Brillouin
Brillouin.jl is a Julia package that provides tools to generate and visualize k-space paths and Brillouin zones that arise for crystalline eigenvalue problems. The functionalities are inspired by the Python SeeK-path package.
Examples
Generate the Brillouin zone of a crystal in space group 147 (Bravais type hP; using Crystalline.jl to easily generate a standard basis):
julia> using Brillouin, Crystalline
julia> Rs = directbasis(147)
julia> Gs = reciprocalbasis(Rs)
julia> cell = wignerseitz(Gs)
Cell{3} (8 faces, 12 vertices):
verts: [-0.0, -0.577, -0.866]
[0.0, 0.577, -0.866]
[0.5, 0.289, -0.866]
[0.5, -0.289, -0.866]
[-0.0, -0.577, 0.866]
[0.0, 0.577, 0.866]
[-0.5, 0.289, 0.866]
[-0.5, -0.289, 0.866]
[-0.5, -0.289, -0.866]
[-0.5, 0.289, -0.866]
[0.5, -0.289, 0.866]
[0.5, 0.289, 0.866]
faces: [4, 3, 12, 11]
[2, 6, 12, 3]
[11, 12, 6, 7, 8, 5]
[10, 9, 8, 7]
[7, 6, 2, 10]
[2, 3, 4, 1, 9, 10]
[5, 8, 9, 1]
[4, 11, 5, 1]
basis: [6.283, 3.628, 0.0]
[0.0, 7.255, 0.0]
[0.0, 0.0, 5.027]The resulting Brillouin zone can be plotted using e.g. PlotlyJS.jl (or 3D-capable backends of AbstractPlotting.jl such as GLMakie.jl):
julia> using PlotlyJS
julia> plot(cell)Examples of interactive visualizations are included in the documentation.
Irreducible k-paths are returned by irrfbz_path, and can similarly be visualized (see examples in documentation):
julia> kp = irrfbz_path(147, Rs)
KPath{3} (7 points, 3 paths, 13 points in paths):
points: :M => [0.5, 0.0, 0.0]
:A => [0.0, 0.0, 0.5]
:H => [0.3333333333333333, 0.3333333333333333, 0.5]
:K => [0.3333333333333333, 0.3333333333333333, 0.0]
:Γ => [0.0, 0.0, 0.0]
:L => [0.5, 0.0, 0.5]
:H₂ => [0.3333333333333333, 0.3333333333333333, -0.5]
paths: [:Γ, :M, :K, :Γ, :A, :L, :H, :A]
[:L, :M]
[:H, :K, :H₂]The resulting object can be interpolated, using either interpolate(kp, N) or splice(kp, N), which produces an KPathInterpolant iterable whose elements interpolate the connected paths (and enable convenient plotting of band structure diagrams).