perconeb 0.1

A tool for finding percolation pathways in crystals

About

Perconeb is the library used for fast identifying of the optimal jumps mobile species required for the percolation in a crystal structure.

The identified jumps can be used for nudged elastic band (NEB) clalculation of the mobile species activation barriers.

Functionality includes:

• 1-3D percolation radius calculations (percolation threshold)

• cutoff search for the shortest ionic jumps between equilibrium positions

• identifying of unique jumps required for 1-3D percolation

• initial trajectory preparation for NEB calculations

Installation

!pip install perconeb

How to use

from core import Perconeb
from ase.io import read

file = '/Users/artemdembitskiy/Desktop/perconeb/LiCoO2.cif'
atoms = read(file)  # can be .cif, POSCAR, or any that is readable by ase
specie = 3          # mobile specie, atomic number
tr = 0.75           # minimum allowed distance between linear segment connecting i,j-th positions of mobile specie
                    # and the framework, angstrom
upper_bound = 10.0  # maximum allowed distance for intersite hops of mobile species, angstrom

calc = Perconeb(atoms, specie, upper_bound = upper_bound)
dim, cutoff = calc.percolation_dimensionality(tr = tr)

dimensions = {2: 1, 4: 2, 8: 3} # we use 2x2x2 supercell to evaluate the percolation dimensionality
                                # if there is a connection between some point in the unitcell 
                                # and its closest replica within supercell then we have the percolation
                                # number of connected unitcell and dimensionality are related as follows
                                # 2 -> 1D, 4 -> 2D, 8 -> 3D
print(f'Maximum percolation dimnesionality is {dimensions[dim]}')
print(f'That requires mobile specie hops up to {round(cutoff, 3)} Angstorm')

Maximum percolation dimnesionality is 3
That requires mobile specie hops up to 4.922 Angstorm

Inequivalent mobile specie hops (edges)

edges, edge_ids, inverse  = calc.unique_edges(tr = tr, dim = dim, cutoff = cutoff)
edges                         # each edge is represented by a 5D vector [i, j, offset_x, offset_y, offset_z]
for edge in edges:
    source, target = edge[:2] # indices of source and target mobile atoms in the mobile sublattice
    offset = edge[2:]
    p_source = atoms[atoms.numbers == specie].positions[source]
    p_target = atoms[atoms.numbers == specie].positions[target]
    distance_vector = p_source - (p_target + np.dot(atoms.cell, offset))
    distance = np.linalg.norm(distance_vector)
    print(f'Source {source}, target {target}, offset {offset}, hop distance {round(distance, 4)}')

Source 0, target 1, offset [0 0 0], hop distance 4.9124
Source 0, target 0, offset [ 1 -1  0], hop distance 4.7593
Source 0, target 0, offset [0 1 0], hop distance 2.4346

Initial gues for NEB

sep_dist = 8.0                                  # minimum size of the supercell, Angstrom
idpp = False                                    # whether to use IDPP or linear interpolation scheme
step = 1.0                                      # interpolation step, Angstroms
out = calc.neb_guess(edges, edge_ids,
                     min_sep_dist = sep_dist,
                     idpp = idpp,
                     step = step
                    )
calc.write_traj(out, f'{file}_traj.cif')        # the whole trajectory can be visualized in jmol

Save percolating pathway within supercell

from ase.io import write

file = '/Users/artemdembitskiy/Desktop/perconeb/LiCoO2.cif'
atoms = read(file)
specie = 3

calc = Perconeb(atoms, specie, upper_bound = 10.0)
dim, cutoff = calc.percolation_dimensionality(tr = 0.75)
mask = calc._filter_edges(tr = 0.75, cutoff = cutoff)
sublattice = calc.mobile_supercell
base = sublattice.copy()
for pair in calc.u[mask][:, :2]:
    p1, p2 = sublattice.positions[pair]
    traj = np.linspace(p1, p2, 10)
    for p in traj[1:-1]:
        base.append('B')
        base.positions[-1] = p
write('percopath.cif', base)