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lammps/src/lattice.cpp
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/* ----------------------------------------------------------------------
LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
http://lammps.sandia.gov, Sandia National Laboratories
Steve Plimpton, sjplimp@sandia.gov
Copyright (2003) Sandia Corporation. Under the terms of Contract
DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
certain rights in this software. This software is distributed under
the GNU General Public License.
See the README file in the top-level LAMMPS directory.
------------------------------------------------------------------------- */
#include "math.h"
#include "string.h"
#include "stdlib.h"
#include "lattice.h"
#include "update.h"
#include "domain.h"
#include "comm.h"
#include "force.h"
#include "memory.h"
#include "error.h"
using namespace LAMMPS_NS;
#define BIG 1.0e30
enum{NONE,SC,BCC,FCC,HCP,DIAMOND,SQ,SQ2,HEX,CUSTOM};
/* ---------------------------------------------------------------------- */
Lattice::Lattice(LAMMPS *lmp, int narg, char **arg) : Pointers(lmp)
{
nbasis = 0;
basis = NULL;
// parse style arg
if (narg < 1) error->all(FLERR,"Illegal lattice command");
if (strcmp(arg[0],"none") == 0) style = NONE;
else if (strcmp(arg[0],"sc") == 0) style = SC;
else if (strcmp(arg[0],"bcc") == 0) style = BCC;
else if (strcmp(arg[0],"fcc") == 0) style = FCC;
else if (strcmp(arg[0],"hcp") == 0) style = HCP;
else if (strcmp(arg[0],"diamond") == 0) style = DIAMOND;
else if (strcmp(arg[0],"sq") == 0) style = SQ;
else if (strcmp(arg[0],"sq2") == 0) style = SQ2;
else if (strcmp(arg[0],"hex") == 0) style = HEX;
else if (strcmp(arg[0],"custom") == 0) style = CUSTOM;
else error->all(FLERR,"Illegal lattice command");
if (style == NONE) {
if (narg != 2) error->all(FLERR,"Illegal lattice command");
xlattice = ylattice = zlattice = force->numeric(FLERR,arg[1]);
if (xlattice <= 0.0) error->all(FLERR,"Illegal lattice command");
return;
}
// check that lattice matches dimension
// style CUSTOM can be either 2d or 3d
int dimension = domain->dimension;
if (dimension == 2) {
if (style == SC || style == BCC || style == FCC || style == HCP ||
style == DIAMOND)
error->all(FLERR,"Lattice style incompatible with simulation dimension");
}
if (dimension == 3) {
if (style == SQ || style == SQ2 || style == HEX)
error->all(FLERR,"Lattice style incompatible with simulation dimension");
}
// scale = conversion factor between lattice and box units
if (narg < 2) error->all(FLERR,"Illegal lattice command");
scale = force->numeric(FLERR,arg[1]);
if (scale <= 0.0) error->all(FLERR,"Illegal lattice command");
// set basis atoms for each style
// x,y,z = fractional coords within unit cell
// style CUSTOM will be defined by optional args
if (style == SC) {
add_basis(0.0,0.0,0.0);
} else if (style == BCC) {
add_basis(0.0,0.0,0.0);
add_basis(0.5,0.5,0.5);
} else if (style == FCC) {
add_basis(0.0,0.0,0.0);
add_basis(0.5,0.5,0.0);
add_basis(0.5,0.0,0.5);
add_basis(0.0,0.5,0.5);
