mirror of https://gitlab.com/QEF/q-e.git
Added partial support to the use of k points label in the Brillouin zone.
git-svn-id: http://qeforge.qe-forge.org/svn/q-e/trunk/espresso@10465 c92efa57-630b-4861-b058-cf58834340f0
This commit is contained in:
dalcorso
parent
49690bc820
commit
4722bfe0eb
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@ -1,7 +1,7 @@
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LATEX = pdflatex
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LATEX2HTML = latex2html
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PDFS = constraints_HOWTO.pdf developer_man.pdf user_guide.pdf plumed_quick_ref.pdf
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PDFS = constraints_HOWTO.pdf developer_man.pdf user_guide.pdf plumed_quick_ref.pdf brillouin_zones.pdf
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AUXS = $(PDFS:.pdf=.aux)
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LOGS = $(PDFS:.pdf=.log)
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OUTS = $(PDFS:.pdf=.out)
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@ -60,3 +60,4 @@ user_guide: user_guide.pdf
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@echo "***"
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@echo ""
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brillouin_zones: brillouin_zones.pdf
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@ -8,6 +8,7 @@ release-notes What is new in the current release + list of fixed bugs
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(only those that were present in some official release)
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user-guide.tex User guide
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developer-man.tex Developers' manual
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brillouin_zone.tex Pictures of the labels defined inside the Brillouin zones.
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plumed_quick_ref.tex
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An introduction to the usage of PLUMED with QE
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constraints_HOWTO.tex
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@ -22,6 +23,7 @@ Printable versions of the *tex files are present in the released version:
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user-guide.pdf
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developer-man.pdf
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plumed_quick_ref.pdf
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brillouin_zone.pdf
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All the material included in this distribution is free software;
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you can redistribute it and/or modify it under the terms of the GNU
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@ -0,0 +1,525 @@
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\documentclass[12pt,a4paper]{article}
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\def\version{$>$5.0.2}
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\def\qe{{\sc Quantum ESPRESSO}}
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\def\qeforge{\texttt{qe-forge.org}}
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\textwidth = 17cm
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\textheight = 24cm
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\topmargin =-1 cm
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\oddsidemargin = 0 cm
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%\usepackage{html}
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% BEWARE: don't revert from graphicx for epsfig, because latex2html
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% doesn't handle epsfig commands !!!
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\usepackage{graphicx}
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\usepackage{amssymb}
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% \def\htmladdnormallink#1#2{#1}
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\def\configure{\texttt{configure}}
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\def\configurac{\texttt{configure.ac}}
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\def\autoconf{\texttt{autoconf}}
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\def\qeImage{../../Doc/quantum_espresso.pdf}
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\def\democritosImage{../../Doc/democritos.pdf}
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%\begin{htmlonly}
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%\def\qeImage{../../Doc/quantum_espresso.png}
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%\def\democritosImage{../../Doc/democritos.png}
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%\end{htmlonly}
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\def\pwx{\texttt{pw.x}}
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\def\phx{\texttt{ph.x}}
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\def\configure{\texttt{configure}}
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\def\PWscf{\texttt{PWscf}}
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\def\PHonon{\texttt{PHonon}}
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\def\make{\texttt{make}}
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\begin{document}
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\author{}
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\date{}
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\title{
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% \includegraphics[width=5cm]{\qeImage} \hskip 2cm
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% \includegraphics[width=6cm]{\democritosImage}\\
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\vskip 1cm
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% title
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\Huge Points inside the Brillouin zone \\
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\Large Notes by Andrea Dal Corso
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}
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\maketitle
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\newpage
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\section{Brillouin zone}
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\qe\ (QE) support for the definition of high symmetry lines inside the Brillouin
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zone (BZ) is still rather limited. However QE can calculate the coordinates
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of the vertexes of the BZ and of particular points inside the BZ. These
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notes show the shape and orientation of the BZ used by QE. The principal
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direct and reciprocal lattice vectors, as implemented
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in the routine \texttt{latgen}, are illustrated here together with the labels
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of each point. These labels can be given as input in a band calculation
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to define paths in the BZ. This feature is available with the option
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\texttt{tpiba\_b} or \texttt{crystal\_b} in \texttt{bands} calculation.
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Lines in reciprocal space are defined by giving the coordinates of the
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starting and ending points and the number of points of each line.
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The coordinates of the starting and ending points can be
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given explicitly with three real numbers or by giving the label of a
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point known to QE.
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For example:
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\begin{verbatim}
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X 10
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gG 25
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0.5 0.5 0.5 1
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\end{verbatim}
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indicate a path composed by two lines. The first line starts at point $X$,
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ends at point $\Gamma$, and has $10$ {\bf k} points. The second line starts
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at $\Gamma$, ends at the point of coordinates \texttt{(0.5,0.5,0.5)} and
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has $25$ {\bf k} points. Greek labels are prefixed by the letter
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\texttt{g}: \texttt{gG} indicates the $\Gamma$ point, \texttt{gS} the
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$\Sigma$ point etc. Subscripts are written after the label: the point $P_1$
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is indicated as \texttt{P1}. In the following section you can find the
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labels of the points defined in each BZ.
