Multi-element spin variable in ATAT

Alloy Theoretic Automated Toolkit (ATAT)
1

Hi every one,

In the cluster expansion formalism, the spin variable is taken \pm 1 for a binary system.
In a ternary, on should use a orthogonal base with 3 variables such as:

[                             [
gamma1 =        [ 0  -1  -1     spin1
gamma1 = -1/2    -2   0   2     spin2
gamma1 =          0   1  -1 ]   spin3
]                             ]

(I think it cames from Barker, Hijmans and de Boer formalism. :shock:
There is a doc somewhere ?

Many thanks in advance.

2

I forgot to reply to myself that I found the answer to my old question in this paper:

https://doi.org/10.1016/j.calphad.2008.12.005