2.2. SQS exploration

2.2.1. Binary systems

2.2.1.1. Example 1

  • Rocksalt structure

  • Exhaustive search

In this tutorial, SQS with 8 cations is explored from a set of derivative structures with 8 cations.

  1. Preparing primitive lattice of rocksalt

    Information of primitive lattice is described in primitive_lattice.

    > mkdir sqs8
> cd sqs8
> vi primitive_lattice
axis1 = [3](0.000000000,2.000000000,2.000000000)
axis2 = [3](2.000000000,0.000000000,2.000000000)
axis3 = [3](2.000000000,2.000000000,0.000000000)
n_atoms = 1 1
position1 = [3](0.000000000,0.000000000,0.000000000)
position2 = [3](0.500000000,0.500000000,0.500000000)

    Non-primitive lattice can be automatically converted to primitive lattice using bin/find_primitive. Non-primitive lattice should be written in clupan structure format.

    bin/find_primitive -f $(structure_name) > primitive_lattice

  2. Preparing structure population (searching for derivative structures)

    SQS is explored from a set of derivative structures.

    Searching for derivative structures

    > mkdir derivative
> cp primitive_lattice derivative/
> cd derivative
> vi derivative.in
n_lattice = 8
n_type = 2
symprec = 1e-5
> bin/derivative

    Converting derivative.out to structure files

    > bin/derivative_to_structure
229 structures are generated.

    229 Independent structures with 8 cations are obtained.

  3. Searching for independent clusters

    Independent pair clusters are explored for calculating correlation functions

    > cd ..
> mkdir cluster_search
> cd cluster_search
> cp primitive_lattice cluster_search/
> vi cluster.in
n_sublattice = 1
max_cluster = 2
trunc_distance = 10.0 0.0 0.0 0.0
symprec = 1e-5
> bin/cluster_search
number of symmetry operations = 48
number of empty cluster = 1
number of 1-body clusters = 1
number of 2-body clusters = 13
number of all clusters = 15

    15 clusters are obtained.

  4. Calculating correlation functions of all structures and finding SQS

    Preparing structures for calculating correlation functions

    > cd ..
> mkdir correlation
> cd correlation
> cp derivative/structure8_* correlation
> cd correlation
> vi setup_correlation.sh
#!/bin/zsh
count=0
for i in `ls ../derivative/structure*`;do
    n1=`grep n_atoms $i | cut -d" " -f4`
    n2=`grep n_atoms $i | cut -d" " -f5`
    count=`expr $count + 1`
    mkdir -p $count
    cp -r $i $count/structure$count
    echo " spin = 1 -1" > $count/correlation.in
    if [ $n1 -ne $n2 ]; then
        count=`expr $count + 1`
        mkdir -p $count
        cp -r $i $count/structure$count
        echo " spin = -1 1" > $count/correlation.in
    fi
done
cd ..
> ./setup_correlation.sh

    377 structures including spin-flip structures are generated from 292 derivative structures.

    Calculating correlation functions of 377 structures

    > for i in `ls -F`;do cp ../cluster_search/cluster.out $i;done
> dir=`pwd`; for i in {1..377};do cd $dir/$i; bin/correlation -f structure$i;done

    Using calculated correlation functions, SQS-8 with the composition of 0.5 can be found.

2.2.1.2. Example 2

  • Rocksalt structure

  • Search of SQS with a larger supercell using simulated annealing

In this tutorial, SQS with 2x2x2 supercell (32 cations) of conventional rocksalt unit cell is explored using simulated annealing.

  1. Preparing conventional unit cell of rocksalt

    Information of conventional unit cell is described in primitive_lattice.