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There are many convention to label high symmetry
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points inside the BZ. The variable \texttt{point\_label\_type} selects the
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set of labels used by QE. The default is \texttt{point\_label\_type='SC'} and
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the labels have been taken from W. Setyawan and S. Curtarolo, Comp. Mat. Sci.
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{\bf 49}, 299 (2010). Many more points can be used in low symmetry
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situations as reported in detail at the web pages
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\texttt{http://www.cryst.ehu.es/cryst/get\_kvec.html}.
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For some BZ some of these points are defined and you can use them by setting
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(\texttt{point\_label\_type='BI'}), others can be added in the future.
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This option is available only with \texttt{ibrav$\ne$0} and for
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all positive \texttt{ibrav} with the exception of the simple monoclinic
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(\texttt{ibrav=12}), base centered monoclinic (\texttt{ibrav=13}), and
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triclinic (\texttt{ibrav=14}) lattices. In these cases you have to
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give all the coordinates of the {\bf k}-points.
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\subsection{\texttt{ibrav=1}, simple cubic lattice}
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The primitive vectors of the direct lattice are:
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\begin{eqnarray}
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{\bf a}_1 &=& a (1, 0, 0), \nonumber \\
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{\bf a}_2 &=& a (0, 1, 0), \nonumber \\
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{\bf a}_3 &=& a (0, 0, 1), \nonumber
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\nonumber
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\end{eqnarray}
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while the reciprocal lattice vectors are:
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\begin{eqnarray}
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{\bf b}_1 &=& {2\pi \over a} (1, 0, 0), \nonumber \\
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{\bf b}_2 &=& {2\pi \over a} (0, 1, 0), \nonumber \\
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{\bf b}_3 &=& {2\pi \over a} (0, 0, 1). \nonumber
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\nonumber
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\end{eqnarray}
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The Brilloin zone is:
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\begin{center}
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\includegraphics[width=7.5cm,angle=0]{images/cubic_bi.png}
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\end{center}
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\texttt{X$_1$} is available only with $\texttt{point\_label\_type='BI'}$.
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\subsection{\texttt{ibrav=2}, face centered cubic lattice}
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The primitive vectors of the direct lattice are:
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\begin{eqnarray}
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{\bf a}_1 &=& {a \over 2} (-1, 0, 1), \nonumber \\
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{\bf a}_2 &=& {a \over 2} (0, 1, 1), \nonumber \\
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{\bf a}_3 &=& {a \over 2} (-1, 1, 0), \nonumber
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\nonumber
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\end{eqnarray}
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while the reciprocal lattice vectors are:
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\begin{eqnarray}
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{\bf b}_1 &=& {2\pi \over a} (-1, -1, 1), \nonumber \\
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{\bf b}_2 &=& {2\pi \over a} (1, 1, 1), \nonumber \\
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{\bf b}_3 &=& {2\pi \over a} (-1, 1, -1). \nonumber
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\nonumber
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\end{eqnarray}
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The Brillouin zone is:
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\begin{center}
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\includegraphics[width=7.5cm,angle=0]{images/fcc_sc.png} \hspace{1.cm}
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\includegraphics[width=7.5cm,angle=0]{images/fcc_bi.png}
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\end{center}
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Labels corresponding to $\texttt{point\_label\_type='SC'}$ and to
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$\texttt{point\_label\_type='BI'}$ are shown on the left and on the right,
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respectively.
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\subsection{\texttt{ibrav=3}, body centered cubic lattice}
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The primitive vectors of the direct lattice are:
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\begin{eqnarray}
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{\bf a}_1 &=&{a \over 2} (1, 1, 1), \nonumber \\
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{\bf a}_2 &=&{a \over 2} (-1, 1, 1), \nonumber \\
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{\bf a}_3 &=&{a \over 2} (-1, -1, 1), \nonumber
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\nonumber
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\end{eqnarray}
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while the reciprocal lattice vectors are:
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\begin{eqnarray}
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{\bf b}_1 &=&{2\pi \over a} (1, 0, 1), \nonumber \\
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{\bf b}_2 &=&{2\pi \over a} (-1, 1, 0), \nonumber \\
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{\bf b}_3 &=&{2\pi \over a} (0, -1, 1). \nonumber
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\nonumber
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\end{eqnarray}
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\begin{center}
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\includegraphics[width=7.5cm,angle=0]{images/bcc_bi.png}
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\end{center}
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\texttt{H$_1$} is available only with $\texttt{point\_label\_type='BI'}$.
