From 259455a3b7b96502cb563e5ff88419df5112282b Mon Sep 17 00:00:00 2001 From: hackbard Date: Tue, 3 Nov 2009 17:48:42 +0100 Subject: [PATCH] defect combos + BC revisited --- posic/talks/upb-ua-xc.tex | 149 +++++++++++++++++++++++++++++++++++++- 1 file changed, 145 insertions(+), 4 deletions(-) diff --git a/posic/talks/upb-ua-xc.tex b/posic/talks/upb-ua-xc.tex index a272ffd..c525f0c 100644 --- a/posic/talks/upb-ua-xc.tex +++ b/posic/talks/upb-ua-xc.tex @@ -1935,6 +1935,43 @@ $z,x'$-axis rotation: $45.0^{\circ}$, $0.0^{\circ}$ \end{slide} +\begin{slide} + + {\large\bf\boldmath + Saddle point configuration check + } + + Simulations: + \begin{itemize} + \item Displacing the C atom in the BC configuration + \begin{itemize} + \item in \hkl<1 -1 0> direction\\ + $(0.1240, 0.1240, 0.0409) \rightarrow + (0.1340, 0.1140, 0.0409)$ + \item in \hkl<1 0 0> direction\\ + $(0.1240, 0.1240, 0.0409) \rightarrow + (0.1440, 0.1240, 0.0409)$ + \end{itemize} + \item Full relaxation of the configuration + \end{itemize} + + Results: + \begin{itemize} + \item Both displacement simulations relax to + the BC configuration + \item Obviously the second derivative with respect to the + migration direction is also positive + \end{itemize} + + \begin{center} + $\Downarrow$\\ + Bond centered configuration is a + {\color{blue}real local minimum} + and {\color{red}not} a saddle point configuration + \end{center} + +\end{slide} + \begin{slide} {\large\bf\boldmath @@ -2287,6 +2324,7 @@ $z,x'$-axis rotation: $45.0^{\circ}$, $0.0^{\circ}$ Initial C \hkl<0 0 -1> insterstital at: $\frac{1}{4}\hkl<1 1 1>$ + {\footnotesize \begin{tabular}{|l|l|l|l|l|l|} \hline & 2 & 3 & 4 & 5 & 6 \\ @@ -2305,15 +2343,26 @@ C \hkl<0 -1 0> & 3.92/-2.39 & 4.15/-2.16 & \hkl<1 0 0> & \hkl<1 0 0> & \hkl <-1 \hline Vacancy & 1.39/-5.39 ($\rightarrow\text{ C}_{\text{S}}$) & 6.19/-0.59 & 3.65/-3.14 & 6.24/-0.54 & 6.50/-0.50 \\ \hline +C$_{\text{sub}}$ & 4.80/0.26 & 4.03/-0.51 & 3.62/-0.93 & 4.39/-0.15 & 5.03/0.49 \\ +\hline \end{tabular}\\[0.2cm] + } + + \begin{minipage}{8cm} Energies: $x/y$\\ $x$: Defect formation energy of the complex\\ $y$: $E_{\text{f}}^{\text{defect combination}}- E_{\text{f}}^{\text{isolated C \hkl<0 0 -1>}}- E_{\text{f}}^{\text{isolated 2nd defect}} - $\\ - That is: If $y<0$ $\rightarrow$ favored compared to far-off isolated defects + $\\[0.3cm] + {\color{blue} + If $y<0$ $\rightarrow$ favored compared to far-off isolated defects + } + \end{minipage} + \begin{minipage}{4.5cm} + \includegraphics[width=5.0cm]{00-1dc/energy.ps} + \end{minipage} \end{slide} @@ -2348,6 +2397,23 @@ Vacancy & 1.39/-5.39 ($\rightarrow\text{ C}_{\text{S}}$) & 6.19/-0.59 & 3.65/-3. \includegraphics[width=2.5cm]{00-1dc/00-1_6.eps} \end{minipage} + \includegraphics[width=5.0cm]{00-1dc/energy_00x.ps} + +\end{slide} + +\begin{slide} + + {\large\bf\boldmath + Combination of defects + } + + \small + + {\color{blue} + For defect position 3 and 5 (image 2 and 4) the unit cell is translated by + $\frac{a}{2} \hkl<0 -1 -1>$ + } + Type of second defect: \hkl<0 0 1> \begin{minipage}{2.5cm} @@ -2366,6 +2432,8 @@ Vacancy & 1.39/-5.39 ($\rightarrow\text{ C}_{\text{S}}$) & 6.19/-0.59 & 3.65/-3. \includegraphics[width=2.5cm]{00-1dc/001_6.eps} \end{minipage} + \includegraphics[width=5.0cm]{00-1dc/energy_001.ps} + \end{slide} \begin{slide} @@ -2399,6 +2467,24 @@ Vacancy & 1.39/-5.39 ($\rightarrow\text{ C}_{\text{S}}$) & 6.19/-0.59 & 3.65/-3. \includegraphics[width=2.5cm]{00-1dc/100_6.eps} \end{minipage} + \includegraphics[width=5.0cm]{00-1dc/energy_100.ps} + +\end{slide} + +\begin{slide} + + {\large\bf\boldmath + Combination of defects + } + + \small + + {\color{blue} + For defect position 3 and 5 (image 2 and 4) the unit cell is translated by + $\frac{a}{2} \hkl<0 -1 -1>$ + } + + Type of second defect: \hkl<-1 0 0> or equivalent one \begin{minipage}{2.5cm} @@ -2417,6 +2503,8 @@ Vacancy & 1.39/-5.39 ($\rightarrow\text{ C}_{\text{S}}$) & 6.19/-0.59 & 3.65/-3. \includegraphics[width=2.5cm]{00-1dc/0-10_6.eps} \end{minipage} + \includegraphics[width=5.0cm]{00-1dc/energy_x00.ps} + \end{slide} \begin{slide} @@ -2450,6 +2538,24 @@ Vacancy & 1.39/-5.39 ($\rightarrow\text{ C}_{\text{S}}$) & 6.19/-0.59 & 3.65/-3. \includegraphics[width=2.5cm]{00-1dc/100_6.eps} \end{minipage} + \includegraphics[width=5.0cm]{00-1dc/energy_010.ps} + +\end{slide} + +\begin{slide} + + {\large\bf\boldmath + Combination of defects + } + + \small + + {\color{blue} + For defect position 3 and 5 (image 2 and 4) the unit cell is translated by + $\frac{a}{2} \hkl<0 -1 -1>$ + } + + Type of second defect: \hkl<0 -1 0> or equivalent one \begin{minipage}{2.5cm} @@ -2468,6 +2574,8 @@ Vacancy & 1.39/-5.39 ($\rightarrow\text{ C}_{\text{S}}$) & 6.19/-0.59 & 3.65/-3. \includegraphics[width=2.5cm]{00-1dc/0-10_6.eps} \end{minipage} + \includegraphics[width=5.0cm]{00-1dc/energy_0x0.ps} + \end{slide} \begin{slide} @@ -2501,9 +2609,42 @@ Vacancy & 1.39/-5.39 ($\rightarrow\text{ C}_{\text{S}}$) & 6.19/-0.59 & 3.65/-3. \includegraphics[width=2.5cm]{00-1dc/vac_6.eps} \end{minipage} - Type of second defect: C Substitutional + \includegraphics[width=5.0cm]{00-1dc/energy_vac.ps} + +\end{slide} + +\begin{slide} + + {\large\bf\boldmath + Combination of defects + } + + \small + + {\color{blue} + For defect position 3 and 5 (image 2 and 4) the unit cell is translated by + $\frac{a}{2} \hkl<0 -1 -1>$ + } + + Type of second defect: C$_{\text{sub}}$ + + \begin{minipage}{2.5cm} + \includegraphics[width=2.5cm]{00-1dc/csub_1.eps} + \end{minipage} + \begin{minipage}{2.5cm} + \includegraphics[width=2.5cm]{00-1dc/csub_3.eps} + \end{minipage} + \begin{minipage}{2.5cm} + \includegraphics[width=2.5cm]{00-1dc/csub_4.eps} + \end{minipage} + \begin{minipage}{2.5cm} + \includegraphics[width=2.5cm]{00-1dc/csub_5.eps} + \end{minipage} + \begin{minipage}{2.5cm} + \includegraphics[width=2.5cm]{00-1dc/csub_6.eps} + \end{minipage} - TODO ... + \includegraphics[width=5.0cm]{00-1dc/energy_csub.ps} \end{slide} -- 2.39.2