    > mkdir sqs_sa
> cd sqs_sa
> vi primitive_lattice
axis1 = [3](4.000000000,0.000000000,0.000000000)
axis2 = [3](0.000000000,4.000000000,0.000000000)
axis3 = [3](0.000000000,0.000000000,4.000000000)
n_atoms = 4 4
position1 = [3](0.000000000,0.000000000,0.000000000)
position2 = [3](0.500000000,0.500000000,0.000000000)
position3 = [3](0.000000000,0.500000000,0.500000000)
position4 = [3](0.500000000,0.000000000,0.500000000)
position5 = [3](0.500000000,0.000000000,0.000000000)
position6 = [3](0.000000000,0.500000000,0.000000000)
position7 = [3](0.000000000,0.000000000,0.500000000)
position8 = [3](0.500000000,0.500000000,0.500000000)

  2. Searching for independent clusters

    Independent pair clusters are explored for finding SQS

    > cd ..
> mkdir cluster_search
> cd cluster_search
> cp primitive_lattice cluster_search/
> vi cluster.in
n_sublattice = 1
max_cluster = 4
trunc_distance = 10.0
symprec = 1e-5
> bin/cluster_search
number of symmetry operations = 192
number of empty cluster = 1
number of 1-body clusters = 1
number of 2-body clusters = 13
number of all clusters = 15

    15 clusters are obtained.

    In order to prepare cluster_function.out, correlation functions of an arbitrary structure are calculated.

    > vi correlation.in
spin = 1 -1
> vi structure_tmp
axis1 = [3](4.000000000,0.000000000,0.000000000)
axis2 = [3](0.000000000,4.000000000,0.000000000)
axis3 = [3](0.000000000,0.000000000,4.000000000)
n_atoms = 4 0 4
position1 = [3](0.000000000,0.000000000,0.000000000)
position2 = [3](0.500000000,0.500000000,0.000000000)
position3 = [3](0.000000000,0.500000000,0.500000000)
position4 = [3](0.500000000,0.000000000,0.500000000)
position5 = [3](0.500000000,0.000000000,0.000000000)
position6 = [3](0.000000000,0.500000000,0.000000000)
position7 = [3](0.000000000,0.000000000,0.500000000)
position8 = [3](0.500000000,0.500000000,0.500000000)
axis_change = [3,3]((1.000000000,0.000000000,0.000000000),(0.000000000,1.000000000,0.000000000),(0.000000000,0.000000000,1.000000000))
n_type = 2
> bin/correlation -f structure_tmp

  3. Exploring SQS using simulated annealing

    Performing simulated annealing

    > cd ..
> mkdir sa
> cd sa
> cp ../cluster_search/{primitive_lattice, cluster.out,cluster_function.out}
> vi sqs.in
cell_expansion = 2 2 2
temp_init = 10000
temp_final = 0.01
temp_mul = 0.99
n_step = 300
spin = 1 -1
comp = 0.5
cluster_index = 2 3 4 5 6
criterion = abs
symprec = 1e-4
> bin/sqs

    Converged structure is generated as structure_sqs.

    If you convert structure_sqs to POSCAR (VASP structure file), type the following command.

    > bin/structure_to_poscar -f structure_sqs

2.2.2. Ternary systems

2.2.2.1. Example 1

  • Rocksalt structure

  • Search of SQS with a large supercell using simulated annealing

In this tutorial, SQS with 4x4x4 supercell (64 cations) of rocksalt primitive cell is explored using simulated annealing.

  1. Preparing primitive cell of rocksalt

    Information of primitive cell is described in primitive_lattice.

    > mkdir sqs_sa
> cd sqs_sa
> vi primitive_lattice
axis1 = [3](0.000000000,2.000000000,2.000000000)
axis2 = [3](2.000000000,0.000000000,2.000000000)
axis3 = [3](2.000000000,2.000000000,0.000000000)
n_atoms = 1 1
position1 = [3](0.000000000,0.000000000,0.000000000)
position2 = [3](0.500000000,0.500000000,0.500000000)

  2. Searching for independent clusters

    Independent pair clusters are explored for finding SQS

    > cd ..
> mkdir cluster_search
> cd cluster_search
> cp primitive_lattice cluster_search/
> vi cluster.in
n_sublattice = 1
max_cluster = 2
trunc_distance = 6.0 0.0 0.0 0.0
symprec = 1e-5
> bin/cluster_search
number of symmetry operations = 48
number of empty cluster = 1
number of 1-body clusters = 1
number of 2-body clusters = 4
number of all clusters = 6

    In order to prepare cluster_function.out, correlation functions of an arbitrary structure are calculated.

