File size: 11,935 Bytes
f614769 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 | import matplotlib.pyplot as plt
import numpy as np
from ase import Atoms
from ase.geometry.analysis import Analysis
from ase.optimize import FIRE
from ase.units import GPa ## 1 GPa = 1 / 160.21766208 eV/ų.
from scipy.stats import linregress
import matplotlib.pyplot as plt
import pandas as pd
def minimize_structure(atoms, fmax=0.05, steps=50):
"""
Perform energy minimization on the given ASE Atoms object using the FIRE optimizer.
Parameters:
atoms (ase.Atoms): The Atoms object to be minimized.
fmax (float): The maximum force tolerance for the optimization (default: 0.01 eV/Å).
steps (int): The maximum number of optimization steps (default: 1000).
Returns:
ase.Atoms: The minimized Atoms object.
"""
dyn = FIRE(atoms, trajectory=None)
dyn.run(fmax=fmax, steps=steps)
return atoms
def min_height(cell_matrix):
"""
Calculate the perpendicular heights in three directions given a 3x3 cell matrix.
"""
a, b, c = cell_matrix[:, 0], cell_matrix[:, 1], cell_matrix[:, 2]
volume = abs(np.dot(a, np.cross(b, c)))
# Calculate the cross products
a_cross_b, b_cross_c, c_cross_a = (
np.linalg.norm(np.cross(a, b)),
np.linalg.norm(np.cross(b, c)),
np.linalg.norm(np.cross(c, a)),
)
# Calculate the perpendicular heights
height_a, height_b, height_c = (
abs(volume / a_cross_b),
abs(volume / b_cross_c),
abs(volume / c_cross_a),
)
return min(height_a, height_b, height_c)
def perturb_config(atoms, displacement_std=0.01):
# Create a new Atoms object with the perturbed positions
positions = atoms.get_positions()
displacements = np.random.normal(scale=displacement_std, size=positions.shape)
new_positions = positions + displacements
new_perturbed_atoms = atoms.copy()
new_perturbed_atoms.set_positions(new_positions)
return new_perturbed_atoms
def plot_pair_rdfs(Pair_rdfs, shift=0):
counter = 0
plt.figure()
for key in Pair_rdfs.keys():
plt.plot(Pair_rdfs[key][0], Pair_rdfs[key][1] + shift * counter, label=key)
counter += 1
plt.legend(loc=(1.2, 0))
plt.xlabel("r (Angstrom)")
plt.ylabel("g(r)")
plt.show()
def replicate_system(atoms: Atoms, replicate_factors: np.ndarray) -> Atoms:
"""
Replicates the given ASE Atoms object according to the specified replication factors.
"""
nx, ny, nz = replicate_factors
original_cell = atoms.get_cell()
original_positions = (
atoms.get_scaled_positions() @ original_cell
) # Scaled or Unscaled ?
original_numbers = atoms.get_atomic_numbers()
x_cell, y_cell, z_cell = original_cell[0], original_cell[1], original_cell[2]
new_numbers = []
for i in range(nx):
for j in range(ny):
for k in range(nz):
new_numbers += [original_numbers]
pos_after_x = np.concatenate([original_positions + i * x_cell for i in range(nx)])
pos_after_y = np.concatenate([pos_after_x + i * y_cell for i in range(ny)])
pos_after_z = np.concatenate([pos_after_y + i * z_cell for i in range(nz)])
new_cell = [nx * original_cell[0], ny * original_cell[1], nz * original_cell[2]]
new_atoms = Atoms(
numbers=np.concatenate(new_numbers),
positions=pos_after_z,
cell=new_cell,
pbc=atoms.get_pbc(),
)
new_atoms.calc = atoms.calc
return new_atoms
def write_xyz(Filepath, atoms):
"""Writes ovito xyz file"""
R = atoms.get_position()
species = atoms.get_atomic_numbers()
cell = atoms.get_cell()
f = open(Filepath, "w")
f.write(str(R.shape[0]) + "\n")
flat_cell = cell.flatten()
f.write(
