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Consider the following bestcorr.out file:

2   0.866025    -0.000000   0.000000    -0.000000
2   0.866025    0.000000    -0.000000   0.000000
2   0.866025    -0.000000   0.000000    -0.000000
2   1.000000    -0.000000   0.000000    -0.000000
2   1.000000    -0.000000   -0.000000   -0.000000
2   1.000000    -0.000000   0.000000    -0.000000
2   1.414214    -0.000000   0.000000    -0.000000
2   1.414214    -0.000000   -0.000000   -0.000000
2   1.414214    0.006944    0.000000    0.006944
Objective_function= -1.630678

This was for a BCC ternary SQS. Let's consider the $1^{st}$ nearest neighbour (NN) pairs. There are three of them; how do we differentiate among them?

Here is the part of clusters.out that concerns these pairs:

4
0.86603
2
1.50000 0.50000 0.50000 1 0
1.00000 -0.00000 1.00000 1 0

8
0.86603
2
1.50000 0.50000 0.50000 1 1
1.00000 -0.00000 1.00000 1 0

4
0.86603
2
1.50000 0.50000 0.50000 1 1
1.00000 -0.00000 1.00000 1 1

mcsqs manual page: https://www.brown.edu/Departments/Engineering/Labs/avdw/atat/manual/node47.html

corrdump manual page: https://www.brown.edu/Departments/Engineering/Labs/avdw/atat/manual/node35.html

Why are there $3$ different kinds of pairs with the same distance? At first, I thought in a ternary alloy it could mean $AB$, $BC$, and $CA$ pairs. $A$, $B$, and $C$ being constituent atoms. Now that I think of it, that doesn't make sense else it would apply to triangles and higher clusters as well but it doesn't.

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