemize} + \begin{center} + \includegraphics[width=10cm]{multiple_impl.eps} + \end{center} + + \end{kasten} \vspace{0.5cm} \begin{kasten} -- 2.20.1 From 84140fe8f39d24049edd24b937f607d71b68d2ac Mon Sep 17 00:00:00 2001 From: hackbard Date: Mon, 29 May 2006 15:07:49 +0000 Subject: [PATCH 02/16] some more topics added --- nlsop/poster/nlsop_ibmm2006.tex | 61 +++++++++++++++++---------------- 1 file changed, 32 insertions(+), 29 deletions(-) diff --git a/nlsop/poster/nlsop_ibmm2006.tex b/nlsop/poster/nlsop_ibmm2006.tex index 2d00cb9..0f7e742 100644 --- a/nlsop/poster/nlsop_ibmm2006.tex +++ b/nlsop/poster/nlsop_ibmm2006.tex @@ -307,7 +307,7 @@ Three contributions to the amorphization process controlled by: \includegraphics[width=11cm]{dosis_entwicklung_ng_e_2-2.eps} \end{center} - \subsection*{4.1 {\color{blue} Carbon distribution}} + \subsection*{4.2 {\color{blue} Carbon distribution}} \begin{center} \includegraphics[width=11cm]{ac_cconc_ver2_e.eps} \end{center} @@ -316,10 +316,15 @@ Three contributions to the amorphization process controlled by: \end{spalte} % fourth column \begin{spalte} + \begin{kasten} + \subsection*{4.3 {\color{blue} More structural information}} + \begin{center} + \includegraphics[width=8cm]{97_98_ng_e.eps} + \end{center} + \end{kasten} \begin{kasten} \section*{5 \hspace{0.1cm} {\color{blue}Broad distribution of lamellar structure}} - \begin{mbox} \begin{itemize} \item $10 \, at.\%$ constant carbon plateau by multiple implantation steps at @@ -341,45 +346,43 @@ Three contributions to the amorphization process controlled by: \begin{kasten} \section*{6 \hspace{0.1cm} {\color{red} \underline{Conclusions}}} \begin{itemize} - \item - - \item + \item 1 - \item + \item 2 - \item + \item 3 + \item 4 + \end{itemize} \end{kasten} \vspace{0.5cm} - \begin{kasten} - - {\small - \begin{thebibliography}{9} - \bibitem{ommen} A. H. van Ommen, - Nucl. Instr. and Meth. B 39 (1989) 194. - \bibitem{specht} E. D. Specht, D. A. Walko, S. J. Zinkle, - Nucl. Instr. and Meth. B 84 (2000) 390. - \bibitem{ishimaru} M. Ishimaru, R. M. Dickerson, K. E. Sickafus, - Nucl. Instr. and Meth. B 166-167 (2000) 390. + \begin{kasten} + {\small + \begin{thebibliography}{9} + \bibitem{ommen} A. H. van Ommen, + Nucl. Instr. and Meth. B 39 (1989) 194. + \bibitem{specht} E. D. Specht, D. A. Walko, S. J. Zinkle, + Nucl. Instr. and Meth. B 84 (2000) 390. + \bibitem{ishimaru} M. Ishimaru, R. M. Dickerson, K. E. Sickafus, + Nucl. Instr. and Meth. B 166-167 (2000) 390. \bibitem{me1} F. Zirkelbach, M. H"aberlen, J. K. N. Lindner, B. Stritzker, Comp. Mater. Sci. 33 (2005) 310. \bibitem{me2} F. Zirkelbach, M. H"aberlen, J. K. N. Lindner, B. Stritzker, Nucl. Instr. and Meth. B 242 (2006) 679. - \bibitem{wong} Dihu Chen, Z. M. Liao, L. Wang, H. Z. Wang, Fuli Zhao, - W. Y. Cheung, S. P. Wong, - Opt. Mater. 23 (2003) 65. Opt. Mater. 23 (2003) 65. - \end{thebibliography} - } - \end{kasten} - \end{spalte} - } - \end{lrbox} + \bibitem{wong} Dihu Chen, Z. M. Liao, L. Wang, H. Z. Wang, Fuli Zhao, + W. Y. Cheung, S. P. Wong, + Opt. Mater. 23 (2003) 65. Opt. Mater. 23 (2003) 65. + \end{thebibliography} + } + \end{kasten} +\end{spalte} +} +\end{lrbox} \resizebox*{0.98\textwidth}{!}{% - \usebox{\spalten}}\hfill\mbox{}\vfill -\end{document} - +\usebox{\spalten}}\hfill\mbox{}\vfill +\end{document} -- 2.20.1 From 34b57344dd865030cdc34c2594f60c72a46af7e3 Mon Sep 17 00:00:00 2001 From: hackbard Date: Tue, 30 May 2006 09:24:14 +0000 Subject: [PATCH 03/16] more updates --- nlsop/poster/nlsop_ibmm2006.tex | 104 +++++++++++--------------------- 1 file changed, 34 insertions(+), 70 deletions(-) diff --git a/nlsop/poster/nlsop_ibmm2006.tex b/nlsop/poster/nlsop_ibmm2006.tex index 0f7e742..43271f5 100644 --- a/nlsop/poster/nlsop_ibmm2006.tex +++ b/nlsop/poster/nlsop_ibmm2006.tex @@ -157,32 +157,16 @@ } \hfill }} -\hfill\mbox{}\\[1.cm] +\hfill\mbox{}\\[0.5cm] %\vspace*{1.3cm} % content, let's rock the columns \begin{lrbox}{\spalten} \parbox[t][\textheight]{1.3\textwidth}{% - \vspace*{0.2cm} + %\vspace*{0.2cm} \hfill % first column -%\begin{spalte} -% \begin{kasten} -% \begin{center} -% {\large{\color{blue}\underline{ABSTRACT}}} -% \end{center} -% -% abstract ... skip it -%High-dose ion implantation into solids usually leads to a disordered distribution of defects or precipitates with variable sizes. -%However materials exist for which high-dose ion irradiation at certain conditions results in periodically arranged, self-organized, nanometric amorphous inclusions. -%This has been observed for a number of ion/target combinations \cite{ommen,specht,ishimaru} which all have in common a largely reduced density of host atoms of the amorphous phase compared to the crystalline host lattice. -%A simple model explaining the phenomenon is introduced and realized in a Monte Carlo simulation code, which focuses on high dose carbon implantation into silicon. -%The simulation is able to reproduce the depth distribution observed by TEM and RBS. -%While first versions of the simulation \cite{me1,me2} just covered a limited depth region of the target in which the selforganization is observed, the new version of this simulation code presented here is able to model the whole depth region affected by the irradiation process, as can be seen in chapter 4. -%Based on simulation results a recipe is proposed for producing broad distributions of lamellar, ordered structures which, according to recent studies \cite{wong}, are the starting point for materials with high photoluminescence. -% \end{kasten} -% \begin{spalte} \begin{kasten} @@ -306,7 +290,8 @@ Three contributions to the amorphization process controlled by: \begin{center} \includegraphics[width=11cm]{dosis_entwicklung_ng_e_2-2.eps} \end{center} - + \end{kasten} + \begin{kasten} \subsection*{4.2 {\color{blue} Carbon distribution}} \begin{center} \includegraphics[width=11cm]{ac_cconc_ver2_e.eps} @@ -317,67 +302,46 @@ Three contributions to the amorphization process controlled by: % fourth column \begin{spalte} \begin{kasten} - \subsection*{4.3 {\color{blue} More structural information}} + \subsection*{4.3 {\color{blue} More structural/compositional + information}} \begin{center} - \includegraphics[width=8cm]{97_98_ng_e.eps} - \end{center} + \includegraphics[width=8cm]{97_98_ng_e.eps} \\ + Plane view of consecutive target layers $z$ and $z+1$ + \end{center} \end{kasten} \begin{kasten} - \section*{5 \hspace{0.1cm} {\color{blue}Broad distribution of - lamellar structure}} - \begin{itemize} - \item $10 \, at.\%$ constant carbon plateau - by multiple implantation steps at - energies between $180$ and $10 \, keV$ - \end{itemize} - \begin{center} - \includegraphics[width=6cm]{multiple_impl_cp.eps} - \end{center} + \subsection*{4.4 \hspace{0.1cm} {\color{blue} Broad distribution + of lamellar structure - the recipe}} + \subsubsection*{4.4.1 Constant carbon concentration} + \makebox[11cm]{% + \parbox[c]{6cm}{% + \includegraphics[width=6cm]{multiple_impl_cp_e.eps} + } + \parbox[c]{5cm}{% \begin{itemize} - \item foloowed by $2 \, MeV$ $C^+$ implantation + \item multiple implantation \\ steps + \item energies: $180$ - $10 \, keV$ \end{itemize} + $\Rightarrow$ nearly constant carbon distribution + ($10 \, at.\%$) + } + } + \subsubsection*{4.4.2 2 MeV C$^+$ implantation + step} \begin{center} - \includegraphics[width=10cm]{multiple_impl.eps} + \includegraphics[width=10cm]{multiple_impl_e.eps} \end{center} \end{kasten} - -\vspace{0.5cm} - \begin{kasten} - \section*{6 \hspace{0.1cm} {\color{red} \underline{Conclusions}}} - \begin{itemize} - \item 1 - - \item 2 - - \item 3 - - \item 4 - - \end{itemize} - \end{kasten} - -\vspace{0.5cm} \begin{kasten} - {\small - \begin{thebibliography}{9} - \bibitem{ommen} A. H. van Ommen, - Nucl. Instr. and Meth. B 39 (1989) 194. - \bibitem{specht} E. D. Specht, D. A. Walko, S. J. Zinkle, - Nucl. Instr. and Meth. B 84 (2000) 390. - \bibitem{ishimaru} M. Ishimaru, R. M. Dickerson, K. E. Sickafus, - Nucl. Instr. and Meth. B 166-167 (2000) 390. - \bibitem{me1} F. Zirkelbach, M. H"aberlen, J. K. N. Lindner, - B. Stritzker, - Comp. Mater. Sci. 33 (2005) 310. - \bibitem{me2} F. Zirkelbach, M. H"aberlen, J. K. N. Lindner, - B. Stritzker, - Nucl. Instr. and Meth. B 242 (2006) 679. - \bibitem{wong} Dihu Chen, Z. M. Liao, L. Wang, H. Z. Wang, Fuli Zhao, - W. Y. Cheung, S. P. Wong, - Opt. Mater. 23 (2003) 65. Opt. Mater. 23 (2003) 65. - \end{thebibliography} - } + \section*{5 \hspace{0.1cm} {\color{red} Conclusions}} + \begin{itemize} + \item selforganized nanometric precipitates by ion irradiation + \item model describing the seoforganization process + \item precipitate structures traceable by simulation + \item detailed structural/compositional information + \item recipe for broad distributions of lamellar structure + \end{itemize} \end{kasten} \end{spalte} } -- 2.20.1 From e553758eb8476a4736350af494a7bb235b9bcd81 Mon Sep 17 00:00:00 2001 From: hackbard Date: Wed, 31 May 2006 10:16:27 +0000 Subject: [PATCH 04/16] firs very beta version --- nlsop/poster/nlsop_ibmm2006.tex | 16 +++++++++++++--- 1 file changed, 13 insertions(+), 3 deletions(-) diff --git a/nlsop/poster/nlsop_ibmm2006.tex b/nlsop/poster/nlsop_ibmm2006.tex index 43271f5..285a42c 100644 --- a/nlsop/poster/nlsop_ibmm2006.tex +++ b/nlsop/poster/nlsop_ibmm2006.tex @@ -277,6 +277,14 @@ Three contributions to the amorphization process controlled by: corresponding to $3 \, nm$ of substrat removal \end{itemize} + + \subsection*{3.3 {\color{blue} TRIM collision statistics}} + \begin{center} + \includegraphics[width=8cm]{trim_coll_e.eps} + \end{center} + \begin{center} + $\Rightarrow$ mean constant energy loss per collision of an ion + \end{center} \end{kasten} \end{spalte} \begin{spalte} @@ -314,17 +322,19 @@ Three contributions to the amorphization process controlled by: of lamellar structure - the recipe}} \subsubsection*{4.4.1 Constant carbon concentration} \makebox[11cm]{% - \parbox[c]{6cm}{% - \includegraphics[width=6cm]{multiple_impl_cp_e.eps} - } \parbox[c]{5cm}{% \begin{itemize} \item multiple implantation \\ steps \item energies: $180$ - $10 \, keV$ + \item higher temeprature\\ + $\rightarrow$ prevent amorphization \end{itemize} $\Rightarrow$ nearly constant carbon distribution ($10 \, at.\%$) } + \parbox[c]{6cm}{% + \includegraphics[width=6cm]{multiple_impl_cp_e.eps} + } } \subsubsection*{4.4.2 2 MeV C$^+$ implantation step} -- 2.20.1 From e86993833978bf71f38e6ca163e3e513e6c27b59 Mon Sep 17 00:00:00 2001 From: hackbard Date: Wed, 14 Jun 2006 15:47:51 +0000 Subject: [PATCH 05/16] - --- posic/thesis/basics.tex | 26 ++++++++++++++++++++++++-- posic/thesis/content.tex | 1 + posic/thesis/literature.tex | 6 ++++++ posic/thesis/title.tex | 1 - 4 files changed, 31 insertions(+), 3 deletions(-) diff --git a/posic/thesis/basics.tex b/posic/thesis/basics.tex index bc9e8a9..c11a832 100644 --- a/posic/thesis/basics.tex +++ b/posic/thesis/basics.tex @@ -2,8 +2,30 @@ \section{Molecular dynamics simulations} +\subsection{Theory of melecular dynamics simulations} -\subsection{Potentials} +Basically molecular dynamics (MD) simulation is a technique to compute a system of particles, referred to as molecules, that evolve in time. +The MD method was introduced by Alder and Wainwright in 1957 \cite{alder1,alder2} to study the interactions of hard spheres. +The basis of the approach are Newton's equations of motion to describe classicaly the many-body system. +MD simulation is the numerical way of solving the $N$-body problem ($N > 3$) which cannot be solved analytically. +Quantum mechanical effects are taken into account by an analytical interaction potential between the nuclei. + +By MD simulation techniques a complete description of the system in the sense of classical mechanics on the microscopic level is obtained. +This microscopic information has to be translated to macroscopic observables by means of statistical mechanics. + +The basic idea is to integrate Newton's equations numerically. +A system of $N$ particles of masses $m_i$ ($i=1,\ldots,N$) at positions ${\bf r}_i$ and velocities $\dot{{\bf r}}_i$ is given by +\begin{equation} +m_i \frac{d^2}{dt^2} {\bf r}_i = {\bf F}_i \, \textrm{.} +\end{equation} +The forces ${\bf F}_i$ are obtained from the potential energy $U(\{{\bf r}\})$: +\begin{equation} +{\bf F}_i = - \nabla_{{\bf r}_i} U({\{\bf r}\}) \, \textrm{.} +\end{equation} +Given the initial conditions ${\bf r}_i(t_0)$ and $\dot{{\bf r}}_i(t_0)$ the equations can be integrated by a certain integration algorithm. +The solution of these equations provides the complete information of a system + +\subsection{Interaction potentials} \subsubsection{The Lennard-Jones potential} @@ -30,7 +52,7 @@ Writing down the derivation of the Lennard-Jones potential in respect to $x_i$ ( \label{eq:lj-d} \end{equation} one can easily identify $\sigma$ by the equilibrium distance of the atoms $r_e=\sqrt[6]{2} \sigma$. -Applying the equilibrium distance into \eqref{eq:lj-p} $\epsilon$ turns out to be half the negative well depth. +Applying the equilibrium distance into \eqref{eq:lj-p} $\epsilon$ turns out to be the negative well depth. The $i$th component of the force $F^j$ on particle $j$ is obtained by \begin{equation} F_i^j = - \frac{\partial}{\partial x_i} U^{LJ}(r) \, \textrm{.