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LatticeMaker

Stable Dev Build Status

This is a package for constructing lattices in Julia.

Installation

using Pkg
Pkg.add(url="https://github.com/nicolasloizeau/LatticeMaker.jl")

Usage

Standard lattices constructors are provided : SquareLattice, CubicLattice, TriangularLattice, HexagonalLattice and KagomeLattice. Custom lattices can be constructed using UnitCell.

Example: Construct a hexagonal lattice with 3*4 cells and periodic boundary conditions along the x-axis, and plot it:

using CairoMakie # for plotting
using LatticeMaker
lattice = HexagonalLattice(4,5; periodic=(true, false))
plot_lattice(lattice)
Example block output
positions(lattice)
40-element Vector{Tuple{Float64, Float64}}:
 (0.0, 0.0)
 (0.5, 0.28867513459481287)
 (0.5, 0.8660254037844386)
 (1.0, 1.1547005383792515)
 (1.0, 1.7320508075688772)
 (1.5, 2.02072594216369)
 (1.5, 2.598076211353316)
 (2.0, 2.886751345948129)
 (2.0, 3.4641016151377544)
 (2.5, 3.7527767497325675)
 ⋮
 (3.5, 0.28867513459481287)
 (3.5, 0.8660254037844386)
 (4.0, 1.1547005383792515)
 (4.0, 1.7320508075688772)
 (4.5, 2.02072594216369)
 (4.5, 2.598076211353316)
 (5.0, 2.886751345948129)
 (5.0, 3.4641016151377544)
 (5.5, 3.7527767497325675)
edges(lattice)
56-element Vector{Vector{Int64}}:
 [1, 2]
 [1, 32]
 [11, 12]
 [2, 11]
 [21, 22]
 [12, 21]
 [31, 32]
 [22, 31]
 [3, 4]
 [3, 34]
 ⋮
 [19, 20]
 [10, 19]
 [18, 19]
 [29, 30]
 [20, 29]
 [28, 29]
 [39, 40]
 [30, 39]
 [38, 39]
LatticeMaker.UnitCell — Type
UnitCell{D}

A unit cell in D dimensions, defined by its lattice vectors, the positions of the sites within the unit cell, and the edges connecting the sites.

source
LatticeMaker.CubicLattice — Method
CubicLattice(Nx, Ny, Nz)

Create a cubic lattice of size (Nx, Ny, Nz). Periodic boundary conditions are not implemented for 3D lattices at the moment.

source
LatticeMaker.HexagonalLattice — Method
HexagonalLattice(Nx, Ny; periodic=(false, false))

Create a hexagonal lattice of size (Nx, Ny). The periodic keyword argument specifies whether the lattice is periodic in the x and y directions, respectively.

source
LatticeMaker.KagomeLattice — Method
KagomeLattice(Nx, Ny; periodic=(false, false))

Create a kagome lattice of size (Nx, Ny). The periodic keyword argument specifies whether the lattice is periodic in the x and y directions, respectively.

source
LatticeMaker.SquareLattice — Method
SquareLattice(Nx, Ny; periodic=(false, false))

Create a square lattice with Nx sites in the x direction and Ny sites in the y direction. The periodic keyword argument specifies whether the lattice is periodic in the x and y directions, respectively.

source
LatticeMaker.TriangularLattice — Method
 TriangularLattice(Nx, Ny; periodic=(false, false))

Create a triangular lattice of size (Nx, Ny). The periodic keyword argument specifies whether the lattice is periodic in the x and y directions, respectively.

source
LatticeMaker.edges — Method
edges(lattice::Lattice; edge_indexes=1:length(lattice.cell.edges))

Returns a list of edges in the lattice, where each edge is represented as a couple of site indexes.

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LatticeMaker.plot_lattice — Method
plot_lattice(lattice::Lattice)

Plot the given lattice. Using GLMakie or CairoMakie if available. Returns a figure.

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LatticeMaker.plot_positions — Method
plot_positions(lattice::Lattice)

Plot the positions of the sites in the given lattice. Using GLMakie or CairoMakie if available. Returns a figure.

source
LatticeMaker.positions — Method
positions(lattice::Lattice)

Returns a vector of the positions of all sites in the lattice. The positions are ordered like sites.

source