Crystal#
The crystal module contains functions for working with Crystallographic Information Files (CIF).
- cartesian(a, b, c, alpha, beta, gamma)[source]#
Transformation matrix from crystal to Cartesian coodinates.
- Parameters:
- a, b, c, alpha, beta, gammafloat
Lattice constants and angles. Angles in radians.
- Returns:
- A2d array
Transformation matrix.
- cartesian_displacement(a, b, c, alpha, beta, gamma)[source]#
Transformation matrix from crystal to Cartesian coodinates for atomic displacement parameters.
- Parameters:
- a, b, c, alpha, beta, gammafloat
Lattice constants and angles. Angles in radians.
- Returns:
- D2d array
Transformation matrix.
- cartesian_moment(a, b, c, alpha, beta, gamma)[source]#
Transformation matrix from crystal to Cartesian coodinates for magnetic moments.
- Parameters:
- a, b, c, alpha, beta, gammafloat
Lattice constants and angles. Angles in radians.
- Returns:
- C2d array
Transformation matrix.
- cartesian_rotation(a, b, c, alpha, beta, gamma)[source]#
Rotation matrix between reciprocal and real Cartesian coodinates.
- Parameters:
- a, b, c, alpha, beta, gammafloat
Lattice constants and angles. Angles in radians.
- Returns:
- R2d array
Rotation matrix.
- d(a, b, c, alpha, beta, gamma, h, k, l)[source]#
Interplanar d-spacing.
- Parameters:
- a, b, c, alpha, beta, gammafloat
Lattice constants and angles. Angles in radians.
- h, k, l1d array
Miller indices
- Returns:
- d1d array
d-spacings.
- disordered(delta, Ux, Uy, Uz, Sx, Sy, Sz, rx, ry, rz, nu, nv, nw, atm, A, name, folder, filename)[source]#
Write disordered supercell information to a CIF file.
- Parameters:
- delta1d array
Relative occupancies.
- Ux, Uy, Uz1d array
Atomic displacementsr in Cartesian coordinates.
- Sx, Sy, Sz1d array
Magnetic momentsr in Cartesian coordinates.
- rx, ry, rz1d array
Spatial vector in Cartesian coordinates.
- nu, nv, nwint
Number of grid points \(N_1\), \(N_2\), \(N_3\) along the \(a\), \(b\), and \(c\)-axis of the supercell.
- atm1d array, str
Atoms, ions, or isotopes.
- A2d array
Transformation matrix from crystal to Cartesian coordinates.
- folderstr,
Name of path excluding filename of reference CIF file.
- filenamestr
Name of filename excluding path of reference CIF file.
- group(folder, filename)[source]#
Reads space group information from a CIF file.
- Parameters:
- folderstr,
Name of path excluding filename.
- filenamestr
Name of filename excluding path.
- Returns:
- groupint
Space group number.
- hmstr
Space group symbol in Hermann–Mauguin notation.
- interplanar(a, b, c, alpha, beta, gamma, h0, k0, l0, h1, k1, l1)[source]#
Interplanar angle.
- Parameters:
- a, b, c, alpha, beta, gammafloat
Lattice constants and angles. Angles in radians.
- h, k, l1d array
Miller indices
- Returns:
- angle1d array
Interplanar angles in radians.
- lattice(a, b, c, alpha, beta, gamma)[source]#
Lattice system of unit cell based on lattice parameters.
- Parameters:
- a, b, c, alpha, beta, gammafloat
Lattice constants and angles. Angles in radians.
- Returns:
- systemstr
One of
'Cubic','Hexagonal','Rhombohedral','Tetragonal','Orthorhombic','Monoclinic', or'Triclinic'.
- laue(folder, filename)[source]#
Determines Laue class from a CIF file.
Laue
Noncentrosymmetric
m-3m
432, -43m
m-3
23
6/mmm
622, -62m, 6mmm
6/m
6, -6
-3m
32, 3m
-3
3
4/mmm
422, -42m, 4mm
4/m
4, -4
mmm
222, 22m
2/m
2, m
-1
1
- Parameters:
- folderstr,
Name of path excluding filename.
- filenamestr
Name of filename excluding path.
- Returns:
- lauestr
One of
'-1','2/m','mmm','4/m','4/mmm','-3','-3m','6/m','6/mmm','m-3', or'm-3m'.
- metric(a, b, c, alpha, beta, gamma)[source]#
Metric tensor.
- Parameters:
- a, b, c, alpha, beta, gammafloat
Lattice constants and angles. Angles in radians.
- Returns:
- G2d array
Components of the \(G\) metric tensor.
- operators(folder, filename)[source]#
Reads symmetry operators from a CIF file.
- Parameters:
- folderstr,
Name of path excluding filename.
- filenamestr
Name of filename excluding path.
- Returns:
- symopslist
Symmetry operators in Jones-faithful notation.
- parameters(folder=None, filename=None)[source]#
Reads lattice parameters from a CIF file.
- Parameters:
- folderstr,
Name of path excluding filename.
- filenamestr
Name of filename excluding path.
- Returns:
- a, b, c, alpha, beta, gammafloat
Lattice constants and angles. Angles in radians.
- reciprocal(a, b, c, alpha, beta, gamma)[source]#
Reciprocal lattice parameters.
- Parameters:
- a, b, c, alpha, beta, gammafloat
Lattice constants and angles. Angles in radians.
- Returns:
- a_, b_, c_, alpha_, beta_, gamma_float
Reciprocal lattice constants and angles. Angles in radians.
- supercell(atm, occ, disp, mom, u, v, w, nu, nv, nw, name, folder, filename)[source]#
Write average supercell information to a CIF file.
- Parameters:
- atm1d array, str
Atoms, ions, or isotopes.
- occ1d array
Site occupancies.
- disp1d array
Atomic displacements.
- mom1d array
Magnetic moments.
- u, v, w1d array
Fractional coordinates.
- nu, nv, nwint
Number of grid points \(N_1\), \(N_2\), \(N_3\) along the \(a\), \(b\), and \(c\)-axis of the supercell.
- folderstr,
Name of path excluding filename of reference CIF file.
- filenamestr
Name of filename excluding path of reference CIF file.
- tolfloat, optional
Tolerance of unique atom coordinates.
- transform(p, q, r, U)[source]#
Transform the components of a vector.
- Parameters:
- p, q, r1d array
Components of a vector.
- U2d array
Transformation matrix.
- Returns:
- x, y, z1d array
Transformed components of a vector.
- twins(folder, filename)[source]#
Reads twin matrices from a CIF file.
- Parameters:
- folderstr,
Name of path excluding filename.
- filenamestr
Name of filename excluding path.
- Returns:
- T3d array
Twin matrices with individual components along last two axes.
- weights1d array
Twin mass fraction.
- unitcell(folder, filename, tol=0.01)[source]#
Reads atom site information from a CIF file.
- Parameters:
- folderstr,
Name of path excluding filename.
- filenamestr
Name of filename excluding path.
- tolfloat, optional
Tolerance of unique atom coordinates.
- Returns:
- unit_celldict
Dictionary of unit cell information.
- vector(h, k, l, B)[source]#
Recirprocal lattice vector in Cartesian coodinates.
- Parameters:
- h, k, l1d array
Miller indices.
- B2d array
Transformation matrix from crystal to Cartesian coodinates in reciprocal space.
- Returns:
- Qx, Qy, Qz1d array
Recirprocal lattice vector in Cartesian coodinates.