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- angles_allowed(alpha=90, beta=90, gamma=90)
- Determine if lattice angles are suitable for basis vectors
https://journals.iucr.org/a/issues/2011/01/00/au5114/index.html
As reported in International Tables for Crystallography:
Donnay & Donnay, 1959 International Tables for X-ray Crystallography, Vol. II.
Koch, 2004 International Tables for Crystallography, Vol. C.
:param alpha: angle in degrees
:param beta: angle in degrees
:param gamma: angle in degrees
:return: bool, True if angles are suitable for creation of basis
- basis2bandl(basis)
- Calculate the Busing and Levy B matrix from a real space UV
"choose the x-axis parallel to a*, the y-axis in the plane of a* and b*, and the z-axis perpendicular to that plane"
From: W. R. Busing and H. A. Levy, Acta Cryst. (1967). 22, 457-464
"Angle calculations for 3- and 4-circle X-ray and neutron diffractometers"
See also: https://docs.mantidproject.org/nightly/concepts/Lattice.html
B = [[b1, b2 * cos(beta3), b3 * cos(beta2)],
[0, b2 * sin(beta3), -b3 * sin(beta2) * cos(alpha1)],
[0, 0, 1 / a3]]
return 2pi * B # equivalent to transpose([a*, b*, c*])
- basis2latpar(basis_vectors)
- Convert UV=[a,b,c] to a,b,c,alpha,beta,gamma
a,b,c,alpha,beta,gamma = UV2latpar(UV)
:param basis_vectors: [3*3] basis vectors array [a[3], b[3], c[3]]
- basis_1(*lattice_parameters, **kwargs)
- Generate direct-space basis-vectors [a, b, c] from lattice parameters
Basis choice equivalent to that of materials project:
https://github.com/materialsproject/pymatgen/blob/v2024.10.3/src/pymatgen/core/lattice.py#L39-L1702
vector c || z-axis
vector a rotated by beta about y-axis from +ve x-axis
vector b* || y-axis
Calculate the lattice positions:
[[x, y, z]] = dot([[u, v, w]], [vec_a, vec_b, vec_c])
:param lattice_parameters: float or list in Angstroms & degrees, see gen_lattice_parameters()
:param kwargs: lattice parameters
:returns: [3x3] array, as [vec_a, vec_b, vec_c] in Angstroms
- basis_2(*lattice_parameters, **kwargs)
- Generate direct-space basis-vectors [a, b, c] from lattice parameters
Basis choice equivalent to that of Vesta:
https://github.com/materialsproject/pymatgen/blob/v2024.10.3/src/pymatgen/core/lattice.py#L39-L1702
vector a || x-axis
vector b rotated by gamma about z-axis from +ve y-axis
vector c* || z-axis
Calculate the lattice positions:
[[x, y, z]] = dot([[u, v, w]], [vec_a, vec_b, vec_c])
:param lattice_parameters: float or list in Angstroms & degrees, see gen_lattice_parameters()
:param kwargs: lattice parameters
:returns: [3x3] array, as [vec_a, vec_b, vec_c] in Angstroms
- basis_3(*lattice_parameters, **kwargs)
- Generate direct-space basis-vectors [a, b, c] from lattice parameters
Basis choice equivalent to the inverse of the Bmatrix of W. R. Busing and H. A. Levy, Acta Cryst. (1967)
https://docs.mantidproject.org/nightly/concepts/Lattice.html
vector a* || x-axis
vector b rotated by alpha about x-axis from +ve z-axis
vector c || z-axis
Calculate the lattice positions:
[[x, y, z]] = dot([[u, v, w]], [vec_a, vec_b, vec_c])
:param lattice_parameters: float or list in Angstroms & degrees, see gen_lattice_parameters()
:param kwargs: lattice parameters
:returns: [3x3] array, as [vec_a, vec_b, vec_c] in Angstroms
- busingandlevy(*lattice_parameters, **kwargs)
- Calculate the Busing and Levy B-matrix from lattice parameters
"we choose the x-axis parallel to a*, the y-axis in the plane of a* and b*,
and the z-axis perpendicular to that plane"
From: W. R. Busing and H. A. Levy, Acta Cryst. (1967). 22, 457-464
"Angle calculations for 3- and 4-circle X-ray and neutron diffractometers"
See also: https://docs.mantidproject.org/nightly/concepts/Lattice.html
