def aucu_phonons():
N = 7
atoms = bulk("Au", crystalstructure="fcc", a=4.08)
calc = EMT()
atoms.set_calculator(calc)
ph = Phonons(atoms, calc, supercell=(N, N, N), delta=0.05)
ph.run()
ph.read(acoustic=True)
ph.clean()
omega_e_au, dos_e_au = ph.dos(kpts=(50, 50, 50), npts=1000, delta=5E-4)
atoms = bulk("Cu", crystalstructure="fcc", a=3.62)
atoms.set_calculator(calc)
ph = Phonons(atoms, calc, supercell=(N, N, N), delta=0.05)
ph.run()
ph.read(acoustic=True)
ph.clean()
omega_e_cu, dos_e_cu = ph.dos(kpts=(13, 13, 13), npts=100, delta=5E-4)
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
ax.plot(omega_e_au * 1000.0, dos_e_au)
ax.plot(omega_e_cu * 1000.0, dos_e_cu)
ax.set_xlabel("Energy (meV)")
logw_au = np.sum(np.log(omega_e_au[1:]) * dos_e_au[1:])
logw_cu = np.sum(np.log(omega_e_cu[1:]) * dos_e_cu[1:])
print(logw_au, logw_cu, logw_au - logw_cu)
plt.show()
def phonon_run(runID, save_to_db=False, plot_bands=False):
print("Running ID %d" % (runID))
db = connect(db_name)
atoms = db.get_atoms(id=runID)
#view(atoms)
#atoms = bulk("Al")
#atoms = atoms*(2,1,1)
#calc = EAM(potential="/home/davidkl/Documents/EAM/Al-LEA.eam.alloy")
calc = EAM(potential="/home/davidkl/Documents/EAM/mg-al-set.eam.alloy")
atoms.set_calculator(calc)
#calc = gp.GPAW( mode=gp.PW(600), xc="PBE", kpts=(4,4,4), nbands="120%", symmetry="off" )
#atoms.set_calculator(calc)
ph = Phonons(atoms,
calc,
supercell=(3, 3, 3),
name=wrk + "/phonon_files/phonon%d" % (runID))
ph.run()
#return
ph.read(acoustic=True)
omega_e, dos_e = ph.dos(kpts=(30, 30, 30), npts=1000, delta=5E-4)
if (plot_bands):
points = ibz_points['fcc']
G = points['Gamma']
X = points['X']
W = points['W']
K = points['K']
L = points['L']
U = points['U']
point_names = ['$\Gamma$', 'X', 'U', 'L', '$\Gamma$', 'K']
path = [G, X, U, L, G, K]
path_kc, q, Q = bandpath(path, atoms.cell, 100)
omega_kn = 1000.0 * ph.band_structure(path_kc)
figb = plt.figure()
axb = figb.add_subplot(1, 1, 1)
for n in range(len(omega_kn[0])):
omega_n = omega_kn[:, n]
axb.plot(q, omega_n)
plt.show()
if (save_to_db):
# Store the results in the database
db.update(runID, has_dos=True)
manager = cpd.PhononDOS_DB(db_name)
# Extract relevant information from the atoms database
row = db.get(id=runID)
name = row.name
atID = row.id
manager.save(name=name, atID=atID, omega_e=omega_e, dos_e=dos_e)
def test_crystal_thermo(asap3, testdir):
atoms = bulk('Al', 'fcc', a=4.05)
calc = asap3.EMT()
atoms.calc = calc
energy = atoms.get_potential_energy()
# Phonon calculator
N = 7
ph = Phonons(atoms, calc, supercell=(N, N, N), delta=0.05)
ph.run()
ph.read(acoustic=True)
phonon_energies, phonon_DOS = ph.dos(kpts=(4, 4, 4), npts=30, delta=5e-4)
thermo = CrystalThermo(phonon_energies=phonon_energies,
phonon_DOS=phonon_DOS,
potentialenergy=energy,
formula_units=4)
thermo.get_helmholtz_energy(temperature=298.15)
def test_thermochemistry():
"""Tests of the major methods (HarmonicThermo, IdealGasThermo,
CrystalThermo) from the thermochemistry module."""
