from math import gcd import numpy as np from numpy.linalg import norm, solve from cmmde_bulk 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)