Special quasi-random structures (SQS) are employed to estimate the physical and electronic properties of disordered materials, such as solid solutions (e.g., Si-Ge, HEAs, and metallic materials in general). This tutorial provides a step-by-step guide to generate an SQS (and evaluate it) via the ATAT package.
In summary, we use two scripts - corrdump and mcsqs - to generate the SQS. The job can be executed offline, in a regular PC, and does not require integration with VASP, QE or similar (at this stage).
ATAT current version (3.36) requires g++ 2.72 or later, and GNU make to compile. Before compiling, it is recommended to update/install the following packages: xsltproc, perl, python-pip and csh.
To download the last (stable) version of ATAT, please check the ATAT official page.
Please refer to the ATAT manual in case of any problems compiling the code.
We need a structure input file named rndstr.in to run corrdump. An example of such a file is presented below.
1 1 1.633 90 90 60
2 0 0
0 2 0
0 0 1
0.000000 0.000000 0.0 Cr
0.000000 1.000000 0.0 Ni=.333333,Fe=.333333,Co=.333334
1.000000 0.000000 0.0 Ni=.333333,Fe=.333333,Co=.333334
1.000000 1.000000 0.0 Ni=.333333,Fe=.333333,Co=.333334
0.666667 0.666667 0.5 Cr
1.666667 0.666667 0.5 Ni=.333333,Fe=.333333,Co=.333334
0.666667 1.666667 0.5 Ni=.333333,Fe=.333333,Co=.333334
1.666667 1.666667 0.5 Ni=.333333,Fe=.333333,Co=.333334
Reading the file from the top to the bottom: the first line defines a coordinate system (Cartesian, as three vectors and three angles); the following lines define the periodic (or primitive) cell expressed in the given coordinate system; finally, float variables (0.000000) define each lattice site (the atomic positions). Concentrations of atomic sites are limited to 6 significant digits. The sum of concentration must always be 1.
As for the lattice in the example above, Cr atoms occupy specific positions, generating a partially-ordered structure, common in intermetallic compounds. In the case of (true) random cells (i.e., atoms can fill any position), the input file can be simplified as follows:
1 1 1 90 90 90
0 0.5 0.5
0.5 0 0.5
0.5 0.5 0
0 0 0 Cu,Au
Which is an FCC random solid-solution of Cu and Au (50 at%). Either Cu or Au can occupy any of the lattice sites. We notice that all input files use 1 as lattice parameter, which makes it easier to set the parameters to run corrdump. We will be able to change it to the real lattice parameter afterward.
Corrdump uses the structure file to check all symmetry operations and permutations of the original cell, which is later written in clusters.out. The most relevant parameter of corrdump is the -2 attribute, which defines the cut-off distance to the calculation of the pair-correlation functions. I recommend you to set -2 = 1.1 to include first and second nearest neighbors in BCC, FCC and HCP based structures. The -3 attribute does the same for triplets interactions. I recommend something between 1.2 and 1.8, depending on the structure and how many neighbors are to be included in the optimization. To run corrdump with this setup:
corrdump -l=rndstr.in -ro -noe -nop -clus -2=1.1 -3=1.5The mcsqs command generates random structures using a Monte-Carlo based algorithm, with a defined supercell size, and sort these structures based on a pair correlation function. The mcsqs code can run indefinitely, depending on the complexity of the system. Since it is a Monte-Carlo based algorithm, one can run multiple seeds to accelerate the process of generation of SQSs.
There are two ways of running this script.
In this case, the number of atoms must be passed on to "-n" - e.g., 16 atoms:
mcsqs -n 16This command enables us to adjust composition precisely the way we want, however, might lead to a non-symmetrical SQS, with long lattice vectors and sharp angles, which are not ideal for DFT calculations.
With this resource, it is possible to control the shape of the SQS setting specific lattice vectors in the sqscell.out file and then running the mcsqs as -rc (which is used to restart a job).
mcsqs -rcFor example, to build a 2-2-2 fcc supercell (32 atoms), sqscell.out should be:
1
2 0 0
0 2 0
0 0 2
The mcsqs code saves the best SQS structure it could find as bestsqs.out. It also saves an interesting log file, with all of the tested SQS and their pair-correlation function.
You can use the script provided by Prof. Liu to convert the SQS to POSCAR (Direct): https://github.com/changning/sqs2poscar - once you have a POSCAR file, it is easy to visualize it with p4v, VESTA, or any other similar software. It is recommended to always visualize your structure before running DFT calculations of any sort. Don't forget to alter the lattice parameter before visualizing or performing further calculations with the structure you generated.
