Input files

Composition and energy

The grand canonical takes into account the local compositional fluctuation and enables to predict the average value of the “property of interest” (PoI) for any composition and temperature. However, it requires the energy and PoI for all possible composition and configurations, which is impractical.

Instead, P5Grand requires the PoI of many (not all, but feasibly large number of) configurations, which are randomly generated at each possible composition.

The PoI of many configuration can be calculated by diverse ways such as

1. all by DFT calculations

2. by machine learning based on some DFT data, etc.

No matter what programs are used, the input data of P5Grand consists of many rows and two columns,

0 -8.675196
0.03125 -8.700504
0.0625 -8.725803
0.0625 -8.726524
0.0625 -8.726524
...

or many rows and three columns.

0.0 -9.189511 0.713310
0.03125 -9.211485 0.676563
0.0625 -9.234508 0.691304
0.0625 -9.233217 0.660815
0.0625 -9.234138 0.672744
...

Each row indicates a configuration. The first and the second column is the composition and energy of a configuration. The third column is PoI like bandgap of a configuration.

The composition of a configuration (the first column) should be within 0~1.

The unit of the energy of a configuration (the second column) can be either eV/[mixing atoms] or J/[mixing atoms].

In this document, the name of input file is referred to as CEL.log, which is the default name of input file to be read in P5Grand.

Strain energy

The grand canonical requires the strain energy induced by local compositional fluctuation. In this document, the strain induced by local compositional fluctuation is referred to as local strain.

P5Grand approximates the local strain energy to Birch-Murnaghan equation of state using several parameters. As a default, P5Grand requires a file which contains four parameters.

\(B_0V_0 \ \ \ B'_0 \ \ \ 1 \ \ \ \frac{V_0(x=1)}{V_0(x=0)}\)

, where V₀ and V are free relaxed volume and strained volume, B₀ and B’₀ are bulk modulus and its derivative.

The first and second values are V₀ B₀ and B’₀, respectively. Fourth value over third value should be the V₀(x=1) divided by V₀(x=0), which limits V/V₀ to be calculated.

The fitting equations can be manually modified by editing the local_strain.py module.

tool/extract_strain

P5Grand provides tool/extract_strain.py script to generate a file containing fitting parameters. tool/extract_strain.py script extracts parameters for local strain from the OUTCAR of VASP, and automatically write them in a file named BM_constant.dat.

You need to prepare a directory which involves calculation output file (OUTCAR) like following structure.

For each configuration, directories must be treed as below.

configuration
├── unstrained
│   └── OUTCAR
├── 0_strain
│   └── OUTCAR
├──    .
│      .
├──    .
│      .
└── n_strain
    └── OUTCAR

Note

Directory named unstrained which calculates freely relaxed state is essential.

Other directories involves the calculation results for strained state.

Overall directory tree is follows.

strain
├── x_equal_0_and_1_must_be_included
│   ├── 0
│   │   ├── 0_strain
│   │   │   └── OUTCAR
│   │   ├──     .
│   │   │       .
│   │   ├──     .
│   │   │       .
│   │   ├── n_strain
│   │   │   └── OUTCAR
│   │   └── unstrained
│   │       └── OUTCAR
│   └── 1
│       ├── 0_strain
│       │   └── OUTCAR
│       ├──     .
│       │       .
│       ├──     .
│       │       .
│       ├── n_strain
│       │   └── OUTCAR
│       └── unstrained
│           └── OUTCAR
├── configuration_1
│   ├── 0_strain
│   │   └── OUTCAR
│   ├──        .
│   │          .
│   ├──        .
│   │          .
│   ├── n_strain
│   │   └── OUTCAR
│   └── unstrained
│       └── OUTCAR
├── configuration_2
│   ├── 0_strain
│   │   └── OUTCAR
│   ├──        .
│   │          .
│   ├──        .
│   │          .
│   ├── n_strain
│   │   └── OUTCAR
│   └── unstrained
│       └── OUTCAR
├──         .
│           .
├──         .
│           .
└── configuration_n
    ├── 0_strain
    │   └── OUTCAR
    ├──        .
    │          .
    ├──        .
    │          .
    ├── n_strain
    │   └── OUTCAR
    └── unstrained
        └── OUTCAR

Note

Directories for x=0 and x=1 must be included.

The basic command to extract the parameters for local strain from the OUTCAR of VASP. Enter this command in strain directory above.

$ python /dir/to/P5Grand/tool/extract_strain.py atomA atomB

We provide an example for testing a command at example/strain. The materials for example is GaAs_xSb_1-x. For the test with example, the command become:

$ python /dir/to/P5Grand/tool/extract_strain.py As Sb

The fitting equations can be manually modified by editing the tool/extract_strain.py script.

Note

The unit of strain energy must be same to the unit of energy in CEL.log, either eV/[mixing atoms] or J/[mixing atoms].

[mixing atoms] indicates the number of atoms in microstates. For an pseudobinary system of GaAs_xSb_1-xas an example, a 2x2x2 zincblende supercell is composed of 32 cations and 32 anions. In this case, the number of mixing atoms is 32.