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1from math import gcd 

2import numpy as np 

3from numpy.linalg import norm, solve 

4 

5from ase.build import bulk 

6 

7 

8def surface(lattice, indices, layers, vacuum=None, tol=1e-10, periodic=False): 

9 """Create surface from a given lattice and Miller indices. 

10 

11 lattice: Atoms object or str 

12 Bulk lattice structure of alloy or pure metal. Note that the 

13 unit-cell must be the conventional cell - not the primitive cell. 

14 One can also give the chemical symbol as a string, in which case the 

15 correct bulk lattice will be generated automatically. 

16 indices: sequence of three int 

17 Surface normal in Miller indices (h,k,l). 

18 layers: int 

19 Number of equivalent layers of the slab. 

20 vacuum: float 

21 Amount of vacuum added on both sides of the slab. 

22 periodic: bool 

23 Whether the surface is periodic in the normal to the surface 

24 """ 

25 

26 indices = np.asarray(indices) 

27 

28 if indices.shape != (3,) or not indices.any() or indices.dtype != int: 

29 raise ValueError('%s is an invalid surface type' % indices) 

30 

31 if isinstance(lattice, str): 

32 lattice = bulk(lattice, cubic=True) 

33 

34 h, k, l = indices # noqa (E741, the variable l) 

35 h0, k0, l0 = (indices == 0) 

36 

37 if h0 and k0 or h0 and l0 or k0 and l0: # if two indices are zero 

38 if not h0: 

39 c1, c2, c3 = [(0, 1, 0), (0, 0, 1), (1, 0, 0)] 

40 if not k0: 

41 c1, c2, c3 = [(0, 0, 1), (1, 0, 0), (0, 1, 0)] 

42 if not l0: 

43 c1, c2, c3 = [(1, 0, 0), (0, 1, 0), (0, 0, 1)] 

44 else: 

45 p, q = ext_gcd(k, l) 

46 a1, a2, a3 = lattice.cell 

47 

48 # constants describing the dot product of basis c1 and c2: 

49 # dot(c1,c2) = k1+i*k2, i in Z 

50 k1 = np.dot(p * (k * a1 - h * a2) + q * (l * a1 - h * a3), 

51 l * a2 - k * a3) 

52 k2 = np.dot(l * (k * a1 - h * a2) - k * (l * a1 - h * a3), 

53 l * a2 - k * a3) 

54 

55 if abs(k2) > tol: 

56 i = -int(round(k1 / k2)) # i corresponding to the optimal basis 

57 p, q = p + i * l, q - i * k 

58 

59 a, b = ext_gcd(p * k + q * l, h) 

60 

61 c1 = (p * k + q * l, -p * h, -q * h) 

62 c2 = np.array((0, l, -k)) // abs(gcd(l, k)) 

63 c3 = (b, a * p, a * q) 

64 

65 surf = build(lattice, np.array([c1, c2, c3]), layers, tol, periodic) 

66 if vacuum is not None: 

67 surf.center(vacuum=vacuum, axis=2) 

68 return surf 

69 

70 

71def build(lattice, basis, layers, tol, periodic): 

72 surf = lattice.copy() 

73 scaled = solve(basis.T, surf.get_scaled_positions().T).T 

74 scaled -= np.floor(scaled + tol) 

75 surf.set_scaled_positions(scaled) 

76 surf.set_cell(np.dot(basis, surf.cell), scale_atoms=True) 

77 surf *= (1, 1, layers) 

78 

79 a1, a2, a3 = surf.cell 

80 surf.set_cell([a1, a2, 

81 np.cross(a1, a2) * np.dot(a3, np.cross(a1, a2)) / 

82 norm(np.cross(a1, a2))**2]) 

83 

84 # Change unit cell to have the x-axis parallel with a surface vector 

85 # and z perpendicular to the surface: 

86 a1, a2, a3 = surf.cell 

87 surf.set_cell([(norm(a1), 0, 0), 

88 (np.dot(a1, a2) / norm(a1), 

89 np.sqrt(norm(a2)**2 - (np.dot(a1, a2) / norm(a1))**2), 0), 

90 (0, 0, norm(a3))], 

91 scale_atoms=True) 

92 

93 surf.pbc = (True, True, periodic) 

94 

95 # Move atoms into the unit cell: 

96 scaled = surf.get_scaled_positions() 

97 scaled[:, :2] %= 1 

98 surf.set_scaled_positions(scaled) 

99 

100 if not periodic: 

101 surf.cell[2] = 0.0 

102 

103 return surf 

104 

105 

106def ext_gcd(a, b): 

107 if b == 0: 

108 return 1, 0 

109 elif a % b == 0: 

110 return 0, 1 

111 else: 

112 x, y = ext_gcd(b, a % b) 

113 return y, x - y * (a // b)