} diff --git a/posic/thesis/content.tex b/posic/thesis/content.tex index c886626..90d5122 100644 --- a/posic/thesis/content.tex +++ b/posic/thesis/content.tex @@ -1,2 +1,3 @@ +\selectlanguage{english} \addcontentsline{toc}{chapter}{Contents} \tableofcontents diff --git a/posic/thesis/literature.tex b/posic/thesis/literature.tex index e2f4f38..d860d2f 100644 --- a/posic/thesis/literature.tex +++ b/posic/thesis/literature.tex @@ -1,5 +1,11 @@ \addcontentsline{toc}{chapter}{References} \begin{thebibliography}{99} + \bibitem{alder1} + B. J. Alder, T.E. Wainwright. + J. Chem. Phys. 27 (1957) 1208. + \bibitem{alder2} + B. J. Alder, T.E. Wainwright. + J. Chem. Phys. 31 (1959) 459. \bibitem{example} \selectlanguage{german} F. Zirkelbach, M. H"aberlen, J. K. N. Lindner, B. Stritzker. diff --git a/posic/thesis/title.tex b/posic/thesis/title.tex index 341e50c..e4625a7 100644 --- a/posic/thesis/title.tex +++ b/posic/thesis/title.tex @@ -53,7 +53,6 @@ \raisebox{600pt}{ } -\selectlanguage{german} \begin{tabular}{ll} Erstkorrektor: & Prof. Dr. Bernd Stritzker \\ Zweitkorrektor: & Prof. Dr. Kai Nordlund \\ -- 2.20.1 From 4774842a09e4f15ab187088ffce234f44a7a11c4 Mon Sep 17 00:00:00 2001 From: hackbard Date: Tue, 20 Jun 2006 13:39:40 +0000 Subject: [PATCH 06/16] jetzt gehts los ... --- posic/thesis/basics.tex | 14 +++++++++++--- 1 file changed, 11 insertions(+), 3 deletions(-) diff --git a/posic/thesis/basics.tex b/posic/thesis/basics.tex index c11a832..24bfc19 100644 --- a/posic/thesis/basics.tex +++ b/posic/thesis/basics.tex @@ -2,9 +2,9 @@ \section{Molecular dynamics simulations} -\subsection{Theory of melecular dynamics simulations} +\subsection{Introduction to molecular dynamics simulations} -Basically molecular dynamics (MD) simulation is a technique to compute a system of particles, referred to as molecules, that evolve in time. +Basically, molecular dynamics (MD) simulation is a technique to compute a system of particles, referred to as molecules, evolving in time. The MD method was introduced by Alder and Wainwright in 1957 \cite{alder1,alder2} to study the interactions of hard spheres. The basis of the approach are Newton's equations of motion to describe classicaly the many-body system. MD simulation is the numerical way of solving the $N$-body problem ($N > 3$) which cannot be solved analytically. @@ -23,7 +23,15 @@ The forces ${\bf F}_i$ are obtained from the potential energy $U(\{{\bf r}\})$: {\bf F}_i = - \nabla_{{\bf r}_i} U({\{\bf r}\}) \, \textrm{.} \end{equation} Given the initial conditions ${\bf r}_i(t_0)$ and $\dot{{\bf r}}_i(t_0)$ the equations can be integrated by a certain integration algorithm. -The solution of these equations provides the complete information of a system +The solution of these equations provides the complete information of a system evolving in time. + +The following chapters cover the tools of the trade necessary for the MD simulation technique. +First a detailed overview of the available integration algorithms is given, including their advantages and disadvantages. +After that the interaction potentials and their accuracy for describing certain systems of elements are discussed. + + + +\subsection{Integration algorithms} \subsection{Interaction potentials} -- 2.20.1 From cbacb767e889a7a8d7196b37286b9eeec2eb802c Mon Sep 17 00:00:00 2001 From: hackbard Date: Wed, 21 Jun 2006 15:47:11 +0000 Subject: [PATCH 07/16] . --- posic/thesis/basics.tex | 15 +++++++++++++-- 1 file changed, 13 insertions(+), 2 deletions(-) diff --git a/posic/thesis/basics.tex b/posic/thesis/basics.tex index 24bfc19..2eda8a2 100644 --- a/posic/thesis/basics.tex +++ b/posic/thesis/basics.tex @@ -28,13 +28,24 @@ The solution of these equations provides the complete information of a system ev The following chapters cover the tools of the trade necessary for the MD simulation technique. First a detailed overview of the available integration algorithms is given, including their advantages and disadvantages. After that the interaction potentials and their accuracy for describing certain systems of elements are discussed. - - +In addition special techniques will be outlined which reduce the complexity of the MD algorithm, though the force/energy evaluation almost inevitably dictates the overall speed. \subsection{Integration algorithms} + \subsection{Interaction potentials} +The potential energy of $N$ interacting atoms can be written in the form +\begin{equation} +U(\{{\bf r}\}) = \sum_i U_1({\bf r}_i) + \sum_i \sum_{j>i} U_2({\bf r}_i,{\bf r}_j) + \sum_i \sum_{j>i} \sum_{k>j>i} U_3({\bf r}_i,{\bf r}_j,{\bf r}_k) \ldots +\end{equation} +where $U$ is the total potential energy. +$U_1$ is a single particle potential describing external forces. +This could for instance be the gravitational force or an electric field. +$U_2$ is a two body pair potential which only depends on the distance $r_{ij}$ between the two atoms $i$ and $j$. + +$U_3$ is a three body potential which may have an additional angular dependence describing covalent bonds, plus higher order terms which are expected to be small and thus neglected. + \subsubsection{The Lennard-Jones potential} The L-J potential is a realistic two body pair potential and is of the form -- 2.20.1 From 19c81fd5d9039d184c432861bdb995503d1959c1 Mon Sep 17 00:00:00 2001 From: hackbard Date: Wed, 5 Jul 2006 14:48:34 +0000 Subject: [PATCH 08/16] foo --- posic/thesis/basics.tex | 53 ++++++++++++++++++++++++++++++------- posic/thesis/literature.tex | 5 ++++ 2 files changed, 49 insertions(+), 9 deletions(-) diff --git a/posic/thesis/basics.tex b/posic/thesis/basics.tex index 2eda8a2..c25e858 100644 --- a/posic/thesis/basics.tex +++ b/posic/thesis/basics.tex @@ -1,13 +1,25 @@ \chapter{Basics} +\begin{quotation} +\dq We may regard the present state of the universe as the effect of the past and the cause of the future. An intellect which at any given moment knew all of the forces that animate nature and the mutual positions of the beings that compose it, if this intellect were vast enough to submit the data to analysis, could condense into a single formula the movement of the greatest bodies of the universe and that of the lightest atom; for such an intellect nothing could be uncertain and the future just like the past would be present before its eyes.\dq{} +\cite{laplace} +\begin{flushright} +{\em Marquis Pierre Simon de Laplace, 1814.} +\end{flushright} +\end{quotation} + \section{Molecular dynamics simulations} +Pierre Simon de Laplace phrased this vision in terms of a controlling, omniscient instance - the {\em Laplace demon} - which would be able to look into the future as well as into the past due to the deterministic nature of processes, governed by the solution of differential equations. +Although Laplace's vision is nowadays corrected by chaos theory and quantum mechanics, it expresses two main features of classical mechanics, the determinism of processes and time reversibility of the fundamental equations. +This understanding was one of the first ideas for doing molecular dynamics simulations, considering an isolated system of particles, the behaviour of which is fully determined by the solution of the classical equations of motion. + \subsection{Introduction to molecular dynamics simulations} -Basically, molecular dynamics (MD) simulation is a technique to compute a system of particles, referred to as molecules, evolving in time. -The MD method was introduced by Alder and Wainwright in 1957 \cite{alder1,alder2} to study the interactions of hard spheres. +Basically, molecular dynamics (MD) simulation is a technique to compute a system of particles, referred to as molecules, with their positions, volocities and forces among each other evolving in time. +The MD method was first introduced by Alder and Wainwright in 1957 \cite{alder1,alder2} to study the interactions of hard spheres. The basis of the approach are Newton's equations of motion to describe classicaly the many-body system. -MD simulation is the numerical way of solving the $N$-body problem ($N > 3$) which cannot be solved analytically. +MD simulation is the numerical way of solving the $N$-body problem which cannot be solved analytically ($N>3$). Quantum mechanical effects are taken into account by an analytical interaction potential between the nuclei. By MD simulation techniques a complete description of the system in the sense of classical mechanics on the microscopic level is obtained. @@ -26,14 +38,23 @@ Given the initial conditions ${\bf r}_i(t_0)$ and $\dot{{\bf r}}_i(t_0)$ the equ The solution of these equations provides the complete information of a system evolving in time. The following chapters cover the tools of the trade necessary for the MD simulation technique. -First a detailed overview of the available integration algorithms is given, including their advantages and disadvantages. -After that the interaction potentials and their accuracy for describing certain systems of elements are discussed. +Three ingredients are required for an MD simulation: +\begin{enumerate} +\item A model for the interaction between system constituents is needed. + Interaction potentials and their accuracy for describing certain systems of elements will be outlined in chapter \ref{subsection:interact_pot}. +\item An integrator is needed, which propagtes the particle positions and velocities from time $t$ to $t+\delta t$, realised by a finite difference scheme which moves trajectories discretely in time. + In chapter \ref{subsection:integrate_algo} a detailed overview of the available integration algorithms is given, including their advantages and disadvantages. +\item A statistical ensemble has to be chosen, which allows certain thermodynamic quantities to be controlled or to stay constant. + This is discussed in chapter \ref{subsection:statistical_ensembles} +\end{enumerate} + In addition special techniques will be outlined which reduce the complexity of the MD algorithm, though the force/energy evaluation almost inevitably dictates the overall speed. \subsection{Integration algorithms} - +\label{subsection:integrate_algo} \subsection{Interaction potentials} +\label{subsection:interact_pot} The potential energy of $N$ interacting atoms can be written in the form \begin{equation} @@ -41,10 +62,17 @@ U(\{{\bf r}\}) = \sum_i U_1({\bf r}_i) + \sum_i \sum_{j>i} U_2({\bf r}_i,{\bf r} \end{equation} where $U$ is the total potential energy. $U_1$ is a single particle potential describing external forces. -This could for instance be the gravitational force or an electric field. +Examples of single particle potentials are the gravitational force or an electric field. $U_2$ is a two body pair potential which only depends on the distance $r_{ij}$ between the two atoms $i$ and $j$. +If not only pair potentials are considered, three body potentials $U_3$ or multi body potentials $U_n$ can be included. +Mainly these higher order terms are avoided since they are not easy to model and it is rather time consuming to evaluate potentials and forces originating from these many body terms. -$U_3$ is a three body potential which may have an additional angular dependence describing covalent bonds, plus higher order terms which are expected to be small and thus neglected. +Ordinary pair potentials have a close-packed structure like face-centered cubic (FCC) or hexagonal close-packed (HCP) as a ground state. +A pair potential is thus unable to describe properly elements with other structures than FCC or HCP. +Silicon and carbon for instance, have a diamand/zincblende structure with four covalent bonded neighbours, which is far from a close-packed structure. +A three body potential has to be included for these types of elements. + +In the following, relevant potentials for this work are discussed. \subsubsection{The Lennard-Jones potential} @@ -53,7 +81,7 @@ The L-J potential is a realistic two body pair potential and is of the form U^{LJ}(r) = 4 \epsilon \Big[ \Big( \frac{\sigma}{r} \Big)^{12} - \Big( \frac{\sigma}{r} \Big)^6 \Big] \, \textrm{,} \label{eq:lj-p} \end{equation} -where $r$ denotes the disatnce between the two atoms. +where $r$ denotes the distance between the two atoms. The attractive tail for large separations $(\sim r^{-6})$ is essentially due to correlations between electron clouds surrounding the atoms. The attractive part is also known as {\em van der Waals} or {\em London} interaction. It can be derived classically by considering how two charged spheres induce dipol-dipol interactions into each other, or by considering the interaction between two oscillators in a quantum mechanical way. @@ -78,3 +106,10 @@ F_i^j = - \frac{\partial}{\partial x_i} U^{LJ}(r) \, \textrm{.} \label{eq:lj-f} \end{equation} +\subsubsection{The Stillinger Weber potential} +\subsubsection{The Stillinger Weber potential} +\subsubsection{The Stillinger Weber potential} + +\subsection{Statistical ensembles} +\label{subsection:statistical_ensembles} + diff --git a/posic/thesis/literature.tex b/posic/thesis/literature.tex index d860d2f..e478cad 100644 --- a/posic/thesis/literature.tex +++ b/posic/thesis/literature.tex @@ -1,5 +1,10 @@ \addcontentsline{toc}{chapter}{References} \begin{thebibliography}{99} + \bibitem{laplace} + P. S. de Laplace. + Th\'eorie analytique des probabilit\'es. + Oeuvres Compl\`etes de Laplace, volume VII. + Paris, 1820, Gauthier-Villars. \bibitem{alder1} B. J. Alder, T.E. Wainwright. J. Chem. Phys. 27 (1957) 1208. -- 2.20.1 From 9761bf24f47daee3d2c82f870321bddbab0e32f4 Mon Sep 17 00:00:00 2001 From: hackbard Date: Tue, 11 Jul 2006 15:48:49 +0000 Subject: [PATCH 09/16] more theory --- posic/thesis/basics.tex | 62 +++++++++++++++++++++++++++++++++++-- posic/thesis/literature.tex | 11 +++++-- 2 files changed, 68 insertions(+), 5 deletions(-) diff --git a/posic/thesis/basics.tex b/posic/thesis/basics.tex index c25e858..8cf717b 100644 --- a/posic/thesis/basics.tex +++ b/posic/thesis/basics.tex @@ -34,6 +34,7 @@ The forces ${\bf F}_i$ are obtained from the potential energy $U(\{{\bf r}\})$: \begin{equation} {\bf F}_i = - \nabla_{{\bf r}_i} U({\{\bf r}\}) \, \textrm{.