MetricTensor(a, b, c, α, β, γ)

Generate a MetricTensor from the six cell parameters.

MetricTensor(𝐚::AbstractVector, 𝐛::AbstractVector, 𝐜::AbstractVector)

Generate a MetricTensor from the three basis vectors.

MetricTensor(lattice::Lattice)

Generate a MetricTensor from a Lattice.

MonkhorstPackGrid(mesh, is_shift)

Represent the Monkhorst–Pack grid.

Arguments

• mesh: A length-three vector specifying the k-point grid ($nk_1 × nk_2 × nk_3$) as in Monkhorst–Pack grids.
• is_shift: A length-three vector specifying whether the grid is displaced by half a grid step in the corresponding directions.

PrimitiveFromStandardized(tf::AbstractMatrix)

Construct the transformation from a standardized cell to a primitive cell.

StandardizedFromPrimitive(tf::AbstractMatrix)

Construct the transformation from a primitive cell to a standardized cell.

Lattice(a, b, c, α, β, γ; axis = :a)

Construct a Lattice from the six cell parameters.

The default convention we used here is that edge vector 𝐚 in the positive x-axis direction, edge vector 𝐛 in the x-y plane with a positive y-axis component, and edge vector 𝐜 with a positive z-axis component in the Cartesian system. See Wikipedia. You can also choose axis = :c.

Lattice(g::MetricTensor)

Construct a Lattice from a MetricTensor.

atomicmass(element::Element)
atomicmass(i::Union{AbstractString,Integer,Symbol})

Return the atomic mass of an element.

cellvolume(a, b, c, α, β, γ)

Calculate the cell volume from 6 cell parameters.

cellvolume(l::Lattice)
cellvolume(c::Cell)

Calculate the cell volume from a Lattice or a Cell.

cellvolume(g::MetricTensor)

Calculate the cell volume from a MetricTensor.

crystaldensity(lattice::Lattice, atoms)
crystaldensity(cell::Cell)

Calculate the density of a crystal structure.

Here, atoms is an iterable of atomic numbers, element names, symbols, or Mendeleev.Elements. You can extend the atomicmass method to work with custom types.

distance(𝐚::ReducedCoordinates, 𝐛::ReducedCoordinates, g::MetricTensor)

Get the distance between two atomic coordinates.

islefthanded(lattice::Lattice)

Test whether the basis vectors are defined to be left-handed.

The basis vectors are left-handed if and only if

\[\mathbf{a} \cdot (\mathbf{b} \times \mathbf{c}) < 0.\]

isrighthanded(lattice::Lattice)

Test whether the basis vectors are defined to be right-handed.

The basis vectors are right-handed if and only if

\[\mathbf{a} \cdot (\mathbf{b} \times \mathbf{c}) > 0.\]

latticeconstants(lattice::Lattice)

Get the six lattice constants from a lattice.

latticeconstants(g::MetricTensor)

Get the six lattice constants from a MetricTensor.

latticesystem(bravais::Bravais)

Get the lattice system of a Bravais lattice.

latticesystem(lattice::Lattice; angletol=1e-5, lengthtol=1e-5)

Get the lattice system of a Lattice.

lengthof(𝐚::ReducedCoordinates, g::MetricTensor)

Get the length of an atomic coordinates.

periodicity(lattice::Lattice)

Get crystal periodicity in $x$, $y$, and $z$ direction from the Lattice.

super(cell::Cell, factors::AbstractMatrix{<:Integer})
super(cell::Cell, factors::AbstractVector{<:Integer})
super(cell::Cell, factor::Integer)

Create a supercell from cell.

super(lattice::Lattice, factors::AbstractMatrix{<:Integer})
super(lattice::Lattice, factors::AbstractVector{<:Integer})
super(lattice::Lattice, factor::Integer)

Create a supercell from lattice.