# coding: utf-8
# Copyright (c) Pymatgen Development Team.
# Distributed under the terms of the MIT License.
"""
This module is intended to be used to compute Pourbaix diagrams
of arbitrary compositions and formation energies. If you use
this module in your work, please consider citing the following:
General formalism for solid-aqueous equilibria from DFT:
Persson et al., DOI: 10.1103/PhysRevB.85.235438
Decomposition maps, or Pourbaix hull diagrams
Singh et al., DOI: 10.1021/acs.chemmater.7b03980
Fast computation of many-element Pourbaix diagrams:
Patel et al., https://arxiv.org/abs/1909.00035 (submitted)
"""
import logging
import numpy as np
import itertools
import re
from copy import deepcopy
from functools import cmp_to_key, partial, lru_cache
from monty.json import MSONable, MontyDecoder
from multiprocessing import Pool
import warnings
from scipy.spatial import ConvexHull, HalfspaceIntersection
try:
from scipy.special import comb
except ImportError:
from scipy.misc import comb
from pymatgen.util.coord import Simplex
from pymatgen.util.string import latexify
from pymatgen.util.plotting import pretty_plot
from pymatgen.core.periodic_table import Element
from pymatgen.core.composition import Composition
from pymatgen.core.ion import Ion
from pymatgen.entries.computed_entries import ComputedEntry
from pymatgen.entries.compatibility import MU_H2O
from pymatgen.analysis.reaction_calculator import Reaction, ReactionError
from pymatgen.analysis.phase_diagram import PhaseDiagram, PDEntry
from tqdm import tqdm
__author__ = "Sai Jayaraman"
__copyright__ = "Copyright 2012, The Materials Project"
__version__ = "0.4"
__maintainer__ = "Joseph Montoya"
__credits__ = "Arunima Singh, Joseph Montoya, Anjli Patel"
__email__ = "joseph.montoya@tri.global"
__status__ = "Production"
__date__ = "Nov 1, 2012"
logger = logging.getLogger(__name__)
PREFAC = 0.0591
# TODO: Revise to more closely reflect PDEntry, invoke from energy/composition
# TODO: PourbaixEntries depend implicitly on having entry energies be
# formation energies, should be a better way to get from raw energies
# TODO: uncorrected_energy is a bit of a misnomer, but not sure what to rename
[docs]class PourbaixEntry(MSONable):
"""
An object encompassing all data relevant to a solid or ion
in a pourbaix diagram. Each bulk solid/ion has an energy
g of the form: e = e0 + 0.0591 log10(conc) - nO mu_H2O
+ (nH - 2nO) pH + phi (-nH + 2nO + q)
Note that the energies corresponding to the input entries
should be formation energies with respect to hydrogen and
oxygen gas in order for the pourbaix diagram formalism to
work. This may be changed to be more flexible in the future.
"""
def __init__(self, entry, entry_id=None, concentration=1e-6):
"""
Args:
entry (ComputedEntry/ComputedStructureEntry/PDEntry/IonEntry): An
entry object
entry_id ():
concentration ():
"""
self.entry = entry
if isinstance(entry, IonEntry):
self.concentration = concentration
self.phase_type = "Ion"
self.charge = entry.ion.charge
else:
self.concentration = 1.0
self.phase_type = "Solid"
self.charge = 0.0
self.uncorrected_energy = entry.energy
if entry_id is not None:
self.entry_id = entry_id
elif hasattr(entry, "entry_id") and entry.entry_id:
self.entry_id = entry.entry_id
else:
self.entry_id = None
@property
def npH(self):
"""
Returns:
"""
return self.entry.composition.get("H", 0.) - 2 * self.entry.composition.get("O", 0.)
@property
def nH2O(self):
"""
Returns: Number of H2O.
"""
return self.entry.composition.get("O", 0.)
@property
def nPhi(self):
"""
Returns: Number of H2O.