f'Lattice="{flat_cell[0]} {flat_cell[1]} {flat_cell[2]} {flat_cell[3]} {flat_cell[4]} {flat_cell[5]} {flat_cell[6]} {flat_cell[7]} {flat_cell[8]}" Properties=species:S:1:pos:R:3 Time=0.0'
)
for i in range(R.shape[0]):
f.write(
"\n"
+ str(species[i])
+ "\t"
+ str(R[i, 0])
+ "\t"
+ str(R[i, 1])
+ "\t"
+ str(R[i, 2])
)
def symmetricize_replicate(curr_atoms: int, max_atoms: int, box_lengths: np.ndarray):
replication = [1, 1, 1]
atom_count = curr_atoms
lengths = box_lengths
while atom_count < (max_atoms // 2):
direction = np.argmin(box_lengths)
replication[direction] += 1
lengths[direction] = box_lengths[direction] * replication[direction]
atom_count = curr_atoms * replication[0] * replication[1] * replication[2]
return replication, atom_count
def get_pairs(atoms):
Atom_types = np.unique(atoms.get_chemical_symbols())
Pairs = []
for i in range(len(Atom_types)):
for j in range(i, len(Atom_types)):
Pairs += [[Atom_types[i], Atom_types[j]]]
return Pairs
def getfirstpeaklength(r, rdf, r_max=6.0):
bin_size = (r[-1] - r[0]) / len(r)
cut_index = int(r_max / bin_size)
cut_index = min(cut_index, len(r))
Peak_index = np.argmax(rdf[:cut_index])
# Returns : Peak index and Bond length
return Peak_index, r[Peak_index]
def get_partial_rdfs(Traj, r_max=6.0, dr=0.01):
rmax = min(r_max, min_height(Traj[0].get_cell()) / 2.7)
analysis = Analysis(Traj)
dr = dr
nbins = int(rmax / dr)
pairs_list = get_pairs(Traj[0])
Pair_rdfs = dict()
for pair in pairs_list:
rdf = analysis.get_rdf(
rmax=rmax, nbins=nbins, imageIdx=None, elements=pair, return_dists=True
)
x = rdf[0][1]
y = np.array([rdf[k][0] for k in range(len(rdf))]).mean(axis=0)
Pair_rdfs["-".join(pair)] = [x, y]
return Pair_rdfs
def get_partial_rdfs_smoothened(
inp_atoms, perturb=10, noise_std=0.01, max_atoms=300, r_max=6.0, dr=0.01
):
atoms = inp_atoms.copy()
replication_factors, _ = symmetricize_replicate(
len(atoms),
max_atoms=max_atoms,
box_lengths=atoms.get_cell_lengths_and_angles()[:3],
)
atoms = replicate_system(atoms, replication_factors)
Traj = [perturb_config(atoms, noise_std) for k in range(perturb)]
return get_partial_rdfs(Traj, r_max=r_max, dr=dr)
def get_bond_lengths_noise(
inp_atoms, perturb=10, noise_std=0.01, max_atoms=300, r_max=6.0, dr=0.01
):
Pair_rdfs = get_partial_rdfs_smoothened(
inp_atoms,
perturb=perturb,
noise_std=noise_std,
max_atoms=max_atoms,
r_max=r_max,
dr=dr,
)
Bond_lengths = dict()
for key in Pair_rdfs:
r, rdf = Pair_rdfs[key]
Bond_lengths[key] = getfirstpeaklength(r, rdf)[1]
return Bond_lengths, Pair_rdfs
def get_bond_lengths_TrajAvg(Traj, r_max=6.0, dr=0.01):
Pair_rdfs = get_partial_rdfs(Traj, r_max=r_max, dr=dr)
Bond_lengths = dict()
for key in Pair_rdfs:
r, rdf = Pair_rdfs[key]
Bond_lengths[key] = getfirstpeaklength(r, rdf)[1]
return Bond_lengths, Pair_rdfs
def get_initial_rdf(
inp_atoms,
perturb=10,
noise_std=0.01,
max_atoms=300,
replicate=False,
Structid=0,
r_max=6.0,
dr=0.01,
):
atoms = inp_atoms.copy()
# write_xyz(f"StabilityXYZData2/{Structid}.xyz",atoms.get_positions(),atoms.get_chemical_symbols(),atoms.get_cell())
if replicate:
replication_factors, size = symmetricize_replicate(
len(atoms),
max_atoms=max_atoms,
box_lengths=atoms.get_cell_lengths_and_angles()[:3],
)
atoms = replicate_system(atoms, replication_factors)
rmax = min(r_max, min_height(atoms.get_cell()) / 2.7)
# atoms.rattle(0.01)
analysis = Analysis([perturb_config(atoms, noise_std) for k in range(perturb)])
