Confusion on SQS at relatively low concentration

[aaron_atat]

Dear Alex and ATAT users,

Recently I was trying to do some calculation for InGaN alloy. But the results I got is weird and hope you could help me with my issue. Thanks in advance.

I was trying to make SQS for wurzite InGaN alloy, with relatively low Indium concentration (~5%).
So I use the rndstr.in file as follows:

[quote]
5.47328055191765 3.16 5.13 90 90 90
1 0 0
0 1 0
0 0 1
0.16667 0.50000 0.00001 Ga=0.944444444444444, In=0.0555555555555556
0.66667 0.00000 0.00001 Ga=0.944444444444444, In=0.0555555555555556
0.33333 0.99999 0.50001 Ga=0.944444444444444, In=0.0555555555555556
0.83333 0.49999 0.50001 Ga=0.944444444444444, In=0.0555555555555556
0.33333 0.99999 0.12362 N
0.83333 0.49999 0.12362 N
0.16667 0.50000 0.62362 N
0.66667 0.00000 0.62362 N
[/quote],
which is a rectangle unit cell of wurzite InGaN.

The I generated the cluster.out file with the command

[quote]
corrdump -l=rndstr.in -ro -noe -nop -clus -2=5 -3=4 -4=4
[/quote].
The sqscell.out file I use is

[quote]
1
3 0 0
0 4 0
0 0 3
[/quote].
Finally I ran the job with

[quote]
mcsqs -n 288 -rc -ip=0
[/quote].
Since my concetration is relatively low, I made a relatively large super cell with 288 atoms.
I thought my settings up to here should be good. But the thing is, after running for several days, what I get for correlation function is:

2       3.147633        0.777778        0.790123        -0.012346
2       3.147633        0.777778        0.790123        -0.012346
2       3.147633        0.777778        0.790123        -0.012346
2       3.147633        0.777778        0.790123        -0.012346
2       3.147680        0.777778        0.790123        -0.012346
2       3.147680        0.777778        0.790123        -0.012346
2       3.147680        0.777778        0.790123        -0.012346
2       3.147680        0.777778        0.790123        -0.012346
2       3.160000        0.777778        0.790123        -0.012346
2       3.160000        0.777778        0.790123        -0.012346
2       3.160000        0.777778        0.790123        -0.012346
2       3.160000        0.777778        0.790123        -0.012346
2       3.160000        0.777778        0.790123        -0.012346
2       3.160000        0.777778        0.790123        -0.012346
2       3.160000        0.777778        0.790123        -0.012346
2       3.160000        0.777778        0.790123        -0.012346
2       4.460167        0.777778        0.790123        -0.012346
2       4.460167        0.777778        0.790123        -0.012346
2       4.460167        0.777778        0.790123        -0.012346
2       4.460167        0.777778        0.790123        -0.012346
2       4.460190        0.777778        0.790123        -0.012346
2       4.460190        0.777778        0.790123        -0.012346
2       4.460190        0.777778        0.790123        -0.012346
2       4.460190        0.777778        0.790123        -0.012346
3       3.160000        -0.666667       -0.702332       0.035665
3       3.160000        -0.666667       -0.702332       0.035665
3       3.160000        -0.666667       -0.702332       0.035665
3       3.160000        -0.666667       -0.702332       0.035665
3       3.160000        -0.666667       -0.702332       0.035665
3       3.160000        -0.666667       -0.702332       0.035665
3       3.160000        -0.666667       -0.702332       0.035665
3       3.160000        -0.666667       -0.702332       0.035665
3       3.160000        -0.666667       -0.702332       0.035665
3       3.160000        -0.666667       -0.702332       0.035665
3       3.160000        -0.666667       -0.702332       0.035665
3       3.160000        -0.666667       -0.702332       0.035665
3       3.160000        -0.666667       -0.702332       0.035665
3       3.160000        -0.666667       -0.702332       0.035665
3       3.160000        -0.666667       -0.702332       0.035665
3       3.160000        -0.666667       -0.702332       0.035665
3       3.160000        -0.666667       -0.702332       0.035665
3       3.160000        -0.666667       -0.702332       0.035665
3       3.160000        -0.666667       -0.702332       0.035665
3       3.160000        -0.666667       -0.702332       0.035665
3       3.160000        -0.666667       -0.702332       0.035665
3       3.160000        -0.666667       -0.702332       0.035665
3       3.160000        -0.666667       -0.702332       0.035665
3       3.160000        -0.666667       -0.702332       0.035665
4       3.160000        0.555556        0.624295        -0.068740
4       3.160000        0.555556        0.624295        -0.068740
4       3.160000        0.555556        0.624295        -0.068740
4       3.160000        0.555556        0.624295        -0.068740
4       3.160000        0.555556        0.624295        -0.068740
4       3.160000        0.555556        0.624295        -0.068740
4       3.160000        0.555556        0.624295        -0.068740
4       3.160000        0.555556        0.624295        -0.068740

,
from which we can see that the structure is far from good.
I was wondering if such result is reasonable or, if there is anything wrong with what I did.