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\subsection{\texttt{ibrav=4}, hexagonal lattice}
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The primitive vectors of the direct lattice are:
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\begin{eqnarray}
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{\bf a}_1 &=& a (1, 0, 0), \nonumber \\
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{\bf a}_2 &=& a (-{1 \over 2}, {\sqrt{3} \over 2}, 0), \nonumber \\
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{\bf a}_3 &=& a (0, 0, {c\over a}), \nonumber
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\nonumber
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\end{eqnarray}
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while the reciprocal lattice vectors are:
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\begin{eqnarray}
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{\bf b}_1 &=& {2\pi \over a} (1, {1 \over \sqrt{3}}, 0), \nonumber \\
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{\bf b}_2 &=& {2\pi \over a} (0, {2 \over \sqrt{3}}, 0), \nonumber \\
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{\bf b}_3 &=& {2\pi \over a} (0, 0, {a\over c}). \nonumber
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\nonumber
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\end{eqnarray}
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The BZ is:
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\begin{center}
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\includegraphics[width=7.5cm,angle=0]{images/hex.png}
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\end{center}
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The figure has been obtained with ${c/a}=1.4$.
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\subsection{\texttt{ibrav=5}, trigonal lattice}
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The primitive vectors of the direct lattice are:
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\begin{eqnarray}
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{\bf a}_1 &=& a ({\sqrt{3}\over 2}\sin{\theta}, -{1\over 2} \sin{\theta},
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\cos{\theta}),
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\nonumber \\
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{\bf a}_2 &=& a (0, \sin{\theta}, \cos{\theta}),
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\nonumber \\
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{\bf a}_3 &=& a (-{\sqrt{3}\over 2} \sin{\theta}, -{1\over 2} \sin{\theta},
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\cos{\theta}),
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\nonumber \\
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\nonumber
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\end{eqnarray}
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while the reciprocal lattice vectors are:
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\begin{eqnarray}
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{\bf b}_1 &=& {2\pi \over a} ({\sqrt{3}\over 2} \sin{\theta},
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-{1 \over 2} \sin{\theta}, \cos{\theta}), \nonumber \\
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{\bf b}_2 &=& {2\pi \over a} (0,
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\sin{\theta}, \cos{\theta}), \nonumber \\
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{\bf b}_3 &=& {2\pi \over a} (-{\sqrt{3}\over 2} \sin{\theta},
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-{1 \over 2} \sin{\theta}, \cos{\theta}), \nonumber
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\end{eqnarray}
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where $\sin{\theta}=\sqrt{2\over 3}\sqrt{1-\cos{\alpha}}$
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and $\cos{\theta}=\sqrt{1\over 3}\sqrt{1 + 2 \cos{\alpha}}$ and $\alpha$
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is the angle between any two primitive direct lattice vectors.
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There are two possible shapes of the BZ, depending on the
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value of the angle $\alpha$. For $\alpha < 90^\circ$ we
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have:
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\begin{center}
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\includegraphics[width=7.5cm,angle=0]{images/tri_1.png}
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\end{center}
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The figure has been obtained with $\alpha=70^\circ$.
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For $90^\circ < \alpha < 120^\circ$ we have:
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\begin{center}
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\includegraphics[width=7.5cm,angle=0]{images/tri_2.png}
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\end{center}
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The figure has been obtained with $\alpha=110^\circ$.
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\subsection{\texttt{ibrav=6}, simple tetragonal lattice}
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The primitive vectors of the direct lattice are:
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\begin{eqnarray}
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{\bf a}_1 &=& a (1, 0, 0), \nonumber \\
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{\bf a}_2 &=& a (0, 1, 0), \nonumber \\
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{\bf a}_3 &=& a (0, 0, {c\over a}), \nonumber
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\nonumber
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\end{eqnarray}
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while the reciprocal lattice vectors are:
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\begin{eqnarray}
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{\bf b}_1 &=& {2\pi \over a} (1, 0, 0), \nonumber \\
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{\bf b}_2 &=& {2\pi \over a} (0, 1, 0), \nonumber \\
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{\bf b}_3 &=& {2\pi \over a} (0, 0, {a\over c}). \nonumber
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\nonumber
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\end{eqnarray}
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\begin{center}
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\includegraphics[width=7.5cm,angle=0]{images/st.png}
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\end{center}
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The figure has been obtained with $c/a=1.4$.
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\subsection{\texttt{ibrav=7}, centered tetragonal lattice}
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The primitive vectors of the direct lattice are:
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\begin{eqnarray}
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{\bf a}_1 &=& {a \over 2} (1, 1, {c\over a}), \nonumber \\
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{\bf a}_2 &=& {a \over 2} (1, -1, {c\over a}), \nonumber \\
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{\bf a}_3 &=& {a \over 2} (-1, -1, {c\over a}), \nonumber
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\nonumber
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\end{eqnarray}
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while the reciprocal lattice vectors are:
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\begin{eqnarray}
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{\bf b}_1 &=& {2\pi \over a} (1, -1, 0), \nonumber \\
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{\bf b}_2 &=& {2\pi \over a} (0, 1, {a\over c}), \nonumber \\
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{\bf b}_3 &=& {2\pi \over a} (-1, 0, {a\over c}). \nonumber
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\nonumber
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\end{eqnarray}
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In this case there are two different shapes of the BZ depending on the
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$c/a$ ratio. For $c/a<1$ we have:
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\begin{center}
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\includegraphics[width=7.5cm,angle=0]{images/stc1.png}
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\end{center}
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The figure has been obtained with $c/a=0.5$ ($a>c$). For $c/a>1$ we have:
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\begin{center}
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\includegraphics[width=7.5cm,angle=0]{images/stc2_sc.png} \hspace{1cm}
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\includegraphics[width=7.5cm,angle=0]{images/stc2.png}
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\end{center}
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The figure has been obtained with $c/a=1.4$ ($a<c$).
