CrystalBase

CrystalBase.jl is a tiny Julia package for working with crystal structures in real and reciprocal space.

The package only defines a few container types and provides some utility functions. It does not involve heavy computations but just to avoid rewriting boilerplate code in other packages.

Example

Real and reciprocal lattice vectors

julia> using CrystalBase

# Define a matrix for lattice vectors
julia> a1, a2, a3 = [1.0, 0.0, 0.0], [0.0, 2.0, 0.0], [0.0, 0.0, 3.0]
julia> lattice = mat3(a1, a2, a3)
3×3 StaticArraysCore.SMatrix{3, 3, Float64, 9} with indices SOneTo(3)×SOneTo(3):
 1.0  0.0  0.0
 0.0  2.0  0.0
 0.0  0.0  3.0

# Compute the reciprocal lattice (as a matrix)
julia> recip_lattice = reciprocal_lattice(lattice)
3×3 StaticArraysCore.SMatrix{3, 3, Float64, 9} with indices SOneTo(3)×SOneTo(3):
 6.28319  0.0      0.0
 0.0      3.14159  0.0
 0.0      0.0      2.0944

# Get the lattice vectors, which are the columns of the matrix
julia> lattice_vectors(recip_lattice)
3-element Vector{StaticArraysCore.SVector{3, Float64}}:
 [6.283185307179586, 0.0, 0.0]
 [0.0, 3.141592653589793, 0.0]
 [0.0, 0.0, 2.0943951023931953]

# Or a convenience function to directly get the vectors
julia> reciprocal_lattice_vectors(a1, a2, a3)
3-element Vector{StaticArraysCore.SVector{3, Float64}}:
 [6.283185307179586, 0.0, 0.0]
 [0.0, 3.141592653589793, 0.0]
 [0.0, 0.0, 2.0943951023931953]

# Compute the real-space lattice vectors
julia> real_lattice(recip_lattice)
3×3 StaticArraysCore.SMatrix{3, 3, Float64, 9} with indices SOneTo(3)×SOneTo(3):
 1.0  0.0  0.0
 0.0  2.0  0.0
 0.0  0.0  3.0

Fractional to Cartesian coordinates interconversion

julia> lattice = mat3([1.0, 0.0, 0.0], [0.0, 2.0, 0.0], [0.0, 0.0, 3.0])
julia> frac_coords = [0.5, 0.5, 0.5]
julia> cart_coords = frac_to_cart(lattice, frac_coords)
3-element StaticArraysCore.SVector{3, Float64} with indices SOneTo(3):
 0.5
 1.0
 1.5

# Also support multiple coordinates at once
julia> frac_to_cart(lattice, [cart_coords, cart_coords])
2-element Vector{StaticArraysCore.SVector{3, Float64}}:
 [0.5, 2.0, 4.5]
 [0.5, 2.0, 4.5]

# Convert back to fractional coordinates
julia> cart_to_frac(lattice, cart_coords)
3-element StaticArraysCore.SVector{3, Float64} with indices SOneTo(3):
 0.5
 0.5
 0.5

K-point paths in the Brillouin zone

# Define a kpoint path with explicit kpoint coordinates along the path
julia> points = [[i/10, 0.0, 0.0] for i in 0:5]
julia> indices = [1, 6]
julia> labels = ["Γ", "X"]
julia> KPath(recip_lattice, points, indices, labels)
KPath{Float64} with 6 k-points and 2 high-symmetry labels:
  Path: Γ → X
  High-symmetry k-points:
    1: Γ  (0.0, 0.0, 0.0)
    6: X  (0.5, 0.0, 0.0)

# Alternatively, only define the high-symmetry kpoints along the path, without
# intermediate kpoints between them
julia> segments = [["Γ", "M"], ["M", "K"]]
julia> coords = Dict("Γ" => [0.0, 0.0, 0.0], "M" => [0.5, 0.5, 0.0], "K" => [1/3, 1/3, 0.0])
julia> KSegment(recip_lattice, segments, coords)
KSegment{Float64} with 2 segments and 3 high-symmetry k-points:
  Segment 1: Γ → M
  Segment 2: M → K
  Coordinates:
    K  (0.3333, 0.3333, 0.0)
    M  (0.5, 0.5, 0.0)
    Γ  (0.0, 0.0, 0.0)