\end{slide}
-% continue here
-\fi
-
\begin{slide}
\headphd
Utilized computational methods
}
-\vspace{0.2cm}
+\vspace{0.3cm}
\small
-{\bf Molecular dynamics (MD)}\\
+{\bf Molecular dynamics (MD)}\\[0.1cm]
\scriptsize
-\begin{tabular}{p{4.5cm} p{7.5cm}}
-Basics & Details\\
+\begin{tabular}{| p{4.5cm} | p{7.5cm} |}
\hline
System of $N$ particles &
$N=5832\pm 1$ (Defects), $N=238328+6000$ (Precipitation)\\
-\hline
Phase space propagation &
Velocity Verlet | timestep: \unit[1]{fs} \\
-\hline
Analytical interaction potential &
Tersoff-like {\color{red}short-range}, {\color{blue}bond order} potential
(Erhart/Albe)
\pot_{ij} = {\color{red}f_C(r_{ij})}
\left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
$\\
-\hline
Observables: time/ensemble averages &
NpT (isothermal-isobaric) | Berendsen thermostat/barostat\\
\hline
\small
-\vspace{0.1cm}
+\vspace{0.3cm}
{\bf Density functional theory (DFT)}
\scriptsize
\begin{minipage}[t]{6cm}
-\underline{Basics}
\begin{itemize}
- \item Born-Oppenheimer approximation:\\
- Decouple electronic \& ionic motion
\item Hohenberg-Kohn theorem:\\
- $n_0(r) \stackrel{\text{uniquely}}{\rightarrow}$
- $V_0$ / $H$ / $\Phi_i$ / \underline{$E_0$}
+ $\Psi_0(r_1,r_2,\ldots,r_N)=\Psi[n_0(r)]$, $E_0=E[n_0]$
+ \item Kohn-Sham approach:\\
+ Single-particle effective theory
\end{itemize}
-\underline{Details}
+\hrule
\begin{itemize}
\item Code: \textsc{vasp}
-\item Plane wave basis set $\{\phi_j\}$\\[0.1cm]
-$\displaystyle
-\Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_j^i \phi_j(r)
-$\\
-$\displaystyle
-E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}=\unit[300]{eV}
-$
+\item Plane wave basis set
+%$\displaystyle
+%\Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_{i,k+G} \exp{\left(i(k+G)r\right)}
+%$\\
+%$\displaystyle
+%E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}=\unit[300]{eV}
+%$
\item Ultrasoft pseudopotential
+\item Exchange \& correlation: GGA
\item Brillouin zone sampling: $\Gamma$-point
+\item Supercell: $N=216\pm2$
\end{itemize}
\end{minipage}
-\begin{minipage}[t]{6cm}
-
-\[
+\begin{minipage}{6cm}
+\begin{pspicture}(0,0)(0,0)
+\pscircle[fillcolor=yellow,fillstyle=solid,linestyle=none](3.5,-2.0){2.5}
+\rput(2.7,-0.7){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
+$\displaystyle
\left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) - \epsilon_i \right] \Phi_i(r) = 0
-\]
-\[
+$
+}}
+\rput(5.2,-2.0){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
+$\displaystyle
n(r)=\sum_i^N|\Phi_i(r)|^2
-\]
-\[
-V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
- +V_{\text{XC}}[n(r)]
-\]
-
-\end{minipage}
-
-\end{slide}
-
-\end{document}
-\ifnum1=0
-
-\begin{slide}
-
- \small
- {\large\bf
- Density functional theory (DFT) calculations
- }
-
- Basic ingredients necessary for DFT
-
- \begin{itemize}
- \item \underline{Hohenberg-Kohn theorem} - ground state density $n_0(r)$ ...