"""
return self.npH - self.charge
@property
def name(self):
"""
Returns: Name for entry
"""
if self.phase_type == "Solid":
return self.entry.composition.reduced_formula + "(s)"
elif self.phase_type == "Ion":
return self.entry.name
@property
def energy(self):
"""
returns energy
Returns (float): total energy of the pourbaix
entry (at pH, V = 0 vs. SHE)
"""
# Note: this implicitly depends on formation energies as input
return self.uncorrected_energy + self.conc_term - (MU_H2O * self.nH2O)
@property
def energy_per_atom(self):
"""
energy per atom of the pourbaix entry
Returns (float): energy per atom
"""
return self.energy / self.composition.num_atoms
[docs] def energy_at_conditions(self, pH, V):
"""
Get free energy for a given pH and V
Args:
pH (float): pH at which to evaluate free energy
V (float): voltage at which to evaluate free energy
Returns:
free energy at conditions
"""
return self.energy + self.npH * PREFAC * pH + self.nPhi * V
[docs] def get_element_fraction(self, element):
"""
Gets the elemental fraction of a given non-OH element
Args:
element (Element or str): string or element corresponding
to element to get from composition
Returns:
fraction of element / sum(all non-OH elements)
"""
return self.composition.get(element) * self.normalization_factor
@property
def normalized_energy(self):
"""
Returns:
energy normalized by number of non H or O atoms, e. g.
for Zn2O6, energy / 2 or for AgTe3(OH)3, energy / 4
"""
return self.energy * self.normalization_factor
[docs] def normalized_energy_at_conditions(self, pH, V):
"""
Energy at an electrochemical condition, compatible with
numpy arrays for pH/V input
Args:
pH (float): pH at condition
V (float): applied potential at condition
Returns:
energy normalized by number of non-O/H atoms at condition
"""
return self.energy_at_conditions(pH, V) * self.normalization_factor
@property
def conc_term(self):
"""
Returns the concentration contribution to the free energy,
and should only be present when there are ions in the entry
"""
return PREFAC * np.log10(self.concentration)
# TODO: not sure if these are strictly necessary with refactor
[docs] def as_dict(self):
"""
Returns dict which contains Pourbaix Entry data.
Note that the pH, voltage, H2O factors are always calculated when
constructing a PourbaixEntry object.
"""
d = {"@module": self.__class__.__module__,
"@class": self.__class__.__name__}
if isinstance(self.entry, IonEntry):
d["entry_type"] = "Ion"
else:
d["entry_type"] = "Solid"
d["entry"] = self.entry.as_dict()
d["concentration"] = self.concentration
d["entry_id"] = self.entry_id
return d
[docs] @classmethod
def from_dict(cls, d):
"""
Invokes
"""
entry_type = d["entry_type"]
if entry_type == "Ion":
entry = IonEntry.from_dict(d["entry"])
else:
entry = PDEntry.from_dict(d["entry"])
entry_id = d["entry_id"]
concentration = d["concentration"]
return PourbaixEntry(entry, entry_id, concentration)
@property
def normalization_factor(self):
"""
Sum of number of atoms minus the number of H and O in composition
"""
return 1.0 / (self.num_atoms - self.composition.get('H', 0)
- self.composition.get('O', 0))
@property
def composition(self):
"""
Returns composition
"""
return self.entry.composition
@property
def num_atoms(self):
"""
Return number of atoms in current formula. Useful for normalization
"""
return self.composition.num_atoms
def __repr__(self):
return "Pourbaix Entry : {} with energy = {:.4f}, npH = {}, nPhi = {}, nH2O = {}, entry_id = {} ".format(
self.entry.composition, self.energy, self.npH, self.nPhi, self.nH2O, self.entry_id)
def __str__(self):
return self.__repr__()
[docs]class MultiEntry(PourbaixEntry):
"""
PourbaixEntry-like object for constructing multi-elemental Pourbaix
diagrams.
"""
def __init__(self, entry_list, weights=None):
"""
Initializes a MultiEntry.
