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Added Python wrapper that handles rotations to and from LAMMPS frame

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This commit is contained in:
Aidan Thompson
2022-05-15 17:43:18 -06:00
parent 223aebe3fb
commit ee8a8b6cd0
5 changed files with 284 additions and 35 deletions
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37
examples/ELASTIC_T/BORN_MATRIX/Silicon/README Normal file
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This directory shows how to use the `fix born` command
to calculate the full matrix of elastic constants
for cubic diamond at finite temperature
running the Stillinger-Weber potential.
The input script `in.elastic` can be run
directly from LAMMPS, or via a Python wrapper
script.
to run directly from LAMMPS, use:
mpirun -np 4 lmp.exe -in in.elastic
This simulates an orthorhombic box with the cubic crystal axes
aligned with x, y, and z.
The default settings replicate the 1477~K benchmark of
Kluge, Ray, and Rahman (1986) that is Ref.[15] in:
Y. Zhen, C. Chu, Computer Physics Communications 183(2012) 261-265
The script contains many adjustable parameters that can be used
to generate different crystal structures, supercell sizes,
and sampling rates.
to run via the Python wrapper, use:
mpirun -np 4 python elastic.py
This will first run the orthorhombic supercell as before,
follows by an equivalent simulation using a triclinic structure.
The script shows how the standard triclinic primitive cell for cubic diamond
can be rotated in to the LAMMPS upper triangular frame. The resultant
elastic constant matrix does not exhibit the standard symmetries of cubic crystals.
However, the matrix is then rotated back to the standard orientation
to recover the cubic symmetry form of the elastic matrix,
resulting in elastic constants that are the same for both
simulations, modulo statistical uncertainty.

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examples/ELASTIC_T/BORN_MATRIX/Silicon/elastic.py Executable file
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#!/usr/bin/env python -i
# preceding line should have path for Python on your machine
# elastic.py
# Purpose: demonstrate elastic constant calculation for
# two different crystal supercells, one with non-standard orientation
#
# Syntax: elastic.py
# uses in.elastic as LAMMPS input script
from __future__ import print_function
import sys
from elastic_utils import *
np.set_printoptions(precision = 3, suppress=True)
# setup MPI, if wanted
me = 0
# uncomment this if running in parallel via mpi4py
from mpi4py import MPI
me = MPI.COMM_WORLD.Get_rank()
nprocs = MPI.COMM_WORLD.Get_size()
# cubic diamond lattice constants
alat = 5.457
# define the cubic diamond orthorhombic supercell
# with 8 atoms
basisstring = ""
origin = np.zeros(3)
bond = np.ones(3)*0.25
b = origin
basisstring += "basis %g %g %g " % (b[0],b[1],b[2])
b = bond
basisstring += "basis %g %g %g " % (b[0],b[1],b[2])
for i in range(3):
b = 2*bond
b[i] = 0
basisstring += "basis %g %g %g " % (b[0],b[1],b[2])
b += bond
basisstring += "basis %g %g %g " % (b[0],b[1],b[2])
hmat = np.eye(3)
varlist = {
"a":alat,
"a1x":hmat[0,0],
"a2x":hmat[0,1],
"a2y":hmat[1,1],
"a3x":hmat[0,2],
"a3y":hmat[1,2],
"a3z":hmat[2,2],
"l":alat,
"basis":basisstring,
"nlat":3,
}
cmdargs = gen_varargs(varlist)
cij_ortho = calculate_cij(cmdargs)
# define the cubic diamond triclinic primitive cell
# with 2 atoms
basisstring = ""
origin = np.zeros(3)
bond = np.ones(3)*0.25
b = origin
basisstring += "basis %g %g %g " % (b[0],b[1],b[2])
b = bond
basisstring += "basis %g %g %g " % (b[0],b[1],b[2])
hmat1 = np.array([[1, 1, 0], [0, 1, 1], [1, 0, 1]]).T/np.sqrt(2)
# rotate primitive cell to LAMMPS orientation (uper triangular)
qmat, rmat = np.linalg.qr(hmat1)
ss = np.diagflat(np.sign(np.diag(rmat)))
rot = ss @ qmat.T
hmat2 = rot @ hmat1
varlist = {
"a":alat,
"a1x":hmat2[0,0],
"a2x":hmat2[0,1],
"a2y":hmat2[1,1],
"a3x":hmat2[0,2],
"a3y":hmat2[1,2],
"a3z":hmat2[2,2],
"l":alat/2**0.5,
"basis":basisstring,
"nlat":5,
}
cmdargs = gen_varargs(varlist)
cij_tri = calculate_cij(cmdargs)
if me == 0:
print("\nPython output:")
print("C_ortho = \n",cij_ortho)
print()
print("C_tri = \n",cij_tri)
print()
cij_tri_rot = rotate_cij(cij_tri, rot.T)
print("C_tri(rotated back) = \n",cij_tri_rot)
print()
print("C_ortho-C_tri = \n", cij_ortho-cij_tri_rot)
print()