Creates a matrix to transform (hkl) into a cartesian basis:
(qx,qy,qz)' = B.(h,k,l)' (where ' indicates a column vector)
The B matrix is related to the reciprocal basis vectors:
(astar, bstar, cstar) = 2 * np.pi * B.T
Where cstar is defined along the z-axis
:param lattice_parameters: float or list in Angstroms & degrees, see gen_lattice_parameters()
:param kwargs: lattice parameters
:returns: [3x3] array B matrix in inverse-Angstroms (no 2pi)
- choose_basis(name)
- Return a basis function based on a name
Available options:
1. 'MaterialsProject': c || z, b* || y
2. 'Vesta': a || x, c* || z
3. 'BusingandLevy': c || z, a* || x, 'default'
:param name: str name of basis
:return: function
- dspacing(h, k, l, *lattice_parameters, **kwargs)
- Calculate the lattice d-spacing for Bragg reflection (h,k,l)
d = lambda / 2 * sin(theta) = 2*pi / |h.a* + k.b* + l.c*|
:param h, k, l: Miller-indices of reflection
:param lattice_parameters: float or list in Angstroms & degrees, see gen_lattice_parameters()
:param kwargs: lattice parameters
:return: float in Angstroms
- gen_lattice_parameters(*lattice_parameters, **kwargs)
- Generate list of lattice parameters:
a,b,c,alpha,beta,gamma = gen_lattice_parameters(*args)
args:
1 -> a=b=c=1,alpha=beta=gamma=90
[1,2,3] -> a=1,b=2,c=3,alpha=beta=gamma=90
[1,2,3,120] -> a=1,b=2,c=3,alpha=beta=90,gamma=120
[1,2,3,10,20,30] -> a=1,b=2,c=3,alpha=10,beta=20,gamma=30
1,2,3,10,20,30 -> a=1,b=2,c=3,alpha=10,beta=20,gamma=30
a=1,b=2,c=3,alpha=10,beta=20,gamma=30 -> a=1,b=2,c=3,alpha=10,beta=20,gamma=30
:param lattice_parameters: float or list in Angstroms & degrees
:param kwargs: lattice parameters
:return: a,b,c,alpha,beta,gamma
- index_lattice(coords, basis_vectors)
- Index cartesian coordinates on a lattice defined by basis vectors
Usage (reciprocal space):
[[h, k, l], ...] = index_lattice([[qx, qy, qz], ...], [a*, b*, c*])
Usage (direct space):
[u, v, w] = index_lattice([x, y, z], [a, b, c])
:param coords: [nx3] array of coordinates
:param basis_vectors: [3*3] array of basis vectors [a[3], b[3], c[3]]
:return: [nx3] array of vectors in units of reciprocal lattice vectors
- lattice_volume(*lattice_parameters, **kwargs)
- Calculate basis volume from lattice parameters
volume = vec_a . (vec_b X vec_c)
:param lattice_parameters: float or list in Angstroms & degrees, see gen_lattice_parameters()
:param kwargs: lattice parameters
:returns: float in Angstroms cubed
- random_basis(symmetry='triclinic', basis_option='default')
- Generate a random basis of unit vectors from a real set of lattice parameters
:param symmetry: string 'cubic', 'tetragona', 'rhobohedral', 'monoclinic-a/b/c', 'triclinic'
:param basis_option: str name of basis, 'materialsproject', 'vesta', 'busingandlevy'
:return: [3x3] array, as [vec_a, vec_b, vec_c] in Angstroms
- random_lattice(symmetry='triclinic')
- Return a random set of real lattice parameters
:param symmetry: string 'cubic', 'tetragona', 'rhobohedral', 'monoclinic-a/b/c', 'triclinic'
:return: (a, b, c, alpha, beta, gamma) lattice parameters in Angstroms/ degrees
- reciprocal_basis(basis_vectors)
- Return the reciprocal basis vectors
[a*, b*, c*] = 2*pi*inv([a, b, c]).T
:param basis_vectors: [3*3] basis vectors array [a[3], b[3], c[3]]
:return: [3*3] array of reciprocal vectors [a*[3], b*[3], c*[3]]
- reciprocal_lattice_parameters(*lattice_parameters, **kwargs)
- Return the reciprocal lattice parameters in inverse-angstroms and degrees
:param lattice_parameters: float or list in Angstroms & degrees, see gen_lattice_parameters()
:param kwargs: lattice parameters
:return: a*, b*, c*, alpha*, beta*, gamma*
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