def getEamValues(p):
mol = read('res_POSCAR_1.0.traj')
calc = get_calc(p)
mol.set_calculator(calc)
forces = mol.get_forces()
energy = [mol.get_potential_energy()]
eps = 0.02
energies = []
lattice = []
initialLattice = mol.get_cell()[0, 0]
for scale in np.linspace(1 - eps, 1 + eps, 3):
mol.set_cell(3 * [initialLattice * scale], scale_atoms=True)
energies = energies + [mol.get_potential_energy()]
lattice = lattice + [[initialLattice * scale / 3.0]]
lattice = np.array(lattice)
energies = np.array(energies)
functions = np.array([lattice**0, lattice, lattice**2])
polyfit = np.linalg.lstsq(functions.T[0], energies)[0]
derivative = [polyfit[1], 2 * polyfit[2]]
a0 = np.linalg.solve([derivative[1]], [-derivative[0]])
forces = forces.reshape(1, forces.size)
print(a0)
print(energy)
ret = np.concatenate((a0, energy, forces), 1)
return (ret)
def calc_lattice_parameter_al(al_bulk, A, lmbd, D, mu2):
q = 0.03
n_points = 14
calc = get_calc((A, lmbd, D, mu2))
# # # Find lattice constant with lowest energy # # #
cell_0 = al_bulk.cell # Unit cell object of the Al bulk
al_bulk.set_calculator(calc)
energies = []
volumes = []
for eps in np.linspace(-q, q, n_points):
al_bulk.cell = (1 + eps) * cell_0 # Adjust lattice constant of unit cell
# Calculate the potential energy for the Al bulk
energies.append(al_bulk.get_potential_energy())
volumes.append(al_bulk.get_volume())
# Plot energies as a function of unit cell volume (directly related to latt. const.)
eos = EquationOfState(volumes, energies)
v0, E, B = eos.fit()
# Latt. const. acc. to ASE doc., but why is this correct?
a_calc = (4 * v0)**(1 / 3.0)
al_bulk.cell = cell_0
print('Lattice_parameter:', a_calc)
return a_calc
def calc_lattice_parameter(al_bulk_ASE, A, lmbd, D, mu2):
q = 0.2
n_points = 15
calc = get_calc((A, lmbd, D, mu2))
# # # Find lattice constant with lowest energy # # #
cell_0 = al_bulk_ASE.get_cell() # Unit cell object of the Al bulk
al_bulk_ASE.set_calculator(calc)
energies = []
volumes = []
for eps in np.linspace(-q, q, n_points):
al_bulk_ASE.set_cell(
(1 + eps) * cell_0) # Adjust lattice constant of unit cell
# Calculate the potential energy for the Al bulk
energies.append(al_bulk_ASE.get_potential_energy())
volumes.append(al_bulk_ASE.get_volume())
#plt.plot(np.asarray(volumes)**(1 / 3), energies)
# plt.show()
# Plot energies as a function of unit cell volume (directly related to latt. const.)
eos = EquationOfState(volumes, energies)
v0, E, B = eos.fit()
# Latt. const. acc. to ASE doc., but why is this correct?
a_calc = v0**(1 / 3.0)
print('a=' + str(a_calc))
al_bulk_ASE.set_cell(cell_0)
return a_calc
def calc_lattice_parameter_al(atom_set, A, lmbd, D, mu2):
global n_sets, cells
q = 0.2
n_points = 10
lattice_param_set = np.zeros(n_sets)
calc = get_calc((A, lmbd, D, mu2))
for index, atoms in enumerate(atom_set):
# # # Find lattice constant with lowest energy # # #
cell_0 = atoms.cells[index] # Unit cell object of the Al bulk
atoms.set_calculator(calc)
energies = []
volumes = []
inval = np.linspace(-q, q, n_points)
for eps in inval:
atoms.cell = (1 + eps) * cell_0 # Adjust lattice constant of unit cell
# Calculate the potential energy for the Al bulk
energies.append(atoms.get_potential_energy())
volumes.append(atoms.get_volume())
# Plot energies as a function of unit cell volume (directly related to latt. const.)
eos = EquationOfState(volumes, energies)
v0, E, B = eos.fit()