- \begin{itemize}
- \item ... uniquely determines the ground state potential
- / wavefunctions
- \item ... minimizes the systems total energy
- \end{itemize}
- \item \underline{Born-Oppenheimer}
- - $N$ moving electrons in an external potential of static nuclei
-\[
-H\Psi = \left[-\sum_i^N \frac{\hbar^2}{2m}\nabla_i^2
- +\sum_i^N V_{\text{ext}}(r_i)
- +\sum_{i<j}^N V_{e-e}(r_i,r_j)\right]\Psi=E\Psi
-\]
- \item \underline{Effective potential}
- - averaged electrostatic potential \& exchange and correlation
-\[
+$
+}}
+\rput(3.0,-4.5){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
+$\displaystyle
V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
+V_{\text{XC}}[n(r)]
-\]
- \item \underline{Kohn-Sham system}
- - Schr\"odinger equation of N non-interacting particles
-\[
-\left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) \right] \Phi_i(r)
-=\epsilon_i\Phi_i(r)
-\quad
-\Rightarrow
-\quad
-n(r)=\sum_i^N|\Phi_i(r)|^2
-\]
- \item \underline{Self-consistent solution}\\
-$n(r)$ depends on $\Phi_i$, which depend on $V_{\text{eff}}$,
-which in turn depends on $n(r)$
- \item \underline{Variational principle}
- - minimize total energy with respect to $n(r)$
- \end{itemize}
-
-\end{slide}
-
-\begin{slide}
-
- {\large\bf
- Density functional theory (DFT) calculations
- }
-
- \small
-
- \vspace*{0.2cm}
-
- Details of applied DFT calculations in this work
-
- \begin{itemize}
- \item \underline{Exchange correlation functional}
- - approximations for the inhomogeneous electron gas
- \begin{itemize}
- \item LDA: $E_{\text{XC}}^{\text{LDA}}[n]=\int \epsilon_{\text{XC}}(n)n(r)d^3r$
- \item GGA: $E_{\text{XC}}^{\text{GGA}}[n]=\int \epsilon_{\text{XC}}(n,\nabla n)n(r)d^3r$
- \end{itemize}
- \item \underline{Plane wave basis set}
- - approximation of the wavefunction $\Phi_i$ by plane waves $\phi_j$
- \item \underline{Brillouin zone sampling} -
- {\color{blue}$\Gamma$-point only} calculations
- \item \underline{Pseudo potential}
- - consider only the valence electrons
- \item \underline{Code} - VASP 4.6
- \end{itemize}
-
- \vspace*{0.2cm}
-
- MD and structural optimization
-
- \begin{itemize}
- \item MD integration: Gear predictor corrector algorithm
- \item Pressure control: Parrinello-Rahman pressure control
- \item Structural optimization: Conjugate gradient method
- \end{itemize}
+$
+}}
+\psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{130}{15}
+\psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{230}{165}
+\psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{345}{310}
-\begin{pspicture}(0,0)(0,0)
-\psellipse[linecolor=blue](1.5,6.75)(0.5,0.3)
\end{pspicture}
+\end{minipage}
\end{slide}
\begin{slide}
+\headphd
{\large\bf
- C and Si self-interstitial point defects in silicon
+ Point defects \& defect migration
}
\small
- \vspace*{0.3cm}
+ \vspace{0.2cm}
-\begin{minipage}{8cm}
-Procedure:\\[0.3cm]
- \begin{pspicture}(0,0)(7,5)
- \rput(3.5,4){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
+\begin{minipage}[b]{7.5cm}
+{\bf Defect structure}\\
+ \begin{pspicture}(0,0)(7,4.4)
+ \rput(3.5,3.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
\parbox{7cm}{
\begin{itemize}
\item Creation of c-Si simulation volume
\item $T=0\text{ K}$, $p=0\text{ bar}$
\end{itemize}
}}}}
-\rput(3.5,2.1){\rnode{insert}{\psframebox{
+\rput(3.5,1.3){\rnode{insert}{\psframebox{
\parbox{7cm}{
\begin{center}
Insertion of interstitial C/Si atoms
\end{center}
}}}}
- \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
+ \rput(3.5,0.2){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
\parbox{7cm}{
\begin{center}
Relaxation / structural energy minimization
\ncline[]{->}{insert}{cool}
\end{pspicture}
\end{minipage}
-\begin{minipage}{5cm}
- \includegraphics[width=5cm]{unit_cell_e.eps}\\
+\begin{minipage}[b]{4.5cm}
+\begin{center}
+\includegraphics[width=3.8cm]{unit_cell_e.eps}\\
+\end{center}
+\begin{minipage}{2.21cm}
+{\scriptsize
+{\color{red}$\bullet$} Tetrahedral\\[-0.1cm]
+{\color{green}$\bullet$} Hexagonal\\[-0.1cm]
+{\color{yellow}$\bullet$} \hkl<1 0 0> DB
+}
+\end{minipage}
+\begin{minipage}{2.21cm}
+{\scriptsize
+{\color{magenta}$\bullet$} \hkl<1 1 0> DB\\[-0.1cm]
+{\color{cyan}$\bullet$} Bond-centered\\[-0.1cm]
+{\color{black}$\bullet$} Vac. / Sub.
