A C++ library for symmetry operations and linear interpolation within an irreducible part of the first Brillouin zone. Wrapped for use in python using pybind11.

irreducible polyhedron

When provided with the lattice parameters or basis vectors of a real space spacegroup and its Hall symbol or number as determined by, e.g., Spglib, brille can

• construct the first Brillouin zone
• determine its high symmetry points
• find a irreducible polyhedron and verify that its conforms to the pointgroup symmetry of the spacegroup.

Constructing and irreducible Brillouin zone polyhedron for a face centered cubic lattice can be accomplished with, e.g.,

    import brille

    direct_lattice = brille.Direct((4.96, 4.96, 4.96), (90, 90, 90), 'Fd-3m')
    brillouin_zone = brille.BrillouinZone(direct_lattice.star)

interpolation

Interpolating eigenvalues and eigenvectors across a degenerate point could lead to misidentified equivalent modes. Since the eigenvectors are distinguishable at all points away from the high-symmetry directions, a hybrid orthogonal/triangulated grid defined in an irreducible part of the Brillouin zone can be used to avoid mode misidentification.

brille can construct

• an orthogonal grid guaranteed to contain the first Brillouin zone
• a triangulated set of points filling an irreducible polyhedron or the first Brillouin zone
• or a hybrid orthogonal/triangulated grid where only the surface cells are triangulated to improve point location time while preserving polyhedral conformity.

Of these options the third is most appropriate for the interpolation of models used in the analysis of inelastic neutron scattering data is the hybrid grid.

Dependencies

TetGen

A modified version of TetGen is used to create refined tetrahedral meshes in the irreducible portion of the first Brillouin zone.

The modified version is included as part of this repository.

Installation

From the root folder of this repository use Python 3 to build and install this library.

python setup.py install

Alternatively, the python module, C++ library, and catch2 based tests can be built directly using cmake.