X-Git-Url: https://hackdaworld.org/gitweb/?a=blobdiff_plain;f=posic%2Ftalks%2Fupb-ua-xc.tex;h=502375bbb17bd3c4d370cb80f90d59b7450a27e0;hb=308a99aefd361f2e795db24e852574f91758a9df;hp=cb717dfcc7cd993f3af3426e98fb0d9bd26e596f;hpb=a75025aeb35286e0960dceaa2684754c9566d7e4;p=lectures%2Flatex.git diff --git a/posic/talks/upb-ua-xc.tex b/posic/talks/upb-ua-xc.tex index cb717df..502375b 100644 --- a/posic/talks/upb-ua-xc.tex +++ b/posic/talks/upb-ua-xc.tex @@ -218,7 +218,7 @@ POTIM = 0.1 \begin{itemize} \item Calculation of cohesive energies for different lattice constants \item No ionic update - \item tetrahedron method with Blöchl corrections for + \item Tetrahedron method with Blöchl corrections for the partial occupancies $f_{nk}$ \item Supercell 3 (8 atoms, 4 primitive cells) \end{itemize} @@ -269,7 +269,7 @@ POTIM = 0.1 \begin{itemize} \item Calculation of cohesive energies for different lattice constants \item No ionic update - \item tetrahedron method with Blöchl corrections for + \item Tetrahedron method with Blöchl corrections for the partial occupancies $f_{nk}$ \end{itemize} \vspace*{0.6cm} @@ -330,65 +330,169 @@ POTIM = 0.1 \begin{slide} {\large\bf - Silicon point defects + Cohesive energies } + {\bf\color{red} From now on ...} + + {\small Energies used: free energy without entropy ($\sigma \rightarrow 0$)} + \small - {\color{red}\bf\LARGE - HIER NOCH NICHT LESEN! :)\\ - } - \begin{minipage}{6.5cm} - <110> Si interstitial \begin{itemize} - \item 2 pc's: - $E_{\textrm{f}}=-5.47342\,\textrm{eV}$ - \item 4 pc's: - $E_{\textrm{f}}=-5.65098\,\textrm{eV}$ - \item 32 pc's: running ... - $E_{\textrm{f}}=\,\textrm{eV}$ + \item $E_{\textrm{free,sp}}$: + energy of spin polarized free atom + \begin{itemize} + \item $k$-points: Monkhorst $1\times 1\times 1$ + \item Symmetry switched off + \item Spin polarized calculation + \item Interpolation formula according to Vosko Wilk and Nusair + for the correlation part of the exchange correlation functional + \item Gaussian smearing for the partial occupancies $f_{nk}$ + ($\sigma=0.05$) + \item Magnetic mixing: AMIX = 0.2, BMIX = 0.0001 + \item Supercell: one atom in cubic + $10\times 10\times 10$ \AA$^3$ box + \end{itemize} + {\color{blue} + $E_{\textrm{free,sp}}(\textrm{Si},250\, \textrm{eV})= + -0.70036911\,\textrm{eV}$ + }, + {\color{gray} + $E_{\textrm{free,sp}}(\textrm{C},xxx\, \textrm{eV})= + yyy\,\textrm{eV}$ + } + \item $E$: + energy (non-polarized) of system of interest composed of\\ + n atoms of type N, m atoms of type M, \ldots \end{itemize} + \vspace*{0.3cm} + {\color{red} + \[ + \Rightarrow + E_{\textrm{coh}}=\frac{ + -\Big(E(N_nM_m\ldots)-nE_{\textrm{free,sp}}(N)-mE_{\textrm{free,sp}}(M) + -\ldots\Big)} + {n+m+\ldots} + \] + } + +\end{slide} + +\begin{slide} + + {\large\bf + Used types of supercells\\ + } + + \footnotesize + + \begin{minipage}{4.3cm} + \includegraphics[width=4cm]{sc_type0.eps}\\[0.3cm] + \underline{Type 0}\\[0.2cm] + Basis: fcc\\ + $x_1=(0.5,0.5,0)$\\ + $x_2=(0,0.5,0.5)$\\ + $x_3=(0.5,0,0.5)$\\ + 1 primitive cell / 2 atoms \end{minipage} - \begin{minipage}{6.5cm} - plain Si - \begin{itemize} - \item 2 pc's: - $E_{\textrm{coh}}=-6.00846\,\textrm{eV}$ - \item 4 pc's: - $E_{\textrm{coh}}=-5.97464\,\textrm{eV}$ - \item 32 pc's: - $E_{\textrm{coh}}=-5.97633\,\textrm{eV}$ - \end{itemize} - \end{minipage}\\[0.2cm] - \begin{minipage}{6.5cm} - hexagonal Si interstitial - \begin{itemize} - \item 2 pc's: - $E_{\textrm{f}}=-5.60654\,\textrm{eV}$ - \item 4 pc's: - $E_{\textrm{f}}=-5.60174\,\textrm{eV}$ - \item 32 pc's: running ... - $E_{\textrm{f}}=\,\textrm{eV}$ - \end{itemize} - tetrahedral Si interstitial - \begin{itemize} - \item 2 pc's: $E_{\textrm{f}}=-5.53623\,\textrm{eV}$ - \item 4 pc's: $E_{\textrm{f}}=-5.64704\,\textrm{eV}$ - \item 32 pc's: $E_{\textrm{f}}=-5.92383\,\textrm{eV}$ - \end{itemize} - Si vacancy + \begin{minipage}{4.3cm} + \includegraphics[width=4cm]{sc_type1.eps}\\[0.3cm] + \underline{Type 1}\\[0.2cm] + Basis:\\ + $x_1=(0.5,-0.5,0)$\\ + $x_2=(0.5,0.5,0)$\\ + $x_3=(0,0,1)$\\ + 2 primitive cells / 4 atoms + \end{minipage} + \begin{minipage}{4.3cm} + \includegraphics[width=4cm]{sc_type2.eps}\\[0.3cm] + \underline{Type 2}\\[0.2cm] + Basis: sc\\ + $x_1=(1,0,0)$\\ + $x_2=(0,1,0)$\\ + $x_3=(0,0,1)$\\ + 4 primitive cells / 8 atoms + \end{minipage}\\[0.4cm] + + {\bf\color{blue} + In the following these types of supercells are used and + are possibly scaled by integers in the different directions! + } + +\end{slide} + +\begin{slide} + + {\large\bf + Silicon point defects\\ + } + + \small + + Calculation of formation energy $E_{\textrm{f}}$ \begin{itemize} - \item 2 pc's: $E_{\textrm{f}}=-5.65965\,\textrm{eV}$ - \item 4 pc's: $E_{\textrm{f}}=-5.56361\,\textrm{eV}$ - \item 32 pc's:$E_{\textrm{f}}=-5.92053\,\textrm{eV}$ + \item $E_{\textrm{coh}}^{\textrm{initial conf}}$: + cohesive energy per atom of the initial system + \item $E_{\textrm{coh}}^{\textrm{interstitial conf}}$: + cohesive energy per atom of the interstitial system + \item N: amount of atoms in the interstitial system \end{itemize} + \vspace*{0.2cm} + {\color{blue} + \[ + \Rightarrow + E_{\textrm{f}}=\Big(E_{\textrm{coh}}^{\textrm{interstitial conf}} + -E_{\textrm{coh}}^{\textrm{initial conf}}\Big) N + \] + } + Influence of supercell size\\ + \begin{minipage}{8cm} + \includegraphics[width=7.0cm]{si_self_int.ps} \end{minipage} - \begin{minipage}{6.5cm} - \begin{center} - \includegraphics[width=6.5cm]{si_self_int.ps} - \end{center} + \begin{minipage}{5cm} + $E_{\textrm{f}}^{\textrm{110},\,32\textrm{pc}}=3.38\textrm{ eV}$\\ + $E_{\textrm{f}}^{\textrm{tet},\,32\textrm{pc}}=3.41\textrm{ eV}$\\ + $E_{\textrm{f}}^{\textrm{hex},\,32\textrm{pc}}=3.42\textrm{ eV}$\\ + $E_{\textrm{f}}^{\textrm{vac},\,32\textrm{pc}}=3.51\textrm{ eV}$ \end{minipage} +\end{slide} + +\begin{slide} + + {\large\bf + Questions so far ...\\ + } + + What configuration to chose for C in Si simulations? + \begin{itemize} + \item Switch to another method for the XC approximation (GGA, PAW)? + \item Reasonable cut-off energy + \item Switch off symmetry? (especially for defect simulations) + \item $k$-points + (Monkhorst? $\Gamma$-point only if cell is large enough?) + \item Switch to tetrahedron method or Gaussian smearing ($\sigma$?) + \item Size and type of supercell + \begin{itemize} + \item connected to choice of $k$-point mesh? + \item hence also connected to choice of smearing method? + \item constraints can only be applied to the lattice vectors! + \end{itemize} + \item \ldots + \end{itemize} + +\end{slide} + +\begin{slide} + + {\large\bf + Review (so far) ...\\ + } + + + + \end{slide} \end{document}