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)
) #__| #| - Phonon Calculation from ase.phonons import Phonons ph = Phonons(new_atoms, calc, supercell=(1, 1, 1)) #ph.run() ph.read(method='frederiksen', acoustic=True) phonon_energies, phonon_DOS = ph.dos(kpts=(40, 40, 40), npts=3000, delta=5e-4) # Calculate the Helmholtz free energy potentialenergy = 0.0 from ase.thermochemistry import CrystalThermo thermo = CrystalThermo(phonon_energies=phonon_energies, phonon_DOS=phonon_DOS, potentialenergy=potentialenergy, formula_units=1) F = thermo.get_helmholtz_energy(temperature=298.15) #dyn = QuasiNewton(atoms, logfile=name+'.log', trajectory=name+'.traj') #dyn.run(fmax=0.05) io.write('final.traj', new_atoms) #__| #| - __old__ # from ase.lattice.spacegroup import crystal # from ase.io import * # # from sys import path
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)
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
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)