wulfric.cell.from_params#

wulfric.cell.from_params(a=1.0, b=1.0, c=1.0, alpha=90.0, beta=90.0, gamma=90.0)[source]#

Constructs the cell from lattice parameters.

The spatial orientation of the cell is decided as

Lattice vector \(\boldsymbol{a_1}\) has the length a and oriented along \({\cal x}\) axis.
Lattice vector \(\boldsymbol{a_2}\) has the length b, is placed in \({\cal xy}\) plane and form an angle gamma with vector \(\boldsymbol{a_1}\), positive in a mathematical sense.
Lattice vector \(\boldsymbol{a_3}\) has the length c and form an angle alpha with the vector \(\boldsymbol{a_2}\) and an angle beta with the vector \(\boldsymbol{a_1}\).

Parameters:

afloat, default 1.0: Length of the \(\boldsymbol{a_1}\) vector.
bfloat, default 1.0: Length of the \(\boldsymbol{a_2}\) vector.
cfloat, default 1.0: Length of the \(\boldsymbol{a_3}\) vector.
alphafloat, default 90.0: Angle between vectors \(\boldsymbol{a_2}\) and \(\boldsymbol{a_3}\) given in degrees.
betafloat, default 90.0: Angle between vectors \(\boldsymbol{a_1}\) and \(\boldsymbol{a_3}\) given in degrees.
gammafloat, default 90.0: Angle between vectors \(\boldsymbol{a_1}\) and \(\boldsymbol{a_2}\) given in degrees.

Returns:

cell(3, 3) numpy.ndarray

Matrix of a direct cell, rows are interpreted as vectors.

cell = [
    [a1_x, a1_y, a1_z],
    [a2_x, a2_y, a2_z],
    [a3_x, a3_y, a3_z],
]

Raises:

ValueError: If parameters could not form a parallelepiped.

See also

get_params
wulfric.geometry.parallelepiped_check: Check if parameters can form a parallelepiped.

Examples

>>> import wulfric
>>> import numpy as np
>>> np.around(wulfric.cell.from_params(1, 2, 3, 90, 90, 60), 6)
array([[1.      , 0.      , 0.      ],
       [1.      , 1.732051, 0.      ],
       [0.      , 0.      , 3.      ]])

>>> wulfric.cell.from_params(1, 2, 3, 60, 60, 130)
Traceback (most recent call last):
...
ValueError: Parameters could not form a parallelepiped:
a = 1
b = 2
c = 3
alpha = 60
beta = 60
gamma = 130
Inequality gamma < alpha + beta is not satisfied with numerical tolerance: 0.0001