2.1. Ground state search and phase diagram calculation¶
2.1.1. Binary systems¶
2.1.1.1. Example 1¶
CaO-SrO pseudobinary system
Without performing cluster analysis of structure population (CASP)
Preparing primitive lattice of rocksalt
Information of primitive lattice is described in primitive_lattice.
> cat 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 find_primitive. Non-primitive lattice should be written in clupan structure format.
tools/find_primitive -f $(structure_name) > primitive_lattice
Preparing structure population (searching for derivative structures)
Structure population is needed for DFT structure selection and CV-CASP estimation. Derivative structures can be regarded as the structure population. In this tutorial, derivative structures with up to 8 cations are regarded as the structure population.
Searching for derivative structures
> cd derivative_structure > ls 5/ derivative.in primitive_lattice > cat 5/derivative.in n_lattice = 5 n_type = 2 symprec = 1e-5 > j=`pwd`;for i in {2..8};do cd $j/$i; derivative;doneConverting derivative.out to structure files
> cd ../ > j=`pwd`;for i in {2..8};do cd $j/$i; derivative_to_structure;done 2 structures are generated. 3 structures are generated. 12 structures are generated. 14 structures are generated. 50 structures are generated. 52 structures are generated. 229 structures are generated.362 structures with up to 8 cations are obtained.
Searching for independent clusters
Independent clusters are required for calculating correlation functions
> cd cluster_search > ls cluster.in primitive_lattice > cat cluster.in n_sublattice = 1 max_cluster = 4 trunc_distance = 6.0 6.0 6.0 0.0 symprec = 1e-5 > 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 3-body clusters = 12 number of 4-body clusters = 35 number of all clusters = 53
53 clusters up to 4-body cluster are obtained.
Calculating correlation functions of all structures in the structure population
Preparing files for calculating correlation functions
> cd derivative_structure > cat setup_correlation.sh #!/bin/zsh mkdir ../correlation count=0 for i in {2..8};do for j in `ls $i/structure*`;do n1=`grep n_atoms $j | cut -d" " -f4` n2=`grep n_atoms $j | cut -d" " -f5` count=`expr $count + 1` mkdir -p ../correlation/$count cp -r $j ../correlation/$count/structure$count echo " spin = 1 -1" > ../correlation/$count/correlation.in if [ $n1 -ne $n2 ]; then count=`expr $count + 1` mkdir -p ../correlation/$count cp -r $j ../correlation/$count/structure$count echo " spin = -1 1" > ../correlation/$count/correlation.in fi done done > ./setup_correlation.sh616 structures including spin-flip structures are prepared.
Calculating correlation functions of 616 structures
> cd ../correlation > for i in `ls -F`;do cp ../cluster_search/cluster.out $i;done > dir=`pwd`; for i in `ls -F`;do name=${i%/}; cd $dir/$name; correlation -f structure$name;doneDFT structure selection
In this tutorials, 55 structures with up to 5 cations and end menbers of CaO and SrO are used for DFT calculation.
DFT calculations
Calculate energies of 57 structures. Then prepare dft_energy file. In order to perform DFT calculations, It may be as well to refine the structures using tools/refine_cell.
> cd ../ > mkdir energy > for i in {1..55};do cp -r correlation/$i energy;done > for i in {1..55};do tools/refine_cell -f $i/structure$i > $i/structure_refine$i;doneWhen using VASP for DFT calculations, POSCAR files can be automatically prepared.
> tools/structure_to_poscar -f $i/structure_refine$i > $i/POSCAR
ECI estimation
Calculated DFT energies are listed in dft_energy file. Energy in dft_energy file has a unit of eV/primitive cell. correlation file is needed for ECI estimation.
> cd ../lsf > ls dft_energy lsf.in ga.in setup_correlation.sh > ./setup_correlation.sh
Genetic algorithm (GA) is performed for optimizing the set of clusters.
