About the correlation function of my SQS structures

Alloy Theoretic Automated Toolkit (ATAT)
1

Dear Axel

I have a question about the correlation function of my generated SQS structure. There are two structures. Here is correlation mismatch:

The first composition is FCC-A2BCD Quaternary (50 atoms). I found the ideal mismatch for the first nn, but I just consider the pair, and the maximum distance is 1.
2 0.707107 0.040000 0.040000 0.000000
2 0.707107 0.000000 0.000000 0.000000
2 0.707107 0.040000 0.040000 0.000000
2 0.707107 -0.000000 0.000000 -0.000000
2 0.707107 0.000000 0.000000 -0.000000
2 0.707107 0.040000 0.040000 -0.000000
2 1.000000 0.013333 0.040000 -0.026667
2 1.000000 -0.006667 0.000000 -0.006667
2 1.000000 0.040000 0.040000 0.000000
2 1.000000 -0.013333 0.000000 -0.013333
2 1.000000 -0.013333 0.000000 -0.013333
2 1.000000 0.040000 0.040000 -0.000000
Objective_function= -28.274271

The second composition is FCC-ABCDE Quinary (50 atoms). I didn’t found ideal mismatch for the first nn. However, I considered the triplets and longer distances. Here is the correlation mismatch:
2 0.707107 -0.015075 0.000000 -0.015075
2 0.707107 -0.002191 0.000000 -0.002191
2 0.707107 0.010417 0.000000 0.010417
2 0.707107 -0.010793 -0.000000 -0.010793
2 0.707107 -0.006198 0.000000 -0.006198
2 0.707107 0.005575 0.000000 0.005575
2 0.707107 0.030746 -0.000000 0.030746
2 0.707107 -0.005758 0.000000 -0.005758
2 0.707107 -0.003544 -0.000000 -0.003544
2 0.707107 -0.022969 0.000000 -0.022969
2 1.000000 -0.013484 0.000000 -0.013484
2 1.000000 -0.005415 0.000000 -0.005415
2 1.000000 0.025000 0.000000 0.025000
2 1.000000 -0.013143 -0.000000 -0.013143
2 1.000000 0.001424 0.000000 0.001424
2 1.000000 0.021266 0.000000 0.021266
2 1.000000 -0.007454 -0.000000 -0.007454
2 1.000000 0.005150 0.000000 0.005150
2 1.000000 0.022940 -0.000000 0.022940
2 1.000000 -0.009757 0.000000 -0.009757
2 1.224745 -0.022121 0.000000 -0.022121
2 1.224745 0.004381 0.000000 0.004381
2 1.224745 -0.001042 0.000000 -0.001042
2 1.224745 0.009876 -0.000000 0.009876
2 1.224745 -0.013788 0.000000 -0.013788
2 1.224745 0.009778 0.000000 0.009778
2 1.224745 -0.016305 -0.000000 -0.016305
2 1.224745 -0.017462 0.000000 -0.017462
2 1.224745 0.007089 -0.000000 0.007089
2 1.224745 -0.009129 0.000000 -0.009129
2 1.414214 -0.013484 0.000000 -0.013484
2 1.414214 -0.005735 0.000000 -0.005735
2 1.414214 -0.006250 0.000000 -0.006250
2 1.414214 0.007766 -0.000000 0.007766
2 1.414214 -0.029271 0.000000 -0.029271
2 1.414214 0.007249 0.000000 0.007249
2 1.414214 0.008385 -0.000000 0.008385
2 1.414214 0.005150 0.000000 0.005150
2 1.414214 -0.001354 -0.000000 -0.001354
2 1.414214 0.004271 0.000000 0.004271
2 1.581139 -0.003675 0.000000 -0.003675
2 1.581139 -0.017882 0.000000 -0.017882
2 1.581139 -0.002083 0.000000 -0.002083
2 1.581139 -0.004061 -0.000000 -0.004061
2 1.581139 -0.033385 0.000000 -0.033385
2 1.581139 -0.017205 0.000000 -0.017205
2 1.581139 -0.021429 -0.000000 -0.021429
2 1.581139 -0.012992 0.000000 -0.012992
2 1.581139 -0.001194 -0.000000 -0.001194
2 1.581139 -0.016615 0.000000 -0.016615
2 1.732051 0.008637 0.000000 0.008637
2 1.732051 -0.015950 0.000000 -0.015950
2 1.732051 0.015625 0.000000 0.015625
2 1.732051 -0.007587 -0.000000 -0.007587
2 1.732051 -0.005998 0.000000 -0.005998
2 1.732051 0.006332 0.000000 0.006332
2 1.732051 -0.009783 -0.000000 -0.009783
2 1.732051 0.022613 0.000000 0.022613
2 1.732051 0.009857 -0.000000 0.009857
2 1.732051 0.024748 0.000000 0.024748
2 1.870829 0.028711 0.000000 0.028711
2 1.870829 0.011230 0.000000 0.011230
2 1.870829 -0.000000 0.000000 -0.000000
2 1.870829 -0.001742 -0.000000 -0.001742
2 1.870829 0.014295 0.000000 0.014295
2 1.870829 -0.016996 0.000000 -0.016996
2 1.870829 0.014441 -0.000000 0.014441
2 1.870829 0.007748 0.000000 0.007748
2 1.870829 -0.015512 -0.000000 -0.015512
2 1.870829 0.013830 0.000000 0.013830
2 2.000000 -0.050000 0.000000 -0.050000
2 2.000000 -0.015851 0.000000 -0.015851
2 2.000000 0.029167 0.000000 0.029167
2 2.000000 -0.003027 -0.000000 -0.003027
2 2.000000 -0.030486 0.000000 -0.030486
2 2.000000 0.012824 0.000000 0.012824