Dr. Changning Liu performed a few modifications in the original code to improve overall functionality. These modifications are listed below:
- If you want to save all the SQS structures and not only the (last) best one, before compiling ATAT add the following lines to
gedit atat/src/mcsqs.c++int tic=0;
Real obj=best.obj;
best.obj=MAXFLOAT;
int count_cniu=1; // added by cniu
while (1) {
if (obj<best.obj) {
// cerr << "Best" << endl;
best=mc(cc);
ofstream strfile;
stringstream out_cniu; // added by cniu
out_cniu << count_cniu++; // added by cniu
std::string str1_cniu = "bestsqs-"; // added by cniu
str1_cniu += out_cniu.str(); // added by cniu
std::string str2_cniu = "bestcorr-"; // added by cniu
str2_cniu += out_cniu.str(); // added by cniu
char *cstr1_cniu = new char[str1_cniu.length()+1]; // added by cniu
char *cstr2_cniu = new char[str2_cniu.length()+1]; // added by cniu
strcpy(cstr1_cniu,str1_cniu.c_str()); // added by cniu
strcpy(cstr2_cniu,str2_cniu.c_str()); // added by cniu
open_numbered_file(strfile,cstr1_cniu,ip,".out"); // changed by cniu
delete [] cstr1_cniu; // added by cniu
strfile.setf(ios::fixed);
strfile.precision(sigdig);
write_structure(best.str,ulat,site_type_list,atom_label,axes,strfile);
ofstream corrfile;
open_numbered_file(corrfile,cstr2_cniu,ip,".out"); // changed by cniu
delete [] cstr2_cniu; // added by cniu
corrfile.setf(ios::fixed);
corrfile.precision(sigdig);
}Then, save it and compile it with your preferred c++ compiler. Keep in mind that after this modification, the code will save many bestsqs-i.out files.
- It is possible to use mcsqs -n NN to generate SQS of varied shape, stop it, then use the python script trim.py (by Prof. Liu) to search for symmetric cells in sqscell.out, trim the others out of it, and finally restart the code with mcsqs -rc.
#! /usr/bin/env python
#
# trim.py
# This script is written for Python 2.7.13.
#
# It copies sqscell.out (generated by mcsqs) to old-sqscell.out.
# Then trim the sqscell.out to three or fewer cells. All cells have
# equal-length lattice vectors. If more than three cells like this
# exist in the original sqscell.out, it keeps three cells with the
# smallest vector lengths.
import numpy as np
# Read the original file
with open('sqscell.out') as f1:
lines = f1.readlines()
# Save the original file
with open('old-sqscell.out', 'w') as f2:
for x in lines: f2.write(x)
# Replace it with a new file with 3 cells.
# The 3 cells have the smallest and equal vector lengths
with open('sqscell.out', 'w') as f3:
tot = int(lines[0].split()[0]) # total number of cells
count = 0
arr1 = np.zeros((tot, 2))
for i in range(tot):
arr1[i][0] = i
a1, a2, a3 = [ float(x) for x in lines[4*i+2].split() ]
b1, b2, b3 = [ float(x) for x in lines[4*i+3].split() ]
c1, c2, c3 = [ float(x) for x in lines[4*i+4].split() ]
l1 = (a1**2 + a2**2 + a3**2)**.5
l2 = (b1**2 + b2**2 + b3**2)**.5
l3 = (c1**2 + c2**2 + c3**2)**.5
if l1 == l2 and l2 == l3:
arr1[i][1] = l1
count += 1
arr1 = arr1[arr1[:,1].argsort()]
if count >= 3:
j = 0
f3.write('3\n\n')
for i in range(tot):
if arr1[i][1] > 0 and j < 3:
f3.write(lines[4*int(arr1[i][0])+2])
f3.write(lines[4*int(arr1[i][0])+3])
f3.write(lines[4*int(arr1[i][0])+4] + '\n')
j += 1
else:
f3.write(str(count) + '\n\n')
for i in range(tot):
if arr1[i][1] > 0:
f3.write(lines[4*int(arr1[i][0])+2])
f3.write(lines[4*int(arr1[i][0])+3])
f3.write(lines[4*int(arr1[i][0])+4] + '\n')This tutorial is a simplified version of this base tutorial, by Dr. Changning Niu, from QuesTek Innovations LLC.
Other useful references are:
- Niu et al 2018, arXiv:1811.04092
- The ATAT manual
- The ATAT users forum
- Ed. M. C. Gao, J. W. Yeh, P. K. Liaw, Y. Zhang, "High-Entropy Alloys", Chapter 10: Applications of Special Quasi-random Structures to High-Entropy Alloys, Springer, 2016
A. Van de Walle, P. Tiwary, M. de Jong, D.L. Olmsted, M. Asta, A. Dick, D. Shin, Y. Wang, L.-Q. Chen, Z.-K. Liu, Efficient stochastic generation of special quasi-random structures, Calphad Journal 42, pp. 13-18 (2013), link
- ATAT - alloy automoted theorical toolkit (software)
- SQS - special quasi-random structures (term)
- HEA - high-entropy alloys (term)
- rndstr.in - the structure input (file)
- bestsqs.out - the best sqs obtained (file)