def generate_uniform_grid(structure, size=3, min_distance_from_atoms=1.0):
"""
Generates a grid of symmetry inequivalent interstitial
positions with a specified minimum distance from the atoms of the
sample. Especially intended for DFT simulations.
:param bulk_structure: A structre data.
:param int size: The number of steps in the three lattice directions.
Only equispaced grids are supported at the moment.
:param float min_distance_from_atoms: Minimum distance between a
interstitial position and the
atoms of the lattice.
Units are Angstrom.
:returns: A list of symmetry inequivalent positions.
:rtype: list
"""
#bulk_structure=Structure.from_file(bulk_structure)
bulk_structure = structure.copy()
tolerance = 7
#build uniform grid
npoints = size**3
x_ = np.linspace(0., 1., size, endpoint=False)
y_ = np.linspace(0., 1., size, endpoint=False)
z_ = np.linspace(0., 1., size, endpoint=False)
uniform_grid = np.meshgrid(x_, y_, z_, indexing='ij')
x, y, z = uniform_grid
equiv = np.ones_like(x) * (npoints)
SA = SpacegroupAnalyzer(bulk_structure)
rot, tran = SA._get_symmetry()
alt = True
nb_cells = np.array([[-1., -1., -1.], [-1., -1., 0.], [-1., -1., 1.],
[-1., 0., -1.], [-1., 0., 0.], [-1., 0., 1.],
[-1., 1., -1.], [-1., 1., 0.], [-1., 1., 1.],
[0., -1., -1.], [0., -1., 0.], [0., -1., 1.],
[0., 0., -1.], [0., 0., 0.], [0., 0., 1.],
[0., 1., -1.], [0., 1., 0.], [0., 1., 1.],
[1., -1., -1.], [1., -1., 0.], [1., -1., 1.],
[1., 0., -1.], [1., 0., 0.], [1., 0., 1.],
[1., 1., -1.], [1., 1., 0.], [1., 1., 1.]])
for i in range(size):
for j in range(size):
for k in range(size):
if equiv[i, j, k] < npoints:
#this point is equivalent to someone else!
continue
for r, t in zip(rot, tran):
# new position for the muon
n = np.zeros(3)
# apply symmetry and bring back to unit cell
n = np.round(
np.dot(r, [x[i, j, k], y[i, j, k], z[i, j, k]]) + t,
decimals=tolerance) % 1
if (np.abs(n * size - np.rint(n * size)) < 10**
-(tolerance)).all():
#get index of point
ii, jj, kk = np.rint(n * size).astype(int)
if (ii * (size**2) + jj * size + kk > i *
(size**2) + j * size + k):
equiv[ii, jj, kk] -= 1
equiv[i, j, k] += 1
reduced_lat = np.array(bulk_structure.lattice)
scaled_pos = bulk_structure.frac_coords
A, B, C = structure.lattice.abc[0], structure.lattice.abc[
1], structure.lattice.abc[2]
alpha, beta, gamma = structure.lattice.angles[0], structure.lattice.angles[
1], structure.lattice.angles[2]
reduced_bases = get_cell_matrix(A, B, C, alpha, beta, gamma)
positions = []
for i in range(size):
for j in range(size):
for k in range(size):
if equiv[i, j, k] >= npoints:
#saves distances with all atoms
distances = []
dists = np.zeros(27 * len(bulk_structure.sites))
center = [x[i, j, k], y[i, j, k], z[i, j, k]]
#check distances form atoms (also in neighbouring cells)
for a in range(len(bulk_structure)):
dists[a * 27:(a + 1) * 27] = np.linalg.norm(np.dot(
scaled_pos[a] - center + nb_cells, reduced_bases),
axis=1)
#
# old method 20 times slower!
#
#for a in range(len(sample._cell)):
# for ii in (-1, 0, 1):
# for jj in (-1, 0, 1):
# for kk in (-1, 0, 1):
# distances.append( np.linalg.norm(
# np.dot(scaled_pos[a] - center + np.array([ii,jj,kk]),
# reduced_bases) ) )
#
#print(np.allclose(dists,distances))
#if min(distances) > min_distance_from_atoms:
if dists.min() > min_distance_from_atoms:
positions.append([x[i, j, k], y[i, j, k], z[i, j, k]])
return positions