+}
+\end{minipage}
\end{minipage}
-\begin{minipage}{9cm}
- \begin{tabular}{l c c}
- \hline
- & size [unit cells] & \# atoms\\
-\hline
-VASP & $3\times 3\times 3$ & $216\pm 1$ \\
-Erhart/Albe & $9\times 9\times 9$ & $5832\pm 1$\\
-\hline
- \end{tabular}
+\vspace{0.2cm}
+
+\begin{minipage}[b]{6cm}
+{\bf Defect formation energy}\\
+\framebox{
+$E_{\text{f}}=E-\sum_i N_i\mu_i$}\\[0.1cm]
+Particle reservoir: Si \& SiC\\[0.2cm]
+{\bf Binding energy}\\
+\framebox{
+$
+E_{\text{b}}=
+E_{\text{f}}^{\text{comb}}-
+E_{\text{f}}^{1^{\text{st}}}-
+E_{\text{f}}^{2^{\text{nd}}}
+$
+}\\[0.1cm]
+\footnotesize
+$E_{\text{b}}<0$: energetically favorable configuration\\
+$E_{\text{b}}\rightarrow 0$: non-interacting, isolated defects\\
\end{minipage}
-\begin{minipage}{4cm}
-{\color{red}$\bullet$} Tetrahedral\\
-{\color{green}$\bullet$} Hexagonal\\
-{\color{yellow}$\bullet$} \hkl<1 0 0> dumbbell\\
-{\color{magenta}$\bullet$} \hkl<1 1 0> dumbbell\\
-{\color{cyan}$\bullet$} Bond-centered\\
-{\color{black}$\bullet$} Vacancy / Substitutional
+\begin{minipage}[b]{6cm}
+{\bf Migration barrier}
+\footnotesize
+\begin{itemize}
+ \item Displace diffusing atom
+ \item Constrain relaxation of (diffusing) atoms
+ \item Record configurational energy
+\end{itemize}
+\begin{picture}(0,0)(-60,-33)
+\includegraphics[width=4.5cm]{crt_mod.eps}
+\end{picture}
\end{minipage}
\end{slide}
\begin{slide}
- \footnotesize
-
-\begin{minipage}{9.5cm}
+\footnotesize
- {\large\bf
- Si self-interstitial point defects in silicon\\
- }
+\headphd
+{\large\bf
+ Si self-interstitial point defects in silicon\\[0.1cm]
+}
+\begin{center}
\begin{tabular}{l c c c c c}
\hline
$E_{\text{f}}$ [eV] & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\
\hline
- VASP & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\
+ \textsc{vasp} & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\
Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\
\hline
-\end{tabular}\\[0.2cm]
+\end{tabular}\\[0.4cm]
+\end{center}
-\begin{minipage}{4.7cm}
-\includegraphics[width=4.7cm]{e_kin_si_hex.ps}
+\begin{minipage}{3cm}
+\begin{center}
+\underline{Vacancy}\\
+\includegraphics[width=2.8cm]{si_pd_albe/vac.eps}
+\end{center}
\end{minipage}
-\begin{minipage}{4.7cm}
+\begin{minipage}{3cm}
\begin{center}
-{\tiny nearly T $\rightarrow$ T}\\
+\underline{\hkl<1 1 0> DB}\\
+\includegraphics[width=2.8cm]{si_pd_albe/110_bonds.eps}
+\end{center}
+\end{minipage}
+\begin{minipage}{3cm}
+\begin{center}
+\underline{\hkl<1 0 0> DB}\\
+\includegraphics[width=2.8cm]{si_pd_albe/100_bonds.eps}
+\end{center}
+\end{minipage}
+\begin{minipage}{3cm}
+\begin{center}
+\underline{Tetrahedral}\\
+\includegraphics[width=2.8cm]{si_pd_albe/tet_bonds.eps}
\end{center}
-\includegraphics[width=4.7cm]{nhex_tet.ps}
\end{minipage}\\
\underline{Hexagonal} \hspace{2pt}
\framebox{
\begin{minipage}{2.7cm}
$E_{\text{f}}^*=4.48\text{ eV}$\\
-\includegraphics[width=2.7cm]{si_pd_albe/hex_a.eps}
+\includegraphics[width=2.7cm]{si_pd_albe/hex_a_bonds.eps}
\end{minipage}
\begin{minipage}{0.4cm}
\begin{center}
\end{minipage}
\begin{minipage}{2.7cm}
$E_{\text{f}}=3.96\text{ eV}$\\
-\includegraphics[width=2.8cm]{si_pd_albe/hex.eps}
