Coupled DoF

Coupled occupation, displacement, and strain DoF

This example constructs the prim for simple cubic crystal system with binary occupation degrees of freedom (DoF), atomic displacement DoF, and strain DoF, using the Green-Lagrange strain metric, and the symmetry-adapted strain basis.

To construct this prim, the following must be specified:

• the lattice vectors

• basis site coordinates

• occupant DoF

• atomic displacement DoF

• strain DoF

import numpy as np
import libcasm.xtal as xtal
from math import sqrt

# Lattice vectors
lattice_column_vector_matrix = np.array([
    [1., 0., 0.],  # a
    [0., 1., 0.],  # a
    [0., 0., 1.],  # a
]).transpose()  # <--- note transpose
lattice = xtal.Lattice(lattice_column_vector_matrix)

# Basis sites positions, as columns of a matrix,
# in fractional coordinates with respect to the lattice vectors
coordinate_frac = np.array([
    [0., 0., 0.],
]).transpose()  # coordinates of basis site, b=0

# Occupation degrees of freedom (DoF)
occ_dof = [
    ["A", "B"],  # occupants allowed on basis site, b=0
]

# Local continuous degrees of freedom (DoF)
disp_dof = xtal.DoFSetBasis("disp")  # Atomic displacement
local_dof = [
    [disp_dof],  # basis site, b=0
]

# Global continuous degrees of freedom (DoF)
GLstrain_dof = xtal.DoFSetBasis(
    dofname="GLstrain",
    axis_names=["e_{1}", "e_{2}", "e_{3}", "e_{4}", "e_{5}", "e_{6}"],
    basis=np.array([
        [1. / sqrt(3), 1. / sqrt(3), 1. / sqrt(3), 0.0, 0.0, 0.0],
        [1. / sqrt(2), -1. / sqrt(2), 0.0, 0.0, 0.0, 0.0],
        [-1. / sqrt(6), -1. / sqrt(6), 2. / sqrt(6), 0.0, 0.0, 0.0],
        [0.0, 0.0, 0.0, 1.0, 0.0, 0.0],
        [0.0, 0.0, 0.0, 0.0, 1.0, 0.0],
        [0.0, 0.0, 0.0, 0.0, 0.0, 1.0],
    ]).transpose())
global_dof = [GLstrain_dof]

# Construct the prim
prim = xtal.Prim(lattice=lattice,
                 coordinate_frac=coordinate_frac,
                 occ_dof=occ_dof,
                 local_dof=local_dof,
                 global_dof=global_dof,
                 title="simple_cubic_coupled")

This prim as JSON: simple_cubic_coupled.json