} else if (style == HCP) {
add_basis(0.0,0.0,0.0);
add_basis(0.5,0.5,0.0);
add_basis(0.5,5.0/6.0,0.5);
add_basis(0.0,1.0/3.0,0.5);
} else if (style == SQ) {
add_basis(0.0,0.0,0.0);
} else if (style == SQ2) {
add_basis(0.0,0.0,0.0);
add_basis(0.5,0.5,0.0);
} else if (style == HEX) {
add_basis(0.0,0.0,0.0);
add_basis(0.5,0.5,0.0);
} else if (style == DIAMOND) {
add_basis(0.0,0.0,0.0);
add_basis(0.0,0.5,0.5);
add_basis(0.5,0.0,0.5);
add_basis(0.5,0.5,0.0);
add_basis(0.25,0.25,0.25);
add_basis(0.25,0.75,0.75);
add_basis(0.75,0.25,0.75);
add_basis(0.75,0.75,0.25);
}
// set defaults for optional args
origin[0] = origin[1] = origin[2] = 0.0;
orientx[0] = 1; orientx[1] = 0; orientx[2] = 0;
orienty[0] = 0; orienty[1] = 1; orienty[2] = 0;
orientz[0] = 0; orientz[1] = 0; orientz[2] = 1;
int spaceflag = 0;
a1[0] = 1.0; a1[1] = 0.0; a1[2] = 0.0;
a2[0] = 0.0; a2[1] = 1.0; a2[2] = 0.0;
a3[0] = 0.0; a3[1] = 0.0; a3[2] = 1.0;
if (style == HEX) a2[1] = sqrt(3.0);
if (style == HCP) {
a2[1] = sqrt(3.0);
a3[2] = sqrt(8.0/3.0);
}
// process optional args
int iarg = 2;
while (iarg < narg) {
if (strcmp(arg[iarg],"origin") == 0) {
if (iarg+4 > narg) error->all(FLERR,"Illegal lattice command");
origin[0] = force->numeric(FLERR,arg[iarg+1]);
origin[1] = force->numeric(FLERR,arg[iarg+2]);
origin[2] = force->numeric(FLERR,arg[iarg+3]);
if (origin[0] < 0.0 || origin[0] >= 1.0 ||
origin[1] < 0.0 || origin[1] >= 1.0 ||
origin[2] < 0.0 || origin[2] >= 1.0)
error->all(FLERR,"Illegal lattice command");
iarg += 4;
} else if (strcmp(arg[iarg],"orient") == 0) {
if (iarg+5 > narg) error->all(FLERR,"Illegal lattice command");
int dim;
if (strcmp(arg[iarg+1],"x") == 0) dim = 0;
else if (strcmp(arg[iarg+1],"y") == 0) dim = 1;
else if (strcmp(arg[iarg+1],"z") == 0) dim = 2;
else error->all(FLERR,"Illegal lattice command");
int *orient;
if (dim == 0) orient = orientx;
else if (dim == 1) orient = orienty;
else if (dim == 2) orient = orientz;
orient[0] = force->inumeric(FLERR,arg[iarg+2]);
orient[1] = force->inumeric(FLERR,arg[iarg+3]);
orient[2] = force->inumeric(FLERR,arg[iarg+4]);
iarg += 5;
} else if (strcmp(arg[iarg],"spacing") == 0) {
if (iarg+4 > narg) error->all(FLERR,"Illegal lattice command");
spaceflag = 1;
xlattice = force->numeric(FLERR,arg[iarg+1]);
ylattice = force->numeric(FLERR,arg[iarg+2]);
zlattice = force->numeric(FLERR,arg[iarg+3]);
iarg += 4;
} else if (strcmp(arg[iarg],"a1") == 0) {
if (iarg+4 > narg) error->all(FLERR,"Illegal lattice command");
if (style != CUSTOM)
error->all(FLERR,
"Invalid option in lattice command for non-custom style");
a1[0] = force->numeric(FLERR,arg[iarg+1]);
a1[1] = force->numeric(FLERR,arg[iarg+2]);
a1[2] = force->numeric(FLERR,arg[iarg+3]);
iarg += 4;
} else if (strcmp(arg[iarg],"a2") == 0) {
if (iarg+4 > narg) error->all(FLERR,"Illegal lattice command");
if (style != CUSTOM)
error->all(FLERR,
"Invalid option in lattice command for non-custom style");
a2[0] = force->numeric(FLERR,arg[iarg+1]);
a2[1] = force->numeric(FLERR,arg[iarg+2]);
a2[2] = force->numeric(FLERR,arg[iarg+3]);
iarg += 4;