+\includegraphics[width=2.8cm]{si_pd_albe/hex_bonds.eps}
\end{minipage}
}
-\begin{minipage}{2.9cm}
-\begin{flushright}
-\underline{Vacancy}\\
-\includegraphics[width=3.0cm]{si_pd_albe/vac.eps}
-\end{flushright}
-\end{minipage}
-
-\end{minipage}
-\begin{minipage}{3.5cm}
-
-\begin{flushright}
-\underline{\hkl<1 1 0> dumbbell}\\
-\includegraphics[width=3.0cm]{si_pd_albe/110.eps}\\
-\underline{Tetrahedral}\\
-\includegraphics[width=3.0cm]{si_pd_albe/tet.eps}\\
-\underline{\hkl<1 0 0> dumbbell}\\
-\includegraphics[width=3.0cm]{si_pd_albe/100.eps}
-\end{flushright}
-
+\begin{minipage}{5.5cm}
+\begin{center}
+{\tiny nearly T $\rightarrow$ T}\\
+\end{center}
+\includegraphics[width=6.0cm]{nhex_tet.ps}
\end{minipage}
\end{slide}
\footnotesize
- {\large\bf
- C interstitial point defects in silicon\\[-0.1cm]
- }
+\headphd
+{\large\bf
+ C interstitial point defects in silicon\\
+}
\begin{tabular}{l c c c c c c r}
\hline
- $E_{\text{f}}$ & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B & \cs{} \& \si\\
+ $E_{\text{f}}$ [eV] & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B &
+ {\color{black} \cs{} \& \si}\\
\hline
- VASP & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\
- Erhart/Albe MD & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & {\color{red}0.75} & 5.59$^*$ & {\color{green}4.43} \\
+ \textsc{vasp} & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\
+ Erhart/Albe & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & {\color{red}0.75} & 5.59$^*$ & {\color{green}4.43} \\
\hline
\end{tabular}\\[0.1cm]
\framebox{
-\begin{minipage}{2.7cm}
+\begin{minipage}{2.8cm}
\underline{Hexagonal} \hspace{2pt}
\href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
$E_{\text{f}}^*=9.05\text{ eV}$\\
-\includegraphics[width=2.7cm]{c_pd_albe/hex.eps}
+\includegraphics[width=2.8cm]{c_pd_albe/hex_bonds.eps}
\end{minipage}
\begin{minipage}{0.4cm}
\begin{center}
$\Rightarrow$
\end{center}
\end{minipage}
-\begin{minipage}{2.7cm}
+\begin{minipage}{2.8cm}
\underline{\hkl<1 0 0>}\\
$E_{\text{f}}=3.88\text{ eV}$\\
-\includegraphics[width=2.7cm]{c_pd_albe/100.eps}
+\includegraphics[width=2.8cm]{c_pd_albe/100_bonds.eps}
\end{minipage}
}
-\begin{minipage}{2cm}
+\begin{minipage}{1.4cm}
\hfill
\end{minipage}
-\begin{minipage}{3cm}
+\begin{minipage}{3.0cm}
\begin{flushright}
\underline{Tetrahedral}\\
-\includegraphics[width=3.0cm]{c_pd_albe/tet.eps}
+\includegraphics[width=3.0cm]{c_pd_albe/tet_bonds.eps}
\end{flushright}
\end{minipage}
\framebox{
-\begin{minipage}{2.7cm}
+\begin{minipage}{2.8cm}
\underline{Bond-centered}\\
$E_{\text{f}}^*=5.59\text{ eV}$\\
-\includegraphics[width=2.7cm]{c_pd_albe/bc.eps}
+\includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}
\end{minipage}
\begin{minipage}{0.4cm}
\begin{center}
$\Rightarrow$
\end{center}
\end{minipage}
-\begin{minipage}{2.7cm}
+\begin{minipage}{2.8cm}
\underline{\hkl<1 1 0> dumbbell}\\
$E_{\text{f}}=5.18\text{ eV}$\\
-\includegraphics[width=2.7cm]{c_pd_albe/110.eps}
+\includegraphics[width=2.8cm]{c_pd_albe/110_bonds.eps}
\end{minipage}
}
-\begin{minipage}{2cm}
+\begin{minipage}{1.4cm}
\hfill
\end{minipage}
