def test_forces_CuZr_glass(self):
"""Calculate interatomic forces in CuZr glass
Reference: tabulated forces from a calculation
with Lammmps (git version patch_29Mar2019-2-g585403d65)
The forces can be re-calculated using the following
Lammps commands:
units metal
atom_style atomic
boundary p p p
read_data CuZr_glass_460_atoms.lammps.data.gz
pair_style eam/alloy
pair_coeff * * ZrCu.onecolumn.eam.alloy Zr Cu
# The initial configuration is in equilibrium
# and the remaining forces are small
# Swap atom types to bring system out of
# equilibrium and create nonzero forces
group originally_Zr type 1
group originally_Cu type 2
set group originally_Zr type 2
set group originally_Cu type 1
run 0
write_dump all custom &
CuZr_glass_460_atoms_forces.lammps.dump.gz &
id type x y z fx fy fz &
modify sort id format float "%.14g"
"""
if "lammps-dump" in io.formats.ioformats.keys():
atoms = io.read("CuZr_glass_460_atoms_forces.lammps.dump.gz",
format="lammps-dump")
elif "lammps-dump-text" in io.formats.ioformats.keys():
atoms = io.read("CuZr_glass_460_atoms_forces.lammps.dump.gz",
format="lammps-dump-text")
else:
raise KeyError(
"ase.io can read neither 'lammps-dump' nor 'lammps-dump-text'")
old_atomic_numbers = atoms.get_atomic_numbers()
sel, = np.where(old_atomic_numbers == 1)
new_atomic_numbers = np.zeros_like(old_atomic_numbers)
new_atomic_numbers[sel] = 40 # Zr
sel, = np.where(old_atomic_numbers == 2)
new_atomic_numbers[sel] = 29 # Cu
atoms.set_atomic_numbers(new_atomic_numbers)
calculator = EAM('ZrCu.onecolumn.eam.alloy')
atoms.set_calculator(calculator)
atoms.pbc = [True, True, True]
forces = atoms.get_forces()
# Read tabulated forces and compare
with gzip.open("CuZr_glass_460_atoms_forces.lammps.dump.gz") as file:
for line in file:
if line.startswith(b"ITEM: ATOMS "): # ignore header
break
dump = np.loadtxt(file)
forces_dump = dump[:, 5:8]
self.assertArrayAlmostEqual(forces,
forces_dump,
tol=self.force_tolerance)
def test_hessian_monoatomic(self):
"""Calculate Hessian matrix of pure Cu
Reference: finite difference approximation of
Hessian from ASE
"""
atoms = FaceCenteredCubic('Cu', size=[4, 4, 4])
calculator = EAM('CuAg.eam.alloy')
self._test_hessian(atoms, calculator)
def test_hessian_amorphous_alloy(self):
"""Calculate Hessian matrix of amorphous alloy
Reference: finite difference approximation of
Hessian from ASE
"""
atoms = io.read('CuZr_glass_460_atoms.gz')
atoms.pbc = [True, True, True]
calculator = EAM('ZrCu.onecolumn.eam.alloy')
self._test_hessian(atoms, calculator)
def test_hessian_monoatomic_with_duplicate_pairs(self):
"""Calculate Hessian matrix of pure Cu
In a small system, the same pair (i,j) will
appear multiple times in the neighbor list,
with different pair distance.
Reference: finite difference approximation of
Hessian from ASE
"""
atoms = FaceCenteredCubic('Cu', size=[2, 2, 2])
calculator = EAM('CuAg.eam.alloy')
self._test_hessian(atoms, calculator)
def test_dynamical_matrix(self):
"""Test dynamical matrix construction
To obtain the dynamical matrix, one could either divide by
masses immediately when constructing the matrix, or one could
first form the complete Hessian and then divide by masses.
The former method is implemented.
"""
atoms = io.read('CuZr_glass_460_atoms.gz')
atoms.pbc = [True, True, True]
calculator = EAM('ZrCu.onecolumn.eam.alloy')
dynamical_matrix = calculator.calculate_hessian_matrix(
atoms, divide_by_masses=True)
# The second method requires a copy of Hessian, since
# sparse matrix does not properly support *= operator
hessian = calculator.calculate_hessian_matrix(atoms)
masses = atoms.get_masses()
mass_row = np.repeat(masses, np.diff(hessian.indptr))
mass_col = masses[hessian.indices]
inverse_mass = np.sqrt(mass_row * mass_col)**-1.0
blocks = (inverse_mass * np.ones(
(inverse_mass.size, 3, 3), dtype=inverse_mass.dtype).T).T
nat = len(atoms)
dynamical_matrix_ref = hessian.multiply(
bsr_matrix((blocks, hessian.indices, hessian.indptr),
shape=(3 * nat, 3 * nat)))
dynamical_matrix = dynamical_matrix.todense()
dynamical_matrix_ref = dynamical_matrix_ref.todense()
self.assertArrayAlmostEqual(dynamical_matrix,
dynamical_matrix.T,
tol=self.hessian_tolerance)
self.assertArrayAlmostEqual(dynamical_matrix_ref,
dynamical_matrix_ref.T,
tol=self.hessian_tolerance)
self.assertArrayAlmostEqual(dynamical_matrix,
dynamical_matrix_ref,
tol=self.hessian_tolerance)
def test_hessian_crystalline_alloy(self):
"""Calculate Hessian matrix of crystalline alloy
Reference: finite difference approximation of
Hessian from ASE
"""
calculator = EAM('ZrCu.onecolumn.eam.alloy')
lattice_size = [4, 4, 4]
# The lattice parameters are not correct, but that should be irrelevant
# CuZr3
atoms = L1_2(['Cu', 'Zr'], size=lattice_size, latticeconstant=4.0)
self._test_hessian(atoms, calculator)
# Cu3Zr
atoms = L1_2(['Zr', 'Cu'], size=lattice_size, latticeconstant=4.0)
self._test_hessian(atoms, calculator)
# CuZr
atoms = B2(['Zr', 'Cu'], size=lattice_size, latticeconstant=3.3)
self._test_hessian(atoms, calculator)
def _test_for_size(size):
atoms = FaceCenteredCubic('Cu', size=size)
calculator = EAM('CuAg.eam.alloy')
self._test_hessian(atoms, calculator)