wulfric.cell.SC_TRI

wulfric.cell.SC_TRI(a: float, b: float, c: float, alpha: float, beta: float, gamma: float, input_reciprocal=False)

Constructs primitive triclinic cell as defined in [1].

\[\begin{split}\begin{matrix} \boldsymbol{a}_1 &=& (a, &0, &0)\\ \boldsymbol{a}_2 &=& (b\cos\gamma, &b\sin\gamma, &0)\\ \boldsymbol{a}_3 &=& (c\cos\beta, &\dfrac{c(\cos\alpha - \cos\beta\cos\gamma)}{\sin\gamma}, &\dfrac{c}{\sin\gamma}\sqrt{\sin^2\gamma - \cos^2\alpha - \cos^2\beta + 2\cos\alpha\cos\beta\cos\gamma}) \end{matrix}\end{split}\]

Parameters:

afloat

Length of the first lattice vector of the conventional cell.

bfloat

Length of the second lattice vector of the conventional cell.

cfloat

Length of the third lattice vector of the conventional cell.

alphafloat

Angle between vectors \(a_2\) and \(a_3\) of the conventional cell in degrees.

betafloat

Angle between vectors \(a_1\) and \(a_3\) of the conventional cell in degrees.

gammafloat

Angle between vectors \(a_1\) and \(a_2\) of the conventional cell in degrees.

input_reciprocalbool, default False

Whether to interpret input as reciprocal parameters.

Returns:

cell(3, 3) numpy.ndarray

Matrix of a primitive 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],
]

References

[1]

Setyawan, W. and Curtarolo, S., 2010. High-throughput electronic band structure calculations: Challenges and tools. Computational materials science, 49(2), pp. 299-312.

Examples

>>> import wulfric
>>> wulfric.cell.SC_TRI(a=3, b=5, c=7, alpha=45, beta=33, gamma=21)
array([[ 3.        ,  0.        ,  0.        ],
       [ 4.66790213,  1.79183975,  0.        ],
       [ 5.87069398, -1.48176621,  3.51273699]])