} else if (strcmp(arg[iarg],"a3") == 0) {
if (iarg+4 > narg) error->all(FLERR,"Illegal lattice command");
if (style != CUSTOM)
error->all(FLERR,
"Invalid option in lattice command for non-custom style");
a3[0] = force->numeric(FLERR,arg[iarg+1]);
a3[1] = force->numeric(FLERR,arg[iarg+2]);
a3[2] = force->numeric(FLERR,arg[iarg+3]);
iarg += 4;
} else if (strcmp(arg[iarg],"basis") == 0) {
if (iarg+4 > narg) error->all(FLERR,"Illegal lattice command");
if (style != CUSTOM)
error->all(FLERR,
"Invalid option in lattice command for non-custom style");
double x = force->numeric(FLERR,arg[iarg+1]);
double y = force->numeric(FLERR,arg[iarg+2]);
double z = force->numeric(FLERR,arg[iarg+3]);
if (x < 0.0 || x >= 1.0 || y < 0.0 || y >= 1.0 || z < 0.0 || z >= 1.0)
error->all(FLERR,"Illegal lattice command");
add_basis(x,y,z);
iarg += 4;
} else error->all(FLERR,"Illegal lattice command");
}
// check settings for errors
if (nbasis == 0) error->all(FLERR,"No basis atoms in lattice");
if (!orthogonal())
error->all(FLERR,"Lattice orient vectors are not orthogonal");
if (!right_handed())
error->all(FLERR,"Lattice orient vectors are not right-handed");
if (collinear())
error->all(FLERR,"Lattice primitive vectors are collinear");
if (dimension == 2) {
if (origin[2] != 0.0)
error->all(FLERR,
"Lattice settings are not compatible with 2d simulation");
if (orientx[2] != 0 || orienty[2] != 0 ||
orientz[0] != 0 || orientz[1] != 0)
error->all(FLERR,
"Lattice settings are not compatible with 2d simulation");
if (a1[2] != 0.0 || a2[2] != 0.0 || a3[0] != 0.0 || a3[1] != 0.0)
error->all(FLERR,
"Lattice settings are not compatible with 2d simulation");
}
if (spaceflag) {
if (xlattice <= 0.0 || ylattice <= 0.0 || zlattice <= 0.0)
error->all(FLERR,"Lattice spacings are invalid");
}
// reset scale for LJ units (input scale is rho*)
// scale = (Nbasis/(Vprimitive * rho*)) ^ (1/dim)
if (strcmp(update->unit_style,"lj") == 0) {
double vec[3];
cross(a2,a3,vec);
double volume = dot(a1,vec);
scale = pow(nbasis/volume/scale,1.0/dimension);
}
// initialize lattice <-> box transformation matrices
setup_transform();
// convert 8 corners of primitive unit cell from lattice coords to box coords
// min to max = bounding box around the pts in box space
// xlattice,ylattice,zlattice = extent of bbox in box space
// set xlattice,ylattice,zlattice to 0.0 initially
// since bbox uses them to shift origin (irrelevant for this computation)
if (spaceflag == 0) {
double xmin,ymin,zmin,xmax,ymax,zmax;
xmin = ymin = zmin = BIG;
xmax = ymax = zmax = -BIG;
xlattice = ylattice = zlattice = 0.0;
bbox(0,0.0,0.0,0.0,xmin,ymin,zmin,xmax,ymax,zmax);
bbox(0,1.0,0.0,0.0,xmin,ymin,zmin,xmax,ymax,zmax);
bbox(0,0.0,1.0,0.0,xmin,ymin,zmin,xmax,ymax,zmax);
bbox(0,1.0,1.0,0.0,xmin,ymin,zmin,xmax,ymax,zmax);
bbox(0,0.0,0.0,1.0,xmin,ymin,zmin,xmax,ymax,zmax);
bbox(0,1.0,0.0,1.0,xmin,ymin,zmin,xmax,ymax,zmax);
bbox(0,0.0,1.0,1.0,xmin,ymin,zmin,xmax,ymax,zmax);
bbox(0,1.0,1.0,1.0,xmin,ymin,zmin,xmax,ymax,zmax);
xlattice = xmax - xmin;
ylattice = ymax - ymin;
zlattice = zmax - zmin;
} else {
