Represent the Miller indices or Miller–Bravais indices.

Miller(i, j, k)

Represent the Miller indices in the real space (crystal directions).

MillerBravais(i, j, k, l)

Represent the Miller–Bravais indices in the real space (crystal directions).

ReciprocalMiller(i, j, k)

Represent the Miller indices in the reciprocal space (planes).

ReciprocalMillerBravais(i, j, k, l)

Represent the Miller–Bravais indices in the reciprocal space (planes).

lengthof(x::Union{AbstractMiller,AbstractMillerBravais}, g::MetricTensor)

Calculate the magnitude of a given indices with respect to a specified metric tensor.

anglebtw(x::Miller, y::Miller, g::MetricTensor)
anglebtw(x::MillerBravais, y::MillerBravais, g::MetricTensor)
anglebtw(x::ReciprocalMiller, y::ReciprocalMiller, g::MetricTensor)
anglebtw(x::ReciprocalMillerBravais, y::ReciprocalMillerBravais, g::MetricTensor)

Calculate the angle (in degrees) between two directions by:

\[\cos\theta = \frac{\mathbf{x} \cdot \mathbf{y}}{\lvert\mathbf{x}\rvert \lvert\mathbf{y}\rvert} = \frac{\sum_{ij} x_i g_{ij} y_j}{\sqrt{\sum_{ij} x_i g_{ij} x_j} \sqrt{\sum_{ij} y_i g_{ij} y_j}}.\]

familyof(x::Union{Miller,MillerBravais,ReciprocalMiller,ReciprocalMillerBravais})

List the all the directions/planes that are equivalent to x by symmetry.

interplanar_spacing(x::Union{ReciprocalMiller,ReciprocalMillerBravais}, g::MetricTensor)

Calculate the interplanar spacing by:

\[d_{h\ k \ l} = \frac{1}{\lvert \mathbf{x}_{h\ k \ l}\rvert}.\]

m_str(s)

Generate the Miller indices or Miller–Bravais indices quickly.

Examples

julia> m"[-1, 0, 1]"
3-element Miller:
 -1
  0
  1

julia> m"<2, -1, -1, 3>"
4-element MillerBravais:
  2
 -1
 -1
  3

julia> m"(-1, 0, 1)"
3-element ReciprocalMiller:
 -1
  0
  1

julia> m"(1, 0, -1, 0)"
4-element ReciprocalMillerBravais:
  1
  0
 -1
  0