Args:
entry_list ([PourbaixEntry]): List of component PourbaixEntries
weights ([float]): Weights associated with each entry. Default is None
"""
if weights is None:
self.weights = [1.0] * len(entry_list)
else:
self.weights = weights
self.entry_list = entry_list
@lru_cache()
def __getattr__(self, item):
"""
Because most of the attributes here are just weighted
averages of the entry_list, we save some space by
having a set of conditionals to define the attributes
"""
# Attributes that are weighted averages of entry attributes
if item in ["energy", "npH", "nH2O", "nPhi", "conc_term",
"composition", "uncorrected_energy"]:
# TODO: Composition could be changed for compat with sum
if item == "composition":
start = Composition({})
else:
start = 0
return sum([getattr(e, item) * w
for e, w in zip(self.entry_list, self.weights)], start)
# Attributes that are just lists of entry attributes
elif item in ["entry_id", "phase_type"]:
return [getattr(e, item) for e in self.entry_list]
# normalization_factor, num_atoms should work from superclass
return self.__getattribute__(item)
@property
def name(self):
"""
MultiEntry name, i. e. the name of each entry joined by ' + '
"""
return " + ".join([e.name for e in self.entry_list])
def __repr__(self):
return "Multiple Pourbaix Entry: energy = {:.4f}, npH = {}, nPhi = {}, nH2O = {}, entry_id = {}, species: {}" \
.format(self.energy, self.npH, self.nPhi, self.nH2O, self.entry_id, self.name)
def __str__(self):
return self.__repr__()
[docs] def as_dict(self):
"""
Returns: MSONable dict
"""
return {"@module": self.__class__.__module__,
"@class": self.__class__.__name__,
"entry_list": [e.as_dict() for e in self.entry_list],
"weights": self.weights}
[docs] @classmethod
def from_dict(cls, d):
"""
Args:
d (): Dict representation
Returns:
MultiEntry
"""
entry_list = [PourbaixEntry.from_dict(e) for e in d.get("entry_list")]
return cls(entry_list, d.get("weights"))
# TODO: this class isn't particularly useful in its current form, could be
# refactored to include information about the reference solid
[docs]class IonEntry(PDEntry):
"""
Object similar to PDEntry, but contains an Ion object instead of a
Composition object.
.. attribute:: name
A name for the entry. This is the string shown in the phase diagrams.
By default, this is the reduced formula for the composition, but can be
set to some other string for display purposes.
"""
def __init__(self, ion, energy, name=None, attribute=None):
"""
Args:
ion: Ion object
energy: Energy for composition.
name: Optional parameter to name the entry. Defaults to the
chemical formula.
"""
self.ion = ion
# Auto-assign name
name = name if name else self.ion.reduced_formula
super(IonEntry, self).__init__(
composition=ion.composition, energy=energy, name=name,
attribute=attribute)
[docs] @classmethod
def from_dict(cls, d):
"""
Returns an IonEntry object from a dict.
"""
return IonEntry(Ion.from_dict(d["ion"]), d["energy"], d.get("name"),
d.get("attribute"))
[docs] def as_dict(self):
"""
Creates a dict of composition, energy, and ion name
"""
d = {"ion": self.ion.as_dict(), "energy": self.energy,
"name": self.name}
return d
def __repr__(self):
return "IonEntry : {} with energy = {:.4f}".format(self.composition,
self.energy)
def __str__(self):
return self.__repr__()
[docs]def ion_or_solid_comp_object(formula):
"""
Returns either an ion object or composition object given
a formula.
Args:
formula: String formula. Eg. of ion: NaOH(aq), Na[+];
Eg. of solid: Fe2O3(s), Fe(s), Na2O
Returns:
Composition/Ion object
"""
m = re.search(r"\[([^\[\]]+)\]|\(aq\)", formula)
if m:
comp_obj = Ion.from_formula(formula)
elif re.search(r"\(s\)", formula):
comp_obj = Composition(formula[:-3])
else:
comp_obj = Composition(formula)
return comp_obj
ELEMENTS_HO = {Element('H'), Element('O')}
# TODO: the solids filter breaks some of the functionality of the
# heatmap plotter, because the reference states for decomposition
# don't include oxygen/hydrogen in the OER/HER regions
# TODO: create a from_phase_diagram class method for non-formation energy
# invocation
# TODO: invocation from a MultiEntry entry list could be a bit more robust
# TODO: serialization is still a bit rough around the edges
[docs]class PourbaixDiagram(MSONable):
"""
Class to create a Pourbaix diagram from entries
"""
def __init__(self, entries, comp_dict=None, conc_dict=None,
filter_solids=False, nproc=None):
"""
Args:
entries ([PourbaixEntry] or [MultiEntry]): Entries list
containing Solids and Ions or a list of MultiEntries
comp_dict ({str: float}): Dictionary of compositions,
defaults to equal parts of each elements
conc_dict ({str: float}): Dictionary of ion concentrations,
defaults to 1e-6 for each element
filter_solids (bool): applying this filter to a pourbaix
diagram ensures all included phases are filtered by
stability on the compositional phase diagram. This
breaks some of the functionality of the analysis,
though, so use with caution.