xlattice *= scale;
ylattice *= scale;
zlattice *= scale;
}
// print lattice spacings
if (comm->me == 0) {
if (screen)
fprintf(screen,"Lattice spacing in x,y,z = %g %g %g\n",
xlattice,ylattice,zlattice);
if (logfile)
fprintf(logfile,"Lattice spacing in x,y,z = %g %g %g\n",
xlattice,ylattice,zlattice);
}
}
/* ---------------------------------------------------------------------- */
Lattice::~Lattice()
{
memory->destroy(basis);
}
/* ----------------------------------------------------------------------
check if 3 orientation vectors are mutually orthogonal
------------------------------------------------------------------------- */
int Lattice::orthogonal()
{
if (orientx[0]*orienty[0] + orientx[1]*orienty[1] +
orientx[2]*orienty[2]) return 0;
if (orienty[0]*orientz[0] + orienty[1]*orientz[1] +
orienty[2]*orientz[2]) return 0;
if (orientx[0]*orientz[0] + orientx[1]*orientz[1] +
orientx[2]*orientz[2]) return 0;
return 1;
}
/* ----------------------------------------------------------------------
check righthandedness of orientation vectors
x cross y must be in same direction as z
------------------------------------------------------------------------- */
int Lattice::right_handed()
{
int xy0 = orientx[1]*orienty[2] - orientx[2]*orienty[1];
int xy1 = orientx[2]*orienty[0] - orientx[0]*orienty[2];
int xy2 = orientx[0]*orienty[1] - orientx[1]*orienty[0];
if (xy0*orientz[0] + xy1*orientz[1] + xy2*orientz[2] <= 0) return 0;
return 1;
}
/* ----------------------------------------------------------------------
check collinearity of each pair of primitive vectors
------------------------------------------------------------------------- */
int Lattice::collinear()
{
double vec[3];
cross(a1,a2,vec);
if (dot(vec,vec) == 0.0) return 1;
cross(a2,a3,vec);
if (dot(vec,vec) == 0.0) return 1;
cross(a1,a3,vec);
if (dot(vec,vec) == 0.0) return 1;
return 0;
}
/* ----------------------------------------------------------------------
initialize lattice <-> box transformation matrices
------------------------------------------------------------------------- */
void Lattice::setup_transform()
{
double length;
// primitive = 3x3 matrix with primitive vectors as columns
primitive[0][0] = a1[0];
primitive[1][0] = a1[1];
primitive[2][0] = a1[2];
primitive[0][1] = a2[0];
primitive[1][1] = a2[1];
primitive[2][1] = a2[2];
primitive[0][2] = a3[0];
primitive[1][2] = a3[1];
primitive[2][2] = a3[2];
// priminv = inverse of primitive
double determinant = primitive[0][0]*primitive[1][1]*primitive[2][2] +
primitive[0][1]*primitive[1][2]*primitive[2][0] +
primitive[0][2]*primitive[1][0]*primitive[2][1] -
primitive[0][0]*primitive[1][2]*primitive[2][1] -
primitive[0][1]*primitive[1][0]*primitive[2][2] -
primitive[0][2]*primitive[1][1]*primitive[2][0];
if (determinant == 0.0)
error->all(FLERR,"Degenerate lattice primitive vectors");
priminv[0][0] = (primitive[1][1]*primitive[2][2] -
primitive[1][2]*primitive[2][1]) / determinant;
priminv[1][0] = (primitive[1][2]*primitive[2][0] -
primitive[1][0]*primitive[2][2]) / determinant;
priminv[2][0] = (primitive[1][0]*primitive[2][1] -