} \end{equation} + Given the initial conditions ${\bf r}_i(t_0)$ and $\dot{{\bf r}}_i(t_0)$ the equations can be integrated by a certain integration algorithm. The solution of these equations provides the complete information of a system evolving in time. @@ -107,8 +108,65 @@ F_i^j = - \frac{\partial}{\partial x_i} U^{LJ}(r) \, \textrm{.} \end{equation} \subsubsection{The Stillinger Weber potential} -\subsubsection{The Stillinger Weber potential} -\subsubsection{The Stillinger Weber potential} + +The Stillinger Weber potential \cite{stillinger_weber} \ldots + +\begin{equation} +U = \sum_{i,j} U_2({\bf r}_i,{\bf r}_j) + \sum_{i,j,k} U_3({\bf r}_i,{\bf r}_j,{\bf r}_k) +\end{equation} + +\begin{equation} +U_2(r_{ij}) = \left\{ + \begin{array}{ll} + \epsilon A \Big( B (r_{ij} / \sigma)^{-p} - 1\Big) \exp \Big[ (r_{ij} / \sigma - 1)^{-1} \Big] & r_{ij} < a \sigma \\ + 0 & r_{ij} \ge a \sigma + \end{array} \right. +\end{equation} + +\begin{equation} +U_3({\bf r}_i,{\bf r}_j,{\bf r}_k) = +\epsilon \Big[ h(r_{ij},r_{ik},\theta_{jik}) + h(r_{ji},r_{jk},\theta_{ijk}) + h(r_{ki},r_{kj},\theta_{ikj}) \Big] +\end{equation} + +\begin{equation} +h(r_{ij},r_{ik},\theta_{jik}) = +\lambda \exp \Big[ \gamma (r_{ij}/\sigma -a)^{-1} + \gamma (r_{ik}/\sigma - a)^{-1} \Big] \Big( \cos \theta_{jik} + \frac{1}{3} \Big)^2 +\end{equation} + +\subsubsection{The Tersoff potential} + +Ther Tersoff potential \cite{tersoff1} \ldots + +\begin{equation} +V_{ij} = f_C(r_{ij}) [ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) ] +\end{equation} + +The total energy is then given by +\begin{equation} +E = \frac{1}{2} \sum_{i \ne j} V_{ij} \, \textrm{.} +\end{equation} + + +\begin{equation} +f_R(r_{ij}) = A_{ij} \exp (- \lambda_{ij} r_{ij} ) \\ +\end{equation} + +\begin{equation} +f_A(r_{ij}) = -B_{ij} \exp (- \mu_{ij} r_{ij} ) \\ +\end{equation} + +The function $f_C$ is the potential cutoff function designed to have a smooth transition between $R_{ij}$ and $S_{ij}$. +\begin{equation} +f_C(r_{ij}) = \left\{ + \begin{array}{ll} + 1 & r_{ij} < R_{ij} \\ + \frac{1}{2} + \frac{1}{2} \cos [ \pi (r_{ij} - R_{ij})/(S_{ij} - R_{ij}) ] & R_{ij} < r_{ij} < S_{ij} \\ + 0 & r_{ij} > S_{ij} + \end{array} \right. +\end{equation} + + +\subsubsection{The Brenner potential} \subsection{Statistical ensembles} \label{subsection:statistical_ensembles} diff --git a/posic/thesis/literature.tex b/posic/thesis/literature.tex index e478cad..002da01 100644 --- a/posic/thesis/literature.tex +++ b/posic/thesis/literature.tex @@ -6,15 +6,20 @@ Oeuvres Compl\`etes de Laplace, volume VII. Paris, 1820, Gauthier-Villars. \bibitem{alder1} - B. J. Alder, T.E. Wainwright. + B. J. Alder, T. E. Wainwright. J. Chem. Phys. 27 (1957) 1208. \bibitem{alder2} - B. J. Alder, T.E. Wainwright. + B. J. Alder, T. E. Wainwright. J. Chem. Phys. 31 (1959) 459. + \bibitem{stillinger_weber} + F. H. Stillinger, T. A. Weber. + Phys. Rev. B 31 (1985) 5262. + \bibitem{tersoff1} + J. Tersoff. + Phys. Rev. B 39 (1989) 5566. \bibitem{example} \selectlanguage{german} F. Zirkelbach, M. H"aberlen, J. K. N. Lindner, B. Stritzker. \selectlanguage{english} - {\em Modelling of a selforganization process leading to periodic arrays of nanometric amorphous precipitates by ion irradiation.} Comp. Mater. Sci. 33 (2005) 310. \end{thebibliography} -- 2.20.1 From 71d8ad22f7c8fd77cc86c966aa209d5cd4c14ac0 Mon Sep 17 00:00:00 2001 From: hackbard Date: Wed, 12 Jul 2006 16:18:34 +0000 Subject: [PATCH 10/16] more theory --- posic/thesis/basics.tex | 9 ++++++++- posic/thesis/literature.tex | 14 +++++++++++++- 2 files changed, 21 insertions(+), 2 deletions(-) diff --git a/posic/thesis/basics.tex b/posic/thesis/basics.tex index 8cf717b..1dbe1c0 100644 --- a/posic/thesis/basics.tex +++ b/posic/thesis/basics.tex @@ -135,7 +135,14 @@ h(r_{ij},r_{ik},\theta_{jik}) = \subsubsection{The Tersoff potential} -Ther Tersoff potential \cite{tersoff1} \ldots +Tersoff proposed an empirical interatomic potential for covalent systems. +The Tersoff potential explicitly incorporates the dependence of bond order on local envirenments, permitting an improved description of covalent materials. +Tersoff applied the potential to silicon \cite{tersoff_silicon1,tersoff_silicon2,tersoff_silicon3}, carbon \cite{tersoff_carbon} and also to multicomponent systems like $SiC$ \cite{tersoff_multi}. + +The basic idea is that, in real systems, the bond order depends upon the local environment. +An atom with many neighbours forms weaker bonds than an atom with few neighbours. + + \begin{equation} V_{ij} = f_C(r_{ij}) [ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) ] diff --git a/posic/thesis/literature.tex b/posic/thesis/literature.tex index 002da01..454bacb 100644 --- a/posic/thesis/literature.tex +++ b/posic/thesis/literature.tex @@ -14,7 +14,19 @@ \bibitem{stillinger_weber} F. H. Stillinger, T. A. Weber. Phys. Rev. B 31 (1985) 5262. - \bibitem{tersoff1} + \bibitem{tersoff_silicon1} + J. Tersoff. + Phys. Rev. Lett. 56 (1986) 632. + \bibitem{tersoff_silicon2} + J. Tersoff. + Phys. Rev. B 37 (1988) 6991. + \bibitem{tersoff_silicon3} + J. Tersoff. + Phys. Rev. B 38 (1988) 9902. + \bibitem{tersoff_carbon} + J. Tersoff. + Phys. Rev. Lett. 61 (1988) 2879. + \bibitem{tersoff_multi} J. Tersoff. Phys. Rev. B 39 (1989) 5566. \bibitem{example} -- 2.20.1 From e393fcd35c73e77fe4eb44139320fd78ad24c6c8 Mon Sep 17 00:00:00 2001 From: hackbard Date: Tue, 18 Jul 2006 15:36:39 +0000 Subject: [PATCH 11/16] more tersoff --- posic/thesis/basics.tex | 73 +++++++++++++++++++++++++++-------------- 1 file changed, 48 insertions(+), 25 deletions(-) diff --git a/posic/thesis/basics.tex b/posic/thesis/basics.tex index 1dbe1c0..e2958ae 100644 --- a/posic/thesis/basics.tex +++ b/posic/thesis/basics.tex @@ -94,7 +94,7 @@ Chosing $12$ as the exponent of the repulsive term it is just the square of the The constants $\epsilon$ and $\sigma$ are usually determined by fitting to experimental data. $\epsilon$ accounts to the depth of the potential well, where $\sigma$ is regarded as the radius of the particle, also known as the van der Waals radius. -Writing down the derivation of the Lennard-Jones potential in respect to $x_i$ (the $i$th component of the distance vector $\vec{r}$) +Writing down the derivation of the Lennard-Jones potential in respect to $x_i$ (the $i$th component of the distance vector ${\bf r}$) \begin{equation} \frac{\partial}{\partial x_i} U^{LJ}(r) = 4 \epsilon x_i \Big( -12 \frac{\sigma^{12}}{r^{14}} + 6 \frac{\sigma^6}{r^8} \Big) \label{eq:lj-d} @@ -138,39 +138,62 @@ h(r_{ij},r_{ik},\theta_{jik}) = Tersoff proposed an empirical interatomic potential for covalent systems. The Tersoff potential explicitly incorporates the dependence of bond order on local envirenments, permitting an improved description of covalent materials. Tersoff applied the potential to silicon \cite{tersoff_silicon1,tersoff_silicon2,tersoff_silicon3}, carbon \cite{tersoff_carbon} and also to multicomponent systems like $SiC$ \cite{tersoff_multi}. - The basic idea is that, in real systems, the bond order depends upon the local environment. An atom with many neighbours forms weaker bonds than an atom with few neighbours. - - -\begin{equation} -V_{ij} = f_C(r_{ij}) [ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) ] -\end{equation} - -The total energy is then given by -\begin{equation} -E = \frac{1}{2} \sum_{i \ne j} V_{ij} \, \textrm{.} -\end{equation} - - +The interatomic potential is taken to have the form +\begin{eqnarray} +E & = & \sum_i E_i = \frac{1}{2} \sum_{i \ne j} V_{ij} \textrm{ ,} \\ +V_{ij} & = & f_C(r_{ij}) [ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) ] \textrm{ .} +\end{eqnarray} +$E$ is the total energy of the system, constituted either by the sum over the site energies $E_i$ or by the bond energies $V_{ij}$. +The indices $i$ and $j$ correspond to the atoms of the system with $r_{ij}$ being the distance from atom $i$ to atom $j$. + +The functions $f_R$ and $f_A$ represent a repulsive and an attractive pair potential. +The repulsive part is due to the orthogonalization energy of overlapped atomic wave functions. +The attractive part is associated with the bonding. +\begin{eqnarray} +f_R(r_{ij}) & = & A_{ij} \exp (- \lambda_{ij} r_{ij} ) \\ +f_A(r_{ij}) & = & -B_{ij} \exp (- \mu_{ij} r_{ij} ) +\end{eqnarray} +The function $f_C$ is the potential cutoff function to limit the range of the potential. +It is designed to have a smooth transition of the potential at distances $R_{ij}$ and $S_{ij}$. \begin{equation} -f_R(r_{ij}) = A_{ij} \exp (- \lambda_{ij} r_{ij} ) \\ +f_C(r_{ij}) = \left\{ + \begin{array}{ll} + 1, & r_{ij} < R_{ij} \\ + \frac{1}{2} + \frac{1}{2} \cos \Big[ \pi (r_{ij} - R_{ij})/(S_{ij} - R_{ij}) \Big], & R_{ij} < r_{ij} < S_{ij} \\ + 0, & r_{ij} > S_{ij} + \end{array} \right. \end{equation} +The function $b_{ij}$ represents a measure of the bond order, monotonically decreasing with the coordination of atoms $i$ and $j$. +It is of the form: +\begin{eqnarray} +b_{ij} & = & \chi_{ij} (1 + \beta_i^{n_i} \zeta^{n_i}_{ij})^{-1/2n_i} \\ +\zeta_{ij} & = & \sum_{k \ne i,j} f_C (r_{ik}) \omega_{ik} g(\theta_{ijk}) \\ +g(\theta_{ijk}) & = & 1 + c_i^2/d_i^2 - c_i^2/[d_i^2 + (h_i - \cos \theta_{ijk})^2] +\end{eqnarray} +where $\theta_{ijk}$ is the bond angle between bonds $ij$ and $ik$. +This is illustrated in Figure \ref{img:tersoff_angle}. + +\printimg{!h}{width=8cm}{tersoff_angle.eps}{Angle between bonds of atoms $i,j$ and $i,k$.}{img:tersoff_angle} + +In order to calculate the forces the derivation of the potential with respect to $x^i_n$ (the $n$th component of the position vector of atom $i$ $\equiv$ ${\bf r}_i$) has to be known. +This is gradually done in the following. +The cutoff function $f_C$ derivated with repect to $x^i_n$ is \begin{equation} -f_A(r_{ij}) = -B_{ij} \exp (- \mu_{ij} r_{ij} ) \\ +\partial_{x^i_n} f_C(r_{ij}) = +\frac{1}{2} \sin \Big( \pi (r_{ij} - R_{ij}) / (S_{ij} - R_{ij}) \Big) \frac{\pi x^i_n}{(S_{ij} - R_{ij}) r_{ij}} \textrm { .} \end{equation} +The angle $\theta_{ijk}$ can be expressed by the atom distances with the law of cosines: +\begin{eqnarray} +\theta_{ijk} & = & \arccos \Big( (r_{ij}^2 + r_{ik}^2 - r_{jk}^2)/(2 r_{ij} r_{ik}) \Big) \\ +\partial_{x^i_n} \theta_{ijk} & = & +\frac{-1}{\sqrt{1 - ((r_{ik}^2+r_{ij}^2-r_{jk}^2)/2r_{ik}r_{ij})^2}} +\Big( \frac{4 r_{ik}r_{ij} (2 x^i_n - x^k_n - x^j_n) + 2(x^j_n - x^i_n)\frac{r_{ik}}{r_{ij}} + 2(x^k_n - x^i_n)\frac{r_{ij}}{r_{ik}} }{4 r^2_{ik} r^2_{ij}}\Big) +\end{eqnarray} -The function $f_C$ is the potential cutoff function designed to have a smooth transition between $R_{ij}$ and $S_{ij}$. -\begin{equation} -f_C(r_{ij}) = \left\{ - \begin{array}{ll} - 1 & r_{ij} < R_{ij} \\ - \frac{1}{2} + \frac{1}{2} \cos [ \pi (r_{ij} - R_{ij})/(S_{ij} - R_{ij}) ] & R_{ij} < r_{ij} < S_{ij} \\ - 0 & r_{ij} > S_{ij} - \end{array} \right. -\end{equation} \subsubsection{The Brenner potential} -- 2.20.1 From b9e8d3d6de1539aedc1cada3cdd34e5ed722209d Mon Sep 17 00:00:00 2001 From: hackbard Date: Tue, 18 Jul 2006 15:37:15 +0000 Subject: [PATCH 12/16] added tersoff angles fig --- posic/thesis/tersoff_angle.fig | 24 ++++++++++++++++++++++++ 1 file changed, 24 insertions(+) create mode 100644 posic/thesis/tersoff_angle.fig diff --git a/posic/thesis/tersoff_angle.fig b/posic/thesis/tersoff_angle.fig new file mode 100644 index 0000000..e402b5b --- /dev/null +++ b/posic/thesis/tersoff_angle.fig @@ -0,0 +1,24 @@ +#FIG 3.2 Produced by xfig version 3.2.5-alpha5 +Landscape +Center +Metric +A4 +100.00 +Single +-2 +1200 2 +5 1 0 1 0 7 50 -1 -1 0.000 0 0 0 0 2150.466 3546.229 2430 3240 2565 3555 2340 3915 +1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 1845 3555 45 45 1845 3555 1890 3555 +1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 5895 1440 45 45 5895 1440 5940 1440 +1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 5355 6075 45 45 5355 6075 5400 6075 +2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 3 + 5310 6030 1845 3555 5895 1440 +2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 0 0 2 + 5400 6075 5895 1440 +4 0 0 50 -1 0 12 0.0000 6 195 720 5085 6390 atom $j$\001 +4 0 0 50 -1 0 12 0.0000 6 165 765 5580 1260 atom $k$\001 +4 0 0 50 -1 0 12 0.0000 6 165 720 1485 3375 atom $i$\001 +4 0 0 50 -1 0 12 0.0000 6 195 1185 2160 3645 $\\theta_{ijk}$\001 +4 0 0 50 -1 0 12 0.0000 6 195 720 3285 2475 $r_{ik}$\001 +4 0 0 50 -1 0 12 0.0000 6 195 720 5715 3870 $r_{jk}$\001 +4 0 0 50 -1 0 12 0.0000 6 195 675 3015 4950 $r_{ij}$\001 -- 2.20.1 From d1ac6c548d593e94735100302640c3fd93984703 Mon Sep 17 00:00:00 2001 From: hackbard Date: Tue, 25 Jul 2006 15:28:19 +0000 Subject: [PATCH 13/16] changed from landscape to portrait style + one new result chapter --- nlsop/poster/nlsop_ibmm2006.tex | 91 ++++++++++++++++++++++----------- 1 file changed, 60 insertions(+), 31 deletions(-) diff --git a/nlsop/poster/nlsop_ibmm2006.tex b/nlsop/poster/nlsop_ibmm2006.tex index 285a42c..1188e13 100644 --- a/nlsop/poster/nlsop_ibmm2006.tex +++ b/nlsop/poster/nlsop_ibmm2006.tex @@ -14,9 +14,11 @@ % % special format, scaled by 2.82 -> A0 % -\def\breite{390mm} -\def\hoehe{319.2mm} -\def\anzspalten{4} +% A4 landscape (?) +% +%\def\breite{390mm} +%\def\hoehe{319.2mm} +%\def\anzspalten{4} % % A3 landscape % @@ -36,6 +38,18 @@ %\def\hoehe{297mm} %\def\anzspalten{2} % +% A0 portrait +% +%\def\breite{841mm} +%\def\hoehe{1189mm} +%\def\anzspalten{3} +% +% A0 / 2.82 portrait +% +\def\breite{298.23mm} +\def\hoehe{421.63mm} +\def\anzspalten{3} +% % % % scaling procedure: @@ -133,15 +147,15 @@ } % header -\vfill +%\vfill \hfill \psshadowbox{\makebox[0.95\textwidth]{% - \hfill - \parbox[c]{0.1\linewidth}{\includegraphics[height=4.5cm]{uni-logo.eps}} - \parbox[c]{0.7\linewidth}{% + %\hfill + \parbox[c]{0.15\linewidth}{\includegraphics[height=4.5cm]{uni-logo.eps}} + \parbox[c]{0.62\linewidth}{% \begin{center} - \textbf{\Huge{Monte Carlo simulation study of a - selforganization process\\ + \textbf{\Huge{Monte Carlo simulation study \\ + of a selforganization process \\ leading to ordered precipitate structures} }\\[0.7em] \textsc{\LARGE \underline{F. Zirkelbach}, M. H"aberlen, @@ -152,12 +166,12 @@ } \end{center} } - \parbox[c]{0.1\linewidth}{% + \parbox[c]{0.15\linewidth}{% \includegraphics[height=4.1cm]{Lehrstuhl-Logo.eps} } - \hfill + %\hfill }} -\hfill\mbox{}\\[0.5cm] +\hfill\mbox{}\\[0.1cm] %\vspace*{1.3cm} @@ -166,6 +180,7 @@ \parbox[t][\textheight]{1.3\textwidth}{% %\vspace*{0.2cm} \hfill + %\hspace{0.5cm} % first column \begin{spalte} \begin{kasten} @@ -216,8 +231,6 @@ $\rightarrow$ {\bf strain induced} lateral amorphization \end{itemize} \end{kasten} -\end{spalte} -\begin{spalte} \begin{kasten} \section*{3 \hspace{0.1cm} {\color{blue}Simulation}} @@ -225,7 +238,21 @@ \begin{center} \includegraphics[width=6cm]{gitter_e.eps} \end{center} + Periodic boundary conditions in $x,y$-direction.