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Labels corresponding to $\texttt{point\_label\_type='SC'}$ are shown on the left,
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those corresponding to $\texttt{point\_label\_type='BI'}$ on the right.
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\subsection{\texttt{ibrav=8}, simple orthorhombic lattice}
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The primitive vectors of the direct lattice are:
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\begin{eqnarray}
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{\bf a}_1 &=& a (1, 0, 0), \nonumber \\
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{\bf a}_2 &=& a (0, {b\over a}, 0), \nonumber \\
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{\bf a}_3 &=& a (0, 0, {c\over a}), \nonumber
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\nonumber
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\end{eqnarray}
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while the reciprocal lattice vectors are:
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\begin{eqnarray}
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{\bf b}_1 &=& {2\pi \over a} (1, 0, 0), \nonumber \\
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{\bf b}_2 &=& {2\pi \over a} (0, {a\over b}, 0), \nonumber \\
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{\bf b}_3 &=& {2\pi \over a} (0, 0, {a\over c}). \nonumber
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\nonumber
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\end{eqnarray}
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\begin{center}
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\includegraphics[width=7.5cm,angle=0]{images/so.png}
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\end{center}
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The figure has been obtained with $b/a=1.2$ and $c/a=1.5$.
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\subsection{\texttt{ibrav=9}, one-face centered orthorhombic lattice}
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The direct lattice vectors are:
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\begin{eqnarray}
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{\bf a}_1 &=& {a \over 2} (1, {b \over a}, 0), \nonumber \\
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{\bf a}_2 &=& {a \over 2} (-1, {b \over a}, 0), \nonumber \\
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{\bf a}_3 &=& a (0, 0, {c \over a}), \nonumber
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\nonumber
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\end{eqnarray}
|
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while the reciprocal lattice vectors are
|
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\begin{eqnarray}
|
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{\bf b}_1 &=& {2\pi \over a} (1, {a \over b}, 0), \nonumber \\
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{\bf b}_2 &=& {2\pi \over a} (-1, {a \over b}, 0), \nonumber \\
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{\bf b}_3 &=& {2\pi \over a} (0, 0, {a \over c}). \nonumber
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\nonumber
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\end{eqnarray}
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There is one shape that can have two orientations depending on the
|
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ratio between of $a$ and $b$:
|
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\begin{center}
|
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\includegraphics[width=7.5cm,angle=0]{images/ofco_2.png} \hspace{1cm}
|
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\includegraphics[width=6.5cm,angle=0]{images/ofco_1.png}
|
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\end{center}
|
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The figures have been obtained with $b/a=0.8$ and $c/a=1.4$ (left part $b<a$)
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and $b/a=1.2$ and $c/a=1.4$ (right part $b>a$).
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\subsection{\texttt{ibrav=10}, face centered orthorhombic lattice}
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The direct lattice vectors are:
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\begin{eqnarray}
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{\bf a}_1 &=& {a \over 2} (1, 0, {c \over a}), \nonumber \\
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{\bf a}_2 &=& {a \over 2} (1, {b \over a}, 0), \nonumber \\
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{\bf a}_3 &=& {a \over 2} (0, {b \over a}, {c \over a}). \nonumber
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\nonumber
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\end{eqnarray}
|
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while the reciprocal lattice vectors are
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\begin{eqnarray}
|
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{\bf b}_1 &=& {2\pi \over a} (1, -{a \over b}, {a \over c}), \nonumber \\
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{\bf b}_2 &=& {2\pi \over a} (1, {a \over b}, -{a \over c}), \nonumber \\
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{\bf b}_3 &=& {2\pi \over a} (-1, {a \over b}, {a \over c}). \nonumber
|
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\nonumber
|
||||
\end{eqnarray}
|
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In this case there are three different shapes
|
||||
that can be rotated in different ways depending on the relative
|
||||
sizes of $a$, $b$, and $c$.
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If $a$ is the shortest side, there are three different shapes according
|
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to
|
||||
\begin{equation}
|
||||
{1\over a^2} \lesseqqgtr
|
||||
{1\over b^2} + {1\over c^2},
|
||||
\label{uno}
|
||||
\end{equation}
|
||||
if $b$ is the shortest side there are three different shapes according to
|
||||
\begin{equation}
|
||||
{1\over b^2} \lesseqqgtr {1\over a^2} + {1\over c^2},
|
||||
\label{due}
|
||||
\end{equation}
|
||||
and if $c$ is the shortest side there are
|
||||
three different shapes according to
|
||||
\begin{equation}
|
||||
{1\over c^2} \lesseqqgtr {1\over a^2}
|
||||
+ {1\over b^2}.
