X-Git-Url: https://hackdaworld.org/gitweb/?a=blobdiff_plain;f=posic%2Ftalks%2Fmpi_app.tex;h=358698d6a10699712337d71d8dff01c5a5c6ba87;hb=01f5420ca3315280e622d8df277abbd73c4ee4f5;hp=3410dca0a91ba27de779d9623b9313d99a562739;hpb=746f2f655599d7f94bf80cd968e6980f3f6f423e;p=lectures%2Flatex.git diff --git a/posic/talks/mpi_app.tex b/posic/talks/mpi_app.tex index 3410dca..358698d 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\\ @@ -1612,327 +1610,366 @@ 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{0.2cm} +\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} +\vspace{0.2cm} -\begin{minipage}{7.0cm} -\includegraphics[width=7cm]{db_along_110_cc.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}{6.0cm} +\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 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 + \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} - Consisten with initial precipitation model -} +{\color{blue}\ci{} agglomeration / no C clustering} \end{center} \end{minipage} +% 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} +}} +\rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{ +\begin{minipage}{8cm} +\begin{center} \vspace{0.2cm} +\scriptsize +Interaction along \hkl[1 1 0] +\includegraphics[width=7cm]{db_along_110_cc.ps} +\end{center} +\end{minipage} +}}} +\end{pspicture} \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} +\headphd +{\large\bf + Defect combinations of C-Si dimers and vacancies +} +\footnotesize -%\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} +\vspace{0.2cm} -\begin{minipage}{6.0cm} -\includegraphics[width=5.8cm]{c_sub_si110.ps} +\begin{minipage}[b]{2.6cm} +\begin{flushleft} +\underline{V at 2: $E_{\text{b}}=-0.59\text{ eV}$}\\[0.1cm] +\includegraphics[width=2.5cm]{00-1dc/0-59.eps} +\end{flushleft} \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} +\begin{minipage}[b]{7cm} +\hfill \end{minipage} +\begin{minipage}[b]{2.6cm} +\begin{flushright} +\underline{V at 3, $E_{\text{b}}=-3.14\text{ eV}$}\\[0.1cm] +\includegraphics[width=2.5cm]{00-1dc/3-14.eps} +\end{flushright} +\end{minipage}\\[0.2cm] \begin{minipage}{6.5cm} -\includegraphics[width=6.0cm]{162-097.ps} -\begin{itemize} - \item Low migration barrier -\end{itemize} +\includegraphics[width=6.0cm]{059-539.ps} +\end{minipage} +\begin{minipage}{5.7cm} +\includegraphics[width=6.0cm]{314-539.ps} \end{minipage} + +\begin{pspicture}(0,0)(0,0) +\psline[linewidth=0.05cm,linecolor=gray](6.3,9.0)(6.3,0) + +\rput(6.3,7.0){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=gray]{ \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} +IBS: Impinging C creates V \& far away \si\\[0.3cm] +Low migration barrier towards C$_{\text{sub}}$\\ +\&\\ +High barrier for reverse process\\[0.3cm] {\color{blue} -Contribution of entropy to structural formation +High probability of stable C$_{\text{sub}}$ configuration } +\end{center} \end{minipage} +}}} +\end{pspicture} \end{slide} \begin{slide} - {\large\bf\boldmath - Migration in C-Si \hkl<1 0 0> and vacancy combinations - } +\headphd +{\large\bf + Combinations of substitutional C and Si self-interstitials +} - \footnotesize +\scriptsize -\vspace{0.1cm} +\vspace{0.3cm} -\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{minipage}{6.2cm} \begin{center} - Low activation energies\\ - High activation energies for reverse processes\\ - $\Downarrow$\\ - {\color{blue}C$_{\text{sub}}$ very stable}\\ -\vspace*{0.1cm} - \hrule -\vspace*{0.1cm} - Without nearby \hkl<1 1 0> Si self-interstitial (IBS)\\ - $\Downarrow$\\ - {\color{blue}Formation of SiC by successive substitution by C} - +{\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction} +\begin{itemize} + \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{} + \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB + \item Interaction drops quickly to zero\\ + $\rightarrow$ low capture radius +\end{itemize} \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} +\begin{minipage}{0.2cm} +\hfill \end{minipage} - - -\framebox{ -\begin{minipage}{5.9cm} -\includegraphics[width=5.9cm]{vasp_mig/comb_mig_3-2_vac_fullct.ps}\\[0.6cm] +\begin{minipage}{6.0cm} \begin{center} -\begin{picture}(0,0)(70,0) -\includegraphics[width=1.4cm]{vasp_mig/comb_2-1_init.eps} -\end{picture} -\begin{picture}(0,0)(30,0) -\includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_03.eps} -\end{picture} -\begin{picture}(0,0)(-10,0) -\includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_06.eps} -\end{picture} -\begin{picture}(0,0)(-48,0) -\includegraphics[width=1.4cm]{vasp_mig/comb_2-1_final.eps} -\end{picture} -\begin{picture}(0,0)(12.5,5) -\includegraphics[width=1cm]{100_arrow.eps} -\end{picture} -\begin{picture}(0,0)(97,-10) -\includegraphics[height=0.9cm]{001_arrow.eps} -\end{picture} +{\bf Transition from the ground state} +\begin{itemize} + \item Low transition barrier + \item Barrier smaller than \ci{} migration barrier + \item Low \si{} migration barrier (\unit[0.67]{eV})\\ + $\rightarrow$ Separation of \cs{} \& \si{} most probable +\end{itemize} \end{center} -\vspace{0.1cm} +\end{minipage}\\[0.3cm] + +\begin{minipage}{6.0cm} +\includegraphics[width=6.0cm]{c_sub_si110.ps} \end{minipage} -} -\begin{minipage}{0.3cm} +\begin{minipage}{0.4cm} \hfill \end{minipage} -\framebox{ -\begin{minipage}{5.9cm} -\includegraphics[width=5.9cm]{vasp_mig/comb_mig_4-2_vac_fullct.ps}\\[0.1cm] +\begin{minipage}{6.0cm} +\begin{flushright} +\includegraphics[width=6.0cm]{162-097.ps} +\end{flushright} +\end{minipage} + +\begin{pspicture}(0,0)(0,0) +\psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5) +\rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{ +\begin{minipage}{8cm} \begin{center} -\begin{picture}(0,0)(60,0) -\includegraphics[width=0.9cm]{vasp_mig/comb_3-1_init.eps} -\end{picture} -\begin{picture}(0,0)(25,0) -\includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_03.eps} -\end{picture} -\begin{picture}(0,0)(-20,0) -\includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_07.eps} -\end{picture} -\begin{picture}(0,0)(-55,0) -\includegraphics[width=0.9cm]{vasp_mig/comb_3-1_final.eps} -\end{picture} -\begin{picture}(0,0)(12.5,5) -\includegraphics[width=1cm]{100_arrow.eps} -\end{picture} -\begin{picture}(0,0)(95,0) -\includegraphics[height=0.9cm]{001_arrow.eps} -\end{picture} -\end{center} \vspace{0.1cm} -\end{minipage} +{\color{black} +\cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm] +IBS --- process far from equilibrium\\ } +\end{center} +\end{minipage} +}}} +\end{pspicture} \end{slide} \begin{slide} - {\large\bf - Conclusion of defect / migration / combined defect simulations - } +\headphd +{\large\bf + Combinations of substitutional C and Si self-interstitials +} - \footnotesize +\scriptsize -\vspace*{0.1cm} +\vspace{0.3cm} -Defect structures +\begin{minipage}{6.2cm} +\begin{center} +{\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction} \begin{itemize} - \item Accurately described by quantum-mechanical simulations - \item Less accurate description by classical potential simulations - \item Underestimated formation energy of \cs{} by classical approach - \item Both methods predict same ground state: \ci{} \hkl<1 0 0> dumbbell + \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{} + \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB + \item Interaction drops quickly to zero\\ + $\rightarrow$ low capture radius \end{itemize} - -Migration -\begin{itemize} - \item C migration pathway in Si identified - \item Consistent with reorientation and diffusion experiments -\end{itemize} +\end{center} +\end{minipage} +\begin{minipage}{0.2cm} +\hfill +\end{minipage} +\begin{minipage}{6.0cm} +\begin{center} +{\bf Transition from the ground state} \begin{itemize} - \item Different path and ... - \item overestimated barrier by classical potential calculations -\end{itemize} + \item Low transition barrier + \item Barrier smaller than \ci{} migration barrier + \item Low \si{} migration barrier (\unit[0.67]{eV})\\ + $\rightarrow$ Separation of \cs{} \& \si{} most probable +\end{itemize} +\end{center} +\end{minipage}\\[0.3cm] -Concerning the precipitation mechanism -\begin{itemize} - \item Agglomeration of C-Si dumbbells energetically favorable - (stress compensation) - \item C-Si indeed favored compared to - C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial - \item Possible low interaction capture radius of - C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial - \item Low barrier for - \ci{} \hkl<1 0 0> $\rightarrow$ \cs{} \& \si{} \hkl<1 1 0> - \item In absence of nearby \hkl<1 1 0> Si self-interstitial: - C-Si \hkl<1 0 0> + Vacancy $\rightarrow$ C$_{\text{sub}}$ (SiC) -\end{itemize} +\begin{minipage}{6.0cm} +\includegraphics[width=6.0cm]{c_sub_si110.ps} +\end{minipage} +\begin{minipage}{0.4cm} +\hfill +\end{minipage} +\begin{minipage}{6.0cm} +\begin{flushright} +\includegraphics[width=6.0cm]{162-097.ps} +\end{flushright} +\end{minipage} + +\begin{pspicture}(0,0)(0,0) +\psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5) +\rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{ +\begin{minipage}{8cm} \begin{center} -{\color{blue}Results suggest increased participation of \cs} +\vspace{0.1cm} +{\color{black} +\cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm] +IBS --- process far from equilibrium\\ +} +\end{center} +\end{minipage} +}}} +\end{pspicture} + +% md support +\begin{pspicture}(0,0)(0,0) +\rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{ +\begin{minipage}{14cm} +\hfill +\vspace{14cm} +\end{minipage} +}} +\rput(6.5,4.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{ +\begin{minipage}{11cm} +\begin{center} +\vspace{0.2cm} +\scriptsize +Ab initio MD at \degc{900}\\[0.4cm] +\begin{minipage}{5.4cm} +\centering +\includegraphics[width=4.3cm]{md01_bonds.eps}\\ +$t=\unit[2230]{fs}$ +\end{minipage} +\begin{minipage}{5.4cm} +\centering +\includegraphics[width=4.3cm]{md02_bonds.eps}\\ +$t=\unit[2900]{fs}$ +\end{minipage}\\[0.5cm] +{\color{blue} +Contribution of entropy to structural formation\\[0.1cm] +} \end{center} +\end{minipage} +}}} +\end{pspicture} \end{slide} \begin{slide} - {\large\bf - Silicon carbide precipitation simulations - } +\headphd +{\large\bf + Silicon carbide precipitation simulations +} - \small +\small + +\vspace{0.2cm} + +{\bf Procedure} {\scriptsize \begin{pspicture}(0,0)(12,6.5) @@ -1951,7 +1988,7 @@ Concerning the precipitation mechanism Insertion of C atoms at constant T \begin{itemize} \item total simulation volume {\pnode{in1}} - \item volume of minimal SiC precipitate {\pnode{in2}} + \item volume of minimal SiC precipitate size {\pnode{in2}} \item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\ precipitate \end{itemize} @@ -1962,51 +1999,76 @@ Concerning the precipitation mechanism }}}} \ncline[]{->}{init}{insert} \ncline[]{->}{insert}{cool} - \psframe[fillstyle=solid,fillcolor=white](7.5,0.7)(13.5,6.3) - \rput(7.8,6){\footnotesize $V_1$} - \psframe[fillstyle=solid,fillcolor=lightgray](9,2)(12,5) - \rput(9.2,4.85){\tiny $V_2$} - \psframe[fillstyle=solid,fillcolor=gray](9.25,2.25)(11.75,4.75) - \rput(9.55,4.45){\footnotesize $V_3$} + \psframe[fillstyle=solid,fillcolor=white](7.3,0.7)(12.8,6.3) + \rput(7.6,6){\footnotesize $V_1$} + \psframe[fillstyle=solid,fillcolor=lightgray](8.7,2)(11.6,5) + \rput(8.9,4.85){\tiny $V_2$} + \psframe[fillstyle=solid,fillcolor=gray](8.95,2.25)(11.35,4.75) + \rput(9.25,4.45){\footnotesize $V_3$} \rput(7.9,3.2){\pnode{ins1}} - \rput(9.22,2.8){\pnode{ins2}} - \rput(11.0,2.4){\pnode{ins3}} + \rput(8.92,2.8){\pnode{ins2}} + \rput(10.8,2.4){\pnode{ins3}} \ncline[]{->}{in1}{ins1} \ncline[]{->}{in2}{ins2} \ncline[]{->}{in3}{ins3} \end{pspicture} } +\vspace{-0.5cm} + +{\bf Note} + +\footnotesize + +\begin{minipage}{5.7cm} \begin{itemize} - \item Restricted to classical potential simulations - \item $V_2$ and $V_3$ considered due to low diffusion - \item Amount of C atoms: 6000 - ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: 2 ... 4 nm) - \item Simulation volume: $31\times 31\times 31$ unit cells + \item Amount of C atoms: 6000\\ + ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: \unit[2--4]{nm}) + \item Simulation volume: $31^3$ Si unit cells\\ (238328 Si atoms) \end{itemize} +\end{minipage} +\begin{minipage}{0.3cm} +\hfill +\end{minipage} +\framebox{ +\begin{minipage}{6.0cm} +Restricted to classical potential caclulations\\ +$\rightarrow$ Low C diffusion / overestimated barrier\\ +$\rightarrow$ Consider $V_2$ and $V_3$ +%\begin{itemize} +% \item $V_2$ and $V_3$ considered due to expected low C diffusion +%\end{itemize} +\end{minipage} +} \end{slide} +% continue here +\fi + \begin{slide} - {\large\bf\boldmath - Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS - } +\headphd +{\large\bf\boldmath + Silicon carbide precipitation simulations at \degc{450} as in IBS +} - \small +\small -\begin{minipage}{6.5cm} -\includegraphics[width=6.4cm]{sic_prec_450_si-si_c-c.ps} +\begin{minipage}{6.2cm} +\hspace{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps} +\hfill \end{minipage} -\begin{minipage}{6.5cm} -\includegraphics[width=6.4cm]{sic_prec_450_energy.ps} +\begin{minipage}{6.2cm} +\includegraphics[width=6.5cm]{sic_prec_450_energy.ps} \end{minipage} -\begin{minipage}{6.5cm} -\includegraphics[width=6.4cm]{sic_prec_450_si-c.ps} +\begin{minipage}{6.2cm} +\hspace{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps} +\hfill \end{minipage} -\begin{minipage}{6.5cm} +\begin{minipage}{6.2cm} \scriptsize \underline{Low C concentration ($V_1$)}\\ \hkl<1 0 0> C-Si dumbbell dominated structure @@ -2026,6 +2088,9 @@ Only short range order observable\\ \end{slide} +\end{document} +\ifnum1=0 + \begin{slide} {\large\bf\boldmath