# Latt. const. acc. to ASE doc., but why is this correct?
a_calc = v0**(1 / 3.0)
n_min = np.argmin(energies)
atoms.cell = (1 + inval[n_min]) * cell_0
lattice_param_set[index] = a_calc
return lattice_param_set
def calc_forces_al(atoms_set, A, lmbd, D, mu2):
forces = []
calc = get_calc((A, lmbd, D, mu2))
for atoms in atoms_set:
atoms.set_calculator(calc)
forces_tmp = atoms.get_forces()
forces = np.hstack([forces, forces_tmp[:, 0], forces_tmp[:, 1], forces_tmp[:, 2]])
return forces
def calc_cohesive_energy_al(atom_set, A, lmbd, D, mu2):
global n_sets
energy_set = np.zeros(n_sets)
calc = get_calc((A, lmbd, D, mu2))
for index, atoms in enumerate(atom_set):
atoms.set_calculator(calc)
energy_set[index] = atoms.get_potential_energy()
return energy_set
def calc_forces(data_input_forces, A, lmbd, D, mu2):
calc = get_calc((A, lmbd, D, mu2))
forces = []
for atoms in data_input_forces:
atoms.set_calculator(calc)
forces_mat = atoms.get_forces()
forces = np.hstack(
[forces, forces_mat[:, 0], forces_mat[:, 1], forces_mat[:, 2]])
return forces
def calc_lattice_parameter(al_bulk_ASE, A, lmbd, D, mu2):
calc = get_calc((A, lmbd, D, mu2))
eps = 0.001
energies = []
volumes = []
al_bulk_ASE.set_calculator(calc)
# # # Find lattice constant with lowest energy # # #
cell_0 = al_bulk_ASE.get_cell() # Unit cell object of the Al bulk
# DIRECTION
cell_orig = cell_0
E1 = al_bulk_ASE.get_potential_energy()
al_bulk_ASE.set_cell((1 + eps) * cell_0)
E2 = al_bulk_ASE.get_potential_energy()
direction = (E2 - E1) / abs((E2 - E1))
print('Direction', direction)
# Go one step in the right
al_bulk_ASE.set_cell(cell_orig)
energies.append(al_bulk_ASE.get_potential_energy())
volumes.append(al_bulk_ASE.get_volume())
cell_0 = al_bulk_ASE.get_cell()
al_bulk_ASE.set_cell(
(1 - direction * eps) * cell_0) # Adjust lattice constant of unit cell
energies.append(al_bulk_ASE.get_potential_energy())
volumes.append(al_bulk_ASE.get_volume())
# Go two steps back
while (energies[-1] - energies[-2]) < 0:
cell_0 = al_bulk_ASE.get_cell()
# Adjust lattice constant of unit cell
al_bulk_ASE.set_cell((1 - direction * eps) * cell_0)
# Calculate the potential energy for the Al bulk
energies.append(al_bulk_ASE.get_potential_energy())
volumes.append(al_bulk_ASE.get_volume())
cell_0 = al_bulk_ASE.get_cell()
al_bulk_ASE.set_cell(
(1 - direction * eps) * cell_0) # Adjust lattice constant of unit cell
# Calculate the potential energy for the Al bulk
energies.append(al_bulk_ASE.get_potential_energy())
volumes.append(al_bulk_ASE.get_volume())
# plt.plot((4 * np.asarray(volumes))**(1 / 3), energies)
# plt.show()
# Plot energies as a function of unit cell volume (directly related to latt. const.)
eos = EquationOfState(volumes, energies)
v0, E, B = eos.fit()
