Symmetry analysis
MatID has extensive symmetry analysis tools for 3D periodic systems. The symmetry detection is powered by spglib, but has been extended with additional analysis and caching functionality for increased performance on closely related queries.
The basis of symmetry analysis is the SymmetryAnalyzer-class. It
takes as input an atomic geometry, and symmetry tolerance settings.
from matid import SymmetryAnalyzer
from ase.build import bulk
from ase.visualize import view
from ase import Atoms
# Prepare a geometry to be analyzed
nacl = bulk("NaCl", "rocksalt", a=5.64).repeat([2, 2, 2])
view(nacl)
# Setup the symmetry analyzer
symm = SymmetryAnalyzer(nacl, symmetry_tol=0.1)
The conventional and primitive systems corresponding to the given structure can be directly queried as ASE.Atoms-objects
# Get the conventional system as an ase.Atoms-object.
conv = symm.get_conventional_system()
view(conv)
# Get the primitive system as an ase.Atoms-object
prim = symm.get_primitive_system()
view(prim)
Further symmetry information can be queried as follows:
space_group_number = symm.get_space_group_number()
space_group_symbol = symm.get_space_group_international_short()
is_chiral = symm.get_is_chiral()
hall_number = symm.get_hall_number()
hall_symbol = symm.get_hall_symbol()
crystal_system = symm.get_crystal_system()
bravais_lattice = symm.get_bravais_lattice()
point_group = symm.get_point_group()
wyckoff_letters_orig = symm.get_wyckoff_letters_original()
wyckoff_letters_prim = symm.get_wyckoff_letters_primitive()
wyckoff_letters_conv = symm.get_wyckoff_letters_conventional()
equivalent_atoms_orig = symm.get_equivalent_atoms_original()
equivalent_atoms_prim = symm.get_equivalent_atoms_primitive()
equivalent_atoms_conv = symm.get_equivalent_atoms_conventional()
print("Space group number: {}".format(space_group_number))
print("Space group international short symbol: {}".format(space_group_symbol))
print("Is chiral: {}".format(is_chiral))
print("Hall number: {}".format(hall_number))
print("Hall symbol: {}".format(hall_symbol))
print("Crystal system: {}".format(crystal_system))
print("Bravais lattice: {}".format(bravais_lattice))
print("Point group: {}".format(point_group))
print("Wyckoff letters original: {}".format(wyckoff_letters_orig))
print("Wyckoff letters primitive: {}".format(wyckoff_letters_prim))
print("Wyckoff letters conventional: {}".format(wyckoff_letters_conv))
Which will output the following:
Space group number: 225
Space group international short symbol: Fm-3m
Is chiral: False
Hall number: 523
Hall symbol: -F 4 2 3
Crystal system: cubic
Bravais lattice: cF
Point group: m-3m
Wyckoff letters original: ['a' 'b' 'a' 'b' 'a' 'b' 'a' 'b' 'a' 'b' 'a' 'b' 'a' 'b' 'a' 'b']
Wyckoff letters primitive: ['a' 'b']
Wyckoff letters conventional: ['a' 'b' 'a' 'b' 'a' 'b' 'a' 'b']
MatID also utilises offline information from the Bilbao crystallographic server to analyze the detailed Wyckoff set information for structures. With this information the details of the Wyckoff sets contained in the structure can be analyzed. Here we demonstrate this functionality on a more complex silicon clathrate structure.