\\ + Start conditions: All volumes crystalline, zero carbon + concentration. + \subsection*{3.3 {\color{blue} TRIM collision statistics}} + \begin{center} + \includegraphics[width=8cm]{trim_coll_e.eps} + \end{center} + \begin{center} + $\Rightarrow$ mean constant energy loss per collision of an ion + \end{center} + \end{kasten} +\end{spalte} +\begin{spalte} + \begin{kasten} \subsection*{3.2 {\color{blue} Simulation algorithm}} \subsubsection*{3.2.1 Amorphization/Recrystallization} @@ -278,16 +305,7 @@ Three contributions to the amorphization process controlled by: removal \end{itemize} - \subsection*{3.3 {\color{blue} TRIM collision statistics}} - \begin{center} - \includegraphics[width=8cm]{trim_coll_e.eps} - \end{center} - \begin{center} - $\Rightarrow$ mean constant energy loss per collision of an ion - \end{center} \end{kasten} -\end{spalte} -\begin{spalte} \begin{kasten} \section*{4 \hspace{0.1cm} {\color{blue}Simulation results}} @@ -298,19 +316,30 @@ Three contributions to the amorphization process controlled by: \begin{center} \includegraphics[width=11cm]{dosis_entwicklung_ng_e_2-2.eps} \end{center} + Simulation parameters:\\ + $p_b=0.01$, $p_c=0.001$, $p_s=0.0001$, $d_r=0.05$, + $d_v=1 \times 10^6$. \end{kasten} \begin{kasten} - \subsection*{4.2 {\color{blue} Carbon distribution}} + \subsection*{4.2 {\color{blue} Variation of the simulation parameters}} \begin{center} - \includegraphics[width=11cm]{ac_cconc_ver2_e.eps} + \includegraphics[width=11cm]{var_sim_paramters_en.eps} \end{center} - + Parameters of initial situation:\\ + $p_b=0.01$, $p_c=0.001$, $p_s=0.0001$, $d_r=0.05$, + $d_v=1 \times 10^6$. \end{kasten} \end{spalte} -% fourth column \begin{spalte} \begin{kasten} - \subsection*{4.3 {\color{blue} More structural/compositional + \subsection*{4.3 {\color{blue} Carbon distribution}} + \begin{center} + \includegraphics[width=11cm]{ac_cconc_ver2_e.eps} + \end{center} + + \end{kasten} + \begin{kasten} + \subsection*{4.4 {\color{blue} More structural/compositional information}} \begin{center} \includegraphics[width=8cm]{97_98_ng_e.eps} \\ @@ -318,9 +347,9 @@ Three contributions to the amorphization process controlled by: \end{center} \end{kasten} \begin{kasten} - \subsection*{4.4 \hspace{0.1cm} {\color{blue} Broad distribution + \subsection*{4.5 \hspace{0.1cm} {\color{blue} Broad distribution of lamellar structure - the recipe}} - \subsubsection*{4.4.1 Constant carbon concentration} + \subsubsection*{4.5.1 Constant carbon concentration} \makebox[11cm]{% \parbox[c]{5cm}{% \begin{itemize} @@ -336,7 +365,7 @@ Three contributions to the amorphization process controlled by: \includegraphics[width=6cm]{multiple_impl_cp_e.eps} } } - \subsubsection*{4.4.2 2 MeV C$^+$ implantation + \subsubsection*{4.5.2 2 MeV C$^+$ implantation step} \begin{center} \includegraphics[width=10cm]{multiple_impl_e.eps} -- 2.20.1 From 1bdf070b8b104915fb6aaece85bf3774fed5e790 Mon Sep 17 00:00:00 2001 From: hackbard Date: Thu, 27 Jul 2006 13:51:46 +0000 Subject: [PATCH 14/16] paper a la elsevier .. --- nlsop/paper/M243.tex | 66 ++ nlsop/paper/elsart.cls | 1435 ++++++++++++++++++++++++++++++++++++++++ 2 files changed, 1501 insertions(+) create mode 100644 nlsop/paper/M243.tex create mode 100644 nlsop/paper/elsart.cls diff --git a/nlsop/paper/M243.tex b/nlsop/paper/M243.tex new file mode 100644 index 0000000..efbf182 --- /dev/null +++ b/nlsop/paper/M243.tex @@ -0,0 +1,66 @@ +\pdfoutput=0 +\documentclass{elsart} +\usepackage[activate]{pdfcprot} +\usepackage{verbatim} +\usepackage[english]{babel} +\usepackage[latin1]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{amsmath} +\usepackage{ae} +\usepackage{aecompl} +\usepackage[dvips]{graphicx} +\graphicspath{{../img/}} +\usepackage{natbib,amssymb} + +\begin{document} + +\hyphenation{TRIM} + +\begin{frontmatter} + +\title{Monte Carlo simulation study\\of a selforganization process\\leading to + ordered precipitate structures} + +\author[augsburg]{F. Zirkelbach\corauthref{cor}} +\author[augsburg]{M. Häberlen} +\author[augsburg]{J. K. N. Lindner} +\author[augsburg]{B. Stritzker} + +\corauth[cor]{Corresponding author.\\ + Tel.: +49-821-5983008; fax: +49-821-5983425.\\ + E-mail address: frank.zirkelbach@physik.uni-augsburg.de (Frank + Zirkelbach)} + +\address[augsburg]{Universität Augsburg, Institut für Physik, + Universitätsstrasse 1,\\D-86135 Augsburg, Germany} + +\begin{abstract} +Periodically arranged, self-organized, nanometric, amorphous precipitates have been observed at high-dose ion implantations for a number of ion/target combinations at certain implantation conditions. +A model describing the ordering process based on compressive stress exerted by the amorphous inclusions as a result of the density change upon amorphization is introduced. +A Monte Carlo simulation code, which focuses on high dose carbon implantation into silicon, is able to reproduce experimentally observed results. +By means of simulation the selforganization process gets traceable and detailed information about the compositional and structural state during the ordering process is obtained. +Based on simulation results, a recipe is proposed for producing broad distributions of lamellar ordered structures. +\end{abstract} + +\begin{keyword} +Monte Carlo simulation; Self-organization; Precipitation; Amorphization; +Nanostructures; Ion irradiation\\ +\PACS 02.70.Uu; 61.72.Tt; 81.16.Rf +\end{keyword} + +\end{frontmatter} + +\section{Introduction} + +High-dose implantations into solids usually results in the formation of unordered ensembles of precipitates with a + + +\section{Modell} + +\section{Simulation} + +\section{Results} + +\section{Summayr and conclusion} + +\end{document} diff --git a/nlsop/paper/elsart.cls b/nlsop/paper/elsart.cls new file mode 100644 index 0000000..1519c04 --- /dev/null +++ b/nlsop/paper/elsart.cls @@ -0,0 +1,1435 @@ +%% +%% This is file `elsart.cls', +%% generated with the docstrip utility. +%% +%% The original source files were: +%% +%% esl.dtx (with options: `package,elsart,ONECOL,DEEPLIST') +%% +%% elsart.cls Copyright (C) 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(Must be + % \z@ \@plus ... ) +\marginparpush 5\p@ % Minimum vertical separation between two marginal + % notes. +\parskip 1pc \@plus 1\p@ % Extra vertical space between paragraphs. +\parindent \z@ % Indentation of each paragraph. +\newskip\eqntopsep % Extra vertical space, in addition to + \eqntopsep 12\p@ \@plus 2\p@ \@minus 2\p@ %\parskip, added above and below +\newdimen\eqnarraycolsep % Half the space between columns +\eqnarraycolsep 1\p@ % in an \eqnarray. +\@lowpenalty 51 % Produced by \nopagebreak[1] or \nolinebreak[1] +\@medpenalty 151 % Produced by \nopagebreak[2] or \nolinebreak[2] +\@highpenalty 301 % Produced by \nopagebreak[3] or \nolinebreak[3] +\@beginparpenalty -\@lowpenalty % Before a list or paragraph environment. +\@endparpenalty -\@lowpenalty % After a list or paragraph environment. +\@itempenalty -\@lowpenalty % Between list items. +\def\section{\@startsection{section}{1}{\z@}{1.5\@bls + \@plus .4\@bls \@minus .1\@bls}{\@bls}{\normalsize\bfseries}} +\def\subsection{\@startsection{subsection}{2}{\z@}{\@bls + \@plus .3\@bls \@minus .1\@bls}{\@bls}{\normalsize\itshape}} +\def\subsubsection{\@startsection{subsubsection}{3}{\z@}{\@bls + \@plus .2\@bls}{0.0001pt}{\normalsize\itshape}} +\def\paragraph{\@startsection{paragraph}{4}{\z@}{3.25ex \@plus + 2ex \@minus 0.2ex}{-1em}{\normalsize\bfseries}} +\setcounter{secnumdepth}{4} +\def\half@em{\hskip 0.5em} +\def\lb@part{PART \thepart.\half@em} + \def\lb@empty@part{PART \thepart} +\def\lb@section{\thesection.\half@em} + \def\lb@empty@section{\thesection} +\def\lb@subsection{\thesubsection.\half@em} + \def\lb@empty@subsection{\thesubsection} +\def\lb@subsubsection{\thesubsubsection.\half@em} + \def\lb@empty@subsubsection{\thesubsubsection} +\def\lb@paragraph{\theparagraph.\half@em} + \def\lb@empty@paragraph{\theparagraph} +\def\lb@subparagraph{\thesubparagraph.\half@em} + \def\lb@empty@subparagraph{\thesubparagraph} +\def\head@format#1#2{#2} +\def\head@style{\interlinepenalty\@M + \hyphenpenalty\@M \exhyphenpenalty\@M + \rightskip \z@ \@plus 0.5\hsize \relax + } +\def\app@number#1{\setcounter{#1}{0}% + \@addtoreset{#1}{section}% + \@namedef{the#1}{\thesection.\arabic{#1}}} +\def\appendix{\@ifstar{\appendix@star}{\appendix@nostar}} +\def\appendix@nostar{% + \def\lb@section{\appendixname\ \thesection.\half@em} + \def\lb@empty@section{\appendixname\ \thesection} + \setcounter{section}{0}\def\thesection{\Alph{section}}% + \setcounter{subsection}{0}% + \setcounter{subsubsection}{0}% + \setcounter{paragraph}{0}% + \app@number{equation}\app@number{figure}\app@number{table}} +\def\appendix@star{% + \def\lb@section{\appendixname}\let\lb@empty@section\lb@section + \setcounter{section}{0}\def\thesection{\Alph{section}}% + \setcounter{subsection}{0}% + \setcounter{subsubsection}{0}% + \setcounter{paragraph}{0}% + \app@number{equation}\app@number{figure}\app@number{table}} +\def\ack{\section*{Acknowledgements}% + \addtocontents{toc}{\protect\vspace{6pt}}% + \addcontentsline{toc}{section}{Acknowledgements}% +} +\@namedef{ack*}{\par\vskip 3.0ex \@plus 1.0ex \@minus 1.0ex} +\let\endack\par +\@namedef{endack*}{\par} +\newdimen\labelwidthi +\newdimen\labelwidthii +\newdimen\labelwidthiii +\newdimen\labelwidthiv +\def\normal@labelsep{0.5em} +\labelsep\normal@labelsep +\settowidth{\labelwidthi}{(iii)} +\settowidth{\labelwidthii}{(d)} +\settowidth{\labelwidthiii}{(iii)} +\settowidth{\labelwidthiv}{(M)} +\leftmargini\labelwidthi \advance\leftmargini\labelsep +\leftmarginii\labelwidthii \advance\leftmarginii\labelsep +\leftmarginiii\labelwidthiii \advance\leftmarginiii\labelsep +\leftmarginiv\labelwidthiv \advance\leftmarginiv\labelsep +\def\setleftmargin#1#2{\settowidth{\@tempdima}{#2}\labelsep\normal@labelsep + \csname labelwidth#1\endcsname\@tempdima + \@tempdimb\@tempdima \advance\@tempdimb\labelsep + \csname leftmargin#1\endcsname\@tempdimb} +\def\@listI{\leftmargin\leftmargini + \labelwidth\labelwidthi \labelsep\normal@labelsep + \topsep \z@ \partopsep\z@ \parsep\z@ \itemsep\z@ + \listparindent 1em} +\def\@listii{\leftmargin\leftmarginii + \labelwidth\labelwidthii \labelsep\normal@labelsep + \topsep\z@ \partopsep\z@ \parsep\z@ \itemsep\z@ + \listparindent 1em} +\def\@listiii{\leftmargin\leftmarginiii + \labelwidth\labelwidthiii \labelsep\normal@labelsep + \topsep\z@ \partopsep\z@ \parsep\z@ \itemsep\z@ + \listparindent 1em} +\def\@listiv{\leftmargin\leftmarginiv + \labelwidth\labelwidthiv \labelsep\normal@labelsep + \topsep\z@ \partopsep\z@ \parsep\z@ \itemsep\z@ + \listparindent 1em} +\let\@listi\@listI +\@listi +\def\left@label#1{{#1}\hss} +\def\right@label#1{\hss\llap{#1}} +\def\thick@label#1{\hspace\labelsep #1} +\newcount\@maxlistdepth +\@maxlistdepth=4 +\def\labelitemi{$\bullet$} \def\labelitemii{$\cdot$} +\def\labelenumi{(\theenumi)} \def\theenumi{\arabic{enumi}} +\def\labelenumii{(\alph{enumii})} \def\theenumii{\theenumi\alph{enumii}} +\def\labelenumiii{(\roman{enumiii})}\def\theenumiii{\theenumii.\roman{enumiii}} +\def\labelenumiv{(\Alph{enumiv})} \def\theenumiv{\theenumiii.