def C44_Calculator(self, EMT, PARAMETERS):
# Return 0 is used when the method is not desired to be used
# return 0
""" This method uses the given EMT calculator to calculate and return the value of the matrix element C44 for
a system of atoms of a given element type. The calculation is done by using that:
C44 = 1 / Volume * d^2/depsilon^2 (E_system) where epsilon is the displacement in one direction of the
system along one axis diveded by the highth of the system. """
# An atom object is created and the calculator attached
atoms = FaceCenteredCubic(size=(self.Size, self.Size, self.Size),
symbol=self.Element)
atoms.set_calculator(EMT)
# The volume of the sample is calculated
Vol = atoms.get_volume()
# The value of the relative displacement, epsilon, is set
epsilon = 1. / 1000
# The matrix used to change the unitcell by n*epsilon is initialized
LMM = numpy.array([[1, 0, -10 * epsilon], [0, 1, 0], [0, 0, 1]])
# The original unit cell is conserved
OCell = atoms.get_cell()
# The array for storing the energies is initialized
E_calc = numpy.zeros(20)
# The numerical value of C44 is calculated
for i in range(20):
# The new system cell based on the pertubation epsilon is set
atoms.set_cell(numpy.dot(OCell, LMM), scale_atoms=True)
# The energy of the system is calculated
E_calc[i] = atoms.get_potential_energy()
# The value of LMM is updated
LMM[0, 2] += epsilon
# A polynomial fit is made for the energy as a function of epsilon
# The displaced axis is defined
da = numpy.arange(-10, 10) * epsilon
# The fit is made
Poly = numpyfit.polyfit(da, E_calc, 2)
# Now C44 can be estimated from this fit by the second derivative of Poly = a * x^2 + b * x + c , multiplied
# with 1 / (2 * Volume) of system
C44 = 2. / Vol * Poly[0]
return C44
# this did not work
# maybe wrong setting of LAMMPS volume optimization for triclinic cell
# from ase.lattice.hexagonal import HexagonalClosedPacked
# atoms = HexagonalClosedPacked(symbol=el1,latticeconstant=(lp,c),size=(5,5,5))
atoms = HCPO(symbol=el1, latticeconstant=(a, b, c), size=(8, 4, 4))
else:
raise RuntimeError, 'unknown structure "' + str + '"'
atoms.set_calculator(calc)
print "el:", el1, "str:", str, "lp:", lp
if str == "hcp":
print "catoi:", catoi
v1 = atoms.get_volume()
print "v1:", v1
n1 = atoms.get_number_of_atoms()
print "n1:", n1
v1pa = v1 / n1
print "v1pa:", v1pa
# initial
ene0 = atoms.get_potential_energy()
print "ene0:", ene0
print "ene0pa:", ene0 / atoms.get_number_of_atoms()
ene0pa = ene0 / atoms.get_number_of_atoms()
# vacancy
atoms.pop(0)
nm1 = n1 - 1
from vasp import Vasp
from ase.lattice.cubic import FaceCenteredCubic
import numpy as np
import matplotlib.pyplot as plt
DELTAS = np.linspace(-0.05, 0.05, 5)
calcs = []
volumes = []
for delta in DELTAS:
atoms = FaceCenteredCubic(symbol='Al')
cell = atoms.cell
T = np.array([[1 + delta, 0, 0], [0, 1, 0], [0, 0, 1]])
newcell = np.dot(cell, T)
atoms.set_cell(newcell, scale_atoms=True)
volumes += [atoms.get_volume()]
calcs += [
Vasp('bulk/Al-c11-{}'.format(delta),
xc='pbe',
kpts=[12, 12, 12],
encut=350,
atoms=atoms)
]
Vasp.run()
energies = [calc.potential_energy for calc in calcs]
# fit a parabola
eos = np.polyfit(DELTAS, energies, 2)
# first derivative
d_eos = np.polyder(eos)
print(np.roots(d_eos))
xfit = np.linspace(min(DELTAS), max(DELTAS))
yfit = np.polyval(eos, xfit)
# this did not work
# maybe wrong setting of LAMMPS volume optimization for triclinic cell
# from ase.lattice.hexagonal import HexagonalClosedPacked
# atoms = HexagonalClosedPacked(symbol=el1,latticeconstant=(lp,c),size=(5,5,5))
atoms = HCPO(symbol=el1, latticeconstant=(a, b, c), size=(8, 4, 4))
else:
raise RuntimeError, "unknown structure \"" + str + "\""
atoms.set_calculator(calc)
print "el:", el1, "str:", str, "lp:", lp
if str == "hcp":
print "catoi:", catoi
v1 = atoms.get_volume()
print "v1:", v1
n1 = atoms.get_number_of_atoms()
print "n1:", n1
v1pa = v1 / n1
print "v1pa:", v1pa
# initial
ene0 = atoms.get_potential_energy()
print "ene0:", ene0
print "ene0pa:", ene0 / atoms.get_number_of_atoms()
ene0pa = ene0 / atoms.get_number_of_atoms()
# vacancy
atoms.pop(0)
nm1 = n1 - 1
ReportTest("Local and global RDF are identical",
max(abs(globalrdf - localrdf)), 0.0, 1e-6)
shellpop = [12, 6, 24, 12, 24, -1]
shell = [sqrt(i+1.0)/sqrt(2.0) for i in range(6)]
print shell
print shellpop
n = 0
dr = maxrdf/nbins
for i in range(nbins):
if (i+1)*dr >= shell[n] * latconst:
if shellpop[n] == -1:
print "Reached the end of the test data"
break
rho = len(atoms) / atoms.get_volume()
expected = shellpop[n] / (4 * pi * ((i+0.5) * dr)**2 * dr * rho)
maxerr = shellpop[n] / (8 * pi * ((i+0.5) * dr)**3 * rho)
print "Shell", n+1, globalrdf[i]
ReportTest(("Shell %d (%d)" % (n+1, i)), globalrdf[i],
expected, maxerr)
n += 1
else:
ReportTest(("Between shells (%d)" % (i,)), globalrdf[i], 0, 0)
ReportTest.Summary()
from vasp import Vasp
from ase.lattice.cubic import FaceCenteredCubic
import numpy as np
import matplotlib.pyplot as plt
DELTAS = np.linspace(-0.05, 0.05, 5)
calcs = []
volumes = []
for delta in DELTAS:
atoms = FaceCenteredCubic(symbol='Al')
cell = atoms.cell
T = np.array([[1 + delta, 0, 0],
[0,1, 0],
[0, 0, 1]])
newcell = np.dot(cell, T)
atoms.set_cell(newcell, scale_atoms=True)
volumes += [atoms.get_volume()]
calcs += [Vasp('bulk/Al-c11-{}'.format(delta),
xc='pbe',
kpts=[12, 12, 12],
encut=350,
atoms=atoms)]
Vasp.run()
energies = [calc.potential_energy for calc in calcs]
# fit a parabola
eos = np.polyfit(DELTAS, energies, 2)
# first derivative
d_eos = np.polyder(eos)
print(np.roots(d_eos))
xfit = np.linspace(min(DELTAS), max(DELTAS))
yfit = np.polyval(eos, xfit)
plt.plot(DELTAS, energies, 'bo', xfit, yfit, 'b-')
