Added hexatic bond orientational order parameter
git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@14231 f3b2605a-c512-4ea7-a41b-209d697bcdaa
This commit is contained in:
athomps
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doc/Eqs/hexorder.jpg
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doc/Eqs/hexorder.jpg
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doc/Eqs/hexorder.tex
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doc/Eqs/hexorder.tex
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\documentclass[12pt]{article}
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\begin{document}
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$$
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q_6 = \frac{1}{N_{neigh}}\sum_{j = 1}^{N_{neigh}} e^{6 i \theta({\bf r}_{ij})}
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$$
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\end{document}
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117
doc/compute_hexorder_atom.txt
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117
doc/compute_hexorder_atom.txt
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"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c
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:link(lws,http://lammps.sandia.gov)
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:link(ld,Manual.html)
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:link(lc,Section_commands.html#comm)
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:line
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compute hexorder/atom command :h3
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[Syntax:]
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compute ID group-ID hexorder/atom cutoff type1 type2 ... :pre
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ID, group-ID are documented in "compute"_compute.html command
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hexorder/atom = style name of this compute command
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cutoff = distance within which to count neighbors (distance units)
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typeN = atom type for Nth order parameter (see asterisk form below) :ul
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[Examples:]
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compute 1 all hexorder/atom 2.0
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compute 1 all hexorder/atom 6.0 1 2
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compute 1 all hexorder/atom 6.0 2*4 5*8 * :pre
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[Description:]
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Define a computation that calculates one or more hexatic bond orientational
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order parameters for each atom in a group. The hexatic bond orientational order
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parameter {q}6 "(Nelson)"_#Nelson for an atom is a complex number (stored as two real numbers).
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It is defined as follows:
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:c,image(Eqs/hexorder.jpg)
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where the sum is over atoms of the specified atom type(s) that are within
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the specified cutoff distance from the central atom. The angle theta
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is formed by the bond vector rij and the {x} axis. theta is calculated
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only using the {x} and {y} components, whereas the distance from the
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central atom is calculated using all three
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{x}, {y}, and {z} components of the bond vector.
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Atoms not in the group
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are included in the order parameter of atoms in the group.
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If the neighbors of the central atom lie on a hexagonal lattice,
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then |{q}6| = 1.
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The complex phase of {q}6 depends on the orientation of the
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lattice relative to the {x} axis. For a liquid in which the
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atomic neighborhood lacks orientational symmettry, |{q}6| << 1.
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The {typeN} keywords allow you to specify which atom types contribute
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to each order parameter. One order parameter is computed for
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each of the {typeN} keywords listed. If no {typeN} keywords are
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listed, a single order parameter is calculated, which includes
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atoms of all types (same as the "*" format, see below).
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The {typeN} keywords can be specified in one of two ways. An explicit
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numeric value can be used, as in the 2nd example above. Or a
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wild-card asterisk can be used to specify a range of atom types. This
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takes the form "*" or "*n" or "n*" or "m*n". If N = the number of
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atom types, then an asterisk with no numeric values means all types
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from 1 to N. A leading asterisk means all types from 1 to n
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(inclusive). A trailing asterisk means all types from n to N
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(inclusive). A middle asterisk means all types from m to n
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(inclusive).
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The value of all order parameters will be 0.0+0.0i for atoms not in the
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specified compute group. An order parameter for atoms that have no
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neighbors of the specified atom type within the cutoff distance will
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be 0.0+0.0i.
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The neighbor list needed to compute this quantity is constructed each
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time the calculation is performed (i.e. each time a snapshot of atoms
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is dumped). Thus it can be inefficient to compute/dump this quantity
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too frequently.
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IMPORTANT NOTE: If you have a bonded system, then the settings of
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"special_bonds"_special_bonds.html command can remove pairwise
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interactions between atoms in the same bond, angle, or dihedral. This
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is the default setting for the "special_bonds"_special_bonds.html
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command, and means those pairwise interactions do not appear in the
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neighbor list. Because this fix uses the neighbor list, it also means
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those pairs will not be included in the order parameter. One way
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to get around this, is to write a dump file, and use the
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"rerun"_rerun.html command to compute the order parameter for snapshots
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in the dump file. The rerun script can use a
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"special_bonds"_special_bonds.html command that includes all pairs in
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the neighbor list.
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[Output info:]
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If single {type1} keyword is specified (or if none are specified),
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this compute calculates a per-atom array with 2 columns, giving the
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real and imaginary parts of the order parameter, respectively.
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If multiple {typeN} keywords are specified, this compute calculates
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a per-atom array with 2*N columns, with each consecutive pair of
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columns giving the real and imaginary parts of one order parameter.
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These values can be accessed by any command that uses
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per-atom values from a compute as input. See "Section_howto
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15"_Section_howto.html#howto_15 for an overview of LAMMPS output
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options.
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The per-atom array values will be floating point numbers, as
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explained above.
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[Restrictions:] none
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[Related commands:]
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"compute coord/atom"_compute_coord_atom.html
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[Default:] none
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:line
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:link(Nelson)
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[(Nelson)] Nelson, Halperin, Phys Rev B, 19, 2457 (1979).
