X-Git-Url: https://hackdaworld.org/gitweb/?a=blobdiff_plain;f=posic%2Ftalks%2Fmpi_app.tex;h=9f6ceb70aebf3a8fb74df8e4cd4038492865a27c;hb=4e0fba333f5b731f132ead813da07d0ebe701df9;hp=687e0ca9592076c908fcc9166191f7de71529ea8;hpb=fb4fac6ca2177733e8994e23d66fdfc25ac77172;p=lectures%2Flatex.git diff --git a/posic/talks/mpi_app.tex b/posic/talks/mpi_app.tex index 687e0ca..9f6ceb7 100644 --- a/posic/talks/mpi_app.tex +++ b/posic/talks/mpi_app.tex @@ -1322,9 +1322,6 @@ $E_{\text{f}}=5.18\text{ eV}$\\ \end{slide} -% continue here -\fi - \begin{slide} \headphd @@ -1366,7 +1363,7 @@ $\Rightarrow$ $sp^2$ hybridization \begin{flushright} {\bf Bond-centered interstitial}\\[0.1cm] \begin{minipage}{4.4cm} -\scriptsize +%\scriptsize \begin{itemize} \item Linear Si-C-Si bond \item Si: one C \& 3 Si neighbours @@ -1376,7 +1373,9 @@ $\Rightarrow$ $sp^2$ hybridization \end{itemize} \end{minipage} \begin{minipage}{2.7cm} -\includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\ +%\includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\ +\vspace{0.2cm} +\includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}\\ \end{minipage} \framebox{ @@ -1436,9 +1435,9 @@ $\Rightarrow$ $sp^2$ hybridization }\\[0.4cm] %\framebox{ -\begin{minipage}{2.8cm} -\scriptsize -Charge density\\ +\begin{minipage}{3.0cm} +%\scriptsize +\underline{Charge density}\\ {\color{gray}$\bullet$} Spin up\\ {\color{green}$\bullet$} Spin down\\ {\color{blue}$\bullet$} Resulting spin up\\ @@ -1453,488 +1452,365 @@ Charge density\\ \end{flushright} \end{minipage} +\begin{pspicture}(0,0)(0,0) +\psline[linecolor=gray,linewidth=0.05cm](-7.8,-8.7)(-7.8,0) +\end{pspicture} \end{slide} -\end{document} -\ifnum1=0 - \begin{slide} - {\large\bf\boldmath - Migration of the C \hkl<1 0 0> dumbbell interstitial - } +\headphd +{\large\bf\boldmath + C interstitial migration --- ab initio +} \scriptsize - {\small Investigated pathways} +\vspace{0.1cm} -\begin{minipage}{8.5cm} -\begin{minipage}{8.3cm} -\underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 0 1>}\\ -\begin{minipage}{2.4cm} -\includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps} -\end{minipage} -\begin{minipage}{0.4cm} -$\rightarrow$ -\end{minipage} -\begin{minipage}{2.4cm} -\includegraphics[width=2.4cm]{c_pd_vasp/bc_2333.eps} -\end{minipage} -\begin{minipage}{0.4cm} -$\rightarrow$ -\end{minipage} -\begin{minipage}{2.4cm} -\includegraphics[width=2.4cm]{c_pd_vasp/100_next_2333.eps} -\end{minipage} -\end{minipage}\\ -\begin{minipage}{8.3cm} -\underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0>}\\ -\begin{minipage}{2.4cm} -\includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps} +\begin{minipage}{6.8cm} +\framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 0 1]}\\ +\begin{minipage}{2.0cm} +\includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps} \end{minipage} -\begin{minipage}{0.4cm} +\begin{minipage}{0.2cm} $\rightarrow$ \end{minipage} -\begin{minipage}{2.4cm} -\includegraphics[width=2.4cm]{c_pd_vasp/00-1-0-10_2333.eps} +\begin{minipage}{2.0cm} +\includegraphics[width=2.0cm]{c_pd_vasp/bc_2333.eps} \end{minipage} -\begin{minipage}{0.4cm} +\begin{minipage}{0.2cm} $\rightarrow$ \end{minipage} -\begin{minipage}{2.4cm} -\includegraphics[width=2.4cm]{c_pd_vasp/0-10_2333.eps} -\end{minipage} -\end{minipage}\\ -\begin{minipage}{8.3cm} -\underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0> (in place)}\\ -\begin{minipage}{2.4cm} -\includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps} +\begin{minipage}{2.0cm} +\includegraphics[width=2.0cm]{c_pd_vasp/100_next_2333.eps} +\end{minipage}\\[0.1cm] +Spin