# Ideal gas thermo.
atoms = Atoms('N2', positions=[(0, 0, 0), (0, 0, 1.1)], calculator=EMT())
QuasiNewton(atoms).run(fmax=0.01)
energy = atoms.get_potential_energy()
vib = Vibrations(atoms, name='idealgasthermo-vib')
vib.run()
vib_energies = vib.get_energies()
thermo = IdealGasThermo(vib_energies=vib_energies,
geometry='linear',
atoms=atoms,
symmetrynumber=2,
spin=0,
potentialenergy=energy)
thermo.get_gibbs_energy(temperature=298.15, pressure=2 * 101325.)
# Harmonic thermo.
atoms = fcc100('Cu', (2, 2, 2), vacuum=10.)
atoms.set_calculator(EMT())
add_adsorbate(atoms, 'Pt', 1.5, 'hollow')
atoms.set_constraint(
FixAtoms(indices=[atom.index for atom in atoms
if atom.symbol == 'Cu']))
QuasiNewton(atoms).run(fmax=0.01)
vib = Vibrations(
atoms,
name='harmonicthermo-vib',
indices=[atom.index for atom in atoms if atom.symbol != 'Cu'])
vib.run()
vib.summary()
vib_energies = vib.get_energies()
thermo = HarmonicThermo(vib_energies=vib_energies,
potentialenergy=atoms.get_potential_energy())
thermo.get_helmholtz_energy(temperature=298.15)
# Crystal thermo.
atoms = bulk('Al', 'fcc', a=4.05)
calc = EMT()
atoms.set_calculator(calc)
energy = atoms.get_potential_energy()
# Phonon calculator
N = 7
ph = Phonons(atoms, calc, supercell=(N, N, N), delta=0.05)
ph.run()
ph.read(acoustic=True)
phonon_energies, phonon_DOS = ph.dos(kpts=(4, 4, 4), npts=30, delta=5e-4)
thermo = CrystalThermo(phonon_energies=phonon_energies,
phonon_DOS=phonon_DOS,
potentialenergy=energy,
formula_units=4)
thermo.get_helmholtz_energy(temperature=298.15)
# Hindered translator / rotor.
# (Taken directly from the example given in the documentation.)
vibs = np.array([
3049.060670, 3040.796863, 3001.661338, 2997.961647, 2866.153162,
2750.855460, 1436.792655, 1431.413595, 1415.952186, 1395.726300,
1358.412432, 1335.922737, 1167.009954, 1142.126116, 1013.918680,
803.400098, 783.026031, 310.448278, 136.112935, 112.939853, 103.926392,
77.262869, 60.278004, 25.825447
])
vib_energies = vibs / 8065.54429 # Convert to eV from cm^-1.
trans_barrier_energy = 0.049313 # eV
rot_barrier_energy = 0.017675 # eV
sitedensity = 1.5e15 # cm^-2
rotationalminima = 6
symmetrynumber = 1
mass = 30.07 # amu
inertia = 73.149 # amu Ang^-2
thermo = HinderedThermo(vib_energies=vib_energies,
trans_barrier_energy=trans_barrier_energy,
rot_barrier_energy=rot_barrier_energy,
sitedensity=sitedensity,
rotationalminima=rotationalminima,
symmetrynumber=symmetrynumber,
mass=mass,
inertia=inertia)
helmholtz = thermo.get_helmholtz_energy(temperature=298.15)
target = 1.593 # Taken from documentation example.
assert (helmholtz - target) < 0.001
from ase.calculators.emt import EMT
from ase.optimize import QuasiNewton
from ase.phonons import Phonons
from ase.thermochemistry import CrystalThermo
# Set up gold bulk and attach EMT calculator
a = 4.078
atoms = crystal('Au', (0., 0., 0.),
spacegroup=225,
cellpar=[a, a, a, 90, 90, 90],
pbc=(1, 1, 1))
calc = EMT()
atoms.set_calculator(calc)
qn = QuasiNewton(atoms)
qn.run(fmax=0.05)
electronicenergy = atoms.get_potential_energy()
# Phonon analysis
N = 5
ph = Phonons(atoms, calc, supercell=(N, N, N), delta=0.05)
ph.run()
ph.read(acoustic=True)
phonon_energies, phonon_DOS = ph.dos(kpts=(40, 40, 40), npts=3000, delta=5e-4)
# Calculate the Helmholtz free energy
thermo = CrystalThermo(phonon_energies=phonon_energies,
phonon_DOS=phonon_DOS,
electronicenergy=electronicenergy,
formula_units=4)
F = thermo.get_helmholtz_energy(temperature=298.15)
class ThermalProperties(object):
"""Class with methods to calculate thermal properties of a structure within the QHA
Attributes
----------
name : str
Base name for the files used for the phonon calculations.