primitive[1][1]*primitive[2][0]) / determinant;
priminv[0][1] = (primitive[0][2]*primitive[2][1] -
primitive[0][1]*primitive[2][2]) / determinant;
priminv[1][1] = (primitive[0][0]*primitive[2][2] -
primitive[0][2]*primitive[2][0]) / determinant;
priminv[2][1] = (primitive[0][1]*primitive[2][0] -
primitive[0][0]*primitive[2][1]) / determinant;
priminv[0][2] = (primitive[0][1]*primitive[1][2] -
primitive[0][2]*primitive[1][1]) / determinant;
priminv[1][2] = (primitive[0][2]*primitive[1][0] -
primitive[0][0]*primitive[1][2]) / determinant;
priminv[2][2] = (primitive[0][0]*primitive[1][1] -
primitive[0][1]*primitive[1][0]) / determinant;
// rotaterow = 3x3 matrix with normalized orient vectors as rows
int lensq = orientx[0]*orientx[0] + orientx[1]*orientx[1] +
orientx[2]*orientx[2];
length = sqrt((double) lensq);
if (length == 0.0) error->all(FLERR,"Zero-length lattice orient vector");
rotaterow[0][0] = orientx[0] / length;
rotaterow[0][1] = orientx[1] / length;
rotaterow[0][2] = orientx[2] / length;
lensq = orienty[0]*orienty[0] + orienty[1]*orienty[1] +
orienty[2]*orienty[2];
length = sqrt((double) lensq);
if (length == 0.0) error->all(FLERR,"Zero-length lattice orient vector");
rotaterow[1][0] = orienty[0] / length;
rotaterow[1][1] = orienty[1] / length;
rotaterow[1][2] = orienty[2] / length;
lensq = orientz[0]*orientz[0] + orientz[1]*orientz[1] +
orientz[2]*orientz[2];
length = sqrt((double) lensq);
if (length == 0.0) error->all(FLERR,"Zero-length lattice orient vector");
rotaterow[2][0] = orientz[0] / length;
rotaterow[2][1] = orientz[1] / length;
rotaterow[2][2] = orientz[2] / length;
// rotatecol = 3x3 matrix with normalized orient vectors as columns
rotatecol[0][0] = rotaterow[0][0];
rotatecol[1][0] = rotaterow[0][1];
rotatecol[2][0] = rotaterow[0][2];
rotatecol[0][1] = rotaterow[1][0];
rotatecol[1][1] = rotaterow[1][1];
rotatecol[2][1] = rotaterow[1][2];
rotatecol[0][2] = rotaterow[2][0];
rotatecol[1][2] = rotaterow[2][1];
rotatecol[2][2] = rotaterow[2][2];
}
/* ----------------------------------------------------------------------
convert lattice coords to box coords
input x,y,z = point in lattice coords
output x,y,z = point in box coords
transformation: xyz_box = Rotate_row * scale * P * xyz_lattice + offset
xyz_box = 3-vector of output box coords
Rotate_row = 3x3 matrix = normalized orient vectors as rows
scale = scale factor
P = 3x3 matrix = primitive vectors as columns
xyz_lattice = 3-vector of input lattice coords
offset = 3-vector = (xlatt*origin[0], ylatt*origin[1], zlatt*origin[2])
------------------------------------------------------------------------- */
void Lattice::lattice2box(double &x, double &y, double &z)
{
double x1 = primitive[0][0]*x + primitive[0][1]*y + primitive[0][2]*z;
double y1 = primitive[1][0]*x + primitive[1][1]*y + primitive[1][2]*z;
double z1 = primitive[2][0]*x + primitive[2][1]*y + primitive[2][2]*z;
x1 *= scale;
y1 *= scale;
z1 *= scale;
double xnew = rotaterow[0][0]*x1 + rotaterow[0][1]*y1 + rotaterow[0][2]*z1;