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examples/ELASTIC_T/BORN_MATRIX/Silicon/elastic_utils.py Normal file
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import numpy as np
from lammps import lammps, LAMMPS_INT, LMP_STYLE_GLOBAL, LMP_VAR_EQUAL, LMP_VAR_ATOM
# method for rotating elastic constants
def rotate_cij(cij, r):
# K_1
# R_11^2 R_12^2 R_13^2
# R_21^2 R_22^2 R_23^2
# R_31^2 R_32^2 R_33^2
k1 = r*r
# K_2
# R_12.R_13 R_13.R_11 R_11.R_12
# R_22.R_23 R_23.R_21 R_21.R_22
# R_32.R_33 R_33.R_31 R_31.R_32
k2 = np.array([
[r[0][1]*r[0][2], r[0][2]*r[0][0], r[0][0]*r[0][1]],
[r[1][1]*r[1][2], r[1][2]*r[1][0], r[1][0]*r[1][1]],
[r[2][1]*r[2][2], r[2][2]*r[2][0], r[2][0]*r[2][1]],
])
# K_3
# R_21.R_31 R_22.R_32 R_23.R_33
# R_31.R_11 R_32.R_12 R_33.R_13
# R_11.R_21 R_12.R_22 R_13.R_23
k3 = np.array([
[r[1][0]*r[2][0], r[1][1]*r[2][1], r[1][2]*r[2][2]],
[r[2][0]*r[0][0], r[2][1]*r[0][1], r[2][2]*r[0][2]],
[r[0][0]*r[1][0], r[0][1]*r[1][1], r[0][2]*r[1][2]],
])
# K_4a
# R_22.R_33 R_23.R_31 R_21.R_32
# R_32.R_13 R_33.R_11 R_31.R_12
# R_12.R_23 R_13.R_21 R_11.R_22
k4a = np.array([
[r[1][1]*r[2][2], r[1][2]*r[2][0], r[1][0]*r[2][1]],
[r[2][1]*r[0][2], r[2][2]*r[0][0], r[2][0]*r[0][1]],
[r[0][1]*r[1][2], r[0][2]*r[1][0], r[0][0]*r[1][1]],
])
# K_4b
# R_23.R_32 R_21.R_33 R_22.R_31
# R_33.R_12 R_31.R_13 R_32.R_11
# R_13.R_22 R_11.R_23 R_12.R_21
k4b = np.array([
[r[1][2]*r[2][1], r[1][0]*r[2][2], r[1][1]*r[2][0]],
[r[2][2]*r[0][1], r[2][0]*r[0][2], r[2][1]*r[0][0]],
[r[0][2]*r[1][1], r[0][0]*r[1][2], r[0][1]*r[1][0]],
])
k = np.block([[k1, 2*k2],[k3, k4a+k4b]])
cijrot = k.dot(cij.dot(k.T))
return cijrot
def calculate_cij(cmdargs):
lmp = lammps(cmdargs=cmdargs)
lmp.file("in.elastic")
C11 = lmp.extract_variable("C11",None, LMP_VAR_EQUAL)
C22 = lmp.extract_variable("C22",None, LMP_VAR_EQUAL)
C33 = lmp.extract_variable("C33",None, LMP_VAR_EQUAL)
C44 = lmp.extract_variable("C44",None, LMP_VAR_EQUAL)
C55 = lmp.extract_variable("C55",None, LMP_VAR_EQUAL)
C66 = lmp.extract_variable("C66",None, LMP_VAR_EQUAL)
C12 = lmp.extract_variable("C12",None, LMP_VAR_EQUAL)
C13 = lmp.extract_variable("C13",None, LMP_VAR_EQUAL)
C14 = lmp.extract_variable("C14",None, LMP_VAR_EQUAL)
C15 = lmp.extract_variable("C15",None, LMP_VAR_EQUAL)
C16 = lmp.extract_variable("C16",None, LMP_VAR_EQUAL)
C23 = lmp.extract_variable("C23",None, LMP_VAR_EQUAL)
C24 = lmp.extract_variable("C24",None, LMP_VAR_EQUAL)
C25 = lmp.extract_variable("C25",None, LMP_VAR_EQUAL)
C26 = lmp.extract_variable("C26",None, LMP_VAR_EQUAL)
C34 = lmp.extract_variable("C34",None, LMP_VAR_EQUAL)
C35 = lmp.extract_variable("C35",None, LMP_VAR_EQUAL)
C36 = lmp.extract_variable("C36",None, LMP_VAR_EQUAL)
C45 = lmp.extract_variable("C45",None, LMP_VAR_EQUAL)
C46 = lmp.extract_variable("C46",None, LMP_VAR_EQUAL)
C56 = lmp.extract_variable("C56",None, LMP_VAR_EQUAL)
cij = np.array([
[C11, C12, C13, C14, C15, C16],
[ 0, C22, C23, C24, C25, C26],
[ 0, 0, C33, C34, C35, C36],
[ 0, 0, 0, C44, C45, C46],
[ 0, 0, 0, 0, C55, C56],
[ 0, 0, 0, 0, 0, C66],
])
cij = np.triu(cij) + np.tril(cij.T, -1)
return cij
def gen_varargs(varlist):
cmdargs = []
for key in varlist:
cmdargs += ["-var",key,str(varlist[key])]
return cmdargs