-\begin{minipage}{3cm}
+\begin{minipage}{3.0cm}
\begin{flushright}
\underline{Substitutional}\\
-\includegraphics[width=3.0cm]{c_pd_albe/sub.eps}
+\includegraphics[width=3.0cm]{c_pd_albe/sub_bonds.eps}
\end{flushright}
\end{minipage}
\begin{slide}
-\footnotesize
+\headphd
+{\large\bf\boldmath
+ C-Si dimer \& bond-centered interstitial configuration
+}
- {\large\bf\boldmath
- C \hkl<1 0 0> dumbbell interstitial configuration\\
- }
+\footnotesize
-{\tiny
-\begin{tabular}{l c c c c c c c c}
-\hline
- Distances [nm] & $r(1C)$ & $r(2C)$ & $r(3C)$ & $r(12)$ & $r(13)$ & $r(34)$ & $r(23)$ & $r(25)$ \\
-\hline
-Erhart/Albe & 0.175 & 0.329 & 0.186 & 0.226 & 0.300 & 0.343 & 0.423 & 0.425 \\
-VASP & 0.174 & 0.341 & 0.182 & 0.229 & 0.286 & 0.347 & 0.422 & 0.417 \\
-\hline
-\end{tabular}\\[0.2cm]
-\begin{tabular}{l c c c c }
-\hline
- Angles [$^{\circ}$] & $\theta_1$ & $\theta_2$ & $\theta_3$ & $\theta_4$ \\
-\hline
-Erhart/Albe & 140.2 & 109.9 & 134.4 & 112.8 \\
-VASP & 130.7 & 114.4 & 146.0 & 107.0 \\
-\hline
-\end{tabular}\\[0.2cm]
-\begin{tabular}{l c c c}
-\hline
- Displacements [nm]& $a$ & $b$ & $|a|+|b|$ \\
-\hline
-Erhart/Albe & 0.084 & -0.091 & 0.175 \\
-VASP & 0.109 & -0.065 & 0.174 \\
-\hline
-\end{tabular}\\[0.6cm]
-}
+\vspace{0.1cm}
-\begin{minipage}{3.0cm}
+\begin{minipage}[t]{4.1cm}
+{\bf\boldmath C \hkl<1 0 0> DB interstitial}\\[0.1cm]
+\begin{minipage}{2.0cm}
\begin{center}
\underline{Erhart/Albe}
-\includegraphics[width=3.0cm]{c_pd_albe/100_cmp.eps}
+\includegraphics[width=2.0cm]{c_pd_albe/100_cmp.eps}
\end{center}
\end{minipage}
-\begin{minipage}{3.0cm}
+\begin{minipage}{2.0cm}
\begin{center}
-\underline{VASP}
-\includegraphics[width=3.0cm]{c_pd_vasp/100_cmp.eps}
+\underline{\textsc{vasp}}
+\includegraphics[width=2.0cm]{c_pd_vasp/100_cmp.eps}
+\end{center}
+\end{minipage}\\[0.2cm]
+Si-C-Si bond angle $\rightarrow$ \unit[180]{$^{\circ}$}\\
+$\Rightarrow$ $sp$ hybridization\\[0.1cm]
+Si-Si-Si bond angle $\rightarrow$ \unit[120]{$^{\circ}$}\\
+$\Rightarrow$ $sp^2$ hybridization
+\begin{center}
+\includegraphics[width=3.4cm]{c_pd_vasp/eden.eps}\\[-0.1cm]
+{\tiny Charge density isosurface}
\end{center}
-\end{minipage}\\
-
-\begin{picture}(0,0)(-185,10)
-\includegraphics[width=6.8cm]{100-c-si-db_cmp.eps}
-\end{picture}
-\begin{picture}(0,0)(-280,-150)
-\includegraphics[width=3.3cm]{c_pd_vasp/eden.eps}
-\end{picture}
-
-\begin{pspicture}(0,0)(0,0)
-\psellipse[linecolor=green](5.18,5.92)(0.5,0.3)
-\psellipse[linecolor=red](3.45,5.92)(1.0,0.4)
-\psellipse[linecolor=blue](2.7,6.92)(0.9,0.2)
-\psellipse[linecolor=blue](4.65,6.92)(0.9,0.2)
-\end{pspicture}
-
-\end{slide}
-
-\begin{slide}
-
-\small
-
-\begin{minipage}{8.5cm}
-
- {\large\bf
- Bond-centered interstitial configuration\\[-0.1cm]
- }
-
-\begin{minipage}{3.0cm}
-\includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\
\end{minipage}
-\begin{minipage}{5.2cm}
+\begin{minipage}{0.2cm}
+\hfill
+\end{minipage}
+\begin{minipage}[t]{8.1cm}
+\begin{flushright}
+{\bf Bond-centered interstitial}\\[0.1cm]
+\begin{minipage}{4.4cm}
+%\scriptsize
\begin{itemize}
\item Linear Si-C-Si bond
\item Si: one C \& 3 Si neighbours
Real local minimum!