double ynew = rotaterow[1][0]*x1 + rotaterow[1][1]*y1 + rotaterow[1][2]*z1;
double znew = rotaterow[2][0]*x1 + rotaterow[2][1]*y1 + rotaterow[2][2]*z1;
x = xnew + xlattice*origin[0];
y = ynew + ylattice*origin[1];
z = znew + zlattice*origin[2];
}
/* ----------------------------------------------------------------------
convert box coords to lattice coords
input x,y,z = point in box coords
output x,y,z = point in lattice coords
transformation: xyz_latt = P_inv * 1/scale * Rotate_col * (xyz_box - offset)
xyz_lattice = 3-vector of output lattice coords
P_inv = 3x3 matrix = inverse of primitive vectors as columns
scale = scale factor
Rotate_col = 3x3 matrix = normalized orient vectors as columns
xyz_box = 3-vector of input box coords
offset = 3-vector = (xlatt*origin[0], ylatt*origin[1], zlatt*origin[2])
------------------------------------------------------------------------- */
void Lattice::box2lattice(double &x, double &y, double &z)
{
x -= xlattice*origin[0];
y -= ylattice*origin[1];
z -= zlattice*origin[2];
double x1 = rotatecol[0][0]*x + rotatecol[0][1]*y + rotatecol[0][2]*z;
double y1 = rotatecol[1][0]*x + rotatecol[1][1]*y + rotatecol[1][2]*z;
double z1 = rotatecol[2][0]*x + rotatecol[2][1]*y + rotatecol[2][2]*z;
x1 /= scale;
y1 /= scale;
z1 /= scale;
x = priminv[0][0]*x1 + priminv[0][1]*y1 + priminv[0][2]*z1;
y = priminv[1][0]*x1 + priminv[1][1]*y1 + priminv[1][2]*z1;
z = priminv[2][0]*x1 + priminv[2][1]*y1 + priminv[2][2]*z1;
}
/* ----------------------------------------------------------------------
add a basis atom to list
x,y,z = fractional coords within unit cell
------------------------------------------------------------------------- */
void Lattice::add_basis(double x, double y, double z)
{
memory->grow(basis,nbasis+1,3,"lattice:basis");
basis[nbasis][0] = x;
basis[nbasis][1] = y;
basis[nbasis][2] = z;
nbasis++;
}
/* ----------------------------------------------------------------------
return x dot y
------------------------------------------------------------------------- */
double Lattice::dot(double *x, double *y)
{
return x[0]*y[0] + x[1]*y[1] + x[2]*y[2];
}
/* ----------------------------------------------------------------------
z = x cross y
------------------------------------------------------------------------- */
void Lattice::cross(double *x, double *y, double *z)
{
z[0] = x[1]*y[2] - x[2]*y[1];
z[1] = x[2]*y[0] - x[0]*y[2];
z[2] = x[0]*y[1] - x[1]*y[0];
}
/* ----------------------------------------------------------------------
convert x,y,z from lattice coords to box coords (flag = 0) or vice versa
use new point to expand bounding box (min to max)
------------------------------------------------------------------------- */
void Lattice::bbox(int flag, double x, double y, double z,
double &xmin, double &ymin, double &zmin,
double &xmax, double &ymax, double &zmax)
{
if (flag == 0) lattice2box(x,y,z);
else box2lattice(x,y,z);
xmin = MIN(x,xmin); ymin = MIN(y,ymin); zmin = MIN(z,zmin);
xmax = MAX(x,xmax); ymax = MAX(y,ymax); zmax = MAX(z,zmax);
}
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