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263
src/compute_hexorder_atom.cpp
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263
src/compute_hexorder_atom.cpp
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/* ----------------------------------------------------------------------
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LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
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http://lammps.sandia.gov, Sandia National Laboratories
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Steve Plimpton, sjplimp@sandia.gov
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Copyright (2003) Sandia Corporation. Under the terms of Contract
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DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
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certain rights in this software. This software is distributed under
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the GNU General Public License.
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See the README file in the top-level LAMMPS directory.
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------------------------------------------------------------------------- */
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/* ----------------------------------------------------------------------
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Contributing author: Aidan Thompson (SNL)
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------------------------------------------------------------------------- */
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#include <math.h>
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#include <string.h>
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#include <stdlib.h>
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#include "compute_hexorder_atom.h"
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#include "atom.h"
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#include "update.h"
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#include "modify.h"
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#include "neighbor.h"
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#include "neigh_list.h"
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#include "neigh_request.h"
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#include "force.h"
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#include "pair.h"
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#include "comm.h"
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#include "memory.h"
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#include "error.h"
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using namespace LAMMPS_NS;
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/* ---------------------------------------------------------------------- */
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ComputeHexOrderAtom::ComputeHexOrderAtom(LAMMPS *lmp, int narg, char **arg) :
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Compute(lmp, narg, arg)
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{
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if (narg < 4) error->all(FLERR,"Illegal compute hexorder/atom command");
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double cutoff = force->numeric(FLERR,arg[3]);
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cutsq = cutoff*cutoff;
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ncol = narg-4 + 1;
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int ntypes = atom->ntypes;
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typelo = new int[ncol];
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typehi = new int[ncol];
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if (narg == 4) {
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ncol = 2;
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typelo[0] = 1;
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typehi[0] = ntypes;
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} else {
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ncol = 0;
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int iarg = 4;
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while (iarg < narg) {
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force->bounds(arg[iarg],ntypes,typelo[ncol],typehi[ncol]);
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if (typelo[ncol] > typehi[ncol])
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error->all(FLERR,"Illegal compute hexorder/atom command");
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typelo[ncol+1] = typelo[ncol];
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typehi[ncol+1] = typehi[ncol];
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ncol+=2;
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iarg++;
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}
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}
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peratom_flag = 1;
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size_peratom_cols = ncol;
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nmax = 0;
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q6array = NULL;
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}
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/* ---------------------------------------------------------------------- */
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ComputeHexOrderAtom::~ComputeHexOrderAtom()
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{
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delete [] typelo;
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delete [] typehi;
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memory->destroy(q6array);
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}
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/* ---------------------------------------------------------------------- */
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void ComputeHexOrderAtom::init()
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{
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if (force->pair == NULL)
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error->all(FLERR,"Compute hexorder/atom requires a pair style be defined");
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if (sqrt(cutsq) > force->pair->cutforce)
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error->all(FLERR,
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"Compute hexorder/atom cutoff is longer than pairwise cutoff");
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// need an occasional full neighbor list
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int irequest = neighbor->request(this,instance_me);
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neighbor->requests[irequest]->pair = 0;
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neighbor->requests[irequest]->compute = 1;
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neighbor->requests[irequest]->half = 0;
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neighbor->requests[irequest]->full = 1;
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neighbor->requests[irequest]->occasional = 1;
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int count = 0;
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for (int i = 0; i < modify->ncompute; i++)
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if (strcmp(modify->compute[i]->style,"hexorder/atom") == 0) count++;
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if (count > 1 && comm->me == 0)
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error->warning(FLERR,"More than one compute hexorder/atom");
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}
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/* ---------------------------------------------------------------------- */
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void ComputeHexOrderAtom::init_list(int id, NeighList *ptr)
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{
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list = ptr;
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}
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/* ---------------------------------------------------------------------- */
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void ComputeHexOrderAtom::compute_peratom()
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{
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int i,j,m,ii,jj,inum,jnum,jtype;
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double xtmp,ytmp,ztmp,delx,dely,delz,rsq;
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int *ilist,*jlist,*numneigh,**firstneigh;
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double *count;
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invoked_peratom = update->ntimestep;
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// grow coordination array if necessary
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if (atom->nlocal > nmax) {
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memory->destroy(q6array);
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nmax = atom->nmax;
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memory->create(q6array,nmax,ncol,"hexorder/atom:q6array");
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array_atom = q6array;
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}
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// invoke full neighbor list (will copy or build if necessary)
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neighbor->build_one(list);
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inum = list->inum;
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ilist = list->ilist;
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numneigh = list->numneigh;
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firstneigh = list->firstneigh;
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// compute order parameter(s) for each atom in group
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// use full neighbor list to count atoms less than cutoff
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double **x = atom->x;
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int *type = atom->type;
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int *mask = atom->mask;
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if (ncol == 2) {
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for (ii = 0; ii < inum; ii++) {
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i = ilist[ii];
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double* q6 = q6array[i];
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q6[0] = q6[1] = 0.0;
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if (mask[i] & groupbit) {
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xtmp = x[i][0];
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ytmp = x[i][1];
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ztmp = x[i][2];