structure : ATAT2EMT
ATAT structure file describing the primitive cell.
atoms : ase.Atoms
Atoms object with the primitive cell.
calc : ase.Calculator
Callable returning a Calculator to use for all energy and force calculations.
n_atoms : int
Number of atoms in the primitive cell.
temperature : Iterable of float
Temperatures at which to calculate temperature dependent properties.
strains : Iterable of float
Strains to apply to the atoms for volume dependent properties.
strained_thermo : list of ThermalProperties
List with classes for the thermal properties of strained versions of the atoms object.
sjeos : SJEOS
Class to fit the equation of state at constant temperature.
base_dir : str
Base directory for the calculations. (WARNING: not fully implemented)
verbosity : int >= 0
Verbosity level.
do_plotting : bool
Determines if the plottings are activated.
supercell_size : tuple of 3 int
Size of the supercell to do the phonon calculations.
thermo : ase.CrystalThermo
Class to delegate the calculation of some thermodynamic properties.
phonons : ase.Phonons
Class to perform phonon calculations using the supercell approach.
phonon_kpts_mp : (N, 3) np.ndarray
Monkhorst-Pack k-point grid.
phonon_energy_mp : (N,) np.ndarray
Energies of the corresponding MP k-points.
phonon_energy : np.ndarray
Energies to calculate the Phonon density of states.
phonon_dos : np.ndarray
Phonon density of states at given energies.
Parameters
----------
atoms :
calc :
supercell_size :
atat_structure :
plot :
verbosity :
name :
"""
def __init__(self,
atoms=None,
calc=None,
supercell_size=5,
atat_structure=None,
plot=False,
verbosity=0,
name='thermo'):
# relaxed structure
self.name = name
self.structure = None
self.atoms = None
self.calc = None
self.n_atoms = 0
self.temperature = None
self.strains = None
self.strained_thermo = []
if atoms is not None and atat_structure is not None:
print('ERROR: only atoms OR atat_structure can be specified')
return
if atoms is not None:
self.atoms = atoms
self.n_atoms = len(self.atoms)
if self.atoms.calc is None:
assert calc is not None
self.atoms.set_calculator(calc())
self.calc = calc
else:
self.calc = atoms.calc
elif atat_structure is not None:
assert calc is not None
self.calc = calc
self.structure = ATAT2EMT(atat_structure,
calc(),
to_niggli=True,
verbosity=verbosity)
self.structure.atoms.wrap()
self.atoms = self.structure.atoms
self.n_atoms = len(self.atoms)
# isgn = spglib.get_symmetry_dataset(self.atoms, symprec=1e-3)['number']
# self.symmetry = el.crystal_system(isgn)
self.sjeos = SJEOS()
self.base_dir = os.getcwd()
self.verbosity = verbosity
self.do_plotting = plot
if isinstance(supercell_size, int):
self.supercell_size = (supercell_size, supercell_size,
supercell_size)
else:
assert len(supercell_size) == 3
self.supercell_size = supercell_size
self.get_phonons()
self.thermo = CrystalThermo(
phonon_energies=self.phonon_energy,
phonon_DOS=self.phonon_dos,
potentialenergy=self.atoms.get_potential_energy(),
formula_units=self.n_atoms)
def set_temperature(self, temperature, save_at='.'):
"""Set the temperature grid.
Parameters
----------
temperature : iterable of float
Iterable containing the temperatures at which to calculate the properties.
save_at : string
Path (relative or absolute) in which to store the value.
"""
if save_at is not None:
if not os.path.exists(save_at):
os.makedirs(save_at)
save_name = os.path.join(save_at, 'T.dat')
np.savetxt(save_name, temperature)
self.temperature = temperature
def get_phonons(self, kpts=(50, 50, 50), npts=5000):
"""Calculate the phonon spectrum and DOS.
Parameters
----------
kpts : tuple
Number of points in each directions of the k-space grid.
npts : int
Number of energy points to calculate the DOS at.
"""
self.phonons = Phonons(self.atoms,
self.calc(),
supercell=self.supercell_size,
delta=0.05,
name=self.name)
self.phonons.run()
# Read forces and assemble the dynamical matrix
self.phonons.read(acoustic=True)
self.phonon_kpts_mp = monkhorst_pack(kpts)
self.phonon_energy_mp = self.phonons.band_structure(
self.phonon_kpts_mp)
self.phonon_energy, self.phonon_dos = \
self.phonons.dos(kpts=kpts, npts=npts, delta=5e-4)
def get_volume_phonons(self, nvolumes=5, max_strain=0.02):
"""Calculate the volume dependent phonons.
