def test_rotation(self):
for make_atoms, calc in [
# ( lambda a0,x :
# FaceCenteredCubic('He', size=[1,1,1],
# latticeconstant=3.5 if a0 is None else a0,
# directions=x),
# LJCut(epsilon=10.2, sigma=2.28, cutoff=5.0, shift=True) ),
( lambda a0,x : FaceCenteredCubic('Au', size=[1,1,1],
latticeconstant=a0, directions=x),
EAM('Au-Grochola-JCP05.eam.alloy') ),
# ( lambda a0,x : Diamond('Si', size=[1,1,1], latticeconstant=a0,
# directions=x),
# Kumagai() )
#( lambda a0,x : FaceCenteredCubic('Au', size=[1,1,1],
# latticeconstant=a0, directions=x),
# EAM(potential='Au-Grochola-JCP05.eam.alloy') ),
]:
a = make_atoms(None, [[1,0,0], [0,1,0], [0,0,1]])
a.set_calculator(calc)
FIRE(StrainFilter(a, mask=[1,1,1,0,0,0]), logfile=None) \
.run(fmax=self.fmax)
latticeconstant = np.mean(a.cell.diagonal())
C6 = measure_triclinic_elastic_constants(a, delta=self.delta,
fmax=self.fmax)
C11, C12, C44 = Voigt_6x6_to_cubic(C6)/GPa
el = CubicElasticModuli(C11, C12, C44)
C_m = measure_triclinic_elastic_constants(a, delta=self.delta,
fmax=self.fmax)/GPa
self.assertArrayAlmostEqual(el.stiffness(), C_m, tol=0.01)
for directions in [ [[1,0,0], [0,1,0], [0,0,1]],
[[0,1,0], [0,0,1], [1,0,0]],
[[1,1,0], [0,0,1], [1,-1,0]],
[[1,1,1], [-1,-1,2], [1,-1,0]] ]:
a, b, c = directions
directions = np.array([ np.array(x)/np.linalg.norm(x)
for x in directions ])
a = make_atoms(latticeconstant, directions)
a.set_calculator(calc)
C = el.rotate(directions)
C_check = el._rotate_explicit(directions)
C_check2 = rotate_cubic_elastic_constants(C11, C12, C44,
directions)
C_check3 = \
rotate_elastic_constants(cubic_to_Voigt_6x6(C11, C12, C44),
directions)
self.assertArrayAlmostEqual(C, C_check, tol=1e-6)
self.assertArrayAlmostEqual(C, C_check2, tol=1e-6)
self.assertArrayAlmostEqual(C, C_check3, tol=1e-6)
C_m = measure_triclinic_elastic_constants(a, delta=self.delta,
fmax=self.fmax)/GPa
self.assertArrayAlmostEqual(C, C_m, tol=1e-2)
def test_measure_triclinic_relaxed(self):
# compare to brute force method with relaxation
C = measure_triclinic_elastic_constants(self.at0,
delta=1e-2,
optimizer=FIRE,
fmax=self.fmax)
self.assertArrayAlmostEqual(C / units.GPa,
self.C_ref_relaxed,
tol=0.2)
if hasattr(params, 'relax_bulk') and params.relax_bulk:
print('Minimising bulk unit cell...')
opt = FIRE(StrainFilter(a, mask=[1, 1, 1, 0, 0, 0]))
opt.run(fmax=params.bulk_fmax)
a0 = a.cell[0, 0]
print('Lattice constant %.3f A\n' % a0)
a.set_calculator(params.calc)
# ******* Find elastic constants *******
# Get 6x6 matrix of elastic constants C_ij
C = measure_triclinic_elastic_constants(a,
optimizer=FIRE,
fmax=params.bulk_fmax)
print('Elastic constants (GPa):')
print((C / units.GPa).round(0))
print('')
E = youngs_modulus(C, params.cleavage_plane)
print('Young\'s modulus %.1f GPa' % (E / units.GPa))
nu = poisson_ratio(C, params.cleavage_plane, params.crack_direction)
print('Poisson ratio % .3f\n' % nu)
# **** Setup crack slab unit cell ******
directions = [
params.crack_direction, params.cleavage_plane, params.crack_front
]
a.set_calculator(params.calc)
if hasattr(params, 'relax_bulk') and params.relax_bulk:
print('Minimising bulk unit cell...')
opt = FIRE(StrainFilter(a, mask=[1, 1, 1, 0, 0, 0]))
opt.run(fmax=params.bulk_fmax)
a0 = a.cell[0, 0]
print('Lattice constant %.3f A\n' % a0)
a.set_calculator(params.calc)
# ******* Find elastic constants *******
# Get 6x6 matrix of elastic constants C_ij
C = measure_triclinic_elastic_constants(a, optimizer=FIRE,
fmax=params.bulk_fmax)
print('Elastic constants (GPa):')
print((C / units.GPa).round(0))
print('')
E = youngs_modulus(C, params.cleavage_plane)
print('Young\'s modulus %.1f GPa' % (E / units.GPa))
nu = poisson_ratio(C, params.cleavage_plane, params.crack_direction)
print('Poisson ratio % .3f\n' % nu)
# **** Setup crack slab unit cell ******
directions = [params.crack_direction,
params.cleavage_plane,
params.crack_front]
print_crack_system(directions)
def test_measure_triclinic_relaxed(self):
# compare to brute force method with relaxation
C = measure_triclinic_elastic_constants(self.at0, delta=1e-2, optimizer=FIRE,
fmax=self.fmax)
self.assertArrayAlmostEqual(C/units.GPa, self.C_ref_relaxed, tol=0.2)