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from math import gcd
import numpy as np
from numpy.linalg import norm, solve
from ase.build import bulk
def surface(lattice, indices, layers, vacuum=None, tol=1e-10, periodic=False):
"""Create surface from a given lattice and Miller indices.
lattice: Atoms object or str
Bulk lattice structure of alloy or pure metal. Note that the
unit-cell must be the conventional cell - not the primitive cell.
One can also give the chemical symbol as a string, in which case the
correct bulk lattice will be generated automatically.
indices: sequence of three int
Surface normal in Miller indices (h,k,l).
layers: int
Number of equivalent layers of the slab.
vacuum: float
Amount of vacuum added on both sides of the slab.
periodic: bool
Whether the surface is periodic in the normal to the surface
"""
indices = np.asarray(indices)
if indices.shape != (3,) or not indices.any() or indices.dtype != int:
raise ValueError('%s is an invalid surface type' % indices)
if isinstance(lattice, str):
lattice = bulk(lattice, cubic=True)
h, k, l = indices
h0, k0, l0 = (indices == 0)
if h0 and k0 or h0 and l0 or k0 and l0: # if two indices are zero
if not h0:
c1, c2, c3 = [(0, 1, 0), (0, 0, 1), (1, 0, 0)]
if not k0:
c1, c2, c3 = [(0, 0, 1), (1, 0, 0), (0, 1, 0)]
if not l0:
c1, c2, c3 = [(1, 0, 0), (0, 1, 0), (0, 0, 1)]
else:
p, q = ext_gcd(k, l)
a1, a2, a3 = lattice.cell
# constants describing the dot product of basis c1 and c2:
# dot(c1,c2) = k1+i*k2, i in Z
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) > tol:
i = -int(round(k1 / k2)) # i corresponding to the optimal basis
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)
surf = build(lattice, np.array([c1, c2, c3]), layers, tol, periodic)
if vacuum is not None:
surf.center(vacuum=vacuum, axis=2)
return surf
def build(lattice, basis, layers, tol, periodic):
surf = lattice.copy()
scaled = solve(basis.T, surf.get_scaled_positions().T).T
scaled -= np.floor(scaled + tol)
surf.set_scaled_positions(scaled)
surf.set_cell(np.dot(basis, surf.cell), scale_atoms=True)
surf *= (1, 1, layers)
a1, a2, a3 = surf.cell
surf.set_cell([a1, a2,
np.cross(a1, a2) * np.dot(a3, np.cross(a1, a2)) /
norm(np.cross(a1, a2))**2])
# Change unit cell to have the x-axis parallel with a surface vector
# and z perpendicular to the surface:
a1, a2, a3 = surf.cell
surf.set_cell([(norm(a1), 0, 0),
(np.dot(a1, a2) / norm(a1),
np.sqrt(norm(a2)**2 - (np.dot(a1, a2) / norm(a1))**2), 0),
(0, 0, norm(a3))],
scale_atoms=True)
surf.pbc = (True, True, periodic)
# Move atoms into the unit cell:
scaled = surf.get_scaled_positions()
scaled[:, :2] %= 1
surf.set_scaled_positions(scaled)
if not periodic:
surf.cell[2] = 0.0
return surf
def ext_gcd(a, b):
if b == 0:
return 1, 0
elif a % b == 0:
return 0, 1
else:
x, y = ext_gcd(b, a % b)
return y, x - y * (a // b)
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