\Alph{enumiv}} +\def\enumerate{% + \ifnum \@enumdepth >\@maxlistdepth + \@toodeep + \else + \advance\@enumdepth \@ne + \edef\@enumctr{enum\romannumeral\the\@enumdepth}% + \list{\csname label\@enumctr\endcsname}% + {\usecounter{\@enumctr} + \let\makelabel=\right@label} + \fi} +\def\itemize{% + \ifnum \@itemdepth >\@maxlistdepth + \@toodeep + \else + \advance\@itemdepth \@ne + \edef\@itemitem{labelitem\romannumeral\the\@itemdepth}% + \setleftmargin{i}{--}% + \setleftmargin{ii}{$\cdot$}% + \list{\csname\@itemitem\endcsname}% + {\let\makelabel\right@label} + \fi} +\def\verse{\let\\=\@centercr + \list{}{\itemsep\z@ + \itemindent \z@ + \listparindent\z@ + \rightmargin 1em + \leftmargin \rightmargin}\item[]} +\let\endverse\endlist +\def\quotation{\list{}{\itemindent\z@ + \leftmargin 1em \rightmargin \z@ + \parsep \z@ \@plus 1pt}\item[]} +\let\endquotation=\endlist +\def\quote{\list{}{\itemindent\z@ + \leftmargin 1em \rightmargin \z@}% +\item[]} +\let\endquote=\endlist +\def\descriptionlabel#1{\hspace\labelsep \bfseries #1} +\def\description{\list{}{\labelwidth\z@ + \leftmargin 1em \itemindent-\leftmargin + \let\makelabel\descriptionlabel}} +\let\enddescription\endlist +\def\@atfmtname{atlplain} +\ifx\fmtname\@atfmtname + \def\neq{\not\nobreak\mkern -2mu =}% + \let\ne\neq +\fi +\def\operatorname#1{\mathop{\mathrm{#1}}\nolimits} +\def\lefteqn#1{\hbox to\z@{$\displaystyle {#1}$\hss}} +\newskip\eqnbaselineskip % Standard interline spacing in an {eqnarray} +\jot=2\p@ +\newskip\eqnlineskip % Minimal space between the bottom of + % a line and the top of the next line. +\eqnbaselineskip=14\p@ \eqnlineskip=2\p@ +\newdimen\mathindent +\if@TwoColumn + \mathindent 0em +\else + \mathindent 2em +\fi +\if@narrowdisplay + \def\calcmathindent{% + \mathindent\linewidth\relax + \advance\mathindent-\@narrowdisplaywidth} +\else + \let\calcmathindent\relax +\fi +\def\[{\relax\ifmmode\@badmath + \else%\bgroup removed on request from BW (1993-05-17) + \@beginparpenalty\predisplaypenalty + \@endparpenalty\postdisplaypenalty +\calcmathindent + \begin{trivlist}\@topsep \eqntopsep % used by first \item + \@topsepadd \eqntopsep % used by \@endparenv + \item[]\leavevmode + \hbox to\linewidth\bgroup$ \displaystyle + \hskip\mathindent\bgroup\fi} +\def\]{\relax\ifmmode \egroup $\hfil \egroup + \end{trivlist}% \egroup removed on request from BW (1993-05-17) + \else \@badmath \fi} +\def\equation{\@beginparpenalty\predisplaypenalty + \@endparpenalty\postdisplaypenalty + \refstepcounter{equation}\trivlist + \@topsep \eqntopsep % used by first \item + \@topsepadd \eqntopsep % used by \@endparenv +\calcmathindent + \item[]\leavevmode + \hbox to\linewidth\bgroup $ \displaystyle \hskip\mathindent\bgroup} +\def\endequation{\egroup$\hfil \displaywidth\linewidth + \@eqnnum\egroup \endtrivlist} +\def\eqnarray{% + \par %BW + \noindent %BW + \baselineskip\eqnbaselineskip\lineskip\eqnlineskip %BW + \lineskiplimit\eqnlineskip %BW +\calcmathindent + \stepcounter{equation}% + \let\@currentlabel=\theequation + \global\@eqnswtrue + \global\@eqcnt\z@ + \tabskip\mathindent + \let\\=\@eqncr + \abovedisplayskip\eqntopsep\ifvmode\advance\abovedisplayskip\partopsep\fi + \belowdisplayskip\abovedisplayskip + \belowdisplayshortskip\abovedisplayskip + \abovedisplayshortskip\abovedisplayskip + $$\halign to \displaywidth\bgroup\@eqnsel + \pre@coli$\displaystyle\tabskip\z@{##}$\post@coli + &\global\@eqcnt\@ne + \pre@colii$\displaystyle{##}$\post@colii + &\global\@eqcnt\tw@ + \pre@coliii $\displaystyle\tabskip\z@{##}$\post@coliii + \tabskip\@centering&\llap{##}\tabskip\z@\cr +} +\def\endeqnarray{\@@eqncr\egroup + \global\advance\c@equation\m@ne$$\global\@ignoretrue } +\def\pre@coli{\hskip\@centering} \def\post@coli{} +\def\pre@colii{\hskip 2\eqnarraycolsep \hfil} \def\post@colii{\hfil} +\def\pre@coliii{\hskip 2\eqnarraycolsep} \def\post@coliii{\hfil} +\arraycolsep 2\p@ % Half the space between columns in array environment. +\tabcolsep 6\p@ % idem in tabular environment. +\def\arraystretch{1.5} % More vertical space in tables +\arrayrulewidth 0.4\p@ % \@Width of rules and space between adjacent +\doublerulesep 2\p@ % rules in any of these two environments. +\newdimen\rulepreskip \newdimen\rulepostskip +\rulepreskip=4\p@ \rulepostskip=6\p@ +\tabbingsep \labelsep % Space used by the \' command. (See LaTeX{} manual.) +\skip\@mpfootins = 6\p@ \@plus 2\p@ % Space between last line of text and + % top of first footnote. +\fboxsep = 7\p@ % Space left between box and text by \fbox and \framebox. +\fboxrule = 0.4\p@ % \@Width of rules in box made by \fbox and \framebox. +\newcounter{section} +\newcounter{subsection}[section] +\newcounter{subsubsection}[subsection] +\newcounter{paragraph}[subsubsection] +\newcounter{subparagraph}[paragraph] +\if@seceqn + \@addtoreset{equation}{section} + \def\theequation{\arabic{section}.\arabic{equation}} +\else + \def\theequation{\arabic{equation}} +\fi +\def\thesection {\arabic{section}} +\def\thesubsection {\thesection.\arabic{subsection}} +\def\thesubsubsection{\thesubsection.\arabic{subsubsection}} +\def\theparagraph {\thesubsubsection.\arabic{paragraph}} +\def\thesubparagraph {\theparagraph.\arabic{subparagraph}} +\@addtoreset{section}{part} % reset section numbers at beginning of part + +\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm} +\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf} +\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt} +\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf} +\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit} +\DeclareOldFontCommand{\sl}{\normalfont\slshape}{\@nomath\sl} +\DeclareOldFontCommand{\sc}{\normalfont\scshape}{\@nomath\sc} +\DeclareRobustCommand*\cal{\@fontswitch\relax\mathcal} +\DeclareRobustCommand*\mit{\@fontswitch\relax\mathnormal} +\RequirePackage{latexsym} +\def\qed{\relax\ifmmode\hskip2em \Box\else\unskip\nobreak\hskip1em $\Box$\fi} +\def\proof@headerfont{\upshape\bfseries} +\if@amsthm + \RequirePackage{amsthm}% + \def\th@plain{% + \thm@preskip\parskip + \thm@postskip\z@ + \itshape % body font + } + \def\th@definition{% + \thm@preskip\parskip + \thm@postskip\z@ + \normalfont % body font + } + \def\th@remark{% + \thm@headfont{\itshape}% + \normalfont % body font + \thm@preskip\parskip \divide\thm@preskip\tw@ + \thm@postskip\z@ + } +\else\let\theoremstyle\@gobble\fi +\newenvironment{pf}% + {\par\addvspace{\@bls \@plus 0.5\@bls \@minus 0.1\@bls}\noindent + {\bfseries\Elproofname}\enspace\ignorespaces}% + {\par\addvspace{\@bls \@plus 0.5\@bls \@minus 0.1\@bls}} +\def\Elproofname{PROOF.} +\@namedef{pf*}#1{\par\begingroup\def\Elproofname{#1}\pf\endgroup\ignorespaces} +\expandafter\let\csname endpf*\endcsname=\endpf +\theoremstyle{plain} +\if@secthm + \newtheorem{thm}{Theorem}[section] + \@addtoreset{thm}{section} +\else + \newtheorem{thm}{Theorem} +\fi +\newtheorem{cor}[thm]{Corollary} +\newtheorem{lem}[thm]{Lemma} +\newtheorem{claim}[thm]{Claim} +\newtheorem{axiom}[thm]{Axiom} +\newtheorem{conj}[thm]{Conjecture} +\newtheorem{fact}[thm]{Fact} +\newtheorem{hypo}[thm]{Hypothesis} +\newtheorem{assum}[thm]{Assumption} +\newtheorem{prop}[thm]{Proposition} +\newtheorem{crit}[thm]{Criterion} +\theoremstyle{definition} +\newtheorem{defn}[thm]{Definition} +\newtheorem{exmp}[thm]{Example} +\newtheorem{rem}[thm]{Remark} +\newtheorem{prob}[thm]{Problem} +\newtheorem{prin}[thm]{Principle} +\newtheorem{alg}{Algorithm} +\long\def\@makealgocaption#1#2{\vskip 2ex \small + \hbox to \hsize{\parbox[t]{\hsize}{{\bfseries #1.} #2}}} +\newcounter{algorithm} +\def\thealgorithm{\@arabic\c@algorithm} +\def\fps@algorithm{tbp} +\def\ftype@algorithm{4} +\def\ext@algorithm{lof} +\def\fnum@algorithm{Algorithm \thealgorithm} +\def\algorithm{\let\@makecaption\@makealgocaption\@float{algorithm}} +\let\endalgorithm\end@float +\newtheorem{note}{Note} +\newtheorem{summ}{Summary} +\newtheorem{case}{Case} +\def\@pnumwidth{2.55em} +\def\@tocrmarg{2.55em \@plus 5em} +\def\@dotsep{-2.5} +\setcounter{tocdepth}{2} +\newcommand\listoffigures{% + \section*{\listfigurename + \@mkboth{\MakeUppercase\listfigurename}% + {\MakeUppercase\listfigurename}}% + \@starttoc{lof}% + } +\newcommand*\l@figure{\@dottedtocline{1}{1.5em}{2.3em}} +\newcommand\listoftables{% + \section*{\listtablename + \@mkboth{% + \MakeUppercase\listtablename}{\MakeUppercase\listtablename}}% + \@starttoc{lot}% + } +\let\l@table\l@figure +\def\tableofcontents{% + \begin{small} + \leftline {{\bfseries \contentsname\/}} + \setcounter{secnumdepth}{4}% + \setcounter{tocdepth}{2}% + {\@starttoc{toc}}% +\end{small} +} +\newcommand*\l@section{\@dottedtocline{1}{1.5em}{2.3em}} +\newcommand*\l@subsection{\@dottedtocline{2}{1.5em}{2.3em}} +\newcommand*\l@subsubsection{\@dottedtocline{3}{3.8em}{3.2em}} +\newcommand*\l@paragraph{\@dottedtocline{4}{7.0em}{4.1em}} +\newcommand*\l@subparagraph{\@dottedtocline{5}{10em}{5em}} +\def\@dotsep{2000} +\def\thebibliography{% + \@startsection{section}{1}{\z@}{20\p@ \@plus 8\p@ \@minus 4pt} + {\@bls}{\normalsize\bfseries}*{\refname}% +\addcontentsline{toc}{section}{\refname}% + \@thebibliography} +\let\endthebibliography=\endlist +\def\@thebibliography#1{\@bibliosize + \list{\@biblabel{\arabic{enumiv}}}{\settowidth\labelwidth{\@biblabel{#1}} + \if@nameyear + \labelwidth\z@ \labelsep\z@ \leftmargin\parindent + \itemindent-\parindent + \else + \labelsep 3\p@ \itemindent\z@ + \leftmargin\labelwidth \advance\leftmargin\labelsep +\fi +\itemsep\@bibitemsep + \usecounter{enumiv}\let\p@enumiv\@empty + \def\theenumiv{\arabic{enumiv}}}% + \tolerance\@M + \hyphenpenalty\@M + \hbadness5000 \sfcode`\.=1000\relax} +\newcommand\newblock{\hskip .11em\@plus.33em\@minus.07em} +\if@nameyear + \def\@biblabel#1{} +\else + \def\@biblabel#1{[#1]\hskip \z@ \@plus 1filll} +\fi +\let\make@bb@error\relax +\def\@mkbberr{\def\bibitem{\ClassError{elsart}% + {Bibitem after note}% + {You are using a bibitem after a note in a subbibitems + environment;\MessageBreak + note should the last item in a subbibitems environment}}} +\def\@itemnote{\make@bb@error\item[]} +\def\mk@noitemnote{\ifx\@tempa\note \let\note\@noitemnote \fi} +\def\@noitemnote{\let\note\@itemnote} +\AtBeginDocument{% + \let\nopeek@bibitem\@bibitem + \let\nopeek@lbibitem\@lbibitem + \def\@bibitem#1{\let\note\@itemnote\nopeek@bibitem{#1}% + \futurelet\@tempa\mk@noitemnote} + \def\@lbibitem[#1]#2{\let\note\@itemnote\nopeek@lbibitem[#1]{#2}% + \futurelet\@tempa\mk@noitemnote} +} +\newif\if@natbibloaded\@natbibloadedfalse +\AtBeginDocument{\@ifpackageloaded{natbib}{\@natbibloadedtrue}{}} +\newenvironment{subbibitems}[1]{% + \if@natbibloaded\def\bib@ctr{NAT@ctr}\else\def\bib@ctr{enumiv}\fi + \if@filesw {\let \protect \noexpand \immediate \write \@auxout + {\string \nocollapse@cites}% + \global\let\nocollapse@cites\relax}\fi + \def\@itemslabel{#1}% + \stepcounter{\bib@ctr}% + \edef\main@bibnum{\the\value{\bib@ctr}}% + \setcounter{\bib@ctr}{0}% + \def\thebib@ctr{\main@bibnum\alph{\bib@ctr}}% + \if@natbibloaded + \def\bibitem{\@ifnextchar [{\@lbibitem }{\global \NAT@stdbsttrue + \stepcounter {\bib@ctr}\@lbibitem [\thebib@ctr]}}% + \else + \def\@bibitem##1{\stepcounter{\bib@ctr}\@lbibitem[\thebib@ctr]{##1}}% + \fi + \let\make@bb@error\@mkbberr +}{% + \if@filesw {% + \if@natbibloaded{% + \let\protect\noexpand + \immediate\write\@auxout {\string\bibcite{\@itemslabel}% + {{\main@bibnum a--\alph {\bib@ctr}}{}{{}}{{}}}}% + \immediate\write\@auxout {\string\bibcite{\@itemslabel :s}% + {{\main@bibnum}{}{{}}{{}}}}% + }\else{% + \let\protect\noexpand + \immediate\write\@auxout {\string\bibcite{\@itemslabel}% + {\main@bibnum a--\alph{\bib@ctr}}}% + \immediate\write\@auxout {\string\bibcite{\@itemslabel :s}% + {\main@bibnum}}% + }\fi + }\fi + \setcounter{\bib@ctr}{\main@bibnum}% +} +\let\nocollapse@citex\@citex +\newcount\@tempcntc +\def\collapse@citex[#1]#2{\if@filesw\immediate\write\@auxout{\string\citation{#2}}\fi + \@tempcnta\z@\@tempcntb\m@ne\def\@citea{}\@cite{\@for\@citeb:=#2\do + {\edef\@citeb{\expandafter\@firstofone\@citeb\@empty}% + \@ifundefined + {b@\@citeb}{\@citeo\@tempcntb\m@ne\@citea\def\@citea{,}{\bfseries ?