# Latt. const. acc. to ASE doc., but why is this correct?
print('asdasdasdasdasd: ', E)
a_calc = (4 * v0)**(1 / 3.0)
# a_calc = v0**(1 / 3.0)
print('a=' + str(a_calc))
al_bulk_ASE.set_cell(cell_0)
return a_calc
def calc_cohesive_energy(al_bulk_ASE, A, lmbd, D, mu2):
calc = get_calc((A, lmbd, D, mu2))
al_bulk_ASE.set_calculator(calc)
energy = al_bulk_ASE.get_potential_energy()
print('Cohesive energy: ', energy)
return energy
def calc_cohesive_energy_al(al_bulk, A, lmbd, D, mu2):
calc = get_calc((A, lmbd, D, mu2))
al_bulk.set_calculator(calc)
energy = al_bulk.get_potential_energy()
return energy
A = 2011
lmbda = 3.21
D = 5.29
mu = 0.93/2
p = (A, lmbda, D, 2*mu)
dE1m2 = []
dE4 = []
dE1p2 = []
e = []
for deformation in (0.2,0.1,0.001):
mol = read('res_POSCAR_1.0.traj')
# mol = bulk('Al','fcc',a = latticeParam)
calc = get_calc(p)
mol.set_calculator(calc)
preEnergy = mol.get_potential_energy()
preVolume = mol.get_volume()
strain_change1m2 = np.array(((deformation, 0, 0),(0,-deformation, 0),(0,0,deformation**2/(1-deformation**2))))
strain_change4 = np.array(((0,0.5*deformation, 0),(0.5*deformation,0, 0),(0,0,deformation**2/(4-deformation**2))))
strain_change1p2 = np.array(((deformation, 0, 0),(0,deformation, 0),(0,0,0)))
strain1m2 = np.identity(3) + strain_change1m2
strain4 = np.identity(3) + strain_change4
strain1p2 = np.identity(3) + strain_change1p2
preCell = mol.get_cell()
def calc_cohesive_energy(al_bulk_ASE, A, lmbd, D, mu2):
calc = get_calc((A, lmbd, D, mu2))
al_bulk_ASE.set_calculator(calc)
return al_bulk_ASE.get_potential_energy()
def main():
''' Read in parameters for EAM calc '''
with open('HA4/results/fit_potential_output_full.txt', 'r') as textfile:
line = next(textfile)
line = line.split(',')
A = float(line[0])
lmbd = float(line[1])
D = float(line[2])
mu2 = float(line[3])
path_BCC = 'HA4/downloads/Al-EV-curves/BCC.dat'
a0_BCC, V_BCC, E_BCC, scale_factors = read_data(path_BCC)
path_DI = 'HA4/downloads/Al-EV-curves/DIAMOND.dat'
a0_DI, V_DI, E_DI, scale_factors = read_data(path_DI)
path_FCC = 'HA4/downloads/Al-EV-curves/FCC.dat'
a0_FCC, V_FCC, E_FCC, scale_factors = read_data(path_FCC)
a0_FCC_experimental = 4.032
E0_FCC_experimental = -3.36
path_SC = 'HA4/downloads/Al-EV-curves/SC.dat'
a0_SC, V_SC, E_SC, scale_factors = read_data(path_SC)
al_bulk_BCC = bulk('Al', 'bcc', a=a0_BCC)
al_bulk_DI = bulk('Al', 'diamond', a=a0_DI)
al_bulk_FCC = bulk('Al', 'fcc', a=a0_FCC)
al_bulk_SC = bulk('Al', 'sc', a=a0_SC)
calc = get_calc((A, lmbd, D, mu2))
al_bulk_BCC.set_calculator(calc)
al_bulk_DI.set_calculator(calc)
al_bulk_FCC.set_calculator(calc)
al_bulk_SC.set_calculator(calc)
V_BCC_sim, V_DI_sim, V_FCC_sim, V_SC_sim = [], [], [], []
E_BCC_sim, E_DI_sim, E_FCC_sim, E_SC_sim = [], [], [], []
for scale_factor in scale_factors:
cell_0 = al_bulk_BCC.get_cell()
al_bulk_BCC.set_cell(cell_0 * scale_factor)
E_BCC_sim.append(al_bulk_BCC.get_potential_energy())