Parameters
----------
nvolumes : int > 0
Number of volumes to calculate the phonon spectrum.
max_strain : float > 0
Maximum (isotropic) strain used to deform equilibrium volume.
"""
strains = np.linspace(-max_strain, max_strain, nvolumes)
load = False
if self.strains is None:
self.strains = strains
else:
if not (strains == self.strains).all():
self.strains = strains
self.strained_thermo = []
else:
load = True
strain_matrices = [np.eye(3) * (1 + s) for s in self.strains]
atoms = self.atoms
cell = atoms.cell
for i, s in enumerate(strain_matrices):
satoms = atoms.copy()
satoms.set_cell(np.dot(cell, s.T), scale_atoms=True)
if load:
pass
else:
satoms.set_calculator(None)
sthermo = ThermalProperties(satoms,
self.calc,
name='thermo_{:.2f}'.format(
self.strains[i]))
self.strained_thermo.append(sthermo)
def get_volume_energy(self, temperature=None, nvolumes=5, max_strain=0.02):
"""Return the volume dependent (Helmholtz) energy.
Parameters
----------
temperature : float > 0
Temeprature at which the volume-energy curve is calculated.
nvolumes : int > 0
Number of volumes to calculate the energy at.
max_strain : float > 0
Maximum (isotropic) strain used to deform equilibrium volume.
save_at : string
Path (relative or absolute) in which to store the value.
Returns
-------
volume : list of double
Volumes at which the entropy was calculated.
energy : list of double
Helmholtz energy for each of the volumes.
"""
if temperature is None and self.temperature is None:
print(
'ERROR. You nee to specify a temperature for the calculations.'
)
return
elif temperature is None:
temperature = self.temperature
if isinstance(temperature, collections.Iterable):
volume_energy = [
self.get_volume_energy(T, nvolumes, max_strain)
for T in temperature
]
return volume_energy
self.get_volume_phonons(nvolumes, max_strain)
energy = []
volume = []
for sthermo in self.strained_thermo:
energy.append(
sthermo.get_helmholtz_energy(temperature, save_at=None))
volume.append(sthermo.atoms.get_volume())
return volume, energy
def get_volume_entropy(self,
temperature=None,
nvolumes=5,
max_strain=0.02):
"""Return the volume dependent entropy.
Parameters
----------
temperature : float > 0
Temeprature at which the volume-entropy curve is calculated.
nvolumes : int > 0
Number of volumes to calculate the entropy at.
max_strain : float > 0
Maximum (isotropic) strain used to deform equilibrium volume.
save_at : string
Path (relative or absolute) in which to store the value.
Returns
-------
volume : list of double
Volumes at which the entropy was calculated.
entropy : list of double
Entropy for each of the volumes.
"""
if temperature is None and self.temperature is None:
print(
'ERROR. You nee to specify a temperature for the calculations.'
)
return
elif temperature is None:
temperature = self.temperature
if isinstance(temperature, collections.Iterable):
volume_entropy = [
self.get_volume_entropy(T, nvolumes, max_strain)
for T in temperature
]
return volume_entropy
self.get_volume_phonons(nvolumes, max_strain)
entropy = []
volume = []
for sthermo in self.strained_thermo:
entropy.append(sthermo.get_entropy(temperature, save_at=None))
volume.append(sthermo.atoms.get_volume())
return volume, entropy
def get_entropy(self, temperature=None, save_at='.'):
"""Return entropy per atom in eV / atom.
Parameters
----------
temperature : float > 0
Temeprature at which the Helmholtz energy is calculated.
save_at : string
Path (relative or absolute) in which to store the value.
Returns
-------
entropy : float
Entropy in eV / atom
Notes
-----
To convert to SI units, divide by units.J.
At the moment only vibrational entropy is included. Electronic entropy can
be included if the calculator provides the electronic DOS.
"""
if temperature is None and self.temperature is None:
print(
'ERROR. You nee to specify a temperature for the calculations.'