nproc (int): number of processes to generate multientries with
in parallel. Defaults to None (serial processing)
"""
entries = deepcopy(entries)
# Get non-OH elements
self.pbx_elts = set(itertools.chain.from_iterable(
[entry.composition.elements for entry in entries]))
self.pbx_elts = list(self.pbx_elts - ELEMENTS_HO)
self.dim = len(self.pbx_elts) - 1
# Process multientry inputs
if isinstance(entries[0], MultiEntry):
self._processed_entries = entries
# Extract individual entries
single_entries = list(set(itertools.chain.from_iterable(
[e.entry_list for e in entries])))
self._unprocessed_entries = single_entries
self._filtered_entries = single_entries
self._conc_dict = None
self._elt_comp = {k: v for k, v in entries[0].composition.items()
if k not in ELEMENTS_HO}
self._multielement = True
# Process single entry inputs
else:
# Set default conc/comp dicts
if not comp_dict:
comp_dict = {elt.symbol: 1. / len(self.pbx_elts) for elt in self.pbx_elts}
if not conc_dict:
conc_dict = {elt.symbol: 1e-6 for elt in self.pbx_elts}
self._conc_dict = conc_dict
self._elt_comp = comp_dict
self.pourbaix_elements = self.pbx_elts
solid_entries = [entry for entry in entries
if entry.phase_type == "Solid"]
ion_entries = [entry for entry in entries
if entry.phase_type == "Ion"]
# If a conc_dict is specified, override individual entry concentrations
for entry in ion_entries:
ion_elts = list(set(entry.composition.elements) - ELEMENTS_HO)
# TODO: the logic here for ion concentration setting is in two
# places, in PourbaixEntry and here, should be consolidated
if len(ion_elts) == 1:
entry.concentration = conc_dict[ion_elts[0].symbol] \
* entry.normalization_factor
elif len(ion_elts) > 1 and not entry.concentration:
raise ValueError("Elemental concentration not compatible "
"with multi-element ions")
self._unprocessed_entries = solid_entries + ion_entries
if not len(solid_entries + ion_entries) == len(entries):
raise ValueError("All supplied entries must have a phase type of "
"either \"Solid\" or \"Ion\"")
if filter_solids:
# O is 2.46 b/c pbx entry finds energies referenced to H2O
entries_HO = [ComputedEntry('H', 0), ComputedEntry('O', 2.46)]
solid_pd = PhaseDiagram(solid_entries + entries_HO)
solid_entries = list(set(solid_pd.stable_entries) - set(entries_HO))
self._filtered_entries = solid_entries + ion_entries
if len(comp_dict) > 1:
self._multielement = True
self._processed_entries = self._preprocess_pourbaix_entries(
self._filtered_entries, nproc=nproc)
else:
self._processed_entries = self._filtered_entries
self._multielement = False
self._stable_domains, self._stable_domain_vertices = \
self.get_pourbaix_domains(self._processed_entries)
def _convert_entries_to_points(self, pourbaix_entries):
"""
Args:
pourbaix_entries ([PourbaixEntry]): list of pourbaix entries
to process into vectors in nph-nphi-composition space
Returns:
list of vectors, [[nph, nphi, e0, x1, x2, ..., xn-1]]
corresponding to each entry in nph-nphi-composition space
"""
vecs = [[entry.npH, entry.nPhi, entry.energy] +
[entry.composition.get(elt) for elt in self.pbx_elts[:-1]]
for entry in pourbaix_entries]
vecs = np.array(vecs)
norms = np.transpose([[entry.normalization_factor
for entry in pourbaix_entries]])
vecs *= norms
return vecs
def _get_hull_in_nph_nphi_space(self, entries):
"""
Generates convex hull of pourbaix diagram entries in composition,
npH, and nphi space. This enables filtering of multi-entries
such that only compositionally stable combinations of entries
are included.