    > vi correlation.in
spin = 1 0 -1
> vi structure_tmp
axis1 = [3](0.000000000,2.000000000,2.000000000)
axis2 = [3](2.000000000,0.000000000,2.000000000)
axis3 = [3](6.000000000,6.000000000,0.000000000)
position1 = [3](0.000000000,0.000000000,0.000000000)
position2 = [3](0.000000000,0.000000000,0.3333333333)
position3 = [3](0.000000000,0.000000000,0.6666666667)
position4 = [3](0.5000000000,0.5000000000,0.1666666667)
position5 = [3](0.5000000000,0.5000000000,0.5000000000)
position6 = [3](0.5000000000,0.5000000000,0.8333333333)
n_atoms = 1 1 1 3
axis_change = [3,3]((1.000000000,0.000000000,0.000000000),(0.000000000,1.000000000,0.000000000),(0.000000000,0.000000000,3.000000000))
n_type = 3
> bin/correlation -f structure_tmp

  3. Exploring SQS using simulated annealing

    Performing simulated annealing

    > cd ..
> mkdir sa
> cd sa
> cp ../cluster_search/{primitive_lattice, cluster.out,cluster_function.out}
> vi sqs.in
cell_expansion = 4 4 4
temp_init = 1000
temp_final = 0.01
temp_mul = 0.95
n_step = 200
spin = 1 0 -1
comp = 0.5 0.25  # comp(B) and comp(C), comp(A) = 1.0-comp(B)-comp(C)
cluster_index = 3 4 5 6 7 8 9 10 11 12 13 14 # first column of cluster_function.out
criterion = abs  # rms or abs
symprec = 1e-5
> bin/sqs

    In this case, cluster functions of up to 3rd NN will be optimized. Converged structure is generated as structure_sqs.

    If you convert structure_sqs to POSCAR (VASP structure file), type the following command.

    > bin/structure_to_poscar -f structure_sqs

2.2.3. Multilattice systems

2.2.3.1. Example 1

  • Wurtzite SiC-AlN system

  • Exhaustive search

SQS for composition of 50%AlN with 8 cations and 8 anions is explored from a set of derivative structures.

  1. Preparing primitive lattice of wurtzite structure

    > vi primitive_lattice
axis1 = [3](2.701133234,-1.559500000,0.000000000)
axis2 = [3](0.000000000,3.119000000,0.000000000)
axis3 = [3](0.000000000,0.000000000,4.991000000)
n_atoms = 2 2
position1 = [3](0.3333333333,0.6666666666,0.000000000)
position2 = [3](0.6666666666,0.3333333333,0.5000000000)
position3 = [3](0.3333333333,0.6666666666,0.3750000000)
position4 = [3](0.6666666666,0.3333333333,0.8750000000)

  2. Searching for derivative structures at the fixed composition

    > mkdir derivative
> cp primitive_lattice derivative/
> cd derivative
> vi derivative.in
n_lattice = 4
n_type = 2 2 # for 2x2 system
comp = 0.5 0.5 # compositions of Al and N (Two compositions should be the same in this case.)

> bin/derivative

> bin/derivative_to_structure
5996 structures are generated.