polarization\\ +$\Rightarrow$ BC configuration constitutes local minimum\\ +$\Rightarrow$ Migration barrier to reach BC | $\Delta E=\unit[1.2]{eV}$ +\end{minipage} +\begin{minipage}{5.4cm} +\includegraphics[width=6.0cm]{im_00-1_nosym_sp_fullct_thesis_vasp_s.ps} +\end{minipage}\\[0.2cm] +%\hrule +% +\begin{minipage}{6.8cm} +\framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 -1 0]}\\ +\begin{minipage}{2.0cm} +\includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps} \end{minipage} -\begin{minipage}{0.4cm} +\begin{minipage}{0.2cm} $\rightarrow$ \end{minipage} -\begin{minipage}{2.4cm} -\includegraphics[width=2.4cm]{c_pd_vasp/00-1_ip0-10_2333.eps} +\begin{minipage}{2.0cm} +\includegraphics[width=2.0cm]{c_pd_vasp/00-1-0-10_2333.eps} \end{minipage} -\begin{minipage}{0.4cm} +\begin{minipage}{0.2cm} $\rightarrow$ \end{minipage} -\begin{minipage}{2.4cm} -\includegraphics[width=2.4cm]{c_pd_vasp/0-10_ip_2333.eps} -\end{minipage} -\end{minipage} -\end{minipage} +\begin{minipage}{2.0cm} +\includegraphics[width=2.0cm]{c_pd_vasp/0-10_2333.eps} +\end{minipage}\\[0.1cm] +$\Delta E=\unit[0.9]{eV}$ | Experimental values: \unit[0.70--0.87]{eV}\\ +$\Rightarrow$ {\color{red}Migration mechanism identified!}\\ +Note: Change in orientation +\end{minipage} +\begin{minipage}{5.4cm} +\includegraphics[width=6.0cm]{00-1_0-10_vasp_s.ps} +\end{minipage}\\[0.1cm] +% +\begin{center} +Reorientation pathway composed of two consecutive processes of the above type +\end{center} \end{slide} \begin{slide} - {\large\bf\boldmath - Migration of the C \hkl<1 0 0> dumbbell interstitial - } +\headphd +{\large\bf\boldmath + C interstitial migration --- analytical potential +} \scriptsize -\framebox{ -\begin{minipage}{5.9cm} -\begin{flushleft} -\includegraphics[width=5.8cm]{im_00-1_nosym_sp_fullct_thesis.ps}\\[0.45cm] -\end{flushleft} -\begin{center} -\begin{picture}(0,0)(60,0) -\includegraphics[width=1cm]{vasp_mig/00-1.eps} -\end{picture} -\begin{picture}(0,0)(-5,0) -\includegraphics[width=1cm]{vasp_mig/bc_00-1_sp.eps} -\end{picture} -\begin{picture}(0,0)(-55,0) -\includegraphics[width=1cm]{vasp_mig/bc.eps} -\end{picture} -\begin{picture}(0,0)(12.5,10) -\includegraphics[width=1cm]{110_arrow.eps} -\end{picture} -\begin{picture}(0,0)(90,0) -\includegraphics[height=0.9cm]{001_arrow.eps} -\end{picture} -\end{center} -\vspace*{0.35cm} -\end{minipage} -} -\begin{minipage}{0.3cm} -\hfill -\end{minipage} -\framebox{ -\begin{minipage}{5.9cm} -\begin{flushright} -\includegraphics[width=5.9cm]{vasp_mig/00-1_0-10_nosym_sp_fullct.ps}\\[0.5cm] -\end{flushright} -\begin{center} -\begin{picture}(0,0)(60,0) -\includegraphics[width=1cm]{vasp_mig/00-1_a.eps} -\end{picture} -\begin{picture}(0,0)(5,0) -\includegraphics[width=1cm]{vasp_mig/00-1_0-10_sp.eps} -\end{picture} -\begin{picture}(0,0)(-55,0) -\includegraphics[width=1cm]{vasp_mig/0-10.eps} -\end{picture} -\begin{picture}(0,0)(12.5,10) -\includegraphics[width=1cm]{100_arrow.eps} -\end{picture} -\begin{picture}(0,0)(90,0) -\includegraphics[height=0.9cm]{001_arrow.eps} -\end{picture} -\end{center} -\vspace*{0.3cm} -\end{minipage}\\ -} - -\vspace*{0.05cm} +\vspace{0.3cm} -\framebox{ -\begin{minipage}{5.9cm} -\begin{flushleft} -\includegraphics[width=5.9cm]{vasp_mig/00-1_ip0-10_nosym_sp_fullct.ps}\\[0.6cm] -\end{flushleft} -\begin{center} -\begin{picture}(0,0)(60,0) -\includegraphics[width=0.9cm]{vasp_mig/00-1_b.eps} -\end{picture} -\begin{picture}(0,0)(10,0) -\includegraphics[width=0.9cm]{vasp_mig/00-1_ip0-10_sp.eps} -\end{picture} -\begin{picture}(0,0)(-60,0) -\includegraphics[width=0.9cm]{vasp_mig/0-10_b.eps} -\end{picture} -\begin{picture}(0,0)(12.5,10) -\includegraphics[width=1cm]{100_arrow.eps} -\end{picture} -\begin{picture}(0,0)(90,0) -\includegraphics[height=0.9cm]{001_arrow.eps} -\end{picture} -\end{center} -\vspace*{0.3cm} +\begin{minipage}[t]{6.0cm} +{\bf\boldmath BC to \hkl[0 0 -1] transition}\\[0.2cm] +\includegraphics[width=6.0cm]{bc_00-1_albe_s.ps}\\ +\begin{itemize} + \item Lowermost migration barrier + \item $\Delta E \approx \unit[2.2]{eV}$ + \item 2.4 times higher than ab initio result + \item Different pathway +\end{itemize} \end{minipage} -} -\begin{minipage}{0.3cm} +\begin{minipage}[t]{0.2cm} \hfill \end{minipage} -\begin{minipage}{6.5cm} -VASP results +\begin{minipage}[t]{6.0cm} +{\bf\boldmath Transition involving a \hkl<1 1 0> configuration} +\vspace{0.1cm} \begin{itemize} - \item Energetically most favorable path - \begin{itemize} - \item Path 2 - \item Activation energy: $\approx$ 0.9 eV - \item Experimental values: 0.73 ... 0.87 eV - \end{itemize} - $\Rightarrow$ {\color{blue}Diffusion} path identified! - \item Reorientation (path 3) - \begin{itemize} - \item More likely composed of two consecutive steps of type 2 - \item Experimental values: 0.77 ... 0.88 eV - \end{itemize} - $\Rightarrow$ {\color{blue}Reorientation} transition identified! + \item Bond-centered configuration unstable\\ + $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell + \item Minima of the \hkl[0 0 -1] to \hkl[0 -1 0] transition\\ + $\rightarrow$ \ci{} \hkl<1 1 0> DB +\end{itemize} +\vspace{0.1cm} +\includegraphics[width=6.0cm]{00-1_110_0-10_mig_albe.ps} +\begin{itemize} + \item $\Delta E \approx \unit[2.2]{eV} \text{ \& } \unit[0.9]{eV}$ + \item 2.4 -- 3.4 times higher than ab initio result + \item After all: Change of the DB orientation \end{itemize} \end{minipage} +\vspace{0.5cm} +\begin{center} +{\color{red}\bf Drastically overestimated diffusion barrier} +\end{center} + +\begin{pspicture}(0,0)(0,0) +\psline[linewidth=0.05cm,linecolor=gray](6.1,1.0)(6.1,9.3) +\end{pspicture} + \end{slide} \begin{slide} - {\large\bf\boldmath - Migration of the C \hkl<1 0 0> dumbbell interstitial - } - -\scriptsize +\headphd +{\large\bf\boldmath + Defect combinations +} - \vspace{0.1cm} +\footnotesize -\begin{minipage}{6.5cm} +\vspace{0.3cm} -\framebox{ -\begin{minipage}[t]{5.9cm} -\begin{flushleft} -\includegraphics[width=5.9cm]{bc_00-1.ps}\\[2.35cm] -\end{flushleft} +\begin{minipage}{9cm} +{\bf + Summary of combinations}\\[0.1cm] +{\scriptsize +\begin{tabular}{l c c c c c c} +\hline + $E_{\text{b}}$ [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} -\begin{pspicture}(0,0)(0,0) -\psframe[linecolor=red,fillstyle=none](-2.8,1.35)(3.3,2.7) -\end{pspicture} -\begin{picture}(0,0)(60,-50) -\includegraphics[width=1cm]{albe_mig/bc_00-1_red_00.eps} -\end{picture} -\begin{picture}(0,0)(5,-50) -\includegraphics[width=1cm]{albe_mig/bc_00-1_red_01.eps} -\end{picture} -\begin{picture}(0,0)(-55,-50) -\includegraphics[width=1cm]{albe_mig/bc_00-1_red_02.eps} -\end{picture} -\begin{picture}(0,0)(12.5,-40) -\includegraphics[width=1cm]{110_arrow.eps} -\end{picture} -\begin{picture}(0,0)(90,-45) -\includegraphics[height=0.9cm]{001_arrow.eps} -\end{picture}\\ -\begin{pspicture}(0,0)(0,0) -\psframe[linecolor=blue,fillstyle=none](-2.8,0)(3.3,1.6) -\end{pspicture} -\begin{picture}(0,0)(60,-15) -\includegraphics[width=0.9cm]{albe_mig/bc_00-1_01.eps} -\end{picture} -\begin{picture}(0,0)(35,-15) -\includegraphics[width=0.9cm]{albe_mig/bc_00-1_02.eps} -\end{picture} -\begin{picture}(0,0)(-5,-15) -\includegraphics[width=0.9cm]{albe_mig/bc_00-1_03.eps} -\end{picture} -\begin{picture}(0,0)(-55,-15) -\includegraphics[width=0.9cm]{albe_mig/bc_00-1_04.eps} -\end{picture} -\begin{picture}(0,0)(12.5,-5) -\includegraphics[width=1cm]{100_arrow.eps} -\end{picture} -\begin{picture}(0,0)(90,-15) -\includegraphics[height=0.9cm]{010_arrow.eps} -\end{picture} +{\color{blue} + $E_{\text{b}}$ explainable by stress compensation / increase +} \end{center} \end{minipage} -}\\[0.1cm] - -\begin{minipage}{5.9cm} -Erhart/Albe results -\begin{itemize} - \item Lowest activation energy: $\approx$ 2.2 eV - \item 2.4 times higher than VASP - \item Different pathway -\end{itemize} +\begin{minipage}{3cm} +\includegraphics[width=3.5cm]{comb_pos.eps} \end{minipage} -\end{minipage} -\begin{minipage}{6.5cm} +\vspace{0.2cm} -\framebox{ -\begin{minipage}{5.9cm} -%\begin{flushright} -%\includegraphics[width=5.9cm]{00-1_0-10.ps}\\[0.75cm] -%\end{flushright} -%\begin{center} -%\begin{pspicture}(0,0)(0,0) -%\psframe[linecolor=red,fillstyle=none](-2.8,-0.25)(3.3,1.1) -%\end{pspicture} -%\begin{picture}(0,0)(60,-5) -%\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_00.eps} -%\end{picture} -%\begin{picture}(0,0)(0,-5) -%\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_min.eps} -%\end{picture} -%\begin{picture}(0,0)(-55,-5) -%\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_03.eps} -%\end{picture} -%\begin{picture}(0,0)(12.5,5) -%\includegraphics[width=1cm]{100_arrow.eps} -%\end{picture} -%\begin{picture}(0,0)(90,0) -%\includegraphics[height=0.9cm]{001_arrow.eps} -%\end{picture} -%\end{center} -%\vspace{0.2cm} -%\end{minipage} -%}\\[0.2cm] -% -%\framebox{ -%\begin{minipage}{5.9cm} -\includegraphics[width=5.9cm]{00-1_110_0-10_mig_albe.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} -}\\[0.1cm] - -\begin{minipage}{5.9cm} -Transition involving \ci{} \hkl<1 1 0> +\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 Bond-centered configuration unstable\\ - $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell - \item Transition minima of path 2 \& 3\\ - $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell - \item Activation energy: $\approx$ 2.2 eV \& 0.9 eV - \item 2.4 - 3.4 times higher than VASP - \item Rotation of dumbbell orientation + \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} -\vspace{0.1cm} \begin{center} -{\color{blue}Overestimated diffusion barrier} +{\color{blue}\ci{} agglomeration / no C clustering} \end{center} \end{minipage} -\end{minipage} - \end{slide} \begin{slide} - {\large\bf\boldmath - Combinations with a C-Si \hkl<1 0 0>-type interstitial - } - -\small - -\vspace*{0.1cm} +\headphd +{\large\bf\boldmath + Defect combinations +} -Binding energy: -$ -E_{\text{b}}= -E_{\text{f}}^{\text{defect combination}}- -E_{\text{f}}^{\text{C \hkl<0 0 -1> dumbbell}}- -E_{\text{f}}^{\text{2nd defect}} -$ +\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 $E_{\text{b}}$ [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}\\ + \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 substitutional (C$_{\text{S}}$) & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\ - Vacancy & -5.39 ($\rightarrow$ C$_{\text{S}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\ + 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} - -\footnotesize +\vspace{0.2cm} -\begin{minipage}[t]{3.8cm} -\underline{\hkl<1 0 0> at position 1}\\[0.1cm] -\includegraphics[width=3.5cm]{00-1dc/2-25.eps} +{\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]{3.5cm} -\underline{\hkl<0 -1 0> at position 1}\\[0.1cm] -\includegraphics[width=3.2cm]{00-1dc/2-39.eps} +\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} -\begin{picture}(0,0)(-295,-130) -\includegraphics[width=3.5cm]{comb_pos.eps} -\end{picture} +% 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 C-Si \hkl<1 0 0>-type interstitials - } - -\small - -\vspace*{0.1cm} +\headphd +{\large\bf + Defect combinations of C-Si dimers and vacancies +} +\footnotesize -Energetically most favorable combinations along \hkl<1 1 0> +\vspace{0.2cm} -\vspace*{0.1cm} +\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}[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] -{\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>\\ -\hline -\end{tabular} -} +\begin{minipage}{6.5cm} +\includegraphics[width=6.0cm]{059-539.ps} +\end{minipage} +\begin{minipage}{5.7cm} +\includegraphics[width=6.0cm]{314-539.ps} +\end{minipage} -\vspace*{0.3cm} +\begin{pspicture}(0,0)(0,0) +\psline[linewidth=0.05cm,linecolor=gray](6.3,9.0)(6.3,0) -\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} +\rput(6.3,7.0){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=gray]{ +\begin{minipage}{6.5cm} \begin{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} - Consisten with initial precipitation model +High probability of stable C$_{\text{sub}}$ configuration } \end{center} \end{minipage} +}}} -\vspace{0.2cm} +\end{pspicture} \end{slide} -\begin{slide} - - {\large\bf\boldmath - Combinations of substitutional C and \hkl<1 1 0> Si self-interstitials - } +% continue here +\fi - \scriptsize +\begin{slide} -%\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 + Combinations of substitutional C and Si self-interstitials +} -%\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} +\scriptsize \begin{minipage}{6.0cm} \includegraphics[width=5.8cm]{c_sub_si110.ps} \end{minipage} -\begin{minipage}{7cm} +\begin{minipage}{6.3cm} \scriptsize \begin{itemize} \item IBS: C may displace Si\\ @@ -1955,13 +1831,10 @@ Type & \hkl<-1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \h \end{center} \end{minipage} -\begin{minipage}{6.5cm} +\begin{minipage}{6.0cm} \includegraphics[width=6.0cm]{162-097.ps} -\begin{itemize} - \item Low migration barrier -\end{itemize} \end{minipage} -\begin{minipage}{6.5cm} +\begin{minipage}{6.2cm} \begin{center} Ab initio MD at \degc{900}\\ \includegraphics[width=3.3cm]{md_vasp_01.eps} @@ -1976,99 +1849,8 @@ Contribution of entropy to structural formation \end{slide} -\begin{slide} - - {\large\bf\boldmath - Migration in C-Si \hkl<1 0 0> and vacancy combinations - } - - \footnotesize - -\vspace{0.1cm} - -\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} - 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} - -\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} -\end{minipage} - - -\framebox{ -\begin{minipage}{5.9cm} -\includegraphics[width=5.9cm]{vasp_mig/comb_mig_3-2_vac_fullct.ps}\\[0.6cm] -\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} -\end{center} -\vspace{0.1cm} -\end{minipage} -} -\begin{minipage}{0.3cm} -\hfill -\end{minipage} -\framebox{ -\begin{minipage}{5.9cm} -\includegraphics[width=5.9cm]{vasp_mig/comb_mig_4-2_vac_fullct.ps}\\[0.1cm] -\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} -} - -\end{slide} +\end{document} +\ifnum1=0 \begin{slide}