Cluster Orbit Set

A description of a set of cluster orbits.

This format is used for the clust.json file generated by CASM when a basis set is constructed using the casm bset --update method.

Cluster Orbit Set attributes:

Name	Description	Format
`bspecs`	Basis set specifications	Basis Set Specs
`orbits`	Cluster orbit set	array of Cluster Orbit
`prim`	Primitive crystal structure and DoF	Prim

Cluster Orbit attributes:

Name	Description	Format
`linear_orbit_index`	Linear cluster orbit index	int
`mult`	Number of equivalent clusters in the orbit	int
`prototype`	Representation of the prototype cluster	Prototype Cluster

Prototype Cluster attributes:

Name	Description	Format
`invariant_group`	Indices of prim factor group operations that leave the prototype cluster invariant	array of int
`invariant_group_descriptions`	Prototype cluster invariant group operation descriptions	array of string
`max_length`	Maximum distance between sites in the cluster.	number
`min_length`	Minimum distance between sites in the cluster.	number
`sites`	Cluster site coordinates	array of integral site coordinates

bspecs: Basis Function Specs

A copy of the basis set specifications (bspecs.json) used to generate the basis set.
orbits: array of Cluster Orbit Set.

An array of cluster orbit objects, one for each orbit generated, including the null cluster orbit.
prim: Prim

A copy of the prim used to generate the basis set.
site_functions: array of Site Functions, shape=(n_sublattice,)

The site_functions array contains one site functions object for each sublattice in the prim.

linear_orbit_index: int

Linear cluster orbit index
mult: int

Cluster multiplicity, the number of symmetrically equivalent clusters in the orbit.
prototype: Prototype Cluster

Information about one cluster (the “prototype”) in the orbit of symmetrically equivalent clusters.

invariant_group: array of int

Indices (begins with 0) of symmetry operations in the prim factor group which leave the prototype cluster invariant (up to lattice vector translations).
invariant_group_descriptions: array of string

Descriptions of the invariant group operations, following the conventions of the International Tables for Crystallography, and using the fractional representation for coordinates and vectors.
Example:
```
"invariant_group_descriptions" : [
  "1",
  "2 x, 0.5, -x",
  "2 0, y, 0",
  "2 x, 0.5-x, x",
  "m x, y, x",
  "m 2*x, 0.5-x+y, -2*y",
  "m x, y, -x",
  "-1 0.0000000 0.5000000 0.0000000"
]
```
max_length: number

Maximum distance between sites in the cluster.
min_length: number

Minimum distance between sites in the cluster.
sites: array of integral site coordinates

Sites are represented using integral site coordinates [b, i, j, k], where b=sublattice index, and i,j,k are lattice vector indices.
Example:
```
"sites" : [
  [ 0, 0, 0, 0 ],
  [ 0, 0, 1, 0 ]
]
```