|
||||
\label{tre}
|
||||
\end{equation}
|
||||
For each case there are two possibilities. If $a$
|
||||
is the shortest side, we can have $b<c$ or $b>c$, if $b$ is
|
||||
the shortest side, we can have $a<c$ or $a>c$, and finally
|
||||
if $c$ is the shortest side we can have $a<b$ or $a>b$. In total we
|
||||
have $18$ distinct cases. Not all cases give different BZ.
|
||||
All the cases with the $<$ sign in Eqs.~\ref{uno}, \ref{due}, \ref{tre} give
|
||||
the same shape of the BZ that differ for the relative sizes of the faces.
|
||||
All the cases with the $>$ sign in Eqs.~\ref{uno}, \ref{due}, \ref{tre} give
|
||||
the same shape with faces of different sizes and oriented in different ways.
|
||||
Finally the particular case with the $=$ sign in Eqs.~\ref{uno},
|
||||
\ref{due}, \ref{tre} give another shape
|
||||
with faces of different size and different orientations.
|
||||
We show all the 18 possibilities and the labels used in each case.
|
||||
|
||||
We start with the case in which $a$ is the shortest side and show on the
|
||||
left the case $b<c$ and on the right the case $b>c$.
|
||||
The first possibility is that ${1\over a^2} <
|
||||
{1\over b^2} + {1\over c^2}$:
|
||||
\begin{center}
|
||||
\includegraphics[width=7.5cm,angle=0]{images/ofc_1.png} \hspace{1cm}
|
||||
\includegraphics[width=6.5cm,angle=0]{images/ofc_2.png}
|
||||
\end{center}
|
||||
The figures have been obtained with $b/a=1.2$ and $c/a=1.4$ (left part $b<c$),
|
||||
and with $b/a=1.4$ and $c/a=1.2$ (right part $b>c$).
|
||||
|
||||
The second possibility is that ${1\over a^2} =
|
||||
{1\over b^2} + {1\over c^2}$:
|
||||
\begin{center}
|
||||
\includegraphics[width=7.5cm,angle=0]{images/ofc_13.png} \hspace{1cm}
|
||||
\includegraphics[width=5.5cm,angle=0]{images/ofc_14.png}
|
||||
\end{center}
|
||||
The figures have been obtained with $b/a=1.2$ and $c/a=1.80906807$
|
||||
(left part $b<c$) and with $b/a=1.80906807$ and $c/a=1.2$ (right part $b>c$).
|
||||
|
||||
The third possibility is that ${1 \over a^2} > {1\over b^2} + {1\over c^2}$:
|
||||
\begin{center}
|
||||
\includegraphics[width=6.5cm,angle=0]{images/ofc_7.png} \hspace{1cm}
|
||||
\includegraphics[width=4.0cm,angle=0]{images/ofc_8.png}
|
||||
\end{center}
|
||||
The figures have been obtained with $b/a=1.2$ and $c/a=2.4$ (left part $b<c$),
|
||||
and with $b/a=2.4$ and $c/a=1.2$ (right part $b>c$).
|
||||
|
||||
Then we consider the cases in which $b$ is the shortest side and show
|
||||
on the left the case in which $a<c$ and on the right the case $a>c$.
|
||||
|
||||
We have the same three possibilities as before. The first possibility
|
||||
is that ${1 \over b^2} < {1\over a^2} + {1\over c^2}$:
|
||||
\begin{center}
|
||||
\includegraphics[width=7.5cm,angle=0]{images/ofc_3.png} \hspace{1cm}
|
||||
\includegraphics[width=7.5cm,angle=0]{images/ofc_4.png} \hspace{1cm}
|
||||
\end{center}
|
||||
The figures have been obtained with $b/a=0.9$ and $c/a=1.2$
|
||||
(left part $a<c$) and $b/a=0.75$ and $c/a=0.95$ (right part $a>c$).
|
||||
|
||||
The second possibility is that ${1 \over b^2}={1\over a^2} + {1\over c^2}$:
|
||||
\begin{center}
|
||||
\includegraphics[width=7.5cm,angle=0]{images/ofc_15.png} \hspace{1cm}
|
||||
\includegraphics[width=7.5cm,angle=0]{images/ofc_16.png}
|
||||
\end{center}
|
||||
The figures have been obtained with $b/a=0.8$ and $c/a=1.33333333333$ (left
|
||||
part $a<c$), and $b/a=0.6$ and $c/a=0.75$ (right part $a>c$).
|
||||
|
||||
The third possibility is than ${1\over b^2}>{1\over a^2} + {1\over c^2}$:
|
||||
\begin{center}
|
||||
\includegraphics[width=7.5cm,angle=0]{images/ofc_9.png} \hspace{1cm}
|
||||
\includegraphics[width=7.5cm,angle=0]{images/ofc_10.png}
|
||||
\end{center}
|
||||
The figures have been obtained with $b/a=0.8$ and $c/a=2.0$ (left part $a<c$),
|
||||
and with $b/a=0.4$ and $c/a=0.5$ (right part $a>c$).
|
||||
|
||||
Finally we consider the case in which $c$ is the shortest side and show on
|
||||
the left the case in which $a<b$ and on the right the case in which $a>b$.
