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from argparse import ArgumentParser
from lammps import PyLammps
def potential(lmp, args):
""" set up potential and minimization """
ff_string = ' '
ff_string = ff_string.join(args.elements) # merge all element string to one string
lmp.kim("interactions", ff_string)
# Setup neighbor style
lmp.neighbor(1.0, "nsq")
lmp.neigh_modify("once no every 1 delay 0 check yes")
# Setup minimization style
lmp.min_style(args.min_style)
lmp.min_modify("dmax ${dmax} line quadratic")
# Setup output
lmp.thermo(1)
lmp.thermo_style("custom step temp pe press pxx pyy pzz pxy pxz pyz lx ly lz")
lmp.thermo_modify("norm no")
return
def displace(lmp, args, idir):
"""computes the response to a small strain """
if idir == 1:
lmp.variable("len0 equal {}".format(lmp.variables["lx0"].value))
elif idir == 2 or idir == 6:
lmp.variable("len0 equal {}".format(lmp.variables["ly0"].value))
else:
lmp.variable("len0 equal {}".format(lmp.variables["lz0"].value))
# Reset box and simulation parameters
lmp.clear()
lmp.box("tilt large")
lmp.kim("init", args.kim_model, "metal", "unit_conversion_mode")
lmp.read_restart("restart.equil")
lmp.change_box("all triclinic")
potential(lmp, args)
# Negative deformation
lmp.variable("delta equal -${up}*${len0}")
lmp.variable("deltaxy equal -${up}*xy")
lmp.variable("deltaxz equal -${up}*xz")
lmp.variable("deltayz equal -${up}*yz")
if idir == 1:
lmp.change_box("all x delta 0 ${delta} xy delta ${deltaxy} xz delta ${deltaxz} remap units box")
elif idir == 2:
lmp.change_box("all y delta 0 ${delta} yz delta ${deltayz} remap units box")
elif idir == 3:
lmp.change_box("all z delta 0 ${delta} remap units box")
elif idir == 4:
lmp.change_box("all yz delta ${delta} remap units box")
elif idir == 5:
lmp.change_box("all xz delta ${delta} remap units box")
else:
lmp.change_box("all xy delta ${delta} remap units box")
# Relax atoms positions
lmp.min_style(args.min_style)
lmp.minimize(args.minimize[0], args.minimize[1], int(args.minimize[2]), int(args.minimize[3]))
# Obtain new stress tensor
lmp.variable("pxx1 equal {}".format(lmp.eval("pxx")))
lmp.variable("pyy1 equal {}".format(lmp.eval("pyy")))
lmp.variable("pzz1 equal {}".format(lmp.eval("pzz")))
lmp.variable("pxy1 equal {}".format(lmp.eval("pxy")))
lmp.variable("pxz1 equal {}".format(lmp.eval("pxz")))
lmp.variable("pyz1 equal {}".format(lmp.eval("pyz")))
# Compute elastic constant from pressure tensor
c1neg = lmp.variables["d1"].value
c2neg = lmp.variables["d2"].value
c3neg = lmp.variables["d3"].value
c4neg = lmp.variables["d4"].value
c5neg = lmp.variables["d5"].value
c6neg = lmp.variables["d6"].value
# Reset box and simulation parameters
lmp.clear()
lmp.box("tilt large")
lmp.kim("init", args.kim_model, "metal", "unit_conversion_mode")
lmp.read_restart("restart.equil")
lmp.change_box("all triclinic")
potential(lmp, args)
# Positive deformation
lmp.variable("delta equal ${up}*${len0}")
lmp.variable("deltaxy equal ${up}*xy")
lmp.variable("deltaxz equal ${up}*xz")
lmp.variable("deltayz equal ${up}*yz")
if idir == 1:
lmp.change_box("all x delta 0 ${delta} xy delta ${deltaxy} xz delta ${deltaxz} remap units box")
