DWBuilder: Domain Wall Builder

Ferroelectric/ferroelastic domain_wall_builder creates domain walls and interface structure for the perovskites and ceramics. The code reads the structure in the vasp format, and then creates domain walls with user-defined sizes and angles.

Overview

There are three main scripts dwbuilder.py, dbuilder.py and hibuilder.py which build domain wall, single domain structures and experimentally observed atomic interface strutures with known orientation relationships (ORs), respectively. For the domain wall and interfaces, you only need to run dwbuilder.py. These scripts can be executed from the command line. I also have included examples of ferroelectric domain walls.

Dependencies

The package requires:

• numpy - http://www.numpy.org/
• metplotlib - https://matplotlib.org/
• ASE - https://wiki.fysik.dtu.dk/ase/
• Pymatgen - https://pymatgen.org/

Installation guide

For installation simply clone or download the code in your terminal and in the main directory of the package type:

> pip install .

This will copy the modules to your active python site-packages, thereby making them importable in any python script and will put the scrpits in the python bin, thereby making them executable in the shell.

After installation, you can start the software by running the following command in your terminal:

> dwbuilder

Usage

To execute the code, one should run the dwbuilder command from the command line. Upon running, the user will be prompted to input the name of the input structure file, as well as the domain wall angle and size (expressed in number of unit cells). This script builds the domain wall structure based on the space group of the input structure with the assumed polarization directions as indicated below.

R3c (Polarization direction (1-11))
R3m (Polarization direction (001))
P4mm (Polarization direction (001))
p6_3cm (Polarization direction (-1-10))
Pnma (Polarization direction (110))
Pmc2_1 (user-defined)
Amm2 (user-defined)

However, if you are unsure about the polarization dirction, you can run polarization.py to determine the polarization direction. This script uses the point charge model and you need to have both optimized CONTCAR and high symmtry structure POSCAR files to determine the polarization.

Example of using dwbuilder.py

ex:

> dwbuilder

    ***************************************************
    *                                                 *
    *                Welcome to DWBuilder             *
    *                                                 *
    ***************************************************
    *        Hey, you must know what you are doing.   *
    *  Otherwise, you might get wrong results.        *
    ***************************************************
    *     Core Developer: M.Z.Khalid                  *
    *     Main Contributors: S.M.Selbach              *
    *     Email: zeeshan.khalid039@gmail.com          *
    ***************************************************
    
Select a script to run:
1: dwbuilder.py                6: supercell.py
2: dbuilder.py                 7: vasp2cif.py
3: hibuilder.py                8: bondanalysis.py
4: slab.py                     9: rotationmatrix.py
5: polarization.py             
Enter the number of the script to run: 1
Enter the input file name (with extension): BiFeO3_R3c.vasp
Space group number: 161
International symbol: R3c
Lattice type: rhombohedral
Select the domain wall angle:
R180 - R180
R71 - R71
R109 - R109
ALL - ALL
ALL
Enter the domain wall size (in number of unit cells): 3
Enter the size of the supercell along the a direction: 1
Enter the size of the supercell along the b direction: 1
Enter the size of the supercell along the c direction: 1
Enter the cutoff distance in angstroms to remove close atoms: 0
Lattice strain for R109 DW:
strain along a (%): 0.00
strain along b (%): 0.00
strain along c (%): 0.00
Lattice strain for R71 DW:
strain along a (%): 0.00
strain along b (%): 0.00
strain along c (%): 0.00
Lattice strain for R180 DW:
strain along a (%): 0.00
strain along b (%): 0.00
strain along c (%): 0.00
Domain wall structures and supercells created successfully! Log file written to LOGFILE.txt

Once you have developed the desired domain wall structure, you can visualize in vesta or ase to further refine domain wall artifacts.

Example of using hibuilder.py

In this example, I have reproduced an orientation relationship reported in the following article CMS.