V_BCC_sim.append(2 * al_bulk_BCC.get_volume())
al_bulk_BCC.set_cell(cell_0)
cell_0 = al_bulk_DI.get_cell()
al_bulk_DI.set_cell(cell_0 * scale_factor)
E_DI_sim.append(al_bulk_DI.get_potential_energy())
V_DI_sim.append(4 * al_bulk_DI.get_volume())
al_bulk_DI.set_cell(cell_0)
cell_0 = al_bulk_FCC.get_cell()
al_bulk_FCC.set_cell(cell_0 * scale_factor)
E_FCC_sim.append(al_bulk_FCC.get_potential_energy())
V_FCC_sim.append(4 * al_bulk_FCC.get_volume())
al_bulk_FCC.set_cell(cell_0)
cell_0 = al_bulk_SC.get_cell()
al_bulk_SC.set_cell(cell_0 * scale_factor)
E_SC_sim.append(al_bulk_SC.get_potential_energy())
V_SC_sim.append(1 * al_bulk_SC.get_volume())
al_bulk_SC.set_cell(cell_0)
fig = plt.figure(1, figsize=(7.1, 7.1))
ax_BCC = fig.add_subplot(221)
ax_BCC.plot(V_BCC, E_BCC, label='DFT', color='blue')
ax_BCC.plot(V_BCC_sim, E_BCC_sim, label='EAM', color='red')
ax_BCC.set_title('BCC unit cell')
ax_BCC.minorticks_on()
ax_BCC.grid(True, which='minor', linestyle='--')
ax_BCC.grid(True, which='major', linestyle='-')
ax_BCC.set_xlim(V_BCC[0], V_BCC[-1])
ax_BCC.legend()
ax_DI = fig.add_subplot(222)
ax_DI.plot(V_DI, E_DI, label='DFT', color='blue')
ax_DI.plot(V_DI_sim, E_DI_sim, label='EAM', color='red')
ax_DI.set_title('Diamond unit cell')
ax_DI.minorticks_on()
ax_DI.grid(True, which='minor', linestyle='--')
ax_DI.grid(True, which='major', linestyle='-')
ax_DI.set_xlim(V_DI[0], V_DI[-1])
ax_DI.legend()
ax_FCC = fig.add_subplot(223)
ax_FCC.plot(V_FCC, E_FCC, label='DFT', color='blue')
ax_FCC.plot(V_FCC_sim, E_FCC_sim, label='EAM', color='red')
ax_FCC.plot(a0_FCC_experimental**3,
E0_FCC_experimental,
marker='*',
color='black')
ax_FCC.set_title('FCC unit cell')
ax_FCC.minorticks_on()
ax_FCC.grid(True, which='minor', linestyle='--')
ax_FCC.grid(True, which='major', linestyle='-')
ax_FCC.set_xlim(V_FCC[0], V_FCC[-1])
ax_FCC.legend()
ax_SC = fig.add_subplot(224)
ax_SC.plot(V_SC, E_SC, label='DFT', color='blue')
ax_SC.plot(V_SC_sim, E_SC_sim, label='EAM', color='red')
ax_SC.set_title('SC unit cell')
ax_SC.minorticks_on()
ax_SC.grid(True, which='minor', linestyle='--')
ax_SC.grid(True, which='major', linestyle='-')
ax_SC.set_xlim(V_SC[0], V_SC[-1])
ax_SC.legend()
fig.subplots_adjust(left=None,
bottom=None,
right=None,
top=None,
wspace=None,
hspace=0.25)
fig.text(0.5, 0.03, 'Volume [Å^3]', ha='center', fontsize=16)
fig.text(0.03,
0.5,
'Energy [eV]',
va='center',
rotation='vertical',
fontsize=16)
fig.savefig("HA4/results/EV_curves.png", bbox_inches='tight')
with open('HA4/results/EV_FCC.txt', 'w') as textfile:
text = 'Volume, Enegy DFT, Energy EAM ' + '\n'
for i in range(len(V_FCC)):
text = text + str(V_FCC[i]) + ',' + str(E_FCC[i]) + ',' + str(
E_FCC_sim[i]) + '\n'
text = text[:-1]
textfile.write(text)
plt.show()
def main():
''' Read in parameters for EAM calc '''
with open('HA4/results/fit_potential_output_full.txt', 'r') as textfile:
line = next(textfile)
line = line.split(',')
A = float(line[0])