elif idir == 2:
lmp.change_box("all y delta 0 ${delta} yz delta ${deltayz} remap units box")
elif idir == 3:
lmp.change_box("all z delta 0 ${delta} remap units box")
elif idir == 4:
lmp.change_box("all yz delta ${delta} remap units box")
elif idir == 5:
lmp.change_box("all xz delta ${delta} remap units box")
else:
lmp.change_box("all xy delta ${delta} remap units box")
# Relax atoms positions
lmp.min_style(args.min_style)
lmp.minimize(args.minimize[0], args.minimize[1], int(args.minimize[2]), int(args.minimize[3]))
# Obtain new stress tensor
lmp.variable("pxx1 equal {}".format(lmp.eval("pxx")))
lmp.variable("pyy1 equal {}".format(lmp.eval("pyy")))
lmp.variable("pzz1 equal {}".format(lmp.eval("pzz")))
lmp.variable("pxy1 equal {}".format(lmp.eval("pxy")))
lmp.variable("pxz1 equal {}".format(lmp.eval("pxz")))
lmp.variable("pyz1 equal {}".format(lmp.eval("pyz")))
# Compute elasic constant from pressure tensor
c1pos = lmp.variables["d1"].value
c2pos = lmp.variables["d2"].value
c3pos = lmp.variables["d3"].value
c4pos = lmp.variables["d4"].value
c5pos = lmp.variables["d5"].value
c6pos = lmp.variables["d6"].value
# Combine positive and negative
lmp.variable("C1{} equal {}".format(idir, 0.5*(c1neg+c1pos)))
lmp.variable("C2{} equal {}".format(idir, 0.5*(c2neg+c2pos)))
lmp.variable("C3{} equal {}".format(idir, 0.5*(c3neg+c3pos)))
lmp.variable("C4{} equal {}".format(idir, 0.5*(c4neg+c4pos)))
lmp.variable("C5{} equal {}".format(idir, 0.5*(c5neg+c5pos)))
lmp.variable("C6{} equal {}".format(idir, 0.5*(c6neg+c6pos)))
return
def elastic():
""" Compute elastic constant tensor for a crystal
In order to calculate the elastic constants correctly, care must be taken to specify
the correct units (units). It is also important to verify that the minimization of energy
w.r.t atom positions in the deformed cell is fully converged.
One indication of this is that the elastic constants are insensitive
to the choice of the variable ${up}. Another is to check
the final max and two-norm forces reported in the log file. If you know
that minimization is not required, you can set maxiter = 0.0 """
parser = ArgumentParser(description='A python script to compute elastic properties of bulk materials')
parser.add_argument("input_data_file", help="The full path & name of the lammps data file.")
parser.add_argument("kim_model", help="the KIM ID of the interatomic model archived in OpenKIM")
parser.add_argument("elements", nargs='+', default=['Au'], help="a list of N chemical species, which defines a mapping between atom types in LAMMPS to the available species in the OpenKIM model")
parser.add_argument("--min_style", default="cg", help="which algorithm will be used for minimization from lammps")
parser.add_argument("--minimize", type=float, nargs=4, default=[1.0e-4, 1.0e-6, 100, 1000], help="minimization parameters")
parser.add_argument("--up", type=float, default=1.0e-6, help="the deformation magnitude (in strain units)")
args = parser.parse_args()
L = PyLammps()
L.units("metal")
# Define the finite deformation size.
#Try several values to verify that results do not depend on it.