> dwbuilder

    ***************************************************
    *                                                 *
    *                Welcome to DWBuilder             *
    *                                                 *
    ***************************************************
    *        Hey, you must know what you are doing.   *
    *  Otherwise, you might get wrong results.        *
    ***************************************************
    *     Core Developer: M.Z.Khalid                  *
    *     Main Contributors: S.M.Selbach              *
    *     Email: zeeshan.khalid039@gmail.com          *
    ***************************************************
    
Select a script to run:
1: dwbuilder.py                6: supercell.py
2: dbuilder.py                 7: vasp2cif.py
3: hibuilder.py                8: bondanalysis.py
4: slab.py                     9: rotationmatrix.py
5: polarization.py             
Enter the number of the script to run: 3
Enter the bulk phase 1file name (with extension): Fe_unitcell.vasp
Enter the bulk phase 2 file name (with extension): Fe2Al5.vasp
Bulk phase 1 Space group number: 229
Bulk phase 1 International symbol: lm-3m
Bulk phase 1 Lattice type: cubic
Bulk phase 2 Space group number: 63
Bulk phase 2 International symbol: Cmcm
Bulk phase 2 Lattice type: orthrhombic
Enter three comma-separated values for bulk 1 lattice direction a: 1,0,1
Enter three comma-separated values for bulk 1 lattice direction b: 1.5,1.5,-1.5
Enter three comma-separated values for bulk 1 lattice direction c: -2,4,2
Enter three comma-separated values for bulk 2 lattice direction a: 0,0,-1
Enter three comma-separated values for bulk 2 lattice direction b: 1,0,0
Enter three comma-separated values for bulk 2 lattice direction c: 0,-2,0
Enter the stacking direction 0 for a, 1 for b and 2 for c): 2
strain along a (%): 1.1378
strain along b (%): -0.5492
strain along c (%): 8.2378
Angular strain along a (radians): 0.0
Angular strain along b (radians): 0.0
Angular strain along c (radians): 0.0
Warning: This code could generate interface/domain wall artifacts (i.e., Oxygen atoms, duplicate atoms etc,) at the interface, thus it requires manual adjustment.

hibuilder.py generates an initial configuration that needs additional refinement along a, b and c-directions. To determine the optimal interface distance along the a, b, and c axes, you can either perform static DFT or forcefield simulations. Additionally, you may need to explore various interfacial configurations to identify the thermodynamically stable structure.

The above code generates the following interface structure (the periodic image) visualized by VESTA:

It is also important to know that all the domain wall and interface structures built in this package follow the orthogonality condition, which means lattice vectors a,b and c are mutually perpendicular (i.e., orthognal) to each other and fulfill these conditions:

a x b = c
a x c = b
b x c = a

• A note on the microscopic degrees of freedom:

To find the global minimum of an interface structure, it is essential to calculate the optimal distance between the different bulk phases at the interface. You also need to identify the termination site that corresponds to the structure with the lowest energy, as well as consider the homogeneous interface structures of the periodic images.

To achieve these goals, I often use first-principles methods such as density functional theory (DFT), specifically with the Vienna Ab-initio Simulation Package VASP at 0 Kelvin. This computational approach helps determine the initial structures for further first-principles calculations.

Method for the development of FDW

R3m

Ferroelectric materials with a rhombohedral space group of R3m exhibit three types of ferroelectric domain walls (FDWs): R71, R109, and R180. Due to neutrality and mechanical compatibility, these FDWs develop along specific planes. For the R180 FDW, the {1-10} plane is used, while for R71 and R109, the FDWs are determined by the sum of the two polarization vectors.

• R71 FDW: Lies parallel to the diagonal (1-10) plane in the primitive cell.
• R180 FDW: Developed along the {1-10} plane.
• R109 FDW: The R109 FDW lies along the (100) plane, and FDWs are simply developed by stacking the primitive cell along this direction.

To analyze the R71 and R180 FDWs, the pseudocubic rhombohedral unit cell is transformed into a 10-atom cell by rotating it 45° around the z-axis relative to the parent cubic unit cell. The transformation matrix applied is given as:

    [ 1  0  1 ]