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111 lines
3.6 KiB
111 lines
3.6 KiB
2 years ago
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import numpy as np
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from cmmde_atoms import Atoms
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from cmmde_clusterutil import get_element_info
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def Icosahedron(symbol, noshells, latticeconstant=None):
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"""
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Returns a cluster with the icosahedra symmetry.
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Parameters
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----------
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symbol: The chemical symbol (or atomic number) of the element.
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noshells: The number of shells (>= 1).
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latticeconstant (optional): The lattice constant. If not given,
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then it is extracted form cmmde.data.
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"""
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symbol, atomic_number, latticeconstant = get_element_info(
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symbol, latticeconstant)
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# Interpret noshells
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if noshells < 1:
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raise ValueError(
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"The number of shells must be equal to or greater than one.")
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t = 0.5 + np.sqrt(5) / 2.0
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verticies = np.array([[t, 0., 1.],
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[t, 0., -1.],
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[-t, 0., 1.],
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[-t, 0., -1.],
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[1., t, 0.],
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[-1., t, 0.],
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[1., -t, 0.],
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[-1., -t, 0.],
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[0., 1., t],
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[0., -1., t],
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[0., 1., -t],
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[0., -1., -t]])
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positions = []
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tags = []
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positions.append(np.zeros(3))
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tags.append(1)
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for n in range(1, noshells):
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# Construct square edges (6)
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for k in range(0, 12, 2):
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v1 = verticies[k]
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v2 = verticies[k + 1]
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for i in range(n + 1):
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pos = i * v1 + (n - i) * v2
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positions.append(pos)
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tags.append(n + 1)
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# Construct triangle planes (12)
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if n > 1:
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map = {0: (8, 9), 1: (10, 11),
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2: (8, 9), 3: (10, 11),
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4: (0, 1), 5: (2, 3),
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6: (0, 1), 7: (2, 3),
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8: (4, 5), 9: (6, 7),
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10: (4, 5), 11: (6, 7)}
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for k in range(0, 12):
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v0 = n * verticies[k]
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v1 = (verticies[map[k][0]] - verticies[k])
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v2 = (verticies[map[k][1]] - verticies[k])
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for i in range(n):
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for j in range(n - i):
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if i == 0 and j == 0:
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continue
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pos = v0 + i * v1 + j * v2
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positions.append(pos)
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tags.append(n + 1)
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# Fill missing triangle planes (8)
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if n > 2:
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map = {0: (9, 6, 8, 4,),
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1: (11, 6, 10, 4),
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2: (9, 7, 8, 5,),
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3: (11, 7, 10, 5)}
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for k in range(0, 4):
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v0 = n * verticies[k]
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v1 = (verticies[map[k][0]] - verticies[k])
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v2 = (verticies[map[k][1]] - verticies[k])
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v3 = (verticies[map[k][2]] - verticies[k])
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v4 = (verticies[map[k][3]] - verticies[k])
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for i in range(1, n):
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for j in range(1, n - i):
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pos = v0 + i * v1 + j * v2
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positions.append(pos)
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tags.append(n + 1)
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pos = v0 + i * v3 + j * v4
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positions.append(pos)
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tags.append(n + 1)
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# Scale the positions
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scaling_factor = latticeconstant / np.sqrt(2 * (1 + t**2))
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positions = np.array(positions) * scaling_factor
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symbols = [atomic_number] * len(positions)
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atoms = Atoms(symbols=symbols, positions=positions, tags=tags)
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atoms.center(about=(0, 0, 0))
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atoms.cell[:] = 0
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return atoms
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