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jlist = firstneigh[i];
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jnum = numneigh[i];
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double usum = 0.0;
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double vsum = 0.0;
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int ncount = 0;
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for (jj = 0; jj < jnum; jj++) {
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j = jlist[jj];
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j &= NEIGHMASK;
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jtype = type[j];
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delx = xtmp - x[j][0];
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dely = ytmp - x[j][1];
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delz = ztmp - x[j][2];
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rsq = delx*delx + dely*dely + delz*delz;
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if (rsq < cutsq && jtype >= typelo[0] && jtype <= typehi[0]) {
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double u, v;
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calc_q6(delx, dely, u, v);
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usum += u;
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vsum += v;
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ncount++;
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}
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}
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if (ncount > 0) {
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double ninv = 1.0/ncount ;
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q6[0] = usum*ninv;
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q6[1] = vsum*ninv;
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}
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}
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}
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} else {
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for (ii = 0; ii < inum; ii++) {
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i = ilist[ii];
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double* q6 = q6array[i];
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for (m = 0; m < ncol; m++) q6[m] = 0.0;
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if (mask[i] & groupbit) {
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xtmp = x[i][0];
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ytmp = x[i][1];
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ztmp = x[i][2];
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jlist = firstneigh[i];
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jnum = numneigh[i];
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for (m = 0; m < ncol; m+=2) {
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double usum = 0.0;
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double vsum = 0.0;
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int ncount = 0;
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for (jj = 0; jj < jnum; jj++) {
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j = jlist[jj];
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j &= NEIGHMASK;
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jtype = type[j];
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delx = xtmp - x[j][0];
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dely = ytmp - x[j][1];
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delz = ztmp - x[j][2];
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rsq = delx*delx + dely*dely + delz*delz;
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if (rsq < cutsq) {
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if (jtype >= typelo[m] && jtype <= typehi[m]) {
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double u, v;
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calc_q6(delx, dely, u, v);
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usum += u;
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vsum += v;
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ncount++;
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}
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}
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if (ncount > 0) {
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double ninv = 1.0/ncount ;
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q6[m] = usum*ninv;
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q6[m+1] = vsum*ninv;
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}
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}
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}
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}
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}
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}
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}
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inline void ComputeHexOrderAtom::calc_q6(double delx, double dely, double &u, double &v) {
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double rinv = 1.0/sqrt(delx*delx+dely*dely);
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double x = delx*rinv;
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double y = dely*rinv;
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double a = x*x;
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double b1 = y*y;
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double b2 = b1*b1;
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double b3 = b2*b1;
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u = (( a - 15*b1)*a + 15*b2)*a - b3;
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v = ((6*a - 20*b1)*a + 6*b2)*x*y;
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}
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/* ----------------------------------------------------------------------
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memory usage of local atom-based array
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------------------------------------------------------------------------- */
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double ComputeHexOrderAtom::memory_usage()
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{
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double bytes = ncol*nmax * sizeof(double);
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return bytes;
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}
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73
src/compute_hexorder_atom.h
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73
src/compute_hexorder_atom.h
Normal file
@ -0,0 +1,73 @@
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/* -*- c++ -*- ----------------------------------------------------------
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LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
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http://lammps.sandia.gov, Sandia National Laboratories
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Steve Plimpton, sjplimp@sandia.gov
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|
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Copyright (2003) Sandia Corporation. Under the terms of Contract
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DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
|
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certain rights in this software. This software is distributed under
|
||||
the GNU General Public License.
|
||||
|
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See the README file in the top-level LAMMPS directory.
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------------------------------------------------------------------------- */
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#ifdef COMPUTE_CLASS
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ComputeStyle(hexorder/atom,ComputeHexOrderAtom)
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#else
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#ifndef LMP_COMPUTE_HEXORDER_ATOM_H
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#define LMP_COMPUTE_HEXORDER_ATOM_H
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#include "compute.h"
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namespace LAMMPS_NS {
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class ComputeHexOrderAtom : public Compute {
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public:
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ComputeHexOrderAtom(class LAMMPS *, int, char **);
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~ComputeHexOrderAtom();
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void init();
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void init_list(int, class NeighList *);
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void compute_peratom();
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double memory_usage();
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private:
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int nmax,ncol;
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double cutsq;
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class NeighList *list;
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int *typelo,*typehi;
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double **q6array;
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void calc_q6(double, double, double&, double&);
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};
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}
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#endif
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#endif
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/* ERROR/WARNING messages:
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E: Illegal ... command
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Self-explanatory. Check the input script syntax and compare to the
|
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documentation for the command. You can use -echo screen as a
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command-line option when running LAMMPS to see the offending line.
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E: Compute hexorder/atom requires a pair style be defined
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Self-explantory.
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E: Compute hexorder/atom cutoff is longer than pairwise cutoff
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Cannot compute order parameter at distances longer than the pair cutoff,
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since those atoms are not in the neighbor list.
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W: More than one compute hexorder/atom
|
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It is not efficient to use compute hexorder/atom more than once.
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*/
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Reference in New Issue
Block a user