ions 0.2.1

A small python library for handling ionic crystals

About

ions is a python library made for studying percolation in ionic crystals

Functionality includes:

• calculating 1-3D percolation radius of mobile species in crystals

• finding percolation pathway and its inequivalent parts (tests are required)

• calculating activation barrier using nudged elastic band method implementing bond valence force field calculator

• searching for a minimum jump distance of a mobile specie required for 1-3D percolation

• handling data associated with ionic crystals

• decoration of ase's Atoms objects with oxidation states (pymatgen's reimplementaion)

Note: The library is under active development. Errors are expected. Most of the features are not well documented for now.

Installation

pip install ions

Percolation barriers

import numpy as np
from ase.io import read, write
from ase.optimize import FIRE

from ions.tools import Perconeb
from ions.decorator import Decorator



file = '/Users/artemdembitskiy/Downloads/LiFePO4.cif'
atoms = read(file)  
Decorator().decorate(atoms)

specie = 3 # Li
upper_bound = 10.0
pn = Perconeb(atoms = atoms, specie = specie, upper_bound = upper_bound, self_interaction=True)

traj = pn.percolating_jumps(tr = 0.5, min_sep_dist=10.0, spacing = 0.5)
for images in traj:
    images, neb = pn.create_neb(images, k = 5.0)
    optimizer = FIRE(neb, logfile = 'log')
    optimizer.run(fmax =.1, steps = 100)
    print(f'Fmax {neb.get_forces().max().round(2)} eV/angstrom |',
          f'Activation barrier {pn.sf.get_barrier(images).round(2)} eV')

Fmax 0.08 eV/angstrom | Activation barrier 3.24 eV
Fmax 0.05 eV/angstrom | Activation barrier 3.56 eV
Fmax 0.08 eV/angstrom | Activation barrier 0.35 eV
Fmax 0.06 eV/angstrom | Activation barrier 3.29 eV

Plot profile

import matplotlib.pyplot as plt
from scipy.interpolate import pchip_interpolate

profile = pn.sf.get_profile(images)
x = np.arange(0, len(images))
x_fit = np.linspace(0, len(images), 100)
y_fit = pchip_interpolate(x, profile, x_fit)

fig, ax = plt.subplots(dpi = 150, figsize = (3,2.5))
ax.plot(x, profile, 'o', label = 'observed')
ax.plot(x_fit, y_fit, zorder = 1, label = 'pchip fit')
ax.set_ylabel('Energy, eV')
ax.set_xlabel('Reaction coordinate')
ax.set_xlim(x.min(), x.max())
ax.legend(fontsize = 8, frameon = False)
plt.tight_layout()

Percolation dimensionality study

emin = []
emax = []
for images in traj:
    emin.append(pn.sf.get_profile(images).min())
    emax.append(pn.sf.get_profile(images).max())

dim, cutoff = pn.mincut_maxdim(tr = 0.5)
edges, ids, inverse = pn.unique_edges(cutoff = cutoff, dim = dim, tr = 0.5)
mask = pn._filter_edges(tr = 0.5, cutoff = cutoff)
percoedges = pn.u[mask][:, :2]

emins = np.array(emin)[inverse]
emaxs = np.array(emax)[inverse]
dims = np.array([2, 4, 8])
dims = dims[dims <= dim]
percolation_profile = {}
dim_edges = {}
for i, dim_ in enumerate(dims):
    e_a, tr_min, tr_max = pn.propagate_barriers(dim_, percoedges, emins, emaxs)
    print(f'Activation barrier of {i + 1}D percolation: {round(e_a, 3)} eV')

Activation barrier of 1D percolation: 0.351 eV
Activation barrier of 2D percolation: 3.24 eV
Activation barrier of 3D percolation: 3.295 eV

Available data

• bv_data - bond valence parameters [1]

• bvse_data - bond valence site energy parameters[2]

• ionic_radii - Shannon ionic radii [3, 4]

• crystal_radii - Shannon crystal radii [3, 4]

• elneg_pauling - Pauling's elenctronegativities [5]

References

[1]. https://www.iucr.org/resources/data/datasets/bond-valence-parameters (bvparam2020.cif)

[2]. He, B., Chi, S., Ye, A. et al. High-throughput screening platform for solid electrolytes combining hierarchical ion-transport prediction algorithms. Sci Data 7, 151 (2020). https://doi.org/10.1038/s41597-020-0474-y

[3] http://abulafia.mt.ic.ac.uk/shannon/ptable.php

[4] https://github.com/prtkm/ionic-radii

[5] https://mendeleev.readthedocs.io/en/stable/

How to handle data

from ions.data import ionic_radii, crystal_radii, bv_data, bvse_data

#ionic radius
symbol, valence = 'V', 4
r_ionic = ionic_radii[symbol][valence]  


#crystal radius
symbol, valence = 'F', -1
r_crystal = crystal_radii[symbol][valence]


# bond valence parameters
source, source_valence = 'Li', 1
target, target_valence = 'O', -2
params = bv_data[source][source_valence][target][target_valence]
r0, b = params['r0'], params['b']


# bond valence site energy parameters
source, source_valence = 'Li', 1
target, target_valence = 'O', -2
params = bvse_data[source][source_valence][target][target_valence]
r0, r_min, alpha, d0  = params['r0'], params['r_min'], params['alpha'], params['d0']

How to decorate ase's Atoms

import numpy as np
from ase.io import read
from ions import Decorator


file = '/Users/artemdembitskiy/Downloads/LiFePO4.cif'
atoms = read(file)
calc = Decorator()
atoms = calc.decorate(atoms)
oxi_states = atoms.get_array('oxi_states')
np.unique(list(zip(atoms.symbols, oxi_states)), axis = 0)

array([['Fe', '2'],
       ['Li', '1'],
       ['O', '-2'],
       ['P', '5']], dtype='<U21')

Example

import numpy as np
from ions import Decorator
from ase.io import read
from ase.neighborlist import neighbor_list
from ions.data import bv_data

file = '/Users/artemdembitskiy/Downloads/LiFePO4.cif'
atoms = read(file)
calc = Decorator()
atoms = calc.decorate(atoms)
ii, jj, dd = neighbor_list('ijd', atoms, 5.0)  

symbols = atoms.symbols
valences = atoms.get_array('oxi_states')
for i in np.unique(ii):
    source = symbols[i]
    source_valence = valences[i]
    neighbors = jj[ii == i]
    distances = dd[ii == i]
    if source_valence > 0:
        bvs = 0
        for n, d in zip(neighbors, distances):
            target = symbols[n]
            target_valence = valences[n]
            if source_valence * target_valence < 0:
                params = bv_data[source][source_valence][target][target_valence]
                r0, b = params['r0'], params['b']
                bvs += np.exp((r0 - d) / b)
        print(f'Bond valence sum for {source} is {round(bvs, 4)}')

Bond valence sum for Li is 1.0775
Bond valence sum for Li is 1.0775
Bond valence sum for Li is 1.0775
Bond valence sum for Li is 1.0775
Bond valence sum for Fe is 1.8394
Bond valence sum for Fe is 1.8394
Bond valence sum for Fe is 1.8394
Bond valence sum for Fe is 1.8394
Bond valence sum for P is 4.6745
Bond valence sum for P is 4.6745
Bond valence sum for P is 4.6745
Bond valence sum for P is 4.6745