Args:
entries ([PourbaixEntry]): list of PourbaixEntries to construct
the convex hull
Returns: list of entries and stable facets corresponding to that
list of entries
"""
ion_entries = [entry for entry in entries
if entry.phase_type == "Ion"]
solid_entries = [entry for entry in entries
if entry.phase_type == "Solid"]
# Pre-filter solids based on min at each composition
logger.debug("Pre-filtering solids by min energy at each composition")
sorted_entries = sorted(
solid_entries, key=lambda x: (x.composition.reduced_composition,
x.entry.energy_per_atom))
grouped_by_composition = itertools.groupby(
sorted_entries, key=lambda x: x.composition.reduced_composition)
min_entries = [list(grouped_entries)[0]
for comp, grouped_entries in grouped_by_composition]
min_entries += ion_entries
logger.debug("Constructing nph-nphi-composition points for qhull")
vecs = self._convert_entries_to_points(min_entries)
maxes = np.max(vecs[:, :3], axis=0)
extra_point = np.concatenate(
[maxes, np.ones(self.dim) / self.dim], axis=0)
# Add padding for extra point
pad = 1000
extra_point[2] += pad
points = np.concatenate([vecs, np.array([extra_point])], axis=0)
logger.debug("Constructing convex hull in nph-nphi-composition space")
hull = ConvexHull(points, qhull_options="QJ i")
# Create facets and remove top
facets = [facet for facet in hull.simplices
if not len(points) - 1 in facet]
if self.dim > 1:
logger.debug("Filtering facets by pourbaix composition")
valid_facets = []
for facet in facets:
comps = vecs[facet][:, 3:]
full_comps = np.concatenate([
comps, 1 - np.sum(comps, axis=1).reshape(len(comps), 1)], axis=1)
# Ensure an compositional interior point exists in the simplex
if np.linalg.matrix_rank(full_comps) > self.dim:
valid_facets.append(facet)
else:
valid_facets = facets
return min_entries, valid_facets
def _preprocess_pourbaix_entries(self, entries, nproc=None):
"""
Generates multi-entries for pourbaix diagram
Args:
entries ([PourbaixEntry]): list of PourbaixEntries to preprocess
into MultiEntries
nproc (int): number of processes to be used in parallel
treatment of entry combos
Returns:
([MultiEntry]) list of stable MultiEntry candidates
"""
# Get composition
tot_comp = Composition(self._elt_comp)
min_entries, valid_facets = self._get_hull_in_nph_nphi_space(entries)
combos = []
for facet in valid_facets:
for i in range(1, self.dim + 2):
these_combos = list()
for combo in itertools.combinations(facet, i):
these_entries = [min_entries[i] for i in combo]
these_combos.append(frozenset(these_entries))
combos.append(these_combos)
all_combos = set(itertools.chain.from_iterable(combos))
list_combos = []
for i in all_combos:
list_combos.append(list(i))
all_combos = list_combos
multi_entries = []
# Parallel processing of multi-entry generation
if nproc is not None:
f = partial(self.process_multientry, prod_comp=tot_comp)
with Pool(nproc) as p:
multi_entries = list(tqdm(p.imap(f, all_combos),
total=len(all_combos)))
multi_entries = list(filter(bool, multi_entries))
else:
# Serial processing of multi-entry generation
for combo in tqdm(all_combos):
multi_entry = self.process_multientry(combo, prod_comp=tot_comp)
if multi_entry:
multi_entries.append(multi_entry)
return multi_entries
def _generate_multielement_entries(self, entries, nproc=None):
"""
Create entries for multi-element Pourbaix construction.
This works by finding all possible linear combinations
of entries that can result in the specified composition
from the initialized comp_dict.
Args:
entries ([PourbaixEntries]): list of pourbaix entries
to process into MultiEntries
nproc (int): number of processes to be used in parallel
treatment of entry combos
"""
N = len(self._elt_comp) # No. of elements
total_comp = Composition(self._elt_comp)
# generate all combinations of compounds that have all elements
entry_combos = [itertools.combinations(
entries, j + 1) for j in range(N)]
entry_combos = itertools.chain.from_iterable(entry_combos)
entry_combos = filter(lambda x: total_comp < MultiEntry(x).composition,
entry_combos)
# Generate and filter entries
processed_entries = []
total = sum([comb(len(entries), j + 1)
for j in range(N)])
if total > 1e6:
warnings.warn("Your pourbaix diagram includes {} entries and may "
"take a long time to generate.".format(total))
# Parallel processing of multi-entry generation
if nproc is not None:
f = partial(self.process_multientry, prod_comp=total_comp)
with Pool(nproc) as p:
processed_entries = list(tqdm(p.imap(f, entry_combos),
total=total))
processed_entries = list(filter(bool, processed_entries))
# Serial processing of multi-entry generation
else:
for entry_combo in entry_combos:
processed_entry = self.process_multientry(entry_combo, total_comp)
if processed_entry is not None:
processed_entries.append(processed_entry)
return processed_entries
[docs] @staticmethod
def process_multientry(entry_list, prod_comp, coeff_threshold=1e-4):
"""
Static method for finding a multientry based on
a list of entries and a product composition.
Essentially checks to see if a valid aqueous
reaction exists between the entries and the
product composition and returns a MultiEntry
with weights according to the coefficients if so.