)
return
elif temperature is None:
temperature = self.temperature
if save_at is not None:
if not os.path.exists(save_at):
os.makedirs(save_at)
save_name = os.path.join(save_at, 'S.dat')
if isinstance(temperature, collections.Iterable):
vib_entropy = [
self.get_entropy(T, save_at=None) for T in temperature
]
if save_at is not None:
np.savetxt(save_name, vib_entropy)
return np.array(vib_entropy)
if temperature == 0.:
if save_at is not None:
np.savetxt(save_name, np.asarray([0.]))
return 0.
vib_entropy = self.thermo.get_entropy(temperature, self.verbosity)
if save_at is not None:
np.savetxt(save_name, vib_entropy)
return vib_entropy
def get_helmholtz_energy(self, temperature=None, save_at='.'):
"""Return Helmholtz energy per atom in eV / atom.
Parameters
----------
temperature : float > 0
Temeprature at which the Helmholtz energy is calculated.
save_at : string
Path (relative or absolute) in which to store the value.
Returns
-------
helmholtz_energy : float
Helmholtz energy in eV / atom
Notes
-----
To convert to SI units, divide by units.J.
"""
if temperature is None and self.temperature is None:
print(
'ERROR. You nee to specify a temperature for the calculations.'
)
return
elif temperature is None:
temperature = self.temperature
if save_at is not None:
if not os.path.exists(save_at):
os.makedirs(save_at)
save_name = os.path.join(save_at, 'F.dat')
if isinstance(temperature, collections.Iterable):
helmholtz_energy = [
self.get_helmholtz_energy(T, save_at=None) for T in temperature
]
if save_at is not None:
np.savetxt(save_name, helmholtz_energy)
return np.array(helmholtz_energy)
if temperature == 0.:
helmholtz_energy = self.get_zero_point_energy(
) + self.thermo.potentialenergy
if save_at is not None:
np.savetxt(save_name, helmholtz_energy)
return helmholtz_energy
helmholtz_energy = self.thermo.get_helmholtz_energy(
temperature, self.verbosity)
if save_at is not None:
np.savetxt(save_name, helmholtz_energy)
return helmholtz_energy
def get_internal_energy(self, temperature=None, save_at='.'):
"""Return internal energy per atom in eV / atom.
Parameters
----------
temperature : float > 0
Temeprature at which the internal energy is calculated.
save_at : string
Path (relative or absolute) in which to store the value.
Returns
-------
internal_energy : float
Internal energy in eV / atom
Notes
-----
To convert to SI units, divide by units.J.
"""
if temperature is None and self.temperature is None:
print(
'ERROR. You nee to specify a temperature for the calculations.'
)
return
elif temperature is None:
temperature = self.temperature
if save_at is not None:
if not os.path.exists(save_at):
os.makedirs(save_at)
save_name = os.path.join(save_at, 'U.dat')
if isinstance(temperature, collections.Iterable):
internal_energy = [
self.get_internal_energy(T, save_at=None) for T in temperature
]
if save_at is not None:
np.savetxt(save_name, internal_energy)
return np.array(internal_energy)
if temperature == 0.:
internal_energy = self.get_zero_point_energy(
) + self.thermo.potentialenergy
if save_at is not None:
np.savetxt(save_name, internal_energy)
return internal_energy
internal_energy = self.thermo.get_internal_energy(
temperature, self.verbosity)
if save_at is not None:
np.savetxt(save_name, internal_energy)
return internal_energy
def get_zero_point_energy(self):
"""Return the Zero Point Energy in eV / atom.
Returns
-------
zpe: float
Zero point energy in eV / atom.
"""
zpe_list = self.phonon_energy / 2.
zpe = np.trapz(zpe_list * self.phonon_dos,
self.phonon_energy) / self.n_atoms
return zpe
def get_specific_heat(self, temperature=None, save_at='.'):
"""Return heat capacity per atom in eV / atom K.
Parameters
----------
temperature : float > 0
Temeprature at which the specific heat is calculated.
save_at : string
Path (relative or absolute) in which to store the value.
Returns
-------
C_V : float
Specific heat in eV / atom K
Notes
-----
To convert to SI units, multiply by (units.mol / units.J).
"""
if temperature is None and self.temperature is None:
print(
'ERROR. You nee to specify a temperature for the calculations.'
