def _build_basis(self, bulk):
"""Get the basis unit cell from bulk unit cell. This
basis is effectively the same as the bulk, but rotated such
that the z-axis is aligned with the surface termination.
The basis is stored separately from the slab generated and is
only intended for internal use.
Returns
-------
basis : atoms object
The basis slab corresponding to the provided bulk.
"""
del bulk.constraints
if len(np.nonzero(self.miller_index)[0]) == 1:
mi = max(np.abs(self.miller_index))
basis = circulant(self.miller_index[::-1] / mi).astype(int)
else:
h, k, l = self.miller_index
p, q = ext_gcd(k, l)
a1, a2, a3 = bulk.cell
k1 = np.dot(p * (k * a1 - h * a2) + q * (l * a1 - h * a3),
l * a2 - k * a3)
k2 = np.dot(l * (k * a1 - h * a2) - k * (l * a1 - h * a3),
l * a2 - k * a3)
if abs(k2) > self.tol:
i = -int(np.round(k1 / k2))
p, q = p + i * l, q - i * k
a, b = ext_gcd(p * k + q * l, h)
c1 = (p * k + q * l, -p * h, -q * h)
c2 = np.array((0, l, -k)) // abs(gcd(l, k))
c3 = (b, a * p, a * q)
basis = np.array([c1, c2, c3])
basis_atoms = Gratoms(positions=bulk.positions,
numbers=bulk.get_atomic_numbers(),
cell=bulk.cell,
pbc=True)
scaled = solve(basis.T, basis_atoms.get_scaled_positions().T).T
scaled -= np.floor(scaled + self.tol)
basis_atoms.set_scaled_positions(scaled)
basis_atoms.set_cell(np.dot(basis, basis_atoms.cell), scale_atoms=True)
a1, a2, a3 = basis_atoms.cell
n1 = np.cross(a1, a2)
a3 = n1 / norm(n1)
rotate(basis_atoms, a3, (0, 0, 1), a1, (1, 0, 0))
return basis_atoms
def align_crystal(self, bulk, miller_index):
"""Return an aligned unit cell from bulk unit cell. This alignment
rotates the a and b basis vectors to be parallel to the Miller index.
Parameters
----------
bulk : Atoms object
Bulk system to be standardized.
miller_index : list (3,)
Miller indices to align with the basis vectors.
Returns
-------
new_bulk : Gratoms object
Standardized bulk unit cell.
"""
del bulk.constraints
if len(np.nonzero(miller_index)[0]) == 1:
mi = max(np.abs(miller_index))
new_lattice = scipy.linalg.circulant(miller_index[::-1] /
mi).astype(int)
else:
h, k, l = miller_index
p, q = utils.ext_gcd(k, l)
a1, a2, a3 = bulk.cell
k1 = np.dot(p * (k * a1 - h * a2) + q * (l * a1 - h * a3),
l * a2 - k * a3)
k2 = np.dot(l * (k * a1 - h * a2) - k * (l * a1 - h * a3),
l * a2 - k * a3)
if abs(k2) > self.tol:
i = -int(np.round(k1 / k2))
p, q = p + i * l, q - i * k
a, b = utils.ext_gcd(p * k + q * l, h)
c1 = (p * k + q * l, -p * h, -q * h)
c2 = np.array((0, l, -k)) // abs(gcd(l, k))
c3 = (b, a * p, a * q)
new_lattice = np.array([c1, c2, c3])
scaled = np.linalg.solve(new_lattice.T,
bulk.get_scaled_positions().T).T
scaled -= np.floor(scaled + self.tol)
new_bulk = Gratoms(positions=bulk.positions,
numbers=bulk.get_atomic_numbers(),
pbc=True)
if not self.attach_graph:
del new_bulk._graph
new_bulk.set_scaled_positions(scaled)
new_bulk.set_cell(np.dot(new_lattice, bulk.cell), scale_atoms=True)
# Align the longest of the ab basis vectors with x
d = np.linalg.norm(new_bulk.cell[:2], axis=1)
if d[1] > d[0]:
new_bulk.cell[[0, 1]] = new_bulk.cell[[1, 0]]
a = new_bulk.cell[0]
a3 = np.cross(a, new_bulk.cell[1]) / np.max(d)
rotate(new_bulk, a3, (0, 0, 1), a, (1, 0, 0))
# Ensure the remaining basis vectors are positive in their
# corresponding axis
for i in range(1, 3):
if new_bulk.cell[i][i] < 0:
new_bulk.cell[i] *= -1
new_bulk.wrap(eps=1e-3)
return new_bulk