Args:
entry_list ([Entry]): list of entries from which to
create a MultiEntry
prod_comp (Composition): composition constraint for setting
weights of MultiEntry
coeff_threshold (float): threshold of stoichiometric
coefficients to filter, if weights are lower than
this value, the entry is not returned
"""
dummy_oh = [Composition("H"), Composition("O")]
try:
# Get balanced reaction coeffs, ensuring all < 0 or conc thresh
# Note that we get reduced compositions for solids and non-reduced
# compositions for ions because ions aren't normalized due to
# their charge state.
entry_comps = [e.composition for e in entry_list]
rxn = Reaction(entry_comps + dummy_oh, [prod_comp])
react_coeffs = [-rxn.get_coeff(comp) for comp in entry_comps]
all_coeffs = react_coeffs + [rxn.get_coeff(prod_comp)]
# Check if reaction coeff threshold met for pourbaix compounds
# All reactant/product coefficients must be positive nonzero
if all([coeff > coeff_threshold for coeff in all_coeffs]):
return MultiEntry(entry_list, weights=react_coeffs)
else:
return None
except ReactionError:
return None
[docs] @staticmethod
def get_pourbaix_domains(pourbaix_entries, limits=None):
"""
Returns a set of pourbaix stable domains (i. e. polygons) in
pH-V space from a list of pourbaix_entries
This function works by using scipy's HalfspaceIntersection
function to construct all of the 2-D polygons that form the
boundaries of the planes corresponding to individual entry
gibbs free energies as a function of pH and V. Hyperplanes
of the form a*pH + b*V + 1 - g(0, 0) are constructed and
supplied to HalfspaceIntersection, which then finds the
boundaries of each pourbaix region using the intersection
points.
Args:
pourbaix_entries ([PourbaixEntry]): Pourbaix entries
with which to construct stable pourbaix domains
limits ([[float]]): limits in which to do the pourbaix
analysis
Returns:
Returns a dict of the form {entry: [boundary_points]}.
The list of boundary points are the sides of the N-1
dim polytope bounding the allowable ph-V range of each entry.
"""
if limits is None:
limits = [[-2, 16], [-4, 4]]
# Get hyperplanes
hyperplanes = [np.array([-PREFAC * entry.npH, -entry.nPhi,
0, -entry.energy]) * entry.normalization_factor
for entry in pourbaix_entries]
hyperplanes = np.array(hyperplanes)
hyperplanes[:, 2] = 1
max_contribs = np.max(np.abs(hyperplanes), axis=0)
g_max = np.dot(-max_contribs, [limits[0][1], limits[1][1], 0, 1])
# Add border hyperplanes and generate HalfspaceIntersection
border_hyperplanes = [[-1, 0, 0, limits[0][0]],
[1, 0, 0, -limits[0][1]],
[0, -1, 0, limits[1][0]],
[0, 1, 0, -limits[1][1]],
[0, 0, -1, 2 * g_max]]
hs_hyperplanes = np.vstack([hyperplanes, border_hyperplanes])
interior_point = np.average(limits, axis=1).tolist() + [g_max]
hs_int = HalfspaceIntersection(hs_hyperplanes, np.array(interior_point))
# organize the boundary points by entry
pourbaix_domains = {entry: [] for entry in pourbaix_entries}
for intersection, facet in zip(hs_int.intersections,
hs_int.dual_facets):
for v in facet:
if v < len(pourbaix_entries):
this_entry = pourbaix_entries[v]
pourbaix_domains[this_entry].append(intersection)
# Remove entries with no pourbaix region
pourbaix_domains = {k: v for k, v in pourbaix_domains.items() if v}
pourbaix_domain_vertices = {}
for entry, points in pourbaix_domains.items():
points = np.array(points)[:, :2]
# Initial sort to ensure consistency
points = points[np.lexsort(np.transpose(points))]
center = np.average(points, axis=0)
points_centered = points - center
# Sort points by cross product of centered points,
# isn't strictly necessary but useful for plotting tools
points_centered = sorted(points_centered,
key=cmp_to_key(lambda x, y: x[0] * y[1] - x[1] * y[0]))
points = points_centered + center
# Create simplices corresponding to pourbaix boundary
simplices = [Simplex(points[indices])
for indices in ConvexHull(points).simplices]
pourbaix_domains[entry] = simplices
pourbaix_domain_vertices[entry] = points
return pourbaix_domains, pourbaix_domain_vertices