}\@warning + {Citation `\@citeb' on page \thepage \space undefined}}% + {\setbox\z@\hbox{\global\@tempcntc0\csname b@\@citeb\endcsname\relax}% + \ifnum\@tempcntc=\z@ \@citeo\@tempcntb\m@ne + \@citea\def\@citea{,}\hbox{\csname b@\@citeb\endcsname}% + \else + \advance\@tempcntb\@ne + \ifnum\@tempcntb=\@tempcntc + \else\advance\@tempcntb\m@ne\@citeo + \@tempcnta\@tempcntc\@tempcntb\@tempcntc\fi\fi}}\@citeo}{#1}} +\let\@citex\collapse@citex +\def\nocollapse@cites{% + \@ifpackageloaded{hyperref}{}{\global\let\@citex\nocollapse@citex}% + \global\let\nocollapse@cites\relax} +\def\@citeo{\ifnum\@tempcnta>\@tempcntb\else\@citea\def\@citea{,}% + \ifnum\@tempcnta=\@tempcntb\the\@tempcnta\else + {\advance\@tempcnta\@ne\ifnum\@tempcnta=\@tempcntb \else \def\@citea{--}\fi + \advance\@tempcnta\m@ne\the\@tempcnta\@citea\the\@tempcntb}\fi\fi} +\@namedef{cv*}{\section*{Curriculum Vitae}\cv} + \def\cv{\hangindent=7pc \hangafter=-12 \parskip\bigskipamount \small} +\def\footnote{\@ifnextchar[{\@xfootnote}{\refstepcounter + {\@mpfn}\protected@xdef\@thefnmark{\thempfn}\@footnotemark\@footnotetext}} +\def\footnotemark{\@ifnextchar[{\@xfootnotemark + }{\refstepcounter{footnote}\xdef\@thefnmark{\thefootnote}\@footnotemark}} +\def\footnoterule{\kern-3\p@ + \hrule \@width 3pc % The \hrule has default \@height of 0.4pt. + \kern 2.6\p@} +\def\thempfootnote{\alph{mpfootnote}} +\def\mpfootnotemark{% + \@ifnextchar[{\@xmpfootnotemark}{\stepcounter{mpfootnote}% + \begingroup + \let\protect\noexpand + \xdef\@thefnmark{\thempfootnote}% + \endgroup + \@footnotemark}} +\def\@xmpfootnotemark[#1]{% + \begingroup + \c@mpfootnote #1\relax + \let\protect\noexpand + \xdef\@thefnmark{\thempfootnote}% + \endgroup + \@footnotemark} +\def\@mpmakefnmark{\,\hbox{$^{\mathrm{\@thefnmark}}$}} +\long\def\@mpmakefntext#1{\noindent + \hbox{$^{\mathrm{\@thefnmark}}$} #1} +\def\@iiiminipage#1#2[#3]#4{% + \leavevmode + \@pboxswfalse + \setlength\@tempdima{#4}% + \def\@mpargs{{#1}{#2}[#3]{#4}}% + \setbox\@tempboxa\vbox\bgroup + \color@begingroup + \hsize\@tempdima + \textwidth\hsize \columnwidth\hsize + \@parboxrestore + \def\@mpfn{mpfootnote}\def\thempfn{\thempfootnote}\c@mpfootnote\z@ + \let\@footnotetext\@mpfootnotetext + \let\@makefntext\@mpmakefntext + \let\@makefnmark\@mpmakefnmark + \let\@listdepth\@mplistdepth \@mplistdepth\z@ + \@minipagerestore\global\@minipagetrue %% \global added 24 May 89 + \everypar{\global\@minipagefalse\everypar{}}} +\def\fn@presym{} +\long\def\@makefntext#1{\noindent\hbox to 1em + {$^{\fn@presym\mathrm{\@thefnmark}}$\hss}#1} +\def\@makefnmark{\,\hbox{$^{\fn@presym\mathrm{\@thefnmark}}$}\,} +\def\patched@end@dblfloat{% + \if@twocolumn + \par\vskip\z@skip %% \par\vskip\z@ added 15 Dec 87 + \global\@minipagefalse + \outer@nobreak + \egroup %% end of vbox + \color@endbox + \ifnum\@floatpenalty <\z@ + \@largefloatcheck + \@cons\@dbldeferlist\@currbox + \fi + \ifnum \@floatpenalty =-\@Mii \@Esphack\fi + \else + \end@float + \fi +} +\setcounter{topnumber}{5} +\def\topfraction{0.99} +\def\textfraction{0.05} +\def\floatpagefraction{0.9} +\setcounter{bottomnumber}{5} +\def\bottomfraction{0.99} +\setcounter{totalnumber}{10} +\def\dbltopfraction{0.99} +\def\dblfloatpagefraction{0.8} +\setcounter{dbltopnumber}{5} +\long\def\@maketablecaption#1#2{\@tablecaptionsize + \global \@minipagefalse + \hbox to \hsize{\parbox[t]{\hsize}{#1 \\ #2}}} +\long\def\@makefigurecaption#1#2{\@figurecaptionsize + \vskip \@overcaptionskip + \setbox\@tempboxa\hbox{#1. #2} + \ifdim \wd\@tempboxa >\hsize % IF longer than one line THEN + \unhbox\@tempboxa\par % set as justified paragraph + \else % ELSE + \global \@minipagefalse + \hbox to\hsize{\hfil\box\@tempboxa\hfil}% center single line. + \fi} +\def\@makecaption{\@makefigurecaption} +\def\conttablecaption{\par \begingroup \@parboxrestore \normalsize + \@makecaption{\fnum@table\,---\,continued}{}\par + \vskip-1pc \endgroup} +\def\contfigurecaption{\vskip-1pc \par \begingroup \@parboxrestore + \@captionsize + \@makecaption{\fnum@figure\,---\,continued}{}\par + \endgroup} +\newcounter{figure} +\def\thefigure{\@arabic\c@figure} +\def\fps@figure{tbp} +\def\ftype@figure{1} +\def\ext@figure{lof} +\def\fnum@figure{\figurename~\thefigure} +\def\figure{% + \let\@makecaption\@makefigurecaption + \let\contcaption\contfigurecaption \@float{figure}} +\let\endfigure\end@float +\@namedef{figure*}{% + \let\@makecaption\@makefigurecaption + \let\contcaption\contfigurecaption \@dblfloat{figure}} +\@namedef{endfigure*}{\end@dblfloat} +\newcounter{table} +\def\thetable{\@arabic\c@table} +\def\fps@table{tbp} +\def\ftype@table{2} +\def\ext@table{lot} +\def\fnum@table{\tablename~\thetable} +\let\old@floatboxreset\@floatboxreset +\def\table{% +\let\@makecaption\@maketablecaption +\def\@floatboxreset{% + \old@floatboxreset + \@tablesize +}% + \let\footnoterule\relax + \let\contcaption\conttablecaption \@float{table}} +\let\endtable\end@float +\@namedef{table*}{% +\let\@makecaption\@maketablecaption +\def\@floatboxreset{% + \old@floatboxreset + \@tablesize +}% + \let\footnoterule\relax + \let\contcaption\conttablecaption \@dblfloat{table}} +\@namedef{endtable*}{\end@dblfloat} +\newtoks\t@glob@notes % List of all notes +\newtoks\t@loc@notes % List of notes for one element +\newcount\note@cnt % Number of notes per element +\newtoks\corauth@text +\newtoks\email@text +\newtoks\url@text +\newcounter{corauth} +\newcounter{author} % Author counter +\newcount\n@author % Total number of authors +\def\n@author@{1} % idem, read from .aux file +\newcounter{collab} % Collaboration counter +\newcount\n@collab % Total number of collaborations +\def\n@collab@{} % idem, read from .aux file +\newcounter{address} % Address counter +\def\theHaddress{\arabic{address}}% for hyperref +\newdimen\sv@mathsurround % Dimen register to save \mathsurround +\newcount\sv@hyphenpenalty % Count register to save \hyphenpenalty +\newcount\prev@elem \prev@elem=0 % Variables to keep track of +\newcount\cur@elem \cur@elem=0 % types of elements that are processed +\chardef\e@title=1 +\chardef\e@subtitle=1 +\chardef\e@author=2 +\chardef\e@collab=3 +\chardef\e@address=4 +\newif\if@newelem % Switch to new type of element? +\newif\if@firstauthor % First author or collaboration? +\newif\if@preface % If preface: omit history and abstract +\newif\if@hasabstract % If abstract / keywords: do not omit rules +\newif\if@haskeywords % If abstract / keywords: do not omit rules +\newbox\fm@box % Box for collected front matter +\newdimen\fm@size % Total height of \fm@box +\newbox\t@abstract % Box for abstract +\newbox\t@keyword % Box for keyword abstract + \let\report@elt\@gobble +\def\add@tok#1#2{\global#1\expandafter{\the#1#2}} +\def\add@xtok#1#2{\begingroup + \no@harm + \xdef\@act{\global\noexpand#1{\the#1#2}}\@act +\endgroup} +\def\beg@elem{\global\t@loc@notes={}\global\note@cnt\z@} +\def\@xnamedef#1{\expandafter\xdef\csname #1\endcsname} +\def\no@harm{% + \let\\=\relax \let\rm\relax + \let\ss=\relax \let\ae=\relax \let\oe=\relax + \let\AE=\relax \let\OE=\relax + \let\o=\relax \let\O=\relax + \let\i=\relax \let\j=\relax + \let\aa=\relax \let\AA=\relax + \let\l=\relax \let\L=\relax + \let\d=\relax \let\b=\relax \let\c=\relax + \let\bar=\relax + \def\protect{\noexpand\protect\noexpand}} +\def\proc@elem#1#2{\begingroup + \no@harm % make a few instructions harmless + \let\thanksref\@gobble % remove \thanksref from element + \let\corauthref\@gobble + \@xnamedef{@#1}{#2}% % and store as \@#1 + \let\thanksref\add@thanksref + \let\corauthref\add@thanksref + \setbox\@tempboxa\hbox{#2}% + \endgroup + \prev@elem=\cur@elem % keep track of type of previous + \cur@elem=\csname e@#1\endcsname % and current element +} +\def\add@thanksref#1{\global\advance\note@cnt\@ne + \ifnum\note@cnt>\@ne \add@xtok\t@loc@notes{\note@sep}\fi + \add@tok\t@loc@notes{\ref{#1}}} +\def\note@sep{,} +\def\thanks{\@ifnextchar[{\@tempswatrue + \thanks@optarg}{\@tempswafalse\thanks@optarg[]}} +\def\thanks@optarg[#1]#2{\refstepcounter{footnote}% + \if@tempswa\label{#1}\else\relax\fi + \add@tok\t@glob@notes{\footnotetext}% + \add@xtok\t@glob@notes{[\the\c@footnote]}% + \add@tok\t@glob@notes{{#2}}% + \ignorespaces} +\def\corauth{\@ifnextchar[{\@tempswatrue + \corauth@optarg}{\@tempswafalse\corauth@optarg[]}} +\def\corauth@optarg[#1]#2{\refstepcounter{corauth}% + \if@tempswa\label{#1}\else\relax\fi + \add@tok\corauth@text{\footnotetext}% + \add@xtok\corauth@text{[\the\c@corauth]}% + \add@tok\corauth@text{{#2}}\ignorespaces} +\newcommand\ead[1][email]{% + \add@eadcomma{#1}% + \expandafter\ifcase\csname has@ead@#1\endcsname + \expandafter\global\expandafter\chardef + \csname has@ead@#1\endcsname=1\relax\else + \expandafter\global\expandafter\chardef + \csname has@ead@#1\endcsname=2\relax\fi + \add@ead{#1}% +} +\def\add@ead#1#2{% + \expandafter\add@tok\csname #1@text\endcsname{\texttt{#2}\ead@au}% + \expandafter\add@xtok\csname #1@text\endcsname{{\@author}}% + \ignorespaces +} +\def\add@eadcomma#1{% + \expandafter\ifcase\csname has@ead@#1\endcsname\else + \expandafter\add@tok\csname #1@text\endcsname{, }\fi +} +\let\@ead@au\@empty +\def\ead@newau{\ifx\@ead@au\@empty\else\ead@addau\@ead@au + \let\@ead@au\@empty\fi} +\let\ead@endau\ead@newau +\def\ead@addau#1{ (#1)} +\def\ead@au#1{\def\@ead@au{#1}} +\def\email@name{Email address} +\def\emails@name{Email addresses} +\chardef\has@ead@email=0 +\def\url@name{URL} +\def\urls@name{URLs} +\chardef\has@ead@url=0 +\let\real@refstepcounter\refstepcounter +\def\footnote{\@ifnextchar[{\@xfootnote}{\real@refstepcounter + {\@mpfn}\protected@xdef\@thefnmark{\thempfn}\@footnotemark\@footnotetext}} +\def\footnotemark{\@ifnextchar[{\@xfootnotemark + }{\real@refstepcounter{footnote}\xdef\@thefnmark{\thefootnote}\@footnotemark}} +\def\footnoterule{\kern-3\p@ + \hrule \@width 3pc % The \hrule has default \@height of 0.4pt. + \kern 2.6\p@} + \let\report@elt\@gobble +\newenvironment{NoHyper}{}{} +\def\frontmatter{% + \NoHyper + \let\@corresp@note\relax + \global\t@glob@notes={}\global\c@author\z@ + \global\c@collab\z@ \global\c@address\z@ + \sv@mathsurround\mathsurround \m@th + \global\n@author=0\n@author@\relax + \global\n@collab=0\n@collab@\relax + \global\advance\n@author\m@ne % In comparisons later on we need + \global\advance\n@collab\m@ne % n@author-1 and n@collab-1 + \global\@firstauthortrue % set to false by first \author or \collab + \global\@hasabstractfalse % Default: no abstract or keywords + \global\@haskeywordsfalse % Default: no abstract or keywords + \global\@prefacefalse % not preface + \ifnum\c@firstpage=\c@lastpage + \gdef\@pagerange{\@pagenumprefix\ESpagenumber{firstpage}} + \else + \gdef\@pagerange{\@pagenumprefix + \ESpagenumber{firstpage}--\@pagenumprefix\ESpagenumber{lastpage}}% + \fi + \parskip 4\p@ + \open@fm \ignorespaces} +\def\preface{\@prefacetrue} +\def\endfrontmatter{% + \ifx\@runauthor\relax + \global\let\@runauthor\@runningauthor + \fi + \global\n@author=\c@author + \global\n@collab=\c@collab \@writecount + \global\@topnum\z@ + \thispagestyle{copyright}% % Format rest of front matter: + \if@preface \else % IF not preface THEN + \vskip \@overhistoryskip + \history@fmt % print history (received, ...) + \newcount\c@sv@footnote + \global\c@sv@footnote=\c@footnote % save current footnote number + \if@hasabstract % IF abstract/ keywords THEN + \vskip \@preabstractskip % Space above rule + \hrule height 0.4\p@ % Rule above abstract/keywords + \vskip 8\p@ + \unvbox\t@abstract % print abstract, if any + \fi + \if@haskeywords % IF keywords THEN + \vskip \@overkeywordskip + \unvbox\t@keyword % Keyword abstract, if any + \fi % FI + \vskip 10\p@ + \hrule height 0.4\p@ % rule below abstract/keywords + \dedicated@fmt % print dedication + \vskip \@belowfmskip % Vertical space below frontmatter +\fi % FI + \close@fm % Close front matter material. + \output@glob@notes % Put notes at bottom of 1st page + \global\c@footnote=\c@sv@footnote % restore footnote number + \global\@prefacefalse + \global\leftskip\z@ % Restore the normal values of + \global\@rightskip\z@ % \leftskip, + \global\rightskip\@rightskip % \rightskip and + \global\mathsurround\sv@mathsurround % \mathsurround. + \let\title\relax \let\author\relax + \let\collab\relax \let\address\relax + \let\frontmatter\relax \let\endfrontmatter\relax + \let\@maketitle\relax \let\@@maketitle\relax + \normal@text +} +\let\maketitle\relax +\newdimen\t@xtheight +\t@xtheight\textheight \advance\t@xtheight-\splittopskip +\def\open@fm{\global\setbox\fm@box=\vbox\bgroup + \hsize=\@frontmatterwidth % Front matter is page-wide by default + \centering % and centered + \sv@hyphenpenalty\hyphenpenalty % (save \hyphenpenalty) + \hyphenpenalty\@M} % and not hyphenated +\def\close@fm{\egroup % close \vbox (\fm@box) + \fm@size=\dp\fm@box \advance\fm@size by \ht\fm@box + \@whiledim\fm@size>\t@xtheight \do{% + \global\setbox\@tempboxa=\vsplit\fm@box to \t@xtheight + \unvbox\@tempboxa \newpage + \fm@size=\dp\fm@box \advance\fm@size by \ht\fm@box} + \if@TwoColumn + \emergencystretch=1pc \twocolumn[\unvbox\fm@box] + \else + \unvbox\fm@box + \fi} +\def\output@glob@notes{\bgroup + \the\t@glob@notes + \egroup} +\def\justify@off{\let\\=\@normalcr + \leftskip\z@ \@rightskip\@flushglue \rightskip\@rightskip} +\def\justify@on{\let\\=\@normalcr + \leftskip\z@ \@rightskip\z@ \rightskip\@rightskip} +\def\normal@text{\global\let\\=\@normalcr + \global\leftskip\z@ \global\@rightskip\z@ \global\rightskip\@rightskip + \global\parfillskip\@flushglue} +\def\@writecount{\write\@mainaux{\string\global + \string\@namedef{n@author@}{\the\n@author}}% + \write\@mainaux{\string\global\string + \@namedef{n@collab@}{\the\n@collab}}} +\def\title#1{% + \beg@elem + \title@note@fmt % formatting instruction + \add@tok\t@glob@notes % for \thanks commands + {\title@note@fmt}% + \proc@elem{title}{#1}% + \def\title@notes{\the\t@loc@notes}% % store the notes of the title, + \title@fmt{\@title}{\title@notes}% % print the title + \ignorespaces} +\def\subtitle#1{% + \beg@elem + \proc@elem{subtitle}{#1}% + \def\title@notes{\the\t@loc@notes}% % store the notes of the title, + \subtitle@fmt{\@subtitle}{\title@notes}% print the title + \ignorespaces} +\newdimen \@logoheight \@logoheight 5pc +\def\@Lhook{\vrule \@height \@logoheight \@width \z@ \vrule \@height 10\p@ \@width 0.2\p@ \vrule \@height 0.2\p@ \@width 10pt} +\def\@Rhook{\vrule \@height 0.2\p@ \@width 10\p@ \vrule \@height 10\p@ \@width 0.2\p@ \vrule \@height \@logoheight \@width \z@} +\def\title@fmt#1#2{% +\@ifundefined{@runtitle}{\global\def\@runtitle{#1}}{}% + \vspace*{12pt} % Vertical space above title + {\@titlesize #1\,\hbox{$^{#2}$}\par}% + \vskip\@undertitleskip +\vskip24\p@ % Vertical space below title + } +\def\subtitle@fmt#1#2{% % No vertical space above sub-title + {\@titlesize #1\,\hbox{$^{#2}$}}\par} +\def\title@note@fmt{\def\thefootnote{\fnstar{footnote}}} +\def\author{\@ifnextchar[{\author@optarg}{\author@optarg[]}} +\def\author@optarg[#1]#2{\stepcounter{author}% + \beg@elem + \add@tok\email@text{\ead@newau}% + \add@tok\url@text{\ead@newau}% + \@for\@tempa:=#1\do{\expandafter\add@thanksref\expandafter{\@tempa}}% + \report@elt{author}\proc@elem{author}{#2}% + \ifnum0\n@collab@=\z@ \runningauthor@fmt \fi + \author@fmt{\the\c@author}{\the\t@loc@notes}{\@author}% +} +\def\runningauthor@fmt{% + \begingroup\no@harm + \if@firstauthor + \ifnum0\n@author@ > 2 + \global\edef\@runningauthor{\@author\ et al.