From 1c838933fa76951ad4deb1164e8d2a950b6771cf Mon Sep 17 00:00:00 2001 From: hackbard Date: Tue, 8 Nov 2011 23:26:06 +0100 Subject: [PATCH] continue with ci and vac --- posic/talks/mpi_app.tex | 284 +++++++++++++++++++++------------------- 1 file changed, 152 insertions(+), 132 deletions(-) diff --git a/posic/talks/mpi_app.tex b/posic/talks/mpi_app.tex index 3410dca..2bf8383 100644 --- a/posic/talks/mpi_app.tex +++ b/posic/talks/mpi_app.tex @@ -1579,9 +1579,6 @@ Reorientation pathway composed of two consecutive processes of the above type \end{slide} -% continue here -\fi - \begin{slide} \headphd @@ -1589,13 +1586,14 @@ Reorientation pathway composed of two consecutive processes of the above type Defect combinations } -\small +\footnotesize -\vspace{0.2cm} +\vspace{0.3cm} \begin{minipage}{9cm} +{\bf + Summary of combinations}\\[0.1cm] {\scriptsize -Combinations of an initially created \ci{} \hkl[0 0 -1] DB\\ \begin{tabular}{l c c c c c c} \hline $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\ @@ -1612,193 +1610,158 @@ Combinations of an initially created \ci{} \hkl[0 0 -1] DB\\ \hline \end{tabular} } +\vspace{0.2cm} +\begin{center} +{\color{blue} + $E_{\text{b}}$ explainable by stress compensation / increase +} +\end{center} \end{minipage} \begin{minipage}{3cm} \includegraphics[width=3.5cm]{comb_pos.eps} \end{minipage} -\vspace*{0.3cm} - -\footnotesize +\vspace{0.2cm} +{\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm] \begin{minipage}[t]{3.2cm} \underline{\hkl[1 0 0] at position 1}\\[0.1cm] \includegraphics[width=2.8cm]{00-1dc/2-25.eps} \end{minipage} -\begin{minipage}[t]{3.2cm} +\begin{minipage}[t]{3.0cm} \underline{\hkl[0 -1 0] at position 1}\\[0.1cm] \includegraphics[width=2.8cm]{00-1dc/2-39.eps} \end{minipage} -\begin{minipage}[t]{5.5cm} +\begin{minipage}[t]{6.1cm} +\vspace{0.7cm} \begin{itemize} - \item $E_{\text{b}}=0$ $\Leftrightarrow$ non-interacting defects\\ - $E_{\text{b}} \rightarrow 0$ for increasing distance (R) - \item Stress compensation / increase - \item Unfavored: antiparallel orientations - \item Indication of energetically favored\\ - agglomeration - \item Most favorable: C clustering - \item However: High barrier ($>4\,\text{eV}$) - \item $4\times{\color{cyan}-2.25}$ versus $2\times{\color{orange}-2.39}$ - (Entropy) + \item \ci{} agglomeration energetically favorable + \item Most favorable: C clustering\\ + {\color{red}However \ldots}\\ + \ldots high migration barrier ($>4\,\text{eV}$)\\ + \ldots entropy: + $4\times{\color{cyan}[-2.25]}$ versus + $2\times{\color{orange}[-2.39]}$ \end{itemize} +\begin{center} +{\color{blue}\ci{} agglomeration / no C clustering} +\end{center} \end{minipage} - \end{slide} -\end{document} -\ifnum1=0 - \begin{slide} - {\large\bf\boldmath - Combinations of C-Si \hkl<1 0 0>-type interstitials - } - -\small - -\vspace*{0.1cm} +\headphd +{\large\bf\boldmath + Defect combinations +} -Energetically most favorable combinations along \hkl<1 1 0> +\footnotesize -\vspace*{0.1cm} +\vspace{0.3cm} +\begin{minipage}{9cm} +{\bf + Summary of combinations}\\[0.1cm] {\scriptsize \begin{tabular}{l c c c c c c} \hline - & 1 & 2 & 3 & 4 & 5 & 6\\ -\hline -$E_{\text{b}}$ [eV] & -2.39 & -1.88 & -0.59 & -0.31 & -0.24 & -0.21 \\ -C-C distance [\AA] & 1.4 & 4.6 & 6.5 & 8.6 & 10.5 & 10.8 \\ -Type & \hkl<-1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0>, \hkl<0 -1 0>\\ + $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\ + \hline + \hkl[0 0 -1] & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\ + \hkl[0 0 1] & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\ + \hkl[0 -1 