\end{itemize}
\end{minipage}
+\begin{minipage}{2.7cm}
+%\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{
\tiny
\end{flushright}
\end{minipage}
\end{minipage}
-}\\[0.1cm]
+}\\[0.4cm]
-\framebox{
-\begin{minipage}{4.5cm}
-\includegraphics[width=4cm]{c_100_mig_vasp/im_spin_diff.eps}
-\end{minipage}
-\begin{minipage}{3.5cm}
+%\framebox{
+\begin{minipage}{3.0cm}
+%\scriptsize
+\underline{Charge density}\\
{\color{gray}$\bullet$} Spin up\\
{\color{green}$\bullet$} Spin down\\
{\color{blue}$\bullet$} Resulting spin up\\
{\color{yellow}$\bullet$} Si atoms\\
{\color{red}$\bullet$} C atom
\end{minipage}
-}
-
+\begin{minipage}{3.6cm}
+\includegraphics[width=3.8cm]{c_100_mig_vasp/im_spin_diff.eps}
\end{minipage}
-\begin{minipage}{4.2cm}
-\begin{flushright}
-\includegraphics[width=4.3cm]{c_pd_vasp/bc_2333_ksl.ps}\\
-{\color{green}$\Box$} {\tiny unoccupied}\\
-{\color{red}$\bullet$} {\tiny occupied}
+%}
+
\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}
+% continue here
+\fi
+
\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}
+\begin{minipage}{6.8cm}
+\underline{\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/bc_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/100_next_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}
-\end{minipage}\\
-\begin{minipage}{8.3cm}
+\begin{minipage}{5.4cm}
+\includegraphics[width=6.0cm]{im_00-1_nosym_sp_fullct_thesis_vasp_s.ps}
+\end{minipage}\\[0.4cm]
+%
+\begin{minipage}{6.8cm}
\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}{2.0cm}
+\includegraphics[width=2.0cm]{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/00-1-0-10_2333.eps}
-\end{minipage}
-\begin{minipage}{0.4cm}
-$\rightarrow$
-\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}
-\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}
+\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}
-\end{minipage}
-\end{minipage}
-\framebox{
-\begin{minipage}{4.2cm}
- {\small Constrained relaxation\\
- technique (CRT) method}\\
-\includegraphics[width=4cm]{crt_orig.eps}
-\begin{itemize}
- \item Constrain diffusing atom
- \item Static constraints
-\end{itemize}
-\vspace*{0.3cm}
- {\small Modifications}\\
-\includegraphics[width=4cm]{crt_mod.eps}
-\begin{itemize}
- \item Constrain all atoms
- \item Update individual\\
- constraints
-\end{itemize}
-\end{minipage}
-}
+\begin{minipage}{5.4cm}
+\includegraphics[width=6.0cm]{00-1_0-10_vasp_s.ps}
+\end{minipage}\\[0.2cm]
+%
+\begin{center}
+Reorientation pathway composed of two consecutive processes of the above type
+\end{center}
\end{slide}
+\end{document}
+\ifnum1=0
+
\begin{slide}
{\large\bf\boldmath