|
||||
|
||||
The first possibility is that ${1\over c^2}<{1\over a^2} + {1\over b^2}$:
|
||||
\begin{center}
|
||||
\includegraphics[width=6.5cm,angle=0]{images/ofc_5.png} \hspace{1cm}
|
||||
\includegraphics[width=7.5cm,angle=0]{images/ofc_6.png}
|
||||
\end{center}
|
||||
The figures have been obtained with $b/a=1.2$ and $c/a=0.85$ (left part $a<b$)
|
||||
and $b/a=0.85$ and $c/a=0.75$ (right part $a>b$).
|
||||
|
||||
The second possibility is that ${1\over c^2}={1\over a^2} + {1\over b^2}$:
|
||||
\begin{center}
|
||||
\includegraphics[width=5.5cm,angle=0]{images/ofc_17.png} \hspace{1cm}
|
||||
\includegraphics[width=7.5cm,angle=0]{images/ofc_18.png}
|
||||
\end{center}
|
||||
The figures have been obtained with $b/a=1.333333333$ and $c/a=0.8$
|
||||
(left part $a<b$) and with $b/a=0.66$ and $c/a=0.5508422$ (right part
|
||||
$a>b$).
|
||||
|
||||
Finally the third possibility is that
|
||||
${1\over c^2} >{1\over a^2} + {1\over b^2}$:
|
||||
\begin{center}
|
||||
\includegraphics[width=5.0cm,angle=0]{images/ofc_11.png} \hspace{1cm}
|
||||
\includegraphics[width=7.5cm,angle=0]{images/ofc_12.png}
|
||||
\end{center}
|
||||
The figures have been obtained with $b/a=2.0$ and $c/a=0.8$ (left part $a<b$),
|
||||
and $b/a=0.5$ and $c/a=0.4$ (right part $a>b$).
|
||||
|
||||
\subsection{\texttt{ibrav=11}, body centered orthorhombic lattice}
|
||||
The direct lattice vectors are:
|
||||
\begin{eqnarray}
|
||||
{\bf a}_1 &=& {a \over 2} (1, {b \over a}, {c \over a}), \nonumber \\
|
||||
{\bf a}_2 &=& {a \over 2} (-1, {b \over a}, {c \over a}), \nonumber \\
|
||||
{\bf a}_3 &=& {a \over 2} (-1, -{b \over a}, {c \over a}). \nonumber
|
||||
\nonumber
|
||||
\end{eqnarray}
|
||||
\begin{eqnarray}
|
||||
{\bf b}_1 &=& {2\pi \over a} (1, 0, {a \over c}), \nonumber \\
|
||||
{\bf b}_2 &=& {2\pi \over a} (-1, {a \over b}, 0), \nonumber \\
|
||||
{\bf b}_3 &=& {2\pi \over a} (0, -{a \over b}, {a \over c}). \nonumber
|
||||
\nonumber
|
||||
\end{eqnarray}
|
||||
In this case the BZ has one shape that can be rotated in
|
||||
different ways depending on the relative sizes of $a$, $b$, and $c$.
|
||||
Similar orientations and BZ that differ only for the relative sizes of
|
||||
the faces are obtained for the cases that have in common the longest side.
|
||||
Therefore we distinguish the cases in which $a$ is the longest side
|
||||
and $b<c$ or $b>c$, the cases in which $b$ is the longest side and
|
||||
$a<c$ or $a>c$ and the cases in which $c$ is the longest side and $a<b$
|
||||
or $a>b$. We have $6$ distinct cases.
|
||||
|
||||
First we take $a$ as the longest side and show
|
||||
on the left the case $b<c$ and on the right the case $b>c$:
|
||||
\begin{center}
|
||||
\includegraphics[width=7.5cm,angle=0]{images/bco_4.png} \hspace{1.0cm}
|
||||
\includegraphics[width=7.5cm,angle=0]{images/bco_5.png}
|
||||
\end{center}
|
||||
The figures have been obtained with $b/a=0.7$ and $c/a=0.85$ (left part
|
||||
$b<c$) and $b/a=0.85$ and $c/a=0.7$ (right part $b>c$).
|
||||
|
||||
Then we take $b$ as the longest side and show on the left the case
|
||||
in which $a<c$ and on the right the case in which $a>c$:
|
||||
\begin{center}
|
||||
\includegraphics[width=7.5cm,angle=0]{images/bco_2.png}\hspace{1cm}
|
||||
\includegraphics[width=7.cm,angle=0]{images/bco_3.png}
|
||||
\end{center}
|
||||
The figures have been obtained with $b/a=1.4$ and $c/a=1.2$ (left part $a<c$)
|
||||
and $b/a=1.2$ and $c/a=0.8$ (right part $a>c$).
|
||||
|
||||
Finally we take $c$ as the longest side and show on the left the case in
|
||||
which $a<b$ and on the right the case in which $b<a$:
|
||||
\begin{center}
|
||||
\includegraphics[width=7.5cm,angle=0]{images/bco_1.png} \hspace{1.0 cm}
|
||||
\includegraphics[width=7.5cm,angle=0]{images/bco_6.png}
|
||||
\end{center}
|
||||
The figures have been obtained with $b/a=1.2$ and $c/a=1.4$ (left part), and
|
||||
$b/a=0.8$ and $c/a=1.2$ (right part).