0] & {\color{orange}-2.39} & -0.17 & {\color{green}-0.10} & {\color{blue}-0.27} & {\color{magenta}-1.88} & {\color{gray}-0.05}\\ + \hkl[0 1 0] & {\color{cyan}-2.25} & -1.90 & {\color{cyan}-2.25} & {\color{purple}-0.12} & {\color{violet}-1.38} & {\color{yellow}-0.06}\\ + \hkl[-1 0 0] & {\color{orange}-2.39} & -0.36 & {\color{cyan}-2.25} & {\color{purple}-0.12} & {\color{magenta}-1.88} & {\color{gray}-0.05}\\ + \hkl[1 0 0] & {\color{cyan}-2.25} & -2.16 & {\color{green}-0.10} & {\color{blue}-0.27} & {\color{violet}-1.38} & {\color{yellow}-0.06}\\ + \hline + C$_{\text{sub}}$ & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\ + Vacancy & -5.39 ($\rightarrow$ C$_{\text{sub}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\ \hline \end{tabular} } - -\vspace*{0.3cm} - -\begin{minipage}{7.0cm} -\includegraphics[width=7cm]{db_along_110_cc.ps} -\end{minipage} -\begin{minipage}{6.0cm} -\begin{itemize} - \item Interaction proportional to reciprocal cube of C-C distance - \item Saturation in the immediate vicinity - \renewcommand\labelitemi{$\Rightarrow$} - \item Agglomeration of \ci{} expected - \item Absence of C clustering -\end{itemize} +\vspace{0.2cm} \begin{center} {\color{blue} - Consisten with initial precipitation model + $E_{\text{b}}$ explainable by stress compensation / increase } \end{center} \end{minipage} +\begin{minipage}{3cm} +\includegraphics[width=3.5cm]{comb_pos.eps} +\end{minipage} \vspace{0.2cm} -\end{slide} - -\begin{slide} - - {\large\bf\boldmath - Combinations of substitutional C and \hkl<1 1 0> Si self-interstitials - } - - \scriptsize - -%\begin{center} -%\begin{minipage}{3.2cm} -%\includegraphics[width=3cm]{sub_110_combo.eps} -%\end{minipage} -%\begin{minipage}{7.8cm} -%\begin{tabular}{l c c c c c c} -%\hline -%C$_{\text{sub}}$ & \hkl<1 1 0> & \hkl<-1 1 0> & \hkl<0 1 1> & \hkl<0 -1 1> & -% \hkl<1 0 1> & \hkl<-1 0 1> \\ -%\hline -%1 & \RM{1} & \RM{3} & \RM{3} & \RM{1} & \RM{3} & \RM{1} \\ -%2 & \RM{2} & A & A & \RM{2} & C & \RM{5} \\ -%3 & \RM{3} & \RM{1} & \RM{3} & \RM{1} & \RM{1} & \RM{3} \\ -%4 & \RM{4} & B & D & E & E & D \\ -%5 & \RM{5} & C & A & \RM{2} & A & \RM{2} \\ -%\hline -%\end{tabular} -%\end{minipage} -%\end{center} - -%\begin{center} -%\begin{tabular}{l c c c c c c c c c c} -%\hline -%Conf & \RM{1} & \RM{2} & \RM{3} & \RM{4} & \RM{5} & A & B & C & D & E \\ -%\hline -%$E_{\text{f}}$ [eV]& 4.37 & 5.26 & 5.57 & 5.37 & 5.12 & 5.10 & 5.32 & 5.28 & 5.39 & 5.32 \\ -%$E_{\text{b}}$ [eV] & -0.97 & -0.08 & 0.22 & -0.02 & -0.23 & -0.25 & -0.02 & -0.06 & 0.05 & -0.03 \\ -%$r$ [nm] & 0.292 & 0.394 & 0.241 & 0.453 & 0.407 & 0.408 & 0.452 & 0.392 & 0.456 & 0.453\\ -%\hline -%\end{tabular} -%\end{center} - -\begin{minipage}{6.0cm} -\includegraphics[width=5.8cm]{c_sub_si110.ps} +{\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm] +\begin{minipage}[t]{3.2cm} +\underline{\hkl[1 0 0] at position 1}\\[0.1cm] +\includegraphics[width=2.8cm]{00-1dc/2-25.eps} \end{minipage} -\begin{minipage}{7cm} -\scriptsize +\begin{minipage}[t]{3.0cm} +\underline{\hkl[0 -1 0] at position 1}\\[0.1cm] +\includegraphics[width=2.8cm]{00-1dc/2-39.eps} +\end{minipage} +\begin{minipage}[t]{6.1cm} +\vspace{0.7cm} \begin{itemize} - \item IBS: C may displace Si\\ - $\Rightarrow$ C$_{\text{sub}}$ + \hkl<1 1 0> Si self-interstitial - \item Assumption:\\ - \hkl<1 1 0>-type $\rightarrow$ favored combination - \renewcommand\labelitemi{$\Rightarrow$} - \item Most favorable: \cs{} along \hkl<1 1 0> chain \si{} - \item Less favorable than C-Si \hkl<1 0 0> dumbbell - \item Interaction drops quickly to zero\\ - $\rightarrow$ low capture radius + \item \ci{} agglomeration energetically favorable + \item Most favorable: C clustering\\ + {\color{red}However \ldots}\\ + \ldots high migration barrier ($>4\,\text{eV}$)\\ + \ldots entropy: + $4\times{\color{cyan}[-2.25]}$ versus + $2\times{\color{orange}[-2.39]}$ \end{itemize} \begin{center} - {\color{blue} - IBS process far from equilibrium\\ - \cs{} \& \si{} instead of thermodynamic ground state - } +{\color{blue}\ci{} agglomeration / no C clustering} \end{center} \end{minipage} -\begin{minipage}{6.5cm} -\includegraphics[width=6.0cm]{162-097.ps} -\begin{itemize} - \item Low migration barrier -\end{itemize} +% insert graph ... +\begin{pspicture}(0,0)(0,0) +\rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{ +\begin{minipage}{14cm} +\hfill +\vspace{12cm} \end{minipage} -\begin{minipage}{6.5cm} +}} +\rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{ +\begin{minipage}{8cm} \begin{center} -Ab initio MD at \degc{900}\\ -\includegraphics[width=3.3cm]{md_vasp_01.eps} -$t=\unit[2230]{fs}$\\ -\includegraphics[width=3.3cm]{md_vasp_02.eps} -$t=\unit[2900]{fs}$ +\vspace{0.2cm} +\scriptsize +Interaction along \hkl[1 1 0] +\includegraphics[width=7cm]{db_along_110_cc.ps} \end{center} -{\color{blue} -Contribution of entropy to structural formation -} \end{minipage} +}}} +\end{pspicture} \end{slide} +% continue here +\fi + \begin{slide} - {\large\bf\boldmath - Migration in C-Si \hkl<1 0 0> and vacancy combinations - } +{\large\bf + Defect combinations +} - \footnotesize +\footnotesize \vspace{0.1cm} +{\bf Combinations of \ci{} \hkl[0 0 -1] and a vacancy}\\ \begin{minipage}[t]{3cm} \underline{Pos 2, $E_{\text{b}}=-0.59\text{ eV}$}\\ \includegraphics[width=2.8cm]{00-1dc/0-59.eps} \end{minipage} + + + \begin{minipage}[t]{7cm} \vspace{0.2cm} \begin{center} @@ -1812,9 +1775,10 @@ Contribution of entropy to structural formation Without nearby \hkl<1 1 0> Si self-interstitial (IBS)\\ $\Downarrow$\\ {\color{blue}Formation of SiC by successive substitution by C} - \end{center} \end{minipage} + + \begin{minipage}[t]{3cm} \underline{Pos 3, $E_{\text{b}}=-3.14\text{ eV}$}\\ \includegraphics[width=2.8cm]{00-1dc/3-14.eps} @@ -1879,6 +1843,62 @@ Contribution of entropy to structural formation \end{slide} +\end{document} +\ifnum1=0 + +\begin{slide} + + {\large\bf\boldmath + Combinations of substitutional C and \hkl<1 1 0> Si self-interstitials + } + + \scriptsize + +\begin{minipage}{6.0cm} +\includegraphics[width=5.8cm]{c_sub_si110.ps} +\end{minipage} +\begin{minipage}{7cm} +\scriptsize +\begin{itemize} + \item IBS: C may displace Si\\ + $\Rightarrow$ C$_{\text{sub}}$ + \hkl<1 1 0> Si self-interstitial + \item Assumption:\\ + \hkl<1 1 0>-type $\rightarrow$ favored combination + \renewcommand\labelitemi{$\Rightarrow$} + \item Most favorable: \cs{} along \hkl<1 1 0> chain \si{} + \item Less favorable than C-Si \hkl<1 0 0> dumbbell + \item Interaction drops quickly to zero\\ + $\rightarrow$ low capture radius +\end{itemize} +\begin{center} + {\color{blue} + IBS process far from equilibrium\\ + \cs{} \& \si{} instead of thermodynamic ground state + } +\end{center} +\end{minipage} + +\begin{minipage}{6.5cm} +\includegraphics[width=6.0cm]{162-097.ps} +\begin{itemize} + \item Low migration barrier +\end{itemize} +\end{minipage} +\begin{minipage}{6.5cm} +\begin{center} +Ab initio MD at \degc{900}\\ +\includegraphics[width=3.3cm]{md_vasp_01.eps} +$t=\unit[2230]{fs}$\\ +\includegraphics[width=3.3cm]{md_vasp_02.eps} +$t=\unit[2900]{fs}$ +\end{center} +{\color{blue} +Contribution of entropy to structural formation +} +\end{minipage} + +\end{slide} + \begin{slide} {\large\bf -- 2.20.1