scaled_positions = [
[0.18370000000000, 0.18370000000000, 0.18370000000000],
[0.18370000000000, 0.18370000000000, 0.81630000000000],
[0.18370000000000, 0.81630000000000, 0.18370000000000],
[0.18370000000000, 0.81630000000000, 0.81630000000000],
[0.31630000000000, 0.31630000000000, 0.31630000000000],
[0.31630000000000, 0.31630000000000, 0.68370000000000],
[0.31630000000000, 0.68370000000000, 0.31630000000000],
[0.31630000000000, 0.68370000000000, 0.68370000000000],
[0.68370000000000, 0.31630000000000, 0.31630000000000],
[0.68370000000000, 0.31630000000000, 0.68370000000000],
[0.68370000000000, 0.68370000000000, 0.31630000000000],
[0.68370000000000, 0.68370000000000, 0.68370000000000],
[0.81630000000000, 0.18370000000000, 0.18370000000000],
[0.81630000000000, 0.18370000000000, 0.81630000000000],
[0.81630000000000, 0.81630000000000, 0.18370000000000],
[0.81630000000000, 0.81630000000000, 0.81630000000000],
[0.00000000000000, 0.11720000000000, 0.30770000000000],
[0.00000000000000, 0.11720000000000, 0.69230000000000],
[0.00000000000000, 0.88280000000000, 0.30770000000000],
[0.00000000000000, 0.88280000000000, 0.69230000000000],
[0.11720000000000, 0.30770000000000, 0.00000000000000],
[0.11720000000000, 0.69230000000000, 0.00000000000000],
[0.19230000000000, 0.38280000000000, 0.50000000000000],
[0.19230000000000, 0.61720000000000, 0.50000000000000],
[0.30770000000000, 0.00000000000000, 0.11720000000000],
[0.30770000000000, 0.00000000000000, 0.88280000000000],
[0.38280000000000, 0.50000000000000, 0.19230000000000],
[0.38280000000000, 0.50000000000000, 0.80770000000000],
[0.50000000000000, 0.19230000000000, 0.38280000000000],
[0.50000000000000, 0.19230000000000, 0.61720000000000],
[0.50000000000000, 0.80770000000000, 0.38280000000000],
[0.50000000000000, 0.80770000000000, 0.61720000000000],
[0.61720000000000, 0.50000000000000, 0.19230000000000],
[0.61720000000000, 0.50000000000000, 0.80770000000000],
[0.69230000000000, 0.00000000000000, 0.11720000000000],
[0.69230000000000, 0.00000000000000, 0.88280000000000],
[0.80770000000000, 0.38280000000000, 0.50000000000000],
[0.80770000000000, 0.61720000000000, 0.50000000000000],
[0.88280000000000, 0.30770000000000, 0.00000000000000],
[0.88280000000000, 0.69230000000000, 0.00000000000000],
[0.00000000000000, 0.25000000000000, 0.50000000000000],
[0.00000000000000, 0.75000000000000, 0.50000000000000],
[0.25000000000000, 0.50000000000000, 0.00000000000000],
[0.50000000000000, 0.00000000000000, 0.25000000000000],
[0.50000000000000, 0.00000000000000, 0.75000000000000],
[0.75000000000000, 0.50000000000000, 0.00000000000000],
]
cell = [
[10.35500000000000, 0.00000000000000, 0.00000000000000],
[0.00000000000000, 10.35500000000000, 0.00000000000000],
[0.00000000000000, 0.00000000000000, 10.35500000000000]
]
labels = ["Si"]*46
clathrate = Atoms(labels, scaled_positions=scaled_positions, cell=cell, pbc=True)
# Setup the symmetry analyzer
symm = SymmetryAnalyzer(clathrate, symmetry_tol=0.1)
has_free_param = symm.get_has_free_wyckoff_parameters()
wyckoff_sets_conv = symm.get_wyckoff_sets_conventional()
for i_group, group in enumerate(wyckoff_sets_conv):
print("Set {}".format(i_group))
print(" Letter: {}".format(group.wyckoff_letter))
print(" Element: {}".format(group.element))
print(" Indices: {}".format(group.indices))
print(" Multiplicity: {}".format(group.multiplicity))
print(" Repr.: {}".format(group.representative))
print(" x: {}".format(group.x))
print(" y: {}".format(group.y))
print(" z: {}".format(group.z))
Which will output the following information:
Set 0
Letter: c
Element: Si
Indices: [40, 41, 42, 43, 44, 45]
Multiplicity: 6
Repr.: ['1/4', '0', '1/2']
x: None
y: None
z: None
Set 1
Letter: i
Element: Si
Indices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]
Multiplicity: 16
Repr.: ['x', 'x', 'x']
x: 0.6836999931629999
y: None
z: None
Set 2
Letter: k
Element: Si
Indices: [16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39]
Multiplicity: 24
Repr.: ['0', 'y', 'z']
x: None
y: 0.6923000000000001
z: 0.8827999999999999
You can find the full example in “examples/symmetry.py”.