)
return
elif temperature is None:
temperature = self.temperature
if save_at is not None:
if not os.path.exists(save_at):
os.makedirs(save_at)
save_name = os.path.join(save_at, 'Cv.dat')
if isinstance(temperature, collections.Iterable):
C_V = [
self.get_specific_heat(T, save_at=None) for T in temperature
]
if save_at is not None:
np.savetxt(save_name, C_V)
return np.array(C_V)
if temperature == 0.:
if save_at is not None:
np.savetxt(save_name, np.asarray([0.]))
return 0.
if self.phonon_energy[0] == 0.:
self.phonon_energy = np.delete(self.phonon_energy, 0)
self.phonon_dos = np.delete(self.phonon_dos, 0)
i2kT = 1. / (2. * units.kB * temperature)
arg = self.phonon_energy * i2kT
C_v = units.kB * arg**2 / np.sinh(arg)**2
C_V = np.trapz(C_v * self.phonon_dos,
self.phonon_energy) / self.n_atoms
if save_at is not None:
np.savetxt(save_name, np.asarray([C_V]))
return C_V
def get_thermal_expansion(self,
temperature=None,
exp_norm_temp=None,
nvolumes=5,
max_strain=0.02,
ntemperatures=5,
delta_t=1.,
save_at='.'):
"""Return the isotropic volumetric thermal expansion in K^-1.
Parameters
----------
temperature : float > 0
Temeprature at which the expansion coefficient is calculated.
exp_norm_temp : float > 0
Temperature for the normalization of the thermal expansion (usually to compare with experiment).
nvolumes : int > 0
Number of volumes to fit the equation of state to extract equilibrium volumes.
max_strain : float > 0
Maximum strain used to fit the equation of state to extract equilibrium volumes.
ntemperatures : int > 0
Number of temperatures to approximate the temperature derivative of the volume.
delta_t : float >0
Temperature step to approximate the temperature derivative of the volume.
save_at : string
Path (relative or absolute) in which to store the value.
Returns
-------
: double
Isotropic volumetric thermal expansion in K^-1
"""
if temperature is None and self.temperature is None:
print(
'ERROR. You nee to specify a temperature for the calculations.'
)
return
elif temperature is None:
temperature = self.temperature
if save_at is not None:
if not os.path.exists(save_at):
os.makedirs(save_at)
save_name = os.path.join(save_at, 'thermal_expansion.dat')
if isinstance(temperature, collections.Iterable):
alpha_v = [
self.get_thermal_expansion(T,
exp_norm_temp,
nvolumes,
max_strain,
ntemperatures,
delta_t,
save_at=None) for T in temperature
]
if save_at is not None:
np.savetxt(save_name, alpha_v)
return np.array(alpha_v)
max_delta_t = (ntemperatures - 1) * delta_t
if temperature - max_delta_t / 2. > 0.:
temperatures = np.linspace(temperature - max_delta_t / 2.,
temperature + max_delta_t / 2.,
ntemperatures)
t0 = (ntemperatures - 1) / 2
mode = 'c'
else:
ntemperatures = (ntemperatures + 2) / 2
temperatures = np.linspace(temperature,
temperature + max_delta_t / 2.,
ntemperatures)
t0 = 0
mode = 'f'
print(temperatures, ntemperatures)
# 1.- Get V-F points
Vs = []
Fs = []
for T in temperatures:
V, F = self.get_volume_energy(T, nvolumes, max_strain)
Vs.append(V)
Fs.append(F)
# 2.- Fit EOS to V-F points for each T
self.sjeos.clean()
for i in range(ntemperatures):
V = np.asarray(Vs[i])
F = np.asarray(Fs[i])
self.sjeos.fit(V, F)
# 3.- Numerical derivative dV/dT
V0s = self.sjeos.get_equilibrium_volume(mean=True)
fd = FD(temperatures)
dV_dT = fd.derivative(1, t0, V0s, acc_order=2, mode=mode)
if self.do_plotting:
plt.plot(temperatures, V0s)
# 4a.- Normalize by volume at temperature (same as derivative)
if exp_norm_temp is None:
return dV_dT / V0s[(ntemperatures - 1) / 2]
# 4b.- Normalize by volume at some give reference temperature (different from derivative)
V, F = self.get_volume_energy(exp_norm_temp, nvolumes, max_strain)
self.sjeos.clean()
self.sjeos.fit(np.asarray(V), np.asarray(F))
V_norm = self.sjeos.get_equilibrium_volume(mean=True)
alpha_v = dV_dT / V_norm
if save_at is not None:
np.savetxt(save_name, alpha_v)
return alpha_v
def get_gruneisen(self,
temperature=None,
nvolumes=5,
max_strain=0.02,
save_at='.'):
r"""Return the Gr\"uneisen parameter.
