Source code for matador.hull.hull

# coding: utf-8
# Distributed under the terms of the MIT License.

""" This file implements convex hull functionality from database
queries.

"""


from copy import deepcopy
from typing import List
from collections import defaultdict
import re
import warnings

from bson.son import SON
import pymongo as pm
import numpy as np

from matador.utils.print_utils import print_notify, print_warning
from matador.utils.chem_utils import parse_element_string, get_padded_composition, get_num_intercalated
from matador.utils.chem_utils import get_generic_grav_capacity, get_formula_from_stoich, get_stoich_from_formula
from matador.utils.chem_utils import get_formation_energy
from matador.utils.cursor_utils import set_cursor_from_array, get_array_from_cursor
from matador.utils.cursor_utils import display_results, recursive_get
from matador.utils.cursor_utils import filter_cursor_by_chempots
from matador.battery import Electrode, VoltageProfile
from matador.hull.phase_diagram import PhaseDiagram

# general small number used when comparing energies to zero
EPS = 1e-8
# small number used for checking boundaries
BOUNDARY_EPS = 1e-12


[docs]class QueryConvexHull: """ Construct a binary or ternary phase diagram from a matador.query.DBQuery object, or a list of structures. Attributes: cursor (list): list of all structures used to create phase diagram. hull_cursor (list): list of all documents within hull_cutoff. chempot_cursor (list): list of chemical potential documents. structures (numpy.ndarray): all structures used to create hull. hull_dist (np.ndarray): array of distances from hull for each structure. species (list): list of chemical potential symbols. num_elements (int): number of elements present in the chemical potentials. elements (list): the elements present in the convex hull. voltage_data (list): if voltage_curve() has been called, then this is a list of VoltageProfile objects containing Q, x, V and reaction pathways. volume_data (dict): if volume_curve() has been called, then this is a dictionary containing x and volumes per B (in AxBy). """ def __init__(self, query=None, cursor=None, elements=None, species=None, voltage=False, volume=False, subcmd=None, plot_kwargs=None, lazy=False, energy_key='enthalpy_per_atom', client=None, collections=None, db=None, **kwargs): """ Initialise the class from either a DBQuery or a cursor (list of matador dicts) and construct the appropriate phase diagram. Keyword arguments: query (matador.query.DBQuery): object containing structures, cursor (list(dict)): alternatively specify list of matador documents. species (list(str)): list of elements/chempots to use, used to provide a useful order, voltage (bool): whether or nto to compute voltages relative for insertion of first entry in species, volume (bool): whether or not to compute volume expansion relative to first entry in species, energy_key (str): key under which the desired energy *per atom* is stored. lazy (bool): if True, do not create hull until `self.create_hull()` is called chempots (list(float)): list of chemical potential values to use. elements (list(str)): deprecated form `species`. kwargs (dict): mostly CLI arguments, see matador hull --help for full options. plot_kwargs (dict): arguments to pass to plot_hull function client (pymongo.MongoClient): optional client to pass to DBQuery. collections (dict of pymongo.collections.Collection): optional dict of collections to pass to DBQuery. db (str): db name to connect to in DBQuery. """ self.args = dict() if query is not None: self.args.update(query.args) self.args.update(kwargs) if subcmd is not None: warnings.warn("subcmd will soon be deprecated, please pass the equivalent flag as a kwarg (e.g. voltage=True)") if subcmd == 'voltage': voltage = True self.args['subcmd'] = subcmd if plot_kwargs is None: plot_kwargs = {} self.args['plot_kwargs'] = plot_kwargs self.from_cursor = False self.plot_params = False self.compute_voltages = voltage self.compute_volumes = volume if query is None and cursor is None: # if no query or cursor passed, push all kwargs to new query from matador.query import DBQuery kwargs.pop('intersection', None) query = DBQuery( subcmd='hull', intersection=True, client=client, collections=collections, **kwargs ) self._query = query if self._query is not None: # this isn't strictly necessary