Coverage for /builds/alexhroom/ase/ase/build/general_surface.py: 83.61%

1from math import gcd 

2import numpy as np 

3from numpy.linalg import norm, solve 

4 

5from ase.build import bulk 

6from ase.build.surface import create_tags 

7 

8 

9def surface(lattice, indices, layers, vacuum=None, tol=1e-10, periodic=False): 

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

11 

12 lattice: Atoms object or str 

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

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

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

16 correct bulk lattice will be generated automatically. 

17 indices: sequence of three int 

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

19 layers: int 

20 Number of equivalent layers of the slab. 

21 vacuum: float 

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

23 periodic: bool 

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

25 """ 

26 

27 indices = np.asarray(indices) 

28 

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

30 raise ValueError(f'{indices} is an invalid surface type') 

31 

32 if isinstance(lattice, str): 

33 lattice = bulk(lattice, cubic=True) 

34 

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

36 h0, k0, l0 = (indices == 0) 

37 

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

39 if not h0: 

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

41 if not k0: 

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

43 if not l0: 

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

45 else: 

46 p, q = ext_gcd(k, l) 

47 a1, a2, a3 = lattice.cell 

48 

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

50 # dot(c1,c2) = k1+i*k2, i in Z 

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

52 l * a2 - k * a3) 

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

54 l * a2 - k * a3) 

55 

56 if abs(k2) > tol: 

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

58 p, q = p + i * l, q - i * k 

59 

60 a, b = ext_gcd(p * k + q * l, h) 

61 

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

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

64 c3 = (b, a * p, a * q) 

65 

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

67 if vacuum is not None: 

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

69 return surf 

70 

71 

72def build(lattice, basis, layers, tol, periodic): 

73 surf = lattice.copy() 

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

75 scaled -= np.floor(scaled + tol) 

76 surf.set_scaled_positions(scaled) 

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

78 surf *= (1, 1, layers) 

79 surf.set_tags(create_tags((1, len(lattice), layers))) 

80 

81 a1, a2, a3 = surf.cell 

82 surf.set_cell([a1, a2, 

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

84 norm(np.cross(a1, a2))**2]) 

85 

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

87 # and z perpendicular to the surface: 

88 a1, a2, a3 = surf.cell 

89 surf.set_cell([(norm(a1), 0, 0), 

90 (np.dot(a1, a2) / norm(a1), 

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

92 (0, 0, norm(a3))], 

93 scale_atoms=True) 

94 

95 surf.pbc = (True, True, periodic) 

96 

97 # Move atoms into the unit cell: 

98 scaled = surf.get_scaled_positions() 

99 scaled[:, :2] %= 1 

100 surf.set_scaled_positions(scaled) 

101 

102 if not periodic: 

103 surf.cell[2] = 0.0 

104 

105 return surf 

106 

107 

108def ext_gcd(a, b): 

109 if b == 0: 

110 return 1, 0 

111 elif a % b == 0: 

112 return 0, 1 

113 else: 

114 x, y = ext_gcd(b, a % b) 

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