Parameters
----------
temperature : float > 0
Temeprature at which the expansion coefficient is calculated.
nvolumes : int > 0
Number of volumes to fit the equation of state to extract equilibrium volumes.
max_strain : float > 0
Maximum strain used to fit the equation of state to extract equilibrium volumes.
save_at : string
Path (relative or absolute) in which to store the value.
Returns
-------
gruneisen : double
Gr\"uneisen parameter.
Notes
-----
The Gr\"uneisen parameter is calculated as
.. math ::
\gamma=\frac{C_v}{V}\left.\frac{\partial S}{\partial V}\right|_T
"""
if temperature is None and self.temperature is None:
print(
'ERROR. You nee to specify a temperature for the calculations.'
)
return
elif temperature is None:
temperature = self.temperature
if save_at is not None:
if not os.path.exists(save_at):
os.makedirs(save_at)
save_name = os.path.join(save_at, 'gruneisen.dat')
if isinstance(temperature, collections.Iterable):
gruneisen = [
self.get_gruneisen(T, nvolumes, max_strain, save_at=None)
for T in temperature
]
if save_at is not None:
np.savetxt(save_name, gruneisen)
return gruneisen
self.get_volume_phonons(nvolumes, max_strain)
C_V = self.get_specific_heat(temperature)
V, F = self.get_volume_energy(temperature, nvolumes, max_strain)
self.sjeos.clean()
self.sjeos.fit(np.asarray(V), np.asarray(F))
V_0 = self.sjeos.get_equilibrium_volume(mean=True)[0]
V, S = self.get_volume_entropy(temperature, nvolumes, max_strain)
fd = FD(V)
dS_dV = fd.derivative(1, nvolumes / 2, S, acc_order=2, mode='c')
gruneisen = dS_dV * V_0 / C_V
"""
phonon_energy_mp = []
volumes = []
hw_V = [[] for i in range(len(self.phonon_energy_mp.ravel()))]
for sthermo in self.strained_thermo:
volumes.append(sthermo.atoms.get_volume())
phonon_energy_mp.append(sthermo.phonon_energy_mp.ravel())
for j, hw in enumerate(phonon_energy_mp[-1]):
hw_V[j].append(hw)
fd = FD(volumes)
gruneisen_i = np.empty_like(phonon_energy_mp[0])
for i, hw in enumerate(hw_V):
dhw_dV = fd.derivative(1, nvolumes/2, hw, acc_order=2, mode='c')
# print(dhw_dV, hw[nvolumes/2], dhw_dV * volumes[nvolumes/2] / hw[nvolumes/2])
gruneisen_i[i]\
= - dhw_dV * volumes[nvolumes/2] / hw[nvolumes/2]
self.hw_V = hw_V
self.volumes = volumes
i2kT = 1. / (2. * units.kB * temperature)
arg = phonon_energy_mp[nvolumes/2] * i2kT
C_v = units.kB * arg ** 2 / np.sinh(arg) ** 2
# print(C_V, C_v, gruneisen_i, volumes)
# gruneisen = np.trapz(C_v * gruneisen_i * self.phonon_dos, self.phonon_energy) / C_V
gruneisen = np.sum(C_v * gruneisen_i) / np.sum(C_v)
print(gruneisen, gruneisen_S)
plt.scatter(temperature, gruneisen, color='r')
plt.scatter(temperature, gruneisen_S, color='g')
"""
if save_at is not None:
np.savetxt(save_name, gruneisen)
return gruneisen
# High-symmetry points in the Brillouin zone
points = ibz_points['bcc']
G = points['Gamma']
H = points['H']
N = points['N']
P = points['P']
point_names = ['$\Gamma$', 'H', 'P', '$\Gamma$', 'N']
path = [G, H, P, G, N]
# Band structure in meV
path_kc, q, Q = bandpath(path, atoms.cell, 100)
omega_kn = 1000 * ph.band_structure(path_kc)
# Calculate phonon DOS
omega_e, dos_e = ph.dos(kpts=(50, 50, 50), npts=5000, delta=5e-4)
omega_e *= 1000
save_atoms(atoms, q, Q, omega_kn, point_names, dos_e, omega_e)