33
examples/ELASTIC_T/BORN_MATRIX/Silicon/init.in
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@ -1,7 +1,6 @@
# NOTE: This script can be modified for different atomic structures, # NOTE: This script can be modified for different atomic structures,
# units, etc. See in.elastic for more info. # units, etc. See in.elastic for more info.
# #
# Define MD parameters # Define MD parameters
# These can be modified by the user # These can be modified by the user
# These settings replicate the 1477~K benchmark of # These settings replicate the 1477~K benchmark of
@ -37,19 +36,34 @@ variable nrepeatborn equal floor(${nfreq}/${neveryborn}) # number of samples
variable nequil equal 10*${nthermo} # length of equilibration run variable nequil equal 10*${nthermo} # length of equilibration run
variable nrun equal 100*${nthermo} # length of equilibrated run variable nrun equal 100*${nthermo} # length of equilibrated run
# generate the box and atom positions using a diamond lattice # this generates a general triclinic cell
# conforming to LAMMPS cell (upper triangular)
units metal units metal
box tilt large
boundary p p p # unit lattice vectors are
# a1 = (a1x 0 0)
# a2 = (a2x a2y 0)
# a3 = (a3x a3y a3z)
# this generates a standard 8-atom cubic cell variable a1x index 1
variable a2x index 0
variable a2y index 1
variable a3x index 0
variable a3y index 0
variable a3z index 1
variable atmp equal $a
variable l index $a
variable basis index "basis 0 0 0 basis 0.25 0.25 0.25 basis 0 0.5 0.5 basis 0.25 0.75 0.75 basis 0.5 0 0.5 basis 0.75 0.25 0.75 basis 0.5 0.5 0 basis 0.75 0.75 0.25"
lattice custom ${l} &
a1 ${a1x} 0 0 &
a2 ${a2x} ${a2y} 0 &
a3 ${a3x} ${a3y} ${a3z} &
${basis} &
spacing 1 1 1
lattice diamond $a region box prism 0 ${a1x} 0 ${a2y} 0 ${a3z} ${a2x} ${a3x} ${a3y}
region box prism 0 1 0 1 0 1 0 0 0
# this generates a 2-atom triclinic cell
#include tri.in
create_box 1 box create_box 1 box
create_atoms 1 box create_atoms 1 box
@ -57,3 +71,4 @@ mass 1 ${mass1}
replicate ${nlat} ${nlat} ${nlat} replicate ${nlat} ${nlat} ${nlat}
velocity all create ${temp} 87287 velocity all create ${temp} 87287

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examples/ELASTIC_T/BORN_MATRIX/Silicon/tri.in
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# this generates a 2-atom triclinic cell
# due to rotation on to x-axis,
# elastic constant analysis is not working yet
# unit lattice vectors are
# a1 = (1 0 0)
# a2 = (1/2 sqrt3/2 0)
# a3 = (1/2 1/(2sqrt3) sqrt2/sqrt3)
variable a1x equal 1
variable a2x equal 1/2
variable a2y equal sqrt(3)/2
variable a3x equal 1/2
variable a3y equal 1/(2*sqrt(3))
variable a3z equal sqrt(2/3)
variable l equal $a/sqrt(2)
lattice custom ${l} &
a1 ${a1x} 0 0 &
a2 ${a2x} ${a2y} 0.0 &
a3 ${a3x} ${a3y} ${a3z} &
basis 0 0 0 &
basis 0.25 0.25 0.25 &
spacing 1 1 1
region box prism 0 ${a1x} 0 ${a2y} 0 ${a3z} ${a2x} ${a3x} ${a3y}