}% + \else + \global\let\@runningauthor\@author% + \fi + \else % \c@author > 1 + \ifnum0\n@author@ = 2 + \global\edef\@runningauthor{\@runningauthor\ \& \noexpand\@author}% + \fi + \fi + \endgroup +} +\def\author@fmt#1#2#3{\@newelemtrue + \if@firstauthor + \first@author \global\@firstauthorfalse \fi + \ifnum\prev@elem=\e@author \global\@newelemfalse \fi + \if@newelem \author@fmt@init \fi + \edef\@tempb{#2}\ifx\@tempb\@empty + \hbox{{\author@font #3}}\else + \hbox{{\author@font #3}\,$^{\mathrm{#2}}$}% + \fi} +\def\first@author{\author@note@fmt + \corauth@mark@fmt + \add@tok\t@glob@notes + {\output@corauth@text + \output@ead@text{email}% + \output@ead@text{url}% + \author@note@fmt}% +}% +\def\author@fmt@init{% + \par + \vskip 8\p@ \@plus 4\p@ \@minus 2\p@ + \@authorsize + \leavevmode} % Vertical space above author list + \def\and{\unskip~and~} +\def\collab{\@ifstar{\collab@arg}{\collab@arg}} +\let\collaboration=\collab +\def\collab@arg#1{\stepcounter{collab}% + \if@firstauthor \first@author \global\@firstauthorfalse \fi + \gdef\@runningauthor{#1}% + \beg@elem + \proc@elem{collab}{#1}% + \collab@fmt{\the\c@collab}{\the\t@loc@notes}{\@collab}% + \ignorespaces} +\def\collab@fmt#1#2#3{\@newelemtrue + \ifnum\prev@elem=\e@collab \global\@newelemfalse \fi + \if@newelem \collab@fmt@init \fi + \par % Start new paragraph + \edef\@tempb{#2}\ifx\@tempb\@empty + {\@authorsize #3}\else + {\@authorsize #3\,$^{\mathrm{#2}}$}} +\def\collab@fmt@init{\vskip 1em} % Vertical space above list +\def\author@note@fmt{\setcounter{footnote}{0}% + \def\thefootnote{\xarabic{footnote}}} +\let\collab@note@fmt=\author@note@fmt +\def\corauth@mark@fmt{\def\thecorauth{\astsymbol{corauth}}} +\def\output@corauth@text{\def\thefootnote{\astsymbol{footnote}}% + \the\corauth@text} +\def\output@ead@text#1{% + \expandafter\add@tok\csname #1@text\endcsname{\ead@endau}% + \expandafter\ifcase\csname has@ead@#1\endcsname\else + {\let\thefootnote\relax + \footnotetext[0]{\raggedright\textit{% + \expandafter\ifcase\csname has@ead@#1\endcsname\or + \csname #1@name\endcsname\else + \csname #1s@name\endcsname\fi + : }% + \expandafter\the\csname #1@text\endcsname.}}% + \fi} +\def\xarabic#1{% + \expandafter\expandafter\expandafter\ifnum\expandafter\the\@nameuse{c@#1}<0 + *\else\arabic{#1} \fi} +\def\xalph#1{% + \expandafter\expandafter\expandafter\ifnum\expandafter\the\@nameuse{c@#1}<0 + *\else\alph{#1} \fi} +\def\xfnsymbol#1{% + \expandafter\expandafter\expandafter\ifnum\expandafter\the\@nameuse{c@#1}<0 + *\else\fnsymbol{#1} \fi} +\def\address{\@ifstar{\address@star}% + {\@ifnextchar[{\address@optarg}{\address@noptarg}}} +\def\address@optarg[#1]#2{\real@refstepcounter{address}% + \beg@elem + \report@elt{address}\proc@elem{address}{#2}% + \address@fmt{\c@address}{\the\t@loc@notes}{\@address}{#1}% + \if@Elproofing\else\label{#1}\fi + \ignorespaces} +\def\address@noptarg#1{\real@refstepcounter{address}% + \beg@elem + \proc@elem{address}{#1}% + \address@fmt{\z@}{\the\t@loc@notes}{\@address}{\theaddress}% + \ignorespaces} +\def\address@star#1{% + \beg@elem + \proc@elem{address}{#1}% + \address@fmt{\m@ne}{\the\t@loc@notes}{\@address}{*}% + \ignorespaces} +\def\theaddress{\alph{address}} +\def\address@fmt#1#2#3#4{\@newelemtrue + \if@Elproofing\def\@eltag{#4}\else\def\@eltag{\theaddress}\fi + \ifnum\prev@elem=\e@address \@newelemfalse \fi + \if@newelem \address@fmt@init \fi + \noindent \bgroup \@addressstyle + \ifnum#1=\z@ + #3\,$^{\mathrm{#2}}$\space% + \else + \ifnum#1=\m@ne + $^{\phantom{\mathrm{\@eltag}}}$\space #3\,$^{\mathrm{#2}}$% + \else + $^{\mathrm{\@eltag}}\space$#3\,$^{\mathrm{#2}}$% + \fi + \fi + \par \egroup} +\def\address@fmt@init{% + \par % Start new paragraph + \vskip 6\p@ \@plus 3\p@ \@minus 1.5pt} +\def\abstract{\@ifnextchar[{\@abstract}{\@abstract[]}} +\def\@abstract[#1]{% + \global\@hasabstracttrue + \hyphenpenalty\sv@hyphenpenalty % restore \hyphenpenalty + \global\setbox\t@abstract=\vbox\bgroup + \leftskip\z@ + \@rightskip\z@ \rightskip\@rightskip \parfillskip\@flushglue + \small + \parindent 1em % \parindent in abstract + \noindent {\bfseries\abstractname} % caption `Abstract' (bold) + \vskip 0.5\@bls % half a line of space below +\noindent\ignorespaces +} + \def\endabstract{\par \egroup} +\def\keyword{% + \global\@haskeywordstrue % Implies rules are to be printed + \hyphenpenalty\sv@hyphenpenalty % restore \hyphenpenalty + \def\sep{\unskip, } % separator for multiple keywords + \def\MSC{\par\leavevmode\hbox {\it 1991 MSC:\ }}% + \def\PACS{\par\leavevmode\hbox {\it PACS:\ }}% + \global\setbox\t@keyword=\vbox\bgroup + \@keywordsize + \parskip\z@ + \vskip 10\p@ \@plus 2\p@ \@minus 2\p@ % One line of space above keywords. + \noindent\@keywordheading + \justify@off % Keywords are not justified. + \ignorespaces} +\def\endkeyword{\par \egroup} +\def\runtitle#1{\gdef\@runtitle{#1}} +\def\runauthor#1{\gdef\@runauthor{#1}} +\let\@runauthor\relax +\let\@runtitle\relax +\let\@runningauthor\relax +\def\RUNDATE{} +\def\RUNJNL{} +\def\RUNART{} +\def\journal#1{\gdef\@journal{#1}} +\def\volume#1{\gdef\@volume{#1}} \def\@volume{0} +\def\issue#1{\gdef\@issue{#1}} \def\@issue{0} +\newcount\@pubyear +\@pubyear=\number\year +\def\company#1{\def\@company{#1}} +\def\@copyrightyear{\number\year} +\def\@shortenyear#1#2#3#4\\{\global\def\@shortyear{#3#4}} +\expandafter\@shortenyear\the\@pubyear\\ +\def\pubyear#1{\global\@pubyear#1 + \expandafter\@shortenyear\the\@pubyear\\% + \ignorespaces} +\def\copyear#1{% + \gdef\@copyrightyear{#1}% + \ignorespaces} +\let\copyrightyear\copyear +\newcounter{firstpage} +\newcounter{lastpage} +\let\ESpagenumber\arabic +\def\firstpage#1{\def\@tempa{#1}\ifx\@tempa\@empty\else + \setcounter{firstpage}{#1}% + \global\c@page=#1 \ignorespaces\fi} +\setcounter{firstpage}{1} +\let\realpageref\pageref +\setcounter{lastpage}{0} +\def\lastpage#1{\def\@tempa{#1}\ifx\@tempa\@empty\else + \setcounter{lastpage}{#1}\ignorespaces\fi + } +\AtEndDocument{% + \clearpage + \addtocounter{page}{-1}% + \immediate\write\@auxout{% + \string\global\string\c@lastpage=\the\c@page}% + \addtocounter{page}{1}% +} +\def\date#1{\gdef\@date{#1}} \def\@date{\today} +\def\aid#1{} +\def\ssdi#1#2{} +\def\received#1{\def\@tempa{#1}\ifx\@tempa\@empty\else\gdef\@received{#1}\fi} + \def\@received{\relax} +\def\revised#1{\def\@tempa{#1}\ifx\@tempa\@empty\else\gdef\@revised{#1}\fi} + \def\@revised{\relax} +\def\accepted#1{\def\@tempa{#1}\ifx\@tempa\@empty\else\gdef\@accepted{#1}\fi} + \def\@accepted{\relax} +\def\communicated#1{\def\@tempa{#1}\ifx\@tempa\@empty\else\gdef\@communicated{#1}\fi} + \def\@communicated{\relax} +\def\dedicated#1{\def\@tempa{#1}\ifx\@tempa\@empty\else\gdef\@dedicated{#1}\fi} + \def\@dedicated{\relax} +\def\presented#1{\def\@tempa{#1}\ifx\@tempa\@empty\else\gdef\@presented{#1}\fi} + \def\@presented{\relax} +\def\articletype#1{\gdef\@articletype{#1}} + \@ifundefined{@articletype}{\def\@articletype{}}{} +\def\received@prefix{Received~} +\def\revised@prefix{; revised~} +\def\accepted@prefix{; accepted~} +\def\communicated@prefix{; communicated~by~} +\def\history@prefix{} +\def\received@postfix{} +\def\revised@postfix{} +\def\accepted@postfix{} +\def\communicated@postfix{} +\def\history@postfix{} +\def\empty@data{\relax} +\def\history@fmt{% + \bgroup + \@historysize + \vskip 6\p@ \@plus 2\p@ \@minus 1\p@ % Vertical space above history + \ifx\@received\empty@data \else % If there is no \received, + % do not print anything + \leavevmode + \history@prefix + \received@prefix\@received \received@postfix% + \ifx\@revised\empty@data \else + \revised@prefix\@revised \revised@postfix% + \fi + \ifx\@accepted\empty@data \else + \accepted@prefix\@accepted \accepted@postfix% + \fi + \ifx\@communicated\empty@data \else + \communicated@prefix\@communicated \communicated@postfix% + \fi + \history@postfix + \fi + \par \egroup} +\def\dedicated@fmt{% + \ifx\@dedicated\empty@data \else + \vskip 4\p@ \@plus 3\p@ + \normalsize\it\centering \@dedicated + \fi} +\def\@alph#1{\ifcase#1\or a\or b\or c\or d\or e\or f\or g\or h\or i\or +j\or k\or \ensuremath{\ell}\or m\or n\or o\or p\or q\or r\or s\or t\or +u\or v\or w\or x\or y\or z\or aa\or ab\or ac\or ad\or ae\or af\or ag\or +ah\or ai\or aj\or ak\or a\ensuremath{\ell}\or am\or an\or ao\or ap\or +aq\or ar\or as\or at\or au\or av\or aw\or ay\or az\or ba\or bb\or bc\or +bd\or be\or bf\or bg\or bh\or bi\or bj\or bk\or b\ensuremath{\ell}\or +bm\or bn\or bo\or bp\or bq\or br\or bs\or bt\or bu\or bw\or bx\or by\or 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\hbox{$\ast\ast\ast\ast$}\or + \hbox{$\ast\ast\ast\ast\ast$}\or + \hbox{$\ast\ast\ast\ast\ast\ast$}% + \else + \@ctrerr + \fi + \relax} +\mark{{}{}} % Initializes TeX's marks +\def\ps@plain{\let\@mkboth\@gobbletwo + \def\@oddhead{}% + \def\@evenhead{}% + \def\@oddfoot{\hfil {\rmfamily\thepage} \hfil}% + \let\@evenfoot\@oddfoot} +\def\@copyright{\@issn/\@shortyear/\$\@price\ $\copyright$\ \the\@pubyear\ + \@company{} All rights reserved} +\def\@jou@vol@pag{\@journal\ \@volume\ (\the\@pubyear)\ \@pagerange} +\def\sectionmark#1{} +\def\subsectionmark#1{} +\let\@j@v@p\@jou@vol@pag % long journal title appears in reprint line +\let\@@j@v@p\@jou@vol@pag % long journal title appears in running headline +\def\sectionmark#1{} +\def\subsectionmark#1{} +\def\ps@copyright{\let\@mkboth\@gobbletwo + \def\@oddhead{}% + \let\@evenhead\@oddhead + \def\@oddfoot{\small\slshape + \def\@tempa{0} + \ifx\@volume\@tempa + Preprint submitted to \@journal\hfil\@date\/% + \else + Article published in \@jou@vol@pag\hfil\hbox{}\fi}% + \let\@evenfoot\@oddfoot +} +\let\ps@noissn\ps@empty +\let\ps@headings\ps@plain +\def\today{\number\day\space\ifcase\month\or + January\or February\or March\or April\or May\or June\or + July\or August\or September\or October\or November\or December\fi + \space\number\year} +\def\nuc#1#2{\relax\ifmmode{}^{#1}{\protect\text{#2}}\else${}^{#1}$#2\fi} +\def\itnuc#1#2{\setbox\@tempboxa=\hbox{\scriptsize\it #1} + \def\@tempa{{}^{\box\@tempboxa}\!\protect\text{\it #2}}\relax + \ifmmode \@tempa \else $\@tempa$\fi} +\let\old@vec\vec % save old definition of \vec +\def\pol#1{\old@vec{#1}} +\def\half{{\textstyle\frac{1}{2}}} +\def\threehalf{{\textstyle\frac{3}{2}}} +\def\quart{{\textstyle\frac{1}{4}}} +\if@symbold\else\def\d{\,\mathrm{d}}\fi +\def\e{\mathop{\mathrm{e}}\nolimits} +\def\int{\intop} +\def\oint{\ointop} +\newbox\slashbox \setbox\slashbox=\hbox{$/$} +\newbox\Slashbox \setbox\Slashbox=\hbox{\large$/$} +\def\pFMslash#1{\setbox\@tempboxa=\hbox{$#1$} + \@tempdima=0.5\wd\slashbox \advance\@tempdima 0.5\wd\@tempboxa + \copy\slashbox \kern-\@tempdima \box\@tempboxa} +\def\pFMSlash#1{\setbox\@tempboxa=\hbox{$#1$} + \@tempdima=0.5\wd\Slashbox \advance\@tempdima 0.5\wd\@tempboxa + \copy\Slashbox \kern-\@tempdima \box\@tempboxa} +\def\FMslash{\protect\pFMslash} +\def\FMSlash{\protect\pFMSlash} + \def\Cset{\mathbb{C}} + \def\Hset{\mathbb{H}} + \def\Nset{\mathbb{N}} + \def\Qset{\mathbb{Q}} + \def\Rset{\mathbb{R}} + \def\Zset{\mathbb{Z}} +\if@TwoColumn + \adjdemerits=100 + \linepenalty=100 + \doublehyphendemerits=5000 % experimental (1993-12-14) + \emergencystretch=1.6pc + \spaceskip=0.3em \@plus 0.17em \@minus 0.12em +\fi +\@frontmatterwidth\textwidth +\ps@headings % 'headings' page style +\pagenumbering{arabic} % Arabic page numbers +\def\thepage{\@pagenumprefix\ESpagenumber{page}} % preceded by \@pagenumprefix +\let\baselinestretch\@blstr +\InputIfFileExists{\@shortjid.cfg}{}{} +\endinput +%% +%% End of file `elsart.cls'. -- 2.20.1 From cfce37621fd37e86a4a5b2ba964fd46921ac6c38 Mon Sep 17 00:00:00 2001 From: hackbard Date: Fri, 28 Jul 2006 13:59:40 +0000 Subject: [PATCH 15/16] intro added --- nlsop/paper/M243.tex | 23 ++++++++++++++++++----- 1 file changed, 18 insertions(+), 5 deletions(-) diff --git a/nlsop/paper/M243.tex b/nlsop/paper/M243.tex index efbf182..ca1dc91 100644 --- a/nlsop/paper/M243.tex +++ b/nlsop/paper/M243.tex @@ -52,15 +52,28 @@ Nanostructures; Ion irradiation\\ \section{Introduction} -High-dose implantations into solids usually results in the formation of unordered ensembles of precipitates with a - - -\section{Modell} +Precipitates, as a result of high-dose ion implantation into solids, are usually statistically arranged and have a broad size distribution. +However, the formation of ordered, lamellar inclusions has been observed for a number of ion/target combinations at certain implantation conditions \cite{ommen,specht,ishimaru}. +An inevitable condition for the material to observe this special self-organized arrangement is a largely reduced density of host atoms in the amorphous phase compared to the crystalline host lattice. +As a consequence stress is exerted by the amorphous inclusions which is responsible for the ordering process. +A model to describe the process is introduced. +The implementation of a simulation code based on that model is discussed. +Simulation results are compared to experimental data, focussing on high-dose carbon implantation into silicon. +Finally a guideline for fabrication of broad ditributions of lamellar ordered structures is suggested. + +\section{Model} +High-dose carbon implantations at $150 \, ^{\circ} \mathrm{C}$ with an energy of $180 \, keV$ result \section{Simulation} \section{Results} -\section{Summayr and