# Plot the band structure and DOS
# import matplotlib.pyplot as plt
# plt.figure(1, (8, 6))
# plt.axes([.1, .07, .67, .85])
# for n in range(len(omega_kn[0])):
# omega_n = omega_kn[:, n]
# plt.plot(q, omega_n, 'k-', lw=2)
#
# plt.xticks(Q, point_names, fontsize=18)
# plt.yticks(fontsize=18)
# plt.xlim(q[0], q[-1])
# plt.ylabel("Frequency ($\mathrm{meV}$)", fontsize=22)
# plt.grid('on')
from ase.optimize import QuasiNewton
from ase.phonons import Phonons
from ase.thermochemistry import CrystalThermo
# Set up gold bulk and attach EMT calculator
a = 4.078
atoms = crystal('Au', (0.,0.,0.),
spacegroup = 225,
cellpar = [a, a, a, 90, 90, 90],
pbc = (1, 1, 1))
calc = EMT()
atoms.set_calculator(calc)
qn = QuasiNewton(atoms)
qn.run(fmax = 0.05)
electronicenergy = atoms.get_potential_energy()
# Phonon analysis
N = 5
ph = Phonons(atoms, calc, supercell=(N, N, N), delta=0.05)
ph.run()
ph.read(acoustic=True)
phonon_energies, phonon_DOS = ph.dos(kpts=(40, 40, 40), npts=3000,
delta=5e-4)
# Calculate the Helmholtz free energy
thermo = CrystalThermo(phonon_energies=phonon_energies,
phonon_DOS = phonon_DOS,
electronicenergy = electronicenergy,
formula_units = 4)
F = thermo.get_helmholtz_energy(temperature=298.15)
vib = Vibrations(atoms,
name='harmonicthermo-vib',
indices=[atom.index for atom in atoms if atom.symbol != 'Cu'])
vib.run()
vib.summary()
vib_energies = vib.get_energies()
thermo = HarmonicThermo(vib_energies=vib_energies,
potentialenergy=atoms.get_potential_energy())
thermo.get_helmholtz_energy(temperature=298.15)
# Crystal thermo.
atoms = bulk('Al', 'fcc', a=4.05)
calc = EMT()
atoms.set_calculator(calc)
energy = atoms.get_potential_energy()
# Phonon calculator
N = 7
ph = Phonons(atoms, calc, supercell=(N, N, N), delta=0.05)
ph.run()
ph.read(acoustic=True)
phonon_energies, phonon_DOS = ph.dos(kpts=(4, 4, 4), npts=30, delta=5e-4)
thermo = CrystalThermo(phonon_energies=phonon_energies,
phonon_DOS=phonon_DOS,
potentialenergy=energy,
formula_units=4)
thermo.get_helmholtz_energy(temperature=298.15)
# High-symmetry points in the Brillouin zone
points = ibz_points['fcc']
G = points['Gamma']
X = points['X']
W = points['W']
K = points['K']
L = points['L']
U = points['U']
point_names = ['$\Gamma$', 'X', 'U', 'L', '$\Gamma$', 'K']
path = [G, X, U, L, G, K]
path_kc, q, Q = get_bandpath(path, atoms.cell, 100)
omega_kn = 1000 * ph.band_structure(path_kc)
# DOS
omega_e, dos_e = ph.dos(kpts=(50, 50, 50), npts=5000, delta=1e-4)
omega_e *= 1000
# Plot phonon dispersion
import matplotlib
#matplotlib.use('Agg')
import pylab as plt
plt.figure(1, (8, 6))
plt.axes([.1, .07, .67, .85])
for n in range(len(omega_kn[0])):
omega_n = omega_kn[:, n]
plt.plot(q, omega_n, 'k-', lw=2)
plt.xticks(Q, point_names, fontsize=18)
plt.yticks(fontsize=18)
indices=[atom.index for atom in atoms
if atom.symbol != 'Cu'])
vib.run()
vib.summary()
vib_energies = vib.get_energies()
thermo = HarmonicThermo(vib_energies=vib_energies,
potentialenergy=atoms.get_potential_energy())
thermo.get_helmholtz_energy(temperature=298.15)
# Crystal thermo.
atoms = bulk('Al', 'fcc', a=4.05)
calc = EMT()
atoms.set_calculator(calc)
energy = atoms.get_potential_energy()
# Phonon calculator
N = 7
ph = Phonons(atoms, calc, supercell=(N, N, N), delta=0.05)
ph.run()
ph.read(acoustic=True)
phonon_energies, phonon_DOS = ph.dos(kpts=(4, 4, 4), npts=30,
delta=5e-4)
thermo = CrystalThermo(phonon_energies=phonon_energies,
phonon_DOS=phonon_DOS,
potentialenergy=energy,
formula_units=4)
thermo.get_helmholtz_energy(temperature=298.15)