> cat ga.in n_loop = 0 temp_init = 1 temp_final = 0.001 temp_mul = 0.9 base_cluster = 0 1 2 3 4 5 n_pop = 25 n_elite = 1 min_index = 6 max_index = 52 n_cluster = 3 max_iteration = 100 p_mating = 0.9 p_mutation = 0.03 > ga default parameter : iweight = 0 default parameter : ex_cluster = generating population generating population using simulated annealing iteration 0 : min_cv_score = 0.00484818 iteration 1 : min_cv_score = 0.004608 iteration 2 : min_cv_score = 0.004608 iteration 3 : min_cv_score = 0.004608 > tail -n 25 ga.out | head -n 1 cv_score = 0.00436178; cluster_index = 34 46 11
By using the result of GA, eci file is prepared.
> cat lsf.in cluster_index = 0 1 2 3 4 5 34 46 11 > lsf > cat eci cluster_index = 0 1 2 3 4 5 34 46 11 eci = [9](-12.48423400,-0.3918767803,-0.03169960820,0.01169224996,-0.03735726419,0.002203187340,-0.01230658445,0.009218152246,-0.005353977333) squared error = 0.0007125008537 cv score = 0.004378791536
Ground state search
By calculating energies of 616 derivative structures, the ground state structure are found. Composition is defined as x=0 at CaO and x=1 at SrO. Practically, a larger number of structures should be prepared for the ground state search.
> cd ../gss > cp ../lsf/eci . > touch correlation > for i in {1..616};do cat ../correlation/$i/correlation.out >> correlation;done > cat gss.in comp_cluster = 1 comp_def = 0.5 -0.5 > gssEnergies of all 616 structures are positive.
Semi-grand canonical Monte Carlo simulation
Semi-grand canonical MC simulations are performed starting from both CaO and SrO at several temperatures and chemical potentials. Chemical potential is defined as mu = mu_Sr(spin=-1) - mu_Ca(spin=+1). cluster.out file is obtained by cluster. cluster_function.out file is obtained by correlation. eci file is botained by lsf.
> cd ../mc > cd start_CaO/100/0.00 > ls cluster.out eci structure_CaO cluster_function.out mc.in > cat mc.in cell_expansion = 10 10 10 i_temp = 0 temp = 100 n_step_ann = 2000 n_step_eqv = 2000 init_structure = structure_CaO spin = 1 -1 simulation_type = gcmc mu = 0.00 > mc
Free energy calculation
In order to obtain the phase diagram, the grand potential is estimated using the thermodynamic integration after performing MC simulation. First, information for thermodynamic integration is prepared in a file. Chemical potential is defined as mu = mu_Sr(spin=-1) - mu_Ca(spin=+1). Composition should be written as composition of Sr.
> cd ../ti > cat ti_path_startc_1000 41 # number of points 0.00 1000 .00000454 -12.93970981 # chem. pot., temp., comp., energy 0.04 1000 .00000686 -12.93970735 0.08 1000 .00001061 -12.93970337 0.12 1000 .00002089 -12.93969246 > cat ti.in initial_potential = -12.93971 > ti -f ti_path_startc_1000
Solubility limit can be found from the difference of the grand potentials of CaO and SrO.
Then, a phase diagram can be obtained.
2.1.1.2. Example 2¶
CaO-SrO pseudobinary system
With performing CASP
Performing CASP
Structure population is divided into 6 groups.
> cd ../casp > touch correlation > for i in {1..616};do cat ../correlation/$i/correlation.out >> correlation;done > tools/correlation_for_casp -f correlation > correlation_casp > R -f casp.rDFT structure selection
In this tutorial, 10 structures are selected from each group. Total number of DFT structures is 60.
> tools/structure_selection -g group -n 10 number of structures in group 1 = 59 number of structures in group 2 = 54 number of structures in group 3 = 136 number of structures in group 4 = 244 number of structures in group 5 = 59 number of structures in group 6 = 64 randomly selected structures = 127,159,181,225,234,240,259,275,505,597,48,115,122,187,221,327,375,388,463,480,26,106,108,143,309,352,390,438,459,539,66,146,217,280,310,363,384,460,478,504,23,89,248,317,355,484,530,608,610,615,78,91,171,193,199,207,356,469,512,574
2.1.2. Ternary systems¶
Coming soon…
2.1.3. Multilattice systems¶
MC simulations for multilattice systems is now unavailable.