but it maintains the sanctity of the query results self.cursor = list(deepcopy(query.cursor)) self.args['use_source'] = False if self._query.args['subcmd'] not in ['hull', 'voltage', 'hulldiff']: print_warning('Query was not prepared with subcmd=hull, so cannot guarantee consistent formation energies.') else: self.cursor = list(cursor) self.from_cursor = True self.args['use_source'] = True # set up attributes for later self.structures = None self.convex_hull = None self.chempot_cursor = None self.hull_cursor = None self.phase_diagram = None self.hull_dist = None self.species = None self.voltage_data: List[VoltageProfile] = [] self.volume_data = defaultdict(list) self.elements = [] self.num_elements = 0 self.species = self._get_species(species, elements) self._dimension = len(self.species) # tracker for whether per_b fields have been setup self._per_b_done = False self.energy_key = energy_key if not self.energy_key.endswith('_per_atom'): warnings.warn('Appending per_atom to energy_key {}'.format(self.energy_key)) self.energy_key += '_per_atom' self._extensive_energy_key = self.energy_key.split('_per_atom')[0] if self.args.get('hull_cutoff') is not None: self.hull_cutoff = float(self.args['hull_cutoff']) else: self.hull_cutoff = 0.0 if self.cursor is None: raise RuntimeError('Failed to find structures to create hull!') self._non_elemental = False assert isinstance(self.species, list) for _species in self.species: if len(parse_element_string(_species, stoich=True)) > 1: self._non_elemental = True if not lazy: self.create_hull()
[docs] def create_hull(self): """ Begin the hull creation routines and perform the post-processing specified by initial arguments. """ if self.args.get('uniq'): from matador.utils.cursor_utils import filter_unique_structures if self.args.get('uniq') is True: sim_tol = 0.1 else: sim_tol = self.args.get('uniq') print_notify('Filtering for unique structures...') self.cursor = filter_unique_structures( self.cursor, args=self.args, quiet=True, sim_tol=sim_tol, hull=True, energy_key=self.energy_key ) self.construct_phase_diagram() if not self.hull_cursor: print_warning('No structures on hull with chosen chemical potentials.') else: print_notify('{} structures found within {} eV of the hull, including chemical potentials.' .format(len(self.hull_cursor), self.hull_cutoff)) display_results(self.hull_cursor, hull=True, energy_key=self.energy_key, **self.args) if self.compute_voltages: print("Constructing electrode system with active ion: {}".format(self.species[0])) self.voltage_curve() if self.compute_volumes: self.volume_curve() if not self.args.get('no_plot'): if self.compute_voltages and self.voltage_data: self.plot_voltage_curve(show=False) if self.compute_volumes and self.volume_data: self.plot_volume_curve(show=False) self.plot_hull(**self.args['plot_kwargs'], debug=self.args.get('debug'), show=True)
def __repr__(self): return display_results(self.hull_cursor, args=self.args, hull=True, energy_key=self.energy_key, return_str=True) @property def savefig(self): """ True if any figure type argument was passed. """ return any([self.args.get('pdf'), self.args.get('png'), self.args.get('svg')]) @property def savefig_ext(self): """ Returns the figure extension to save with. """ for ext in ['pdf', 'png', 'svg']: if self.args.get(ext): return ext
[docs] def plot_hull(self, **kwargs): """ Hull plot helper function. """ from matador import plotting if self._dimension == 3: ax = plotting.plot_ternary_hull(self, **kwargs) elif self._dimension == 2: ax = plotting.plot_2d_hull(self, **kwargs) else: print_notify('Unable to plot phase diagram of dimension {}.'.format(self._dimension)) return ax
[docs] def plot_voltage_curve(self, **kwargs): """ Voltage plot helper function. """ from matador import plotting savefig = None if self.savefig: savefig = '{}_voltage.{}'.format(''.join(self.elements), self.savefig_ext) keys = ['expt', 'labels', 'expt_label'] plot_args = {key: self.args.get(key) for key in keys} plot_args["savefig"] = savefig plot_args.update(kwargs) plotting.plot_voltage_curve( self.voltage_data, **plot_args )
[docs] def plot_volume_curve(self, **kwargs): """ Volume plot helper function. """ from matador import plotting plotting.plot_volume_curve( self, **self.args['plot_kwargs'], show=False )