[docs] def find_stable_entry(self, pH, V):
"""
Finds stable entry at a pH,V condition
Args:
pH (float): pH to find stable entry
V (float): V to find stable entry
Returns:
"""
energies_at_conditions = [e.normalized_energy_at_conditions(pH, V)
for e in self.stable_entries]
return self.stable_entries[np.argmin(energies_at_conditions)]
[docs] def get_decomposition_energy(self, entry, pH, V):
"""
Finds decomposition to most stable entries in eV/atom,
supports vectorized inputs for pH and V
Args:
entry (PourbaixEntry): PourbaixEntry corresponding to
compound to find the decomposition for
pH (float, [float]): pH at which to find the decomposition
V (float, [float]): voltage at which to find the decomposition
Returns:
Decomposition energy for the entry, i. e. the energy above
the "pourbaix hull" in eV/atom at the given conditions
"""
# Check composition consistency between entry and Pourbaix diagram:
pbx_comp = Composition(self._elt_comp).fractional_composition
entry_pbx_comp = Composition(
{elt: coeff for elt, coeff in entry.composition.items()
if elt not in ELEMENTS_HO}).fractional_composition
if entry_pbx_comp != pbx_comp:
raise ValueError("Composition of stability entry does not match "
"Pourbaix Diagram")
entry_normalized_energy = entry.normalized_energy_at_conditions(pH, V)
hull_energy = self.get_hull_energy(pH, V)
decomposition_energy = entry_normalized_energy - hull_energy
# Convert to eV/atom instead of eV/normalized formula unit
decomposition_energy /= entry.normalization_factor
decomposition_energy /= entry.composition.num_atoms
return decomposition_energy
[docs] def get_hull_energy(self, pH, V):
"""
Gets the minimum energy of the pourbaix "basin" that is formed
from the stable pourbaix planes. Vectorized.
Args:
pH (float or [float]): pH at which to find the hull energy
V (float or [float]): V at which to find the hull energy
Returns:
(float or [float]) minimum pourbaix energy at conditions
"""
all_gs = np.array([e.normalized_energy_at_conditions(
pH, V) for e in self.stable_entries])
base = np.min(all_gs, axis=0)
return base
[docs] def get_stable_entry(self, pH, V):
"""
Gets the stable entry at a given pH, V condition
Args:
pH (float): pH at a given condition
V (float): V at a given condition
Returns:
(PourbaixEntry or MultiEntry): pourbaix or multi-entry
corresponding ot the minimum energy entry at a given
pH, V condition
"""
all_gs = np.array([e.normalized_energy_at_conditions(
pH, V) for e in self.stable_entries])
return self.stable_entries[np.argmin(all_gs)]
@property
def stable_entries(self):
"""
Returns the stable entries in the Pourbaix diagram.
"""
return list(self._stable_domains.keys())
@property
def unstable_entries(self):
"""
Returns all unstable entries in the Pourbaix diagram
"""
return [e for e in self.all_entries if e not in self.stable_entries]
@property
def all_entries(self):
"""
Return all entries used to generate the pourbaix diagram
"""
return self._processed_entries
@property
def unprocessed_entries(self):
"""
Return unprocessed entries
"""
return self._unprocessed_entries
[docs] def as_dict(self, include_unprocessed_entries=False):
"""
Args:
include_unprocessed_entries (): Whether to include unprocessed entries.
Returns:
MSONable dict.
"""
if include_unprocessed_entries:
entries = [e.as_dict() for e in self._unprocessed_entries]
else:
entries = [e.as_dict() for e in self._processed_entries]
d = {"@module": self.__class__.__module__,
"@class": self.__class__.__name__,
"entries": entries,
"comp_dict": self._elt_comp,
"conc_dict": self._conc_dict}
return d
[docs] @classmethod
def from_dict(cls, d):
"""
Args:
d (): Dict representation.
Returns:
PourbaixDiagram
"""
decoded_entries = MontyDecoder().process_decoded(d['entries'])
return cls(decoded_entries, d.get('comp_dict'),
d.get('conc_dict'))
[docs]class PourbaixPlotter:
"""
A plotter class for phase diagrams.
"""
def __init__(self, pourbaix_diagram):
"""
Args:
pourbaix_diagram (PourbaixDiagram): A PourbaixDiagram object.