What made me more confused is that, when I visualized the structure I got from above calculation, the In atoms tend to stay at or close to the boundary of the unit cell, they never appear in the central region of the cell. This is rather contrary to my physical intuition that one should distribute uniformly in lattice if its concentration is rather low.
Hope you can help me with the issue. Thanks!

Best
Aaron

[avdw]

Note that it’s the last column of bestcorr.out file that tells you how close your correlations are from the random state’s correlations. Here 0.01 discrepancy is not to bad!
BTW, one strange thing is that when I run your case I get

2       3.147633        0.787037        0.790123        -0.003086
2       3.160000        0.787037        0.790123        -0.003086
2       4.460167        0.787037        0.790123        -0.003086
3       3.160000        -0.694444       -0.702332       0.007888
3       3.160000        -0.694444       -0.702332       0.007888
3       3.160000        -0.694444       -0.702332       0.007888
3       3.160000        -0.694444       -0.702332       0.007888
4       3.160000        0.611111        0.624295        -0.013184
4       3.160000        0.611111        0.624295        -0.013184

while you only get pairs (2 in the first column). I am not sure why that would be…

One issues with SQS at low concentration is that it may be indeed difficult to get all the correlations to match if your concentration are not simple fraction. Here you have 1/18, so the pair correlation could only be matched exactly if the number of p pairs in your cell is such that p*(1/18)^2 is an integer.

BTW, the -n=288 in your case is overridden by specifiying your own sqscell.out file.

[aaron_atat]

Hi Alex,

Thanks for the reply.
I checked and tried my system for one more time and still get the same results as in my post.
Based on your reply, I have several questions, listed below:

1. In my bestcorr.out file (the one posted in my original post), I have many many interaction clusters, not only "pairs" as stated in your reply. Please pay attention to the scrollbar on the right…
   For pair interactions, I get the correlation discrepancy around 0.012, but for triple- and quadra- interactions, I get 0.035 and 0.069. So this is why I said "the structure is far from good" in my post.
   BTW, in your post, your correlation function only has 9 lines, did you paste all the lines here? Or you just pasted the first few lines?

2. what do you mean by "the -n=288 in your case is overridden by specifiying your own sqscell.out file" ? I think the number 288 is correct. In my rndstr.in structure I have 8 atoms per cell(see my original post), and there are 3x4x3=36 cells according to my sqscell.out file. So there should be in total 8x36=288 atoms. Is there anything wrong here?

3. I think I understand your comment on the number of p pairs need for getting exactly matched structure. I don’t expect to get the "exact" one, but at least good enough one (say, all the correlation discrepancies are within 0.01?).

Thank you for helping me with my problem.

Aaron

[avdw]

1. In my bestcorr.out file (the one posted in my original post), I have many many interaction clusters, not only "pairs" as stated in your reply. Please pay attention to the scrollbar on the right…
   For pair interactions, I get the correlation discrepancy around 0.012, but for triple- and quadra- interactions, I get 0.035 and 0.069. So this is why I said "the structure is far from good" in my post.
   BTW, in your post, your correlation function only has 9 lines, did you paste all the lines here? Or you just pasted the first few lines?

Ok I see the multiplet (Sorry!). Still, 0.035 or 0.069 may not be that bad. Keep in mind that many researchers don’t even try to match beyond pairs!
These 9 lines are all I have.

2. what do you mean by "the -n=288 in your case is overridden by specifiying your own sqscell.out file" ? I think the number 288 is correct. In my rndstr.in structure I have 8 atoms per cell(see my original post), and there are 3x4x3=36 cells according to my sqscell.out file. So there should be in total 8x36=288 atoms. Is there anything wrong here?

The number is correct but I just wanted to mention that the code ignores it if you specify the -rc option (to read your sqscell.out file)

3. I think I understand your comment on the number of p pairs need for getting exactly matched structure. I don’t expect to get the "exact" one, but at least good enough one (say, all the correlation discrepancies are within 0.01?).

Hard to tell what can be achieved in a given system. You could always try two different SQS and if they have similar properties (e.g. energy) then that is a measure of their quality.