CMMDE/lib/cmmde_surface.py

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)