"""
self._pbx = pourbaix_diagram
[docs] def show(self, *args, **kwargs):
"""
Shows the pourbaix plot
Args:
*args: args to get_pourbaix_plot
**kwargs: kwargs to get_pourbaix_plot
Returns:
None
"""
plt = self.get_pourbaix_plot(*args, **kwargs)
plt.show()
[docs] def get_pourbaix_plot(self, limits=None, title="",
label_domains=True, plt=None):
"""
Plot Pourbaix diagram.
Args:
limits: 2D list containing limits of the Pourbaix diagram
of the form [[xlo, xhi], [ylo, yhi]]
title (str): Title to display on plot
label_domains (bool): whether to label pourbaix domains
plt (pyplot): Pyplot instance for plotting
Returns:
plt (pyplot) - matplotlib plot object with pourbaix diagram
"""
if limits is None:
limits = [[-2, 16], [-3, 3]]
plt = plt or pretty_plot(16)
xlim = limits[0]
ylim = limits[1]
h_line = np.transpose([[xlim[0], -xlim[0] * PREFAC],
[xlim[1], -xlim[1] * PREFAC]])
o_line = np.transpose([[xlim[0], -xlim[0] * PREFAC + 1.23],
[xlim[1], -xlim[1] * PREFAC + 1.23]])
neutral_line = np.transpose([[7, ylim[0]], [7, ylim[1]]])
V0_line = np.transpose([[xlim[0], 0], [xlim[1], 0]])
ax = plt.gca()
ax.set_xlim(xlim)
ax.set_ylim(ylim)
lw = 3
plt.plot(h_line[0], h_line[1], "r--", linewidth=lw)
plt.plot(o_line[0], o_line[1], "r--", linewidth=lw)
plt.plot(neutral_line[0], neutral_line[1], "k-.", linewidth=lw)
plt.plot(V0_line[0], V0_line[1], "k-.", linewidth=lw)
for entry, vertices in self._pbx._stable_domain_vertices.items():
center = np.average(vertices, axis=0)
x, y = np.transpose(np.vstack([vertices, vertices[0]]))
plt.plot(x, y, 'k-', linewidth=lw)
if label_domains:
plt.annotate(generate_entry_label(entry), center, ha='center',
va='center', fontsize=20, color="b").draggable()
plt.xlabel("pH")
plt.ylabel("E (V)")
plt.title(title, fontsize=20, fontweight='bold')
return plt
[docs] def plot_entry_stability(self, entry, pH_range=None, pH_resolution=100,
V_range=None, V_resolution=100, e_hull_max=1,
cmap='RdYlBu_r', **kwargs):
"""
Args:
entry ():
pH_range ():
pH_resolution ():
V_range ():
V_resolution ():
e_hull_max ():
cmap ():
**kwargs ():
Returns:
"""
if pH_range is None:
pH_range = [-2, 16]
if V_range is None:
V_range = [-3, 3]
# plot the Pourbaix diagram
plt = self.get_pourbaix_plot(**kwargs)
pH, V = np.mgrid[pH_range[0]:pH_range[1]:pH_resolution * 1j, V_range[0]:V_range[1]:V_resolution * 1j]
stability = self._pbx.get_decomposition_energy(entry, pH, V)
# Plot stability map
plt.pcolor(pH, V, stability, cmap=cmap, vmin=0, vmax=e_hull_max)
cbar = plt.colorbar()
cbar.set_label("Stability of {} (eV/atom)".format(
generate_entry_label(entry)))
# Set ticklabels
# ticklabels = [t.get_text() for t in cbar.ax.get_yticklabels()]
# ticklabels[-1] = '>={}'.format(ticklabels[-1])
# cbar.ax.set_yticklabels(ticklabels)
return plt
[docs] def domain_vertices(self, entry):
"""
Returns the vertices of the Pourbaix domain.
Args:
entry: Entry for which domain vertices are desired
Returns:
list of vertices
"""
return self._pbx._stable_domain_vertices[entry]
[docs]def generate_entry_label(entry):
"""
Generates a label for the pourbaix plotter
Args:
entry (PourbaixEntry or MultiEntry): entry to get a label for
"""
if isinstance(entry, MultiEntry):
return " + ".join([latexify_ion(latexify(e.name)) for e in entry.entry_list])
else:
return latexify_ion(latexify(entry.name))
[docs]def latexify_ion(formula):
"""
Convert a formula to latex format.
Args:
formula (str): Formula
Returns:
Latex string.
"""
return re.sub(r"()\[([^)]*)\]", r"\1$^{\2}$", formula)