|
||||
|
||||
\subsection{\texttt{ibrav=12,13,14}, monoclinic, base centered monoclinic,
|
||||
triclinic}
|
||||
These lattices are not supported by this feature, you have to give
|
||||
explicitly the coordinates of the path.
|
||||
|
||||
\section{Bibliography}
|
||||
|
||||
\noindent [1] G.F. Koster, Space groups and their representations, Academic press,
|
||||
New York and London, (1957).
|
||||
|
||||
\noindent [2] C.J. Bradley and A.P. Cracknell, The mathematical theory of symmetry
|
||||
in solids, Oxford University Press, (1972).
|
||||
|
||||
\noindent [3] W. Setyawan and S. Curtarolo, Comp. Mat. Sci. {\bf 49}, 299 (2010).
|
||||
|
||||
\noindent [4] E.S. Tasci, G. de la Flor, D. Orobengoa, C. Capillas,
|
||||
J.M. Perez-Mato, M.I. Aroyo, ``An introduction to the tools hosted in the
|
||||
Bilbao Crystallographic Server''. EPJ Web of Conferences 22 00009 (2012).
|
||||
|
||||
\end{document}
|
||||
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|
|
@ -12,6 +12,7 @@ basic_algebra_routines.o \
|
|||
becmod.o \
|
||||
bfgs_module.o \
|
||||
bspline.o \
|
||||
bz_form.o \
|
||||
cell_base.o \
|
||||
check_stop.o \
|
||||
clocks.o \
|
||||
|
|
|
|||
File diff suppressed because it is too large
Load Diff
|
|
@ -251,6 +251,8 @@ MODULE input_parameters
|
|||
|
||||
CHARACTER(len=256) :: vdw_table_name = ' '
|
||||
|
||||
CHARACTER(len=10) :: point_label_type='SC'
|
||||
|
||||
CHARACTER(len=80) :: memory = 'default'
|
||||
! controls memory usage
|
||||
CHARACTER(len=80) :: memory_allowed(3)
|
||||
|
|
@ -271,7 +273,7 @@ MODULE input_parameters
|
|||
forc_conv_thr, pseudo_dir, disk_io, tefield, dipfield, lberry, &
|
||||
gdir, nppstr, wf_collect, printwfc, lelfield, nberrycyc, refg, &
|
||||
tefield2, saverho, tabps, lkpoint_dir, use_wannier, lecrpa, &
|
||||
vdw_table_name, lorbm, memory
|
||||
vdw_table_name, lorbm, memory, point_label_type
|
||||
|
||||
|
||||
#if defined ( __MS2)
|
||||
|
|
|
|||
|
|
@ -632,13 +632,22 @@ CONTAINS
|
|||
!
|
||||
SUBROUTINE card_kpoints( input_line )
|
||||
!
|
||||
USE bz_form, ONLY : bz, set_label_type, allocate_bz, deallocate_bz, &
|
||||
init_bz, find_bz_type, find_letter_coordinate
|
||||
USE input_parameters, ONLY : ibrav, celldm, point_label_type
|
||||
IMPLICIT NONE
|
||||
!
|
||||
CHARACTER(len=256) :: input_line
|
||||
INTEGER :: i, j, ijk
|
||||
CHARACTER(len=256) :: input_line, buffer
|
||||
INTEGER :: i, j
|
||||
INTEGER :: nkaux
|
||||
INTEGER, ALLOCATABLE :: wkaux(:)
|
||||
REAL(DP), ALLOCATABLE :: xkaux(:,:)
|
||||
INTEGER :: npk_label, nch
|
||||
CHARACTER(LEN=3), ALLOCATABLE :: letter(:)
|
||||
INTEGER, ALLOCATABLE :: label_list(:)
|
||||
INTEGER :: bzt
|
||||
TYPE(bz) :: bz_struc
|
||||
REAL(DP) :: at(3,3), bg(3,3), omega, xk_buffer(3)
|
||||
REAL(DP) :: delta, wk0
|
||||
REAL(DP) :: dkx(3), dky(3)
|
||||
LOGICAL, EXTERNAL :: matches
|
||||
|
|
@ -704,14 +713,96 @@ CONTAINS
|
|||
!
|
||||
nkaux=nkstot
|
||||
ALLOCATE(xkaux(3,nkstot), wkaux(nkstot))
|
||||
ALLOCATE ( letter(nkstot) )
|
||||
ALLOCATE ( label_list(nkstot) )
|
||||
npk_label=0
|
||||
DO i = 1, nkstot
|
||||
CALL read_line( input_line, end_of_file = tend, error = terr )
|
||||
IF (tend) GOTO 10
|
||||
IF (terr) GOTO 20
|
||||
READ(input_line,*, END=10, ERR=20) xkaux(1,i), xkaux(2,i), &
|
||||
xkaux(3,i), wk0
|
||||
wkaux(i) = NINT ( wk0 ) ! beware: wkaux is integer
|
||||
DO j=1,256 ! loop over all characters of input_line
|
||||
IF ((ICHAR(input_line(j:j)) < 58 .AND. & ! a digit
|
||||
ICHAR(input_line(j:j)) > 47) &
|
||||
.OR. ICHAR(input_line(j:j)) == 43 .OR. & ! the + sign
|
||||
ICHAR(input_line(j:j))== 45 .OR. & ! the - sign
|
||||
ICHAR(input_line(j:j))== 46 ) THEN ! a dot .
