Calculate Warren-Cowley short-range-order

[dgehringer]

Calculate Warren-Cowley short-range-order

[dgehringer]

Many thanks for this report! Honestly, I still have to find the problem. The input is fine, and I can reproduce the error. Once I know more I let you know

[QQQsupermans]

Many thanks for this report! Honestly, I still have to find the problem. The input is fine from the input, and I can reproduce the error. Once I know more I let you know

Thank you very much for your reply! I think the difference may be due to the formula. The theoretical SRO formula is α=1-(Pij/Cj), where Pij is probability of j around i atom, and Cj is concentration of j. Taking 1st nearest neighbor as an example.

(1) For pure Ni (fcc), the theoretical SRO is 1-1/1=0. For your formula, the SRO of Ni-Ni is α=1-(12/2 N)/(N * 12 * 1 * 1)=0.5.
(2) For Ni3Al (L12), the theoretical SRO of Ni-Ni is 1-(2/3)/(3/4)=1/9. For your formula, the SRO of Ni-Ni is α=1-3N/(N * 12 * 0.75 * 0.75)=5/9. There are 6N bonds in Ni3Al (L12), 3N for Ni-Al, and 3N for Ni-Ni.

By the way, how to cite your code? Have you published papers by using this code.
Thank you!

[dgehringer]

The reason why the the value is wrong is that the computation of the occupations of the coordination shells is "wrong".

The programm basically creates a histogramm of the distance matrix, to determine how many atoms are in the individual coordination shells. As in this small cell there are only 4 atoms, all the other three atoms are in the first coordination shell. Therefore, we get with 3 Ni-Ni bonds, α=1 - 3/(4 * 3 * (3/4)^2) = 1 - 4/9 = 5/9 = 0.55555555559. This is how we get to this wrong answer.

The reason why that is so is that, we usually deal with super-cells where this case does never happen (for us at least).

By the way, how to cite your code? Have you published papers by using this code.

Actually not yet! I'm working on it! I'm intensively working on a new version of it where I want to fix all those problems

[QQQsupermans]

Great! Looking forward to your excellent job!
In other words, at present, this code can correctly deal with the short-range order of A-B bonds when A and B are different, is it right?
For Ni3Al, I use 108-atom (3 * 3 * 3) supercell, and the result is same.

[dgehringer]

For Ni3Al, I use 108-atom (3 * 3 * 3) supercell, and the result is same.

Indeed I can confirm that

I think the difference may be due to the formula. The theoretical SRO formula is α=1-(Pij/Cj), where Pij is probability of j around i atom, and Cj is concentration of j. Taking 1st nearest neighbor as an example.
(1) For pure Ni (fcc), the theoretical SRO is 1-1/1=0. For your formula, the SRO of Ni-Ni is α=1-(12/2 N)/(N * 12 * 1 * 1)=0.5.
(2) For Ni3Al (L12), the theoretical SRO of Ni-Ni is 1-(2/3)/(3/4)=1/9. For your formula, the SRO of Ni-Ni is α=1-3N/(N * 12 * 0.75 * 0.75)=5/9. There are 6N bonds in Ni3Al (L12), 3N for Ni-Al, and 3N for Ni-Ni.

I also double checked that. Tt seems that you were right! I do get one half for the pure systems
So I have to correct myself as it seems the the computation of the shell occupation is alright, and the difference comes from, as you already said, the different definition