# write_xyz(f"StabilityXYZDataReplicated2/{Structid}.xyz",atoms.get_positions(),atoms.get_chemical_symbols(),atoms.get_cell())
dr = dr
nbins = int(rmax / dr)
rdf = analysis.get_rdf(
rmax=rmax, nbins=nbins, imageIdx=None, elements=None, return_dists=True
)
x = rdf[0][1]
y = np.array([rdf[k][0] for k in range(len(rdf))]).mean(axis=0)
return x, y
def get_rdf(Traj, r_max=6.0, dr=0.01):
rmax = min(r_max, min_height(Traj[0].get_cell()) / 2.7)
analysis = Analysis(Traj)
dr = dr
nbins = int(rmax / dr)
rdf = analysis.get_rdf(
rmax=rmax, nbins=nbins, imageIdx=None, elements=None, return_dists=True
)
x = rdf[0][1]
y = np.array([rdf[k][0] for k in range(len(rdf))]).mean(axis=0)
return x, y
def get_density(atoms: Atoms) -> float:
amu_to_grams = 1.66053906660e-24 # 1 amu = 1.66053906660e-24 grams
angstrom_to_cm = 1e-8 # 1 Å = 1e-8 cm
mass_amu = atoms.get_masses().sum()
mass_g = (
mass_amu * amu_to_grams
) # Get the volume of the atoms object in cubic angstroms (ų)
volume_A3 = atoms.get_volume()
volume_cm3 = volume_A3 * (angstrom_to_cm**3) # 1 ų = 1e-24 cm³
density = mass_g / volume_cm3
return density
def elastic_tensor_calculation(atoms, calculator,filename):
atoms.calc = calculator
# Minimize the structure before stress calculations
dyn = FIRE(atoms)
dyn.run(fmax=0.01, steps=1000) # Converge forces below 0.01 eV/Å
# Define small strain range
eps = 1e-4 # Maximum strain
n_points = 20 # Number of points from -eps to +eps
strain_values = np.linspace(-eps, eps, n_points)
Cij = np.zeros((6, 6)) # Elastic tensor storage
# Define strain matrices for Voigt notation (6 independent strains)
strain_matrices = [
[[1, 0, 0], [0, 0, 0], [0, 0, 0]], # e_xx
[[0, 0, 0], [0, 1, 0], [0, 0, 0]], # e_yy
[[0, 0, 0], [0, 0, 0], [0, 0, 1]], # e_zz
[[0, 0, 0], [0, 0, 0.5], [0, 0.5, 0]], # e_yz
[[0, 0, 0.5], [0, 0, 0], [0.5, 0, 0]], # e_xz
[[0, 0.5, 0], [0.5, 0, 0], [0, 0, 0]], # e_xy
]
# Labels for the strain components in Voigt notation
voigt_labels = ['11', '22', '33', '23', '13', '12']
# Compute reference stress
ref_stress = atoms.get_stress(voigt=True)
elastic_data=[]
for i, strain_matrix in enumerate(strain_matrices):
stresses = np.zeros((n_points, 6))
intercepts=np.zeros((1,6))
r_values=np.zeros((1,6))
std_errs=np.zeros((1,6))
for j, strain in enumerate(strain_values):
strained_atoms = atoms.copy()
deformation_matrix = np.eye(3) + strain * np.array(strain_matrix)
strained_atoms.set_cell(atoms.cell @ deformation_matrix, scale_atoms=True)
strained_atoms.calc = calculator
dyn = FIRE(strained_atoms)
dyn.run(fmax=0.05, steps=1000) # Minimize structure
stresses[j, :] = strained_atoms.get_stress(voigt=True) - ref_stress
elastic_data.append([strain] + list(stresses[j, :]))
# Perform linear regression to find the best slope
for k in range(6):
slope, intercept, r_value, p_value, std_err = linregress(strain_values, stresses[:, k])
Cij[i, k] = slope
intercepts[:,k]=intercept
r_values[:,k]=r_value
std_errs[:,k]=std_err
# Convert the elastic tensor to GPa
Cij_GPa = Cij / GPa # Convert the elastic tensor to GPa (Cij_GPa)
# print("Elastic Stiffness Tensor (Cij) in GPa:")
# print(np.array2string(Cij_GPa, precision=2, suppress_small=True,
# formatter={'float_kind': lambda x: f"{x:6.2f}"}))
# Save data as CSV using pandas
columns = ["Strain"] + [f"Stress_{label}" for label in voigt_labels]
df = pd.DataFrame(elastic_data, columns=columns)
df.to_csv(filename, index=False)
return Cij_GPa |