|
||||
!
|
||||
! This is a digit, therefore this line contains the coordinates of the
|
||||
! k point. We read it and exit from the loop on the characters
|
||||
!
|
||||
READ(input_line,*, END=10, ERR=20) xkaux(1,i), &
|
||||
xkaux(2,i), xkaux(3,i), wk0
|
||||
wkaux(i) = NINT ( wk0 ) ! beware: wkaux is integer
|
||||
EXIT
|
||||
ELSEIF ((ICHAR(input_line(j:j)) < 123 .AND. &
|
||||
ICHAR(input_line(j:j)) > 64)) THEN
|
||||
!
|
||||
! This is a letter, not a space character. We read the next three
|
||||
! characters and save them in the letter array, save also which k point
|
||||
! it is
|
||||
!
|
||||
npk_label=npk_label+1
|
||||
READ(input_line(j:),'(a3)') letter(npk_label)
|
||||
label_list(npk_label)=i
|
||||
!
|
||||
! now we remove the letters from input_line and read the number of points
|
||||
! of the line. The next two line should account for the case in which
|
||||
! there is only one space between the letter and the number of points.
|
||||
!
|
||||
nch=3
|
||||
IF ( ICHAR(input_line(j+1:j+1))==32 .OR. &
|
||||
ICHAR(input_line(j+2:j+2))==32 ) nch=2
|
||||
buffer=input_line(j+nch:)
|
||||
READ(buffer,*,err=20) wkaux(i)
|
||||
EXIT
|
||||
ENDIF
|
||||
ENDDO
|
||||
ENDDO
|
||||
IF ( npk_label > 0 ) THEN
|
||||
!
|
||||
! In this case some k points have been specified as letters.
|
||||
! We need to transform these letters in coordinates
|
||||
! Find the brillouin zone type
|
||||
!
|
||||
CALL find_bz_type(ibrav, celldm, bzt)
|
||||
!
|
||||
! generate direct lattice vectors
|
||||
!
|
||||
CALL latgen(ibrav,celldm,at(:,1),at(:,2),at(:,3),omega)
|
||||
!
|
||||
! we use at in units of celldm(1)
|
||||
!
|
||||
at=at/celldm(1)
|
||||
!
|
||||
! generate reciprocal lattice vectors
|
||||
!
|
||||
CALL recips( at(:,1), at(:,2), at(:,3), bg(:,1), bg(:,2), &
|
||||
bg(:,3) )
|
||||
!
|
||||
! load the information on the Brillouin zone
|
||||
!
|
||||
CALL set_label_type(bz_struc, point_label_type)
|
||||
CALL allocate_bz(ibrav, bzt, bz_struc, celldm, at, bg )
|
||||
CALL init_bz(bz_struc)
|
||||
!
|
||||
! find for each label the corresponding coordinates and save them
|
||||
! on the k point list
|
||||
!
|
||||
DO i=1, npk_label
|
||||
CALL find_letter_coordinate(bz_struc, letter(i), xk_buffer)
|
||||
!
|
||||
! The output of this routine is in cartesian coordinates. If the other
|
||||
! k points are in crystal coordinates we transform xk_buffer to the bg
|
||||
! base.
|
||||
!
|
||||
IF (k_points=='crystal') &
|
||||
CALL cryst_to_cart( 1, xk_buffer, at, -1 )
|
||||
xkaux(:,label_list(i))=xk_buffer(:)
|
||||
ENDDO
|
||||
CALL deallocate_bz(bz_struc)
|
||||
ENDIF
|
||||
DEALLOCATE(letter)
|
||||
DEALLOCATE(label_list)
|
||||
! Count k-points first
|
||||
nkstot=SUM(wkaux(1:nkaux-1))+1
|
||||
DO i=1,nkaux-1
|
||||
|
|
|
|||
|
|
@ -672,6 +672,7 @@ MODULE read_namelists_module
|
|||
CALL mp_bcast( lberry, ionode_id, intra_image_comm )
|
||||
CALL mp_bcast( gdir, ionode_id, intra_image_comm )
|
||||
CALL mp_bcast( nppstr, ionode_id, intra_image_comm )
|
||||
CALL mp_bcast( point_label_type, ionode_id, intra_image_comm )
|
||||
CALL mp_bcast( lkpoint_dir, ionode_id, intra_image_comm )
|
||||
CALL mp_bcast( wf_collect, ionode_id, intra_image_comm )
|
||||
CALL mp_bcast( printwfc, ionode_id, intra_image_comm )
|
||||
|
|
|
|||
Loading…
Reference in New Issue