  3. Searching for independent pair clusters

    > cd ..
> mkdir cluster_search
> cd cluster_search
> cp primitive_lattice cluster_search/
> vi cluster.in
n_sublattice = 2  # for 2x2 system
max_cluster = 2
trunc_distance = 4.0 0.0 0.0 0.0
symprec = 1e-5

> bin/cluster_search
number of symmetry operations = 4
number of empty cluster = 1
number of 1-body clusters = 2
number of 2-body clusters = 9
number of all clusters = 12

  4. Calculating correlation functions of all structures

    > cd ..
> mkdir correlation
> cd correlation
> cp ../cluster_search/cluster.out .
> echo "spin = 1 -1 1 -1" > correlation.in # spins for Si, Al, C and N

> for i in {1..5996};do ~/git/clupan/version-1.0/bin/correlation -f ../derivative_lattice/structure16_$i; mv correlation.out correlation.out.$i;done

  5. Finding SQS-16 using calculated correlation functions.

2.2.3.2. Example 2

  • Rocksalt structure

  • Search of SQS with a large supercell using simulated annealing

In this tutorial, SQS with 4x4x4 supercell (64 cations) of rocksalt primitive cell is explored using simulated annealing.

  1. Preparing primitive cell of rocksalt

    Information of primitive cell is described in primitive_lattice.

    > mkdir sqs_sa
> cd sqs_sa
> vi primitive_lattice
axis1 = [3](0.000000000,2.000000000,2.000000000)
axis2 = [3](2.000000000,0.000000000,2.000000000)
axis3 = [3](2.000000000,2.000000000,0.000000000)
n_atoms = 1 1
position1 = [3](0.000000000,0.000000000,0.000000000)
position2 = [3](0.500000000,0.500000000,0.500000000)

  2. Searching for independent clusters

    Independent pair clusters are explored for finding SQS

    > cd ..
> mkdir cluster_search
> cd cluster_search
> cp primitive_lattice cluster_search/
> vi cluster.in
n_sublattice = 2
max_cluster = 2
trunc_distance = 6.0 0.0 0.0 0.0
symprec = 1e-5
> bin/cluster_search
number of symmetry operations = 48
number of empty cluster = 1
number of 1-body clusters = 2
number of 2-body clusters = 13
number of all clusters = 16

    In order to prepare cluster_function.out, correlation functions of an arbitrary structure are calculated.

    > vi correlation.in
spin = 1 -1 1 -1
> vi structure_tmp
axis1 = [3](0.000000000,2.000000000,2.000000000)
axis2 = [3](2.000000000,0.000000000,2.000000000)
axis3 = [3](6.000000000,6.000000000,0.000000000)
position1 = [3](0.000000000,0.000000000,0.000000000)
position2 = [3](0.000000000,0.000000000,0.3333333333)
position3 = [3](0.000000000,0.000000000,0.6666666667)
position4 = [3](0.5000000000,0.5000000000,0.1666666667)
position5 = [3](0.5000000000,0.5000000000,0.5000000000)
position6 = [3](0.5000000000,0.5000000000,0.8333333333)
n_atoms = 2 1 2 1
axis_change = [3,3]((1.000000000,0.000000000,0.000000000),(0.000000000,1.000000000,0.000000000),(0.000000000,0.000000000,3.000000000))
n_type = 2 2
> bin/correlation -f structure_tmp

  3. Exploring SQS using simulated annealing

    Performing simulated annealing

    > cd ..
> mkdir sa
> cd sa
> cp ../cluster_search/{primitive_lattice, cluster.out,cluster_function.out}
> vi sqs.in
cell_expansion = 4 4 4
temp_init = 1000
temp_final = 0.01
temp_mul = 0.95
n_step = 200
spin = 1 -1 1 -1
comp = 0.5 0.5  # comp(B, sublattice 1) and comp(D, sublattice 2),
                # comp(A, sublattice 1) = 1.0-comp(B),
                # comp(C, sublattice 2) = 1.0-comp(D)
cluster_index = 3 4 5 6 7 8 # first column of cluster_function.out
criterion = abs  # rms or abs
symprec = 1e-5
> bin/sqs

    In this case, cluster functions of up to 6th NN will be optimized. Converged structure is generated as structure_sqs.

    If you convert structure_sqs to POSCAR (VASP structure file), type the following command.

    > bin/structure_to_poscar -f structure_sqs