L.variable("up equal {}".format(args.up))
# Define the amount of random jiggle for atoms. It prevents atoms from staying on saddle points
atomjiggle = 1.0e-5
# metal units, elastic constants in GPa
cfac = 1.0e-4
# Define minimization parameters
L.variable("dmax equal 1.0e-2")
L.boundary("p", "p", "p") # periodic boundary conditions in all three directions
L.box("tilt large") # to avoid termination if the final simulation box has a high tilt factor
# use the OpenKIM model to set the energy interactions
L.kim("init", args.kim_model, "metal", "unit_conversion_mode")
L.read_data(args.input_data_file)
potential(L, args)
# Need to set mass to something, just to satisfy LAMMPS
mass_dictionary = {'H': 1.00797, 'He': 4.00260, 'Li': 6.941, 'Be': 9.01218, 'B': 10.81, 'C': 12.011, 'N': 14.0067, 'O': 15.9994, 'F': 18.998403, 'Ne': 20.179, 'Na': 22.98977, 'Mg': 24.305, 'Al': 26.98154, 'Si': 28.0855, 'P': 30.97376, 'S': 32.06, 'Cl': 35.453, 'K': 39.0983, 'Ar': 39.948, 'Ca': 40.08, 'Sc': 44.9559, 'Ti': 47.90, 'V': 50.9415, 'Cr': 51.996, 'Mn': 54.9380, 'Fe': 55.847, 'Ni': 58.70, 'Co': 58.9332, 'Cu': 63.546, 'Zn': 65.38, 'Ga': 69.72, 'Ge': 72.59, 'As': 74.9216, 'Se': 78.96, 'Br': 79.904, 'Kr': 83.80, 'Rb': 85.4678, 'Sr': 87.62, 'Y': 88.9059, 'Zr': 91.22, 'Nb': 92.9064, 'Mo': 95.94, 'Tc': 98, 'Ru': 101.07, 'Rh': 102.9055, 'Pd': 106.4, 'Ag': 107.868, 'Cd': 112.41, 'In': 114.82, 'Sn': 118.69, 'Sb': 121.75, 'I': 126.9045, 'Te': 127.60, 'Xe': 131.30, 'Cs': 132.9054, 'Ba': 137.33, 'La': 138.9055, 'Ce': 140.12, 'Pr': 140.9077, 'Nd': 144.24, 'Pm': 145, 'Sm': 150.4, 'Eu': 151.96, 'Gd': 157.25, 'Tb': 158.9254, 'Dy': 162.50, 'Ho': 164.9304, 'Er': 167.26, 'Tm': 168.9342, 'Yb': 173.04, 'Lu': 174.967, 'Hf': 178.49, 'Ta': 180.9479, 'W': 183.85, 'Re': 186.207, 'Os': 190.2, 'Ir': 192.22, 'Pt': 195.09, 'Au': 196.9665, 'Hg': 200.59, 'Tl': 204.37, 'Pb': 207.2, 'Bi': 208.9804, 'Po': 209, 'At': 210, 'Rn': 222, 'Fr': 223, 'Ra': 226.0254, 'Ac': 227.0278, 'Pa': 231.0359, 'Th': 232.0381, 'Np': 237.0482, 'U': 238.029}
for itype in range(1, len(args.elements)+1):
L.mass(itype, mass_dictionary.get(args.elements[itype-1], 1.0e-20))
# Compute initial state at zero pressure
L.fix(3, "all", "box/relax", "aniso", 0.0)
L.min_style(args.min_style)
L.minimize(args.minimize[0], args.minimize[1], int(args.minimize[2]), int(args.minimize[3]))
L.variable("lx0 equal {}".format(L.eval("lx")))
L.variable("ly0 equal {}".format(L.eval("ly")))
L.variable("lz0 equal {}".format(L.eval("lz")))
# These formulas define the derivatives w.r.t. strain components
L.variable("d1 equal -(v_pxx1-{})/(v_delta/v_len0)*{}".format(L.eval("pxx"), cfac))
L.variable("d2 equal -(v_pyy1-{})/(v_delta/v_len0)*{}".format(L.eval("pyy"), cfac))
L.variable("d3 equal -(v_pzz1-{})/(v_delta/v_len0)*{}".format(L.eval("pzz"), cfac))
L.variable("d4 equal -(v_pyz1-{})/(v_delta/v_len0)*{}".format(L.eval("pyz"), cfac))
L.variable("d5 equal -(v_pxz1-{})/(v_delta/v_len0)*{}".format(L.eval("pxz"), cfac))
L.variable("d6 equal -(v_pxy1-{})/(v_delta/v_len0)*{}".format(L.eval("pxy"), cfac))
L.displace_atoms("all", "random", atomjiggle, atomjiggle, atomjiggle, 87287, "units box")
# Write restart
L.unfix(3)
L.write_restart("restart.equil")
for idir in range(1, 7):
displace(L, args, idir)
postprocess_and_output(L)
return
def postprocess_and_output(lmp):
"""Compute the moduli and print everything to screen """
# Output final values
c11all = lmp.variables["C11"].value