conclusion} +\section{Summary and conclusion} + +\begin{thebibliography}{20} +\bibitem{ommen} A. H. van Ommen. Nucl. Instr. and Meth. B 39 (1989) 194. +\bibitem{specht} E. D. Specht, D. A. Walko, S. J. Zinkle. Nucl. Instr. and Meth. B 84 (2000) 390. +\bibitem{ishimaru} M. Ishimaru, R. M. Dickerson, K. E. Sickafus. Nucl. Instr. and Meth. B 166-167 (2000) 390. +\end{thebibliography} \end{document} -- 2.20.1 From a15f3c73944bcd75505f403340744d3dad7e6c9e Mon Sep 17 00:00:00 2001 From: hackbard Date: Mon, 31 Jul 2006 19:05:01 +0000 Subject: [PATCH 16/16] finished model and began simulation chapter --- nlsop/paper/M243.tex | 146 ++++++++++++++++++++++++++++++++++++++++--- 1 file changed, 137 insertions(+), 9 deletions(-) diff --git a/nlsop/paper/M243.tex b/nlsop/paper/M243.tex index ca1dc91..99cccce 100644 --- a/nlsop/paper/M243.tex +++ b/nlsop/paper/M243.tex @@ -1,5 +1,5 @@ \pdfoutput=0 -\documentclass{elsart} +\documentclass[12pt]{elsart} \usepackage[activate]{pdfcprot} \usepackage{verbatim} \usepackage[english]{babel} @@ -12,6 +12,8 @@ \graphicspath{{../img/}} \usepackage{natbib,amssymb} +\linespread{1.4} + \begin{document} \hyphenation{TRIM} @@ -35,9 +37,9 @@ Universitätsstrasse 1,\\D-86135 Augsburg, Germany} \begin{abstract} -Periodically arranged, self-organized, nanometric, amorphous precipitates have been observed at high-dose ion implantations for a number of ion/target combinations at certain implantation conditions. +Periodically arranged, self-organized, nanometric, amorphous precipitates have been observed after high-fluence ion implantations into solids for a number of ion/target combinations at certain implantation conditions. A model describing the ordering process based on compressive stress exerted by the amorphous inclusions as a result of the density change upon amorphization is introduced. -A Monte Carlo simulation code, which focuses on high dose carbon implantation into silicon, is able to reproduce experimentally observed results. +A Monte Carlo simulation code, which focuses on high fluence carbon implantation into silicon, is able to reproduce experimentally observed results. By means of simulation the selforganization process gets traceable and detailed information about the compositional and structural state during the ordering process is obtained. Based on simulation results, a recipe is proposed for producing broad distributions of lamellar ordered structures. \end{abstract} @@ -52,28 +54,154 @@ Nanostructures; Ion irradiation\\ \section{Introduction} -Precipitates, as a result of high-dose ion implantation into solids, are usually statistically arranged and have a broad size distribution. +Precipitates, as a result of high-fluence ion implantation into solids, are usually statistically arranged and have a broad size distribution. However, the formation of ordered, lamellar inclusions has been observed for a number of ion/target combinations at certain implantation conditions \cite{ommen,specht,ishimaru}. An inevitable condition for the material to observe this special self-organized arrangement is a largely reduced density of host atoms in the amorphous phase compared to the crystalline host lattice. As a consequence stress is exerted by the amorphous inclusions which is responsible for the ordering process. A model to describe the process is introduced. The implementation of a simulation code based on that model is discussed. -Simulation results are compared to experimental data, focussing on high-dose carbon implantation into silicon. +Simulation results are compared to experimental data, focussing on high-fluence carbon implantations into silicon. Finally a guideline for fabrication of broad ditributions of lamellar ordered structures is suggested. \section{Model} -High-dose carbon implantations at $150 \, ^{\circ} \mathrm{C}$ with an energy of $180 \, keV$ result +High-fluence carbon implantations at temperatures between $150$ and $400 \, ^{\circ} \mathrm{C}$ with an energy of $180 \, keV$ result in an amorphous $SiC_x$ layer along with spherical and lamellar amorphous $SiC_x$ inclusions at the layer interface \cite{lamellar_inclusions}, as can be ssen in Fig. \ref{img:tem}. +A model is proposed in \cite{model_joerg}, which is schematically displayed in Fig. \ref{img:model}, showing the evolution into ordered lamellae with increasingamount of implanted carbon. + +With increasing fluence the silcon is supersaturated of carbon atoms which results in a nucleation of spherical $SiC_x$ precipitates. +By the precipitation into the amorphous $SiC_x$ ($a-SiC_x$) phase an enormous interfacial energy \cite{int_eng} required for cubic $SiC$ ($3C-SiC$, $a=0.536 \, nm$) in crystalline silicon ($c-Si$, $a=0.543 \, nm$) due to a $20 \, \%$ lattice mismatch can be saved. +Since amorphous silicon ($a-Si$) is not stable against ion beam induced epitaxial recrystallization at temperatures above $130 \, ^{\circ} \mathrm{C}$ \cite{ibic}, the existence of the amorphous precipitates must be due to the accumulation of carbon (carbon induced amorphization), which stabilizes the amorphous phase \cite{ap_stab}. +In fact, energy filtered XTEM studies \cite{eftem_maik} revealed the carbon-rich nature of the precipitates. + +The $Si$ atomic density of $a-SiC$ is about $20$ to $30 \, \%$ lower compared to $3C-SiC$ \cite{si_dens1,si_dens2}. +The same is assumed for substoicheometrc $a-SiC_x$ compared to $c-Si$. +Therefor the amorphous volumes tend to expand and as a result compressive stress - which is relaxing in the vertical direction since the process occurs near the target surface - is applied on the $Si$ host lattice, represented by black arrows in Fig \ref{img:model}. +Volumes between amorphous inclusions will more likely turn into an amorphous state as the stress aggravates the rearrangement of atoms on regular lattice sites (stress enhanced amorphization). +In contrast, randomly originated amorphous precipitates (ballistic amorphization) located in a crystalline neighbourhood not containing high amounts of carbon will recrystallize in all probability under the present implantation conditions. + +Since the solid solubility of carbon in $c-Si$ is essentially zero, once formed, $a-SiC_x$ inclusions serve as diffusional sinks for excess carbon atoms in the $c-Si$ phase, represented by the white arrows in Fig. \ref{img:model}. +As a consequence the amorphous volumes accumulate carbon enhancing the selforganization process. \section{Simulation} +For the Monte Carlo simulation the target is devided into cells with a side length of $3 \, nm$. +Each cell has a crystalline or amorphous state and stores the local carbon concentration. +It is addressed by a position vector $\vec{r} = (k,l,m)$ where $k$, $l$ and $m$ are integers. +The simulation starts with a complete crytsalline target and zero carbon inside. + +The model proposes three mechanisms of amorphization. +In the simulation, each of this mechanisms contributes to a local amorphization probability of cell $\vec{r}$. +The influence of the mechanisms are controlled by simulation parameters. +The local amorphization probability at volume $\vec{r}$ is calculated by +\begin{equation} +p_{c \rightarrow a}(\vec{r}) = p_b + p_c c_C(\vec{r}) + \sum_{\textrm{amorphous neighbours}} \frac{p_s c_C(\vec{r'})}{(r-r')^2} \textrm{ .} +\end{equation} + +The ballistic amorphization is constant and controlled by $p_b$. +This choice is justified by analysing {\em TRIM} \cite{trim} collision data that show a mean constant energy loss per collision of an ion. +The carbon induced amorphization is proportional to the local amount of carbon $c_C(\vec{r})$ and controlled by the simulation parameter $p_c$. +The stress enhanced amorphization is controlled by $p_s$. +The forces originating from the amorphous volumes $\vec{r}'$ in the vicinity are assumed to be proportional to the amount of carbon $c_C(\vec{r}')$. +The sum is just taken over volumes located in the layer and since the stress amplitude is decreasing with the square of the distance $r-r'$ a cutoff radius is used in the simulation. +In case of an amorphous volume, a recrystallization probability is given by +\begin{equation} +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{,} +\end{equation} +\[ +\delta (\vec r) = \left\{ +\begin{array}{ll} + 1 & \textrm{volume at position $\vec r$ amorphous} \\ + 0 & \textrm{otherwise} \\ +\end{array} +\right. +\] +which is basically $1$ minus the amorphization probability and a term taking into account the crystalline neighbourhood which is needed for epitaxial recrystallization. + +The simulation algorithm consists of three parts. +The first part is the amorphization/recrystallization step. +Random values are computed to specify the volume $\vec{r}$ which is hit by an impinging carbon ion. +Two uniformly distributed random numbers $x$ and $y$ are mapped to the coordinates $k$ and $l$. +A random number $z$ corresponding to the depth coordinate $m$ is distributed according to the nuclear stopping power gained by {\em TRIM} using the rejection method. + +Again analysing {\em TRIM} collision data shows the nuclear stopping power being essentially +The amorphization or recrystallization probability is computed and another random number decides whether there is amorphization or recrystallization or + + \section{Results} \section{Summary and conclusion} \begin{thebibliography}{20} -\bibitem{ommen} A. H. van Ommen. Nucl. Instr. and Meth. B 39 (1989) 194. -\bibitem{specht} E. D. Specht, D. A. Walko, S. J. Zinkle. Nucl. Instr. and Meth. B 84 (2000) 390. -\bibitem{ishimaru} M. Ishimaru, R. M. Dickerson, K. E. Sickafus. Nucl. Instr. and Meth. B 166-167 (2000) 390. +\bibitem{ommen} A. H. van Ommen, Nucl. Instr. and Meth. B 39 (1989) 194. +\bibitem{specht} E. D. Specht, D. A. Walko, S. J. Zinkle, Nucl. Instr. and Meth. B 84 (2000) 390. +\bibitem{ishimaru} M. Ishimaru, R. M. Dickerson, K. E. Sickafus, Nucl. Instr. and Meth. B 166-167 (2000) 390. +\bibitem{lamellar_inclusions} J. K. N. Lindner, M. Häberlen, M. Schmidt, W. Attenberger, B. Stritzker, Nucl. Instr. Meth. B 186 (2002) 206. +\bibitem{model_joerg} J. K. N. Lindner, Nucl. Instr. Meth. B 178 (2001) 44. +\bibitem{int_eng} W. J. Taylor, T. Y. Tan, U. Gösele, Appl. Phys. Lett. 62 (1993) 3336. +\bibitem{ibic} J. Linnross, R. G. Elliman, W. L. Brown, J. Matter. Res. 3 (1988) 1208. +\bibitem{ap_stab} E. F. Kennedy, L. Csepregi, J. W. Mayer, J. Appl. Phys. 48 (1977) 4241. +\bibitem{eftem_maik} M. Häberlen, Bildung und Ausheilverhalten nanometrischer amorpher Einschlüsse in Kohlenstoff-implantierten Silizium, Diploma thesis, Augsburg, 2002 (in Germany). +\bibitem{si_dens1} L. L. Horton, J. Bentley, L. Romana, A. Perez, C. J. McHargue, J. C. McCallum, Nucl. Instr. Meth. B 65 (1992) 345. +\bibitem{si_dens2} W. Skorupa, V. Heera, Y. Pacaud, H. Weishart, in: F. Priolo, J. K. N. Lindner, A. Nylandsted Larsen, J. M. Poate (Eds.), New Trends in Ion Beam Processing of Materials, Eur. Mater. Res. Soc. Symp. Proc. 65, Part 1, Elsevier,Amsterdam, 1997,p. 114. +\bibitem{trim} J. F. Ziegler, J. P. Biersack, U. Littmark, The Stopping and Range of Ions in Solids, Pergamon, New York, 1985. \end{thebibliography} +\newpage + +\section*{Figure Captions} + +\begin{enumerate} +\item Cross-sectional transmission electron microscopy (XTEM) image of a $Si(100)$ sample implanted with $180 \, keV$ $C^+$ ions at a fluence of $4.3 \times 10^{17} \, cm^{-2}$ and a substrate temperature of $150 \, ^{\circ} \mathrm{C}$. Lamellar and spherical amorphous inclusions at the interface of the continuous amorphous layer are marked by L and S. +\item Schematic explaining the selforganization of amorphous $SiC_x$ precipitates and the evolution into ordered lamellae with increasing fluence (see text). +\item Comparison of simulation results and XTEM images ($180 \, keV$ $C^+$ implantation into silicon at $150 \, ^{\circ} mathrm{C}$) for several fluence. Amorphous cells are white. Simulation parameters: $p_b=0.01$, $p_c=0.001$, $p_s=0.0001$, $d_r=0.05$, $d_v=1 \times 10^6$. +\item Amorphous cell distribution and corresponding carbon implantation profile. The implantation profile shows the mean amount of carbon in amorphous and crystalline volumes as well as the sum for a fluence of $4.3 \times 10^{17} \, cm^{-2}$. +\item Simulation result for a $2 \, MeV$ $C^+$ irradiation into silicon doped with $10 \, at. \%$ carbon by multiple implantation steps between $180$ and $10 \, keV$. $20 \times 10^6$ simulation steps correspond to a fluence of $0.54 \times 10^{17} \, cm^{-2}$. +\end{enumerate} + +\newpage +\section*{Figures} + +\begin{figure}[!h] +\begin{center} +\includegraphics[width=14cm]{k393abild1_e.eps} +\caption[foo]{} +\end{center} +\label{img:tem} +\end{figure} + +\newpage +\begin{figure}[!h] +\begin{center} +\includegraphics[width=14cm]{modell_ng_e.eps} +\caption[foo]{} +\end{center} +\label{img:model} +\end{figure} + +\newpage +\begin{figure}[!h] +\begin{center} +\includegraphics[width=14cm]{dosis_entwicklung_all_e.eps} +\caption[foo]{} +\end{center} +\label{img:dose_cmp} +\end{figure} + +\newpage +\begin{figure}[!h] +\begin{center} +\includegraphics[width=14cm]{ac_cconc_ver2_e.eps} +\caption[foo]{} +\end{center} +\label{img:carbon_distr} +\end{figure} + +\newpage +\begin{figure}[!h] +\begin{center} +\includegraphics[width=14cm]{multiple_impl_e.eps} +\caption[foo]{} +\end{center} +\label{img:broad_lam} +\end{figure} + \end{document} -- 2.20.1