lmbd = float(line[1])
D = float(line[2])
mu2 = float(line[3])
# with open('HAlea')
# ''' Optimization parameters '''
# A = 1000 # eV
# lmbd = 3 # Å^(-1)
# D = 5 # Å
# mu2 = 1 # 2 # Å^(-1)
# param_0 = [A, lmbd, D, mu2]
''' Strains and stuff '''
eV_to_J = 1.60217662 * 10**(-19)
angstrom_to_meter = 1e-10
calc = get_calc((A, lmbd, D, mu2))
# calc = EMT()
e1 = 0.01
e6 = 0.01
energies = []
C11_vec = []
C12_vec = []
B_vec = []
x = np.linspace(0, 0.5, 100)
for i in x:
e1 = i
e6 = i
# C11-C12
al_bulk = bulk('Al', 'fcc', a=4.032, cubic=True)
al_bulk.set_calculator(calc)
ep_mat_1 = np.array([[e1, 0, 0], [0, -e1, 0],
[0, 0, e1**2 / (1 - e1**2)]])
energies.append(al_bulk.get_potential_energy())
cell_0 = al_bulk.get_cell()
# al_bulk.set_cell(np.dot((np.eye(3) + ep_mat_1), np.transpose(cell_0)))
al_bulk.set_cell(np.dot((np.eye(3) + ep_mat_1),
cell_0)) # Yields same result
energies.append(al_bulk.get_potential_energy())
# print(cell_0 / al_bulk.get_cell())
# print(cell_0)
# print(al_bulk.get_cell())
V = al_bulk.get_volume() #4 * al_bulk.get_volume()
delta_E = energies[-1] - energies[0]
C11_minus_C12 = delta_E / (V * e1**2)
# print('Hola', C11_minus_C12 * eV_to_J / (angstrom_to_meter**3 * 1e9))
# C11+C12
al_bulk = bulk('Al', 'fcc', a=4.032, cubic=True)
al_bulk.set_calculator(calc)
e2 = e1
ep_mat_12 = np.array([[e1, 0, 0], [0, e2, 0], [0, 0, 0]])
energies.append(al_bulk.get_potential_energy())
V = al_bulk.get_volume(
) #4 * al_bulk.get_volume() # Equilibrium cell volume
cell_0 = al_bulk.get_cell()
al_bulk.set_cell(np.dot((np.eye(3) + ep_mat_12), cell_0))
energies.append(al_bulk.get_potential_energy())
delta_E = energies[-1] - energies[0]
C11_plus_C12 = delta_E / (V * e1**2)
# print(C11_plus_C12)
# C11 and C12
C11 = (C11_minus_C12 + C11_plus_C12) / 2
C12 = C11_plus_C12 - C11
C11_vec.append(C11 * eV_to_J / (angstrom_to_meter**3 * 1e9))
C12_vec.append(C12 * eV_to_J / (angstrom_to_meter**3 * 1e9))
B_vec.append(
((C11 + 2 * C12) / 3) * eV_to_J / (angstrom_to_meter**3 * 1e9))
plt.figure()
plt.plot(x, C11_vec)
plt.plot(x, C12_vec)
plt.plot(x, B_vec)
plt.set_xlabel(
r'Displacement factor $\varepsilon_1 = \varepsilon_2 \varepsilon_6 $')
plt.set_ylabel('Elastic constants/Bulk modulus [GPa]')
plt.show()
# C44
al_bulk = bulk('Al', 'fcc', a=4.032, cubic=True)
al_bulk.set_calculator(calc)
cell_0 = al_bulk.get_cell()
ep_mat_6 = np.array([[0, 0.5 * e6, 0], [0.5 * e6, 0, 0],
[0, 0, e6**2 / (4 - e6**2)]])
al_bulk.set_cell(np.dot((np.eye(3) + ep_mat_6), cell_0))
energies.append(al_bulk.get_potential_energy())
V = 4 * al_bulk.get_volume()
delta_E = energies[-1] - energies[0]
C44 = 2 * delta_E / (V * e6**2)
# print(C44)
B = (C11 + 2 * C12) / 3
# print('C11: ', C11 * eV_to_J / (angstrom_to_meter**3 * 1e9))
# print('C12: ', C12 * eV_to_J / (angstrom_to_meter**3 * 1e9))
B_SI = B * eV_to_J / (angstrom_to_meter)**3
B_GPa = B_SI / 1e9
# print('B', B_GPa)
c_prim = (C11 * C12) / 2
