X-Git-Url: https://hackdaworld.org/gitweb/?p=lectures%2Flatex.git;a=blobdiff_plain;f=posic%2Ftalks%2Fupb-ua-xc.tex;h=7b953ffafa28429c1e0274314340d37373e7db7d;hp=78b1ef52853e8a7d4e4c74621057bb611e31e2f9;hb=e08a97849ebaf34c088eef126bf83fa8a4267119;hpb=a9b873c00599fbcfa38cbaf058f9846732a4f773 diff --git a/posic/talks/upb-ua-xc.tex b/posic/talks/upb-ua-xc.tex index 78b1ef5..7b953ff 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 @@ -1955,10 +1992,31 @@ $z,x'$-axis rotation: $45.0^{\circ}$, $0.0^{\circ}$ \begin{slide} {\large\bf\boldmath - \hkl<0 0 -1> to \hkl<0 0 1> migration + BC to \hkl<0 0 -1> migration in the $3\times 3\times 3$ Type 2 supercell } + \begin{minipage}{6cm} + Method: + \begin{itemize} + \item Starting configuration:\\ + C bond centered + \item CRT towards \hkl<0 0 -1> configuration + \item Spin polarized calculations + \end{itemize} + Results:\\ + Video \href{../video/c_im_00-1_vasp.avi}{$\rhd_{\text{local}}$ } $|$ + \href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/c_im_00-1_vasp.avi}{$\rhd_{\text{remote url}}$} + \begin{itemize} + \item Still abrupt changes in configuration and energy + \item Migration barrier $>$ 1 eV + \end{itemize} + \end{minipage} + \begin{minipage}{6cm} + \includegraphics[width=6cm]{c_im_001_mig_vasp.ps} + \includegraphics[width=6cm]{c_im_001_mig_rc_vasp.ps} + \end{minipage} + \end{slide} \begin{slide} @@ -1971,6 +2029,92 @@ $z,x'$-axis rotation: $45.0^{\circ}$, $0.0^{\circ}$ \includegraphics[width=6cm]{c_00-1_0-10_mig_vasp.ps} \includegraphics[width=6cm]{c_00-1_0-10_mig_dis_vasp.ps} + Calculations without spin:\\ + Video \href{../video/c_00-1_0-10_vasp.avi}{$\rhd_{\text{local}}$ } $|$ + \href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/c_00-1_0-10_vasp.avi}{$\rhd_{\text{remote url}}$} ... WAAAAH!!! + \begin{itemize} + \item Refined starting from 70\% due to + abrubt jumps in energy and configuration + \item Displacement from 80 to 85\% disastrous + \item Subsequent displacements too large + \end{itemize} + + Waiting for spin polarized calculations before deciding what to do ... + +\end{slide} + +\begin{slide} + + {\large\bf\boldmath + C \hkl<1 0 0> migration - yet another method! + } + + {\color{red}Problem:} + + Abrubt changes in atomic configurations (and energy) + in consecutive steps. + In addition - sometimes - the final configuration is not obtained! + + {\color{blue}New method:} + + Displace {\color{red}all} atoms towards the final configuration + and apply corresponding constraints for each atom. + + Usage: + (\href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/sd_rot_all-atoms.patch}{Patch}) + +\footnotesize + +\begin{verbatim} +cubic diamond + 5.48000000000000 + 2.9909698580839312 0.0039546630279804 -0.0039658085666586 + 0.0039548953566878 2.9909698596656376 -0.0039660323646892 + -0.0039680658132861 -0.0039674231313905 2.9909994291263242 + 216 1 +Transformed selective dynamics +Direct + 0.994174 0.994174 -0.000408732 T F T 45 36.5145 + 0.182792 0.182792 0.981597 T F T -135 -5.95043 + ... + 0.119896 0.119896 0.0385525 T F T -135 21.8036 +\end{verbatim} + +\end{slide} + +\begin{slide} + + {\large\bf\boldmath + BC to \hkl<0 0 -1> migration (all atoms CRT) + } + + \includegraphics[width=6cm]{im_00-1_nosym_sp_fullct.ps} + \includegraphics[width=6cm]{im_00-1_nosym_sp_fullct_rc.ps} + +\end{slide} + +\begin{slide} + + {\large\bf\boldmath + \hkl<0 0 -1> to \hkl<0 -1 0> migration (all atoms CRT) + } + + \includegraphics[width=6cm]{00-1_0-10_nosym_sp_fullct.ps} + \includegraphics[width=6cm]{00-1_0-10_nosym_sp_fullct_rc.ps} + +\end{slide} + +\begin{slide} + + {\large\bf\boldmath + \hkl<0 0 -1> to \hkl<0 -1 0> migration in place (all atoms CRT) + } + + \includegraphics[width=6cm]{00-1_ip0-10_nosym_sp_fullct.ps} + \includegraphics[width=6cm]{00-1_ip0-10_nosym_sp_fullct_rc.ps} + + in progress ... + \end{slide} \begin{slide} @@ -2071,6 +2215,28 @@ $z,x'$-axis rotation: $45.0^{\circ}$, $0.0^{\circ}$ \end{slide} +\begin{slide} + + {\large\bf\boldmath + Silicon point defects + } + + \begin{minipage}{3.1cm} + \underline{\hkl<1 0 0> interstitial} + \begin{itemize} + \item $E_{\text{f}}=4.41\text{ eV}$ + \end{itemize} + \includegraphics[width=3cm]{si_pd_vasp/100_2333.eps}\\ + \end{minipage} + \begin{minipage}{3.7cm} + \begin{center} + \includegraphics[height=8cm]{si_pd_vasp/100_2333_ksl.ps}\\ + {\scriptsize \hkl<1 0 0> interstitial} + \end{center} + \end{minipage} + +\end{slide} + \begin{slide} {\large\bf\boldmath @@ -2111,22 +2277,40 @@ $z,x'$-axis rotation: $45.0^{\circ}$, $0.0^{\circ}$ } \begin{minipage}{3.2cm} - \underline{C tetrahedral}\\ - Relaxes into \hkl<0 0 1> configuration\\[0.2cm] - \underline{C hexagonal}\\ - Relaxes into \hkl<0 0 1> configuration\\[0.4cm] + \underline{C bond centered} + \begin{itemize} + \item $E_{\text{f}}=4.10\text{ eV}$ + \end{itemize} + \includegraphics[width=3cm]{c_pd_vasp/bc_2333.eps} \underline{\hkl<1 1 0> interstitial} \begin{itemize} \item $E_{\text{f}}=3.60\text{ eV}$ \end{itemize} \includegraphics[width=3cm]{c_pd_vasp/110_2333.eps} \end{minipage} - \begin{minipage}{9cm} + \begin{minipage}{4.5cm} \begin{center} \includegraphics[height=8cm]{c_pd_vasp/110_2333_ksl.ps} {\scriptsize \hkl<1 1 0> interstitial} \end{center} \end{minipage} + \begin{minipage}{4.5cm} + \begin{center} + \includegraphics[height=8cm]{c_pd_vasp/bc_2333_ksl.ps} + {\scriptsize C bond centered} + \end{center} + \end{minipage} + +\end{slide} + +\begin{slide} + + {\large\bf\boldmath + Carbon point defects in silicon + } + + The hexagonal and tetrahedral C configurations both relax into the + \hkl<0 0 1> interstitial configuration! \end{slide} @@ -2232,25 +2416,331 @@ $z,x'$-axis rotation: $45.0^{\circ}$, $0.0^{\circ}$ Combination of defects } + \small + + 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 \\ \hline -\hkl<0 0 -1> & 6.23 & 5.16 & 6.23 & 6.35 & 4.65\\ +C \hkl<0 0 -1> & 6.23/-0.08 & 5.16/-1.15 & 6.23/-0.08 & 6.35/0.04 & 4.65/-1.66\\ \hline -\hkl<0 0 1> & 6.64 & 6.31 & 4.26 & 6.57 & 4.78 \\ +C \hkl<0 0 1> & 6.64/0.34 & 6.31/0.01 & 4.26/-2.05 & 6.57/0.26 & 4.78/-1.53 \\ \hline -\hkl<1 0 0> & 4.06 & 6.13 & 6.21 & 6.03 & 4.93 \\ +C \hkl<1 0 0> & 4.06/-2.25 & 6.13/-0.17 & 6.21/-0.10 & 6.03/-0.27 & 4.93/-1.38 \\ \hline -\hkl<-1 0 0> & \hkl<0 -1 0> & 4.41 & 4.06 & 6.19 & 4.43 \\ +C \hkl<-1 0 0> & \hkl<0 -1 0> & 4.41/-1.90 & 4.06/-2.25 & 6.19/-0.12 & 4.43/-1.88 \\ \hline -\hkl<0 1 0> & \hkl<1 0 0> & 5.95 & \hkl<-1 0 0> & \hkl<-1 0 0> & \hkl<1 0 0> \\ +C \hkl<0 1 0> & \hkl<1 0 0> & 5.95/-0.36 & \hkl<-1 0 0> & \hkl<-1 0 0> & \hkl<1 0 0> \\ \hline -\hkl<0 -1 0> & 3.92 & 4.15 & \hkl<1 0 0> & \hkl<1 0 0> & \hkl <-1 0 0> \\ +C \hkl<0 -1 0> & 3.92/-2.39 & 4.15/-2.16 & \hkl<1 0 0> & \hkl<1 0 0> & \hkl <-1 0 0> \\ \hline -Vacancy & 1.39 & 6.19 & 3.65 & 6.24 & 6.50 \\ +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 - \end{tabular} +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}} + $\\[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} + +\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} + \includegraphics[width=2.5cm]{00-1dc/00-1_1.eps} + \end{minipage} + \begin{minipage}{2.5cm} + \includegraphics[width=2.5cm]{00-1dc/00-1_3.eps} + \end{minipage} + \begin{minipage}{2.5cm} + \includegraphics[width=2.5cm]{00-1dc/00-1_4.eps} + \end{minipage} + \begin{minipage}{2.5cm} + \includegraphics[width=2.5cm]{00-1dc/00-1_5.eps} + \end{minipage} + \begin{minipage}{2.5cm} + \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} + \includegraphics[width=2.5cm]{00-1dc/001_1.eps} + \end{minipage} + \begin{minipage}{2.5cm} + \includegraphics[width=2.5cm]{00-1dc/001_3.eps} + \end{minipage} + \begin{minipage}{2.5cm} + \includegraphics[width=2.5cm]{00-1dc/001_4.eps} + \end{minipage} + \begin{minipage}{2.5cm} + \includegraphics[width=2.5cm]{00-1dc/001_5.eps} + \end{minipage} + \begin{minipage}{2.5cm} + \includegraphics[width=2.5cm]{00-1dc/001_6.eps} + \end{minipage} + + \includegraphics[width=5.0cm]{00-1dc/energy_001.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} + \includegraphics[width=2.5cm]{00-1dc/100_1.eps} + \end{minipage} + \begin{minipage}{2.5cm} + \includegraphics[width=2.5cm]{00-1dc/100_3.eps} + \end{minipage} + \begin{minipage}{2.5cm} + \includegraphics[width=2.5cm]{00-1dc/100_4.eps} + \end{minipage} + \begin{minipage}{2.5cm} + \includegraphics[width=2.5cm]{00-1dc/100_5.eps} + \end{minipage} + \begin{minipage}{2.5cm} + \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} + \includegraphics[width=2.5cm]{00-1dc/0-10_1.eps} + \end{minipage} + \begin{minipage}{2.5cm} + \includegraphics[width=2.5cm]{00-1dc/-100_3.eps} + \end{minipage} + \begin{minipage}{2.5cm} + \includegraphics[width=2.5cm]{00-1dc/-100_4.eps} + \end{minipage} + \begin{minipage}{2.5cm} + \includegraphics[width=2.5cm]{00-1dc/-100_5.eps} + \end{minipage} + \begin{minipage}{2.5cm} + \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} + + {\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} + \includegraphics[width=2.5cm]{00-1dc/100_1.eps} + \end{minipage} + \begin{minipage}{2.5cm} + \includegraphics[width=2.5cm]{00-1dc/010_3.eps} + \end{minipage} + \begin{minipage}{2.5cm} + \includegraphics[width=2.5cm]{00-1dc/-100_4.eps} + \end{minipage} + \begin{minipage}{2.5cm} + \includegraphics[width=2.5cm]{00-1dc/-100_5.eps} + \end{minipage} + \begin{minipage}{2.5cm} + \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} + \includegraphics[width=2.5cm]{00-1dc/0-10_1.eps} + \end{minipage} + \begin{minipage}{2.5cm} + \includegraphics[width=2.5cm]{00-1dc/0-10_3.eps} + \end{minipage} + \begin{minipage}{2.5cm} + \includegraphics[width=2.5cm]{00-1dc/100_4.eps} + \end{minipage} + \begin{minipage}{2.5cm} + \includegraphics[width=2.5cm]{00-1dc/100_5.eps} + \end{minipage} + \begin{minipage}{2.5cm} + \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} + + {\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: Vacancy + + \begin{minipage}{2.5cm} + \includegraphics[width=2.5cm]{00-1dc/vac_1.eps} + \end{minipage} + \begin{minipage}{2.5cm} + \includegraphics[width=2.5cm]{00-1dc/vac_3.eps} + \end{minipage} + \begin{minipage}{2.5cm} + \includegraphics[width=2.5cm]{00-1dc/vac_4.eps} + \end{minipage} + \begin{minipage}{2.5cm} + \includegraphics[width=2.5cm]{00-1dc/vac_5.eps} + \end{minipage} + \begin{minipage}{2.5cm} + \includegraphics[width=2.5cm]{00-1dc/vac_6.eps} + \end{minipage} + + \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} + + \includegraphics[width=5.0cm]{00-1dc/energy_csub.ps} \end{slide} @@ -2262,7 +2752,7 @@ Vacancy & 1.39 & 6.19 & 3.65 & 6.24 & 6.50 \\ \small - Supercell size: $2$ - $2000 \cdot 10^{-21}\text{ cm}^3$ + Supercell size: $2$ -- $2000 \cdot 10^{-21}\text{ cm}^3$ \underline{After crystal growth} \begin{itemize}