c22all = lmp.variables["C22"].value
c33all = lmp.variables["C33"].value
c12all = 0.5*(lmp.variables["C12"].value + lmp.variables["C21"].value)
c13all = 0.5*(lmp.variables["C13"].value + lmp.variables["C31"].value)
c23all = 0.5*(lmp.variables["C23"].value + lmp.variables["C32"].value)
c44all = lmp.variables["C44"].value
c55all = lmp.variables["C55"].value
c66all = lmp.variables["C66"].value
c14all = 0.5*(lmp.variables["C14"].value + lmp.variables["C41"].value)
c15all = 0.5*(lmp.variables["C15"].value + lmp.variables["C51"].value)
c16all = 0.5*(lmp.variables["C16"].value + lmp.variables["C61"].value)
c24all = 0.5*(lmp.variables["C24"].value + lmp.variables["C42"].value)
c25all = 0.5*(lmp.variables["C25"].value + lmp.variables["C52"].value)
c26all = 0.5*(lmp.variables["C26"].value + lmp.variables["C62"].value)
c34all = 0.5*(lmp.variables["C34"].value + lmp.variables["C43"].value)
c35all = 0.5*(lmp.variables["C35"].value + lmp.variables["C53"].value)
c36all = 0.5*(lmp.variables["C36"].value + lmp.variables["C63"].value)
c45all = 0.5*(lmp.variables["C45"].value + lmp.variables["C54"].value)
c46all = 0.5*(lmp.variables["C46"].value + lmp.variables["C64"].value)
c56all = 0.5*(lmp.variables["C56"].value + lmp.variables["C65"].value)
# Average moduli for cubic crystals
c11cubic = (c11all + c22all + c33all)/3.0
c12cubic = (c12all + c13all + c23all)/3.0
c44cubic = (c44all + c55all + c66all)/3.0
bulkmodulus = (c11cubic + 2*c12cubic)/3.0
shearmodulus1 = c44cubic
shearmodulus2 = (c11cubic - c12cubic)/2.0
poisson_ratio = 1.0/(1.0 + c11cubic/c12cubic)
# print results to screen
print("=========================================")
print("Components of the Elastic Constant Tensor")
print("=========================================")
print("Elastic Constant C11all = {} GPa".format(c11all))
print("Elastic Constant C22all = {} GPa".format(c22all))
print("Elastic Constant C33all = {} GPa".format(c33all))
print("Elastic Constant C12all = {} GPa".format(c12all))
print("Elastic Constant C13all = {} GPa".format(c13all))
print("Elastic Constant C23all = {} GPa".format(c23all))
print("Elastic Constant C44all = {} GPa".format(c44all))
print("Elastic Constant C55all = {} GPa".format(c55all))
print("Elastic Constant C66all = {} GPa".format(c66all))
print("Elastic Constant C14all = {} GPa".format(c14all))
print("Elastic Constant C15all = {} GPa".format(c15all))
print("Elastic Constant C16all = {} GPa".format(c16all))
print("Elastic Constant C24all = {} GPa".format(c24all))
print("Elastic Constant C25all = {} GPa".format(c25all))
print("Elastic Constant C26all = {} GPa".format(c26all))
print("Elastic Constant C34all = {} GPa".format(c34all))
print("Elastic Constant C35all = {} GPa".format(c35all))
print("Elastic Constant C36all = {} GPa".format(c36all))
print("Elastic Constant C45all = {} GPa".format(c45all))
print("Elastic Constant C46all = {} GPa".format(c46all))
print("Elastic Constant C56all = {} GPa".format(c56all))
print("=========================================")
print("Average properties for a cubic crystal")
print("=========================================")
print("Bulk Modulus = {} GPa".format(bulkmodulus))
print("Shear Modulus 1 = {} GPa".format(shearmodulus1))
print("Shear Modulus 2 = {} GPa".format(shearmodulus2))
print("Poisson Ratio = {}".format(poisson_ratio))
return
if __name__ == "__main__":
elastic()
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