2 2.000000 -0.005590 -0.000000 -0.005590
2 2.000000 -0.050000 0.000000 -0.050000
2 2.000000 -0.009796 -0.000000 -0.009796
2 2.000000 -0.052847 0.000000 -0.052847
3 0.707107 -0.004319 0.000000 -0.004319
3 0.707107 0.004849 0.000000 0.004849
3 0.707107 0.000890 0.000000 0.000890
3 0.707107 0.009230 -0.000000 0.009230
3 0.707107 0.000288 0.000000 0.000288
3 0.707107 -0.005421 0.000000 -0.005421
3 0.707107 -0.000390 -0.000000 -0.000390
3 0.707107 -0.006098 0.000000 -0.006098
3 0.707107 0.002126 -0.000000 0.002126
3 0.707107 0.003177 0.000000 0.003177
3 0.707107 -0.003913 0.000000 -0.003913
3 0.707107 -0.013594 0.000000 -0.013594
3 0.707107 -0.010633 -0.000000 -0.010633
3 0.707107 -0.008990 0.000000 -0.008990
3 0.707107 -0.004036 -0.000000 -0.004036
3 0.707107 -0.006572 0.000000 -0.006572
3 0.707107 -0.011306 0.000000 -0.011306
3 0.707107 0.001901 -0.000000 0.001901
3 0.707107 0.000754 0.000000 0.000754
3 0.707107 -0.012276 -0.000000 -0.012276
3 1.000000 0.003617 0.000000 0.003617
3 1.000000 -0.016707 0.000000 -0.016707
3 1.000000 0.001826 0.000000 0.001826
3 1.000000 -0.009534 -0.000000 -0.009534
3 1.000000 0.007587 0.000000 0.007587
3 1.000000 0.019132 0.000000 0.019132
3 1.000000 0.012500 0.000000 0.012500
3 1.000000 -0.008202 -0.000000 -0.008202
3 1.000000 -0.012688 0.000000 -0.012688
3 1.000000 -0.002031 0.000000 -0.002031
3 1.000000 -0.017972 0.000000 -0.017972
3 1.000000 -0.006098 -0.000000 -0.006098
3 1.000000 0.004799 -0.000000 0.004799
3 1.000000 -0.001999 -0.000000 -0.001999
3 1.000000 0.006357 -0.000000 0.006357
3 1.000000 0.000338 0.000000 0.000338
3 1.000000 0.017760 0.000000 0.017760
3 1.000000 -0.004993 0.000000 -0.004993
3 1.000000 -0.006077 -0.000000 -0.006077
3 1.000000 -0.003206 0.000000 -0.003206
3 1.000000 0.012683 0.000000 0.012683
3 1.000000 0.013725 -0.000000 0.013725
3 1.000000 -0.005402 0.000000 -0.005402
3 1.000000 0.025334 0.000000 0.025334
3 1.000000 -0.003473 -0.000000 -0.003473
3 1.000000 0.011888 -0.000000 0.011888
3 1.000000 0.003777 -0.000000 0.003777
3 1.000000 -0.004375 0.000000 -0.004375
3 1.000000 0.010605 0.000000 0.010605
3 1.000000 0.008602 -0.000000 0.008602
3 1.000000 -0.011728 0.000000 -0.011728
3 1.000000 -0.008249 -0.000000 -0.008249
3 1.000000 -0.005700 0.000000 -0.005700
3 1.000000 0.006652 -0.000000 0.006652
3 1.000000 0.006332 -0.000000 0.006332
3 1.000000 0.007951 0.000000 0.007951
3 1.000000 -0.017514 0.000000 -0.017514
3 1.000000 -0.007347 0.000000 -0.007347
3 1.000000 0.000990 0.000000 0.000990
3 1.000000 0.000757 -0.000000 0.000757
Objective_function= -34.990317

It seems that the second one has lower objective function, but it doe not have ideal mismatch like the first one. So I am going to wait one more week to see if I can find a good one.

My question is which of the following structures are better? Although the second one has lower objective function, this is because I considered longer distance and triplet. It does not have ideal mismatch for the first nn.

2

The value of the objective function can’t be compared across runs that have different range of correlations included. It also can’t be compared across different number of components.
The objective function is just there to guide the code in the right direction. Ultimately, you have to look at the correlation mismatch and decide if this is what you want.
Clealry, in your second run, having NO correlation matched exactly is not ideal. Then again, if the error is just 1%, maybe that gives an acceptable error. To give you an idea of the magnitude of the error introduced, you can compute the property of interest with two sqs that have similar, but not identical, correlations.

3

Thanks Dr Axel.
By the way, for my second composition, I didn’t find good mismatch. If it is possible to get an ideal mismatch (at least for the 1st nn pairs?) with a larger supercell?

4

There always exists a larger that will provide an exact match. I have explain elsewhere in this forum how to estimate the required size of the cell.

5

Thank you Dr Axel, I will search the relevant questions from this forum.