''' Phonon calculator '''
al_bulk = bulk('Al', 'fcc', a=4.032)
N = 7
ph = Phonons(al_bulk, calc, supercell=(N, N, N), delta=0.05)
ph.run()
# Read forces and assemble the dynamical matrix
ph.read(acoustic=True, banana=True)
# High-symmetry points in the Brillouin zone
points = ibz_points['fcc']
G = points['Gamma']
X = points['X']
W = points['W']
K = points['K']
L = points['L']
U = points['U']
point_names = ['$\Gamma$', 'X', 'U', 'L', '$\Gamma$', 'K']
path = [G, X, U, L, G, K]
# Band structure in meV
path_kc, q, Q = bandpath(path, al_bulk.cell, 100)
omega_kn = 1000 * ph.band_structure(path_kc)
# # Check band path
# fig = plt.figure()
# ax = fig.add_subplot(111, projection='3d')
# ax.plot(path_kc[:,0], path_kc[:,1], path_kc[:,2])
# plt.show()
# Calculate phonon DOS
# omega_e, dos_e = ph.dos(kpts=(50, 50, 50), npts=5000, delta=5e-4)
# omega_e *= 1000
#
# # Plot the band structure and DOS
# plt.figure(1, (8, 6))
# plt.axes([.1, .07, .67, .85])
# for n in range(len(omega_kn[0])):
# omega_n = omega_kn[:, n]
# plt.plot(q, omega_n, 'k-', lw=2)
#
# plt.xticks(Q, point_names, fontsize=18)
# plt.yticks(fontsize=18)
# plt.xlim(q[0], q[-1])
# plt.ylabel("Frequency ($\mathrm{meV}$)", fontsize=22)
# plt.grid('on')
#
# plt.axes([.8, .07, .17, .85])
# plt.fill_between(dos_e, omega_e, y2=0, color='lightgrey', edgecolor='k', lw=1)
# plt.ylim(0, 35)
# plt.xticks([], [])
# plt.yticks([], [])
# plt.xlabel("DOS", fontsize=18)
# plt.show()
''' Sound velocity '''
# point_names = ['$\Gamma$', 'X']
path_100 = [G, X]
# Band structure in meV
# Return list of k-points, list of x-coordinates and list of x-coordinates of special points.
path_kc_100, q_100, Q_100 = bandpath(path_100, al_bulk.cell, 100)
omega_kn_100 = 1000 * ph.band_structure(path_kc_100)
# # Find the longitudinal curve (the one that is not initially overlapping)
# print(omega_kn_100[0:10,0])
# print(omega_kn_100[0:10,1])
# print(omega_kn_100[0:10,2]) # <-- This one!
k = np.sqrt(path_kc_100[:, 0]**2 + path_kc_100[:, 1]**2 +
path_kc_100[:, 2]**2) # [Å^-1]
convert_meV_to_1_over_s = (1 / 1000) * (1 / (6.582119514 * 10**(-16)))
# print(omega_kn_100[1,2])
omega_long_at_q_to_0 = omega_kn_100[1, 2] * convert_meV_to_1_over_s
# omega_long_at_q_to_1 = omega_kn_100[2,2] * convert_meV_to_1_over_s
c_s = omega_long_at_q_to_0 * 10**(-10) / k[1] # Speed of sound, [m/s]
# c_s = 10**(-10) * ((omega_long_at_q_to_1 - omega_long_at_q_to_0) / (k[2] - k[1])) # Speed of sound, [m/s]
print(c_s)
#
# convert_u_to_kg = 1.66054 * 10**(-27)
# convert_kg_to_eV_c2 = (2.99792 * 10**8)**2
# m_Al = al_bulk.get_masses()[0] * convert_u_to_kg * convert_kg_to_eV_c2 # [eV * (s^2/m^2)]
# nbr_of_atoms_UC = 4 # Number of atoms per unit cell for fcc
# V_Al = nbr_of_atoms_UC * al_bulk.get_volume() # [Å^3]
# rho_Al = m_Al * nbr_of_atoms_UC / V_Al # [eV * (s^2/m^2) / Å^3]
# young = c_s**2 * rho_Al
#
# print(C11)
# print(young)
plt.figure()
plt.plot(q_100, omega_kn_100)
plt.show()