[docs] def fake_chempots(self, custom_elem=None): """ Spoof documents for command-line chemical potentials. Keyword arguments: custom_elem (list(str)): list of element symbols to generate chempots for. """ self.chempot_cursor = [] print('Generating fake chempots...') if custom_elem is None: custom_elem = self.species if len(custom_elem) != len(self.species): raise RuntimeError('Wrong number of compounds/chemical potentials specified: {} vs {}' .format(custom_elem, self.args.get('chempots'))) for i, _ in enumerate(self.args.get('chempots')): self.chempot_cursor.append(dict()) self.chempot_cursor[i]['stoichiometry'] = get_stoich_from_formula(custom_elem[i]) self.chempot_cursor[i][self.energy_key] = -1*abs(self.args.get('chempots')[i]) self.chempot_cursor[i][self._extensive_energy_key] = self.chempot_cursor[i][self.energy_key] * \ sum(elem[1] for elem in self.chempot_cursor[i]['stoichiometry']) self.chempot_cursor[i]['num_fu'] = 1 self.chempot_cursor[i]['num_atoms'] = 1 self.chempot_cursor[i]['text_id'] = ['command', 'line'] self.chempot_cursor[i]['_id'] = None self.chempot_cursor[i]['source'] = ['command_line'] self.chempot_cursor[i]['space_group'] = 'xxx' self.chempot_cursor[i][self._extensive_energy_key + '_per_b'] = self.chempot_cursor[i][self.energy_key] self.chempot_cursor[i]['num_a'] = 0 self.chempot_cursor[i]['cell_volume'] = 1 self.chempot_cursor[i]['concentration'] = [1 if i == ind else 0 for ind in range(self._dimension-1)] self.chempot_cursor[0]['num_a'] = float('inf') notify = 'Custom chempots:' for chempot in self.chempot_cursor: notify += '{:3} = {} eV/fu, '.format(get_formula_from_stoich(chempot['stoichiometry'], sort=False), chempot[self._extensive_energy_key]) if self.args.get('debug'): for match in self.chempot_cursor: print(match) print(len(notify) * '─') print(notify) print(len(notify) * '─')
[docs] def construct_phase_diagram(self): """ Create a phase diagram with arbitrary chemical potentials. Expects self.cursor to be populated with structures and chemical potential labels to be set under self.species. """ self.set_chempots() self.cursor = filter_cursor_by_chempots(self.species, self.cursor) formation_key = 'formation_{}'.format(self.energy_key) extensive_formation_key = 'formation_{}'.format(self._extensive_energy_key) for ind, doc in enumerate(self.cursor): self.cursor[ind][formation_key] = get_formation_energy(self.chempot_cursor, doc, energy_key=self.energy_key) self.cursor[ind][extensive_formation_key] = doc[formation_key] * doc['num_atoms'] if self._non_elemental and self.args.get('subcmd') in ['voltage', 'volume']: raise NotImplementedError('Pseudo-binary/pseudo-ternary voltages not yet implemented.') self.phase_diagram = PhaseDiagram(self.cursor, formation_key, self._dimension) # aliases for data stored in phase diagram self.structures = self.phase_diagram.structures self.hull_dist = self.phase_diagram.hull_dist self.convex_hull = self.phase_diagram.convex_hull # ensure hull cursor is sorted by enthalpy_per_atom, # then by concentration, as it will be by default if from database hull_cursor = [self.cursor[idx] for idx in np.where(self.hull_dist <= self.hull_cutoff + EPS)[0]] # TODO: check why this fails when the opposite way around hull_cursor = sorted(hull_cursor, key=lambda doc: (doc['concentration'], recursive_get(doc, self.energy_key))) # by default hull cursor includes all structures within hull_cutoff # if summary requested and we're in hulldiff mode, filter hull_cursor for lowest per stoich if self.args.get('summary') and self.args['subcmd'] == 'hulldiff': tmp_hull_cursor = [] compositions = set() for ind, member in enumerate(hull_cursor): formula = get_formula_from_stoich(member['stoichiometry'], sort=True) if formula not in compositions: compositions.add(formula) tmp_hull_cursor.append(member) hull_cursor = tmp_hull_cursor self.hull_cursor = hull_cursor
[docs] def set_chempots(self, energy_key=None): """ Search for chemical potentials that match the structures in the query cursor and add them to the cursor. Also set the concentration of chemical potentials in :attr:`cursor`, if not already set. """ if energy_key is None: energy_key = self.energy_key query = self._query query_dict = dict() species_stoich = [sorted(get_stoich_from_formula(spec, sort=False)) for spec in self.species] self.chempot_cursor = [] if self.args.get('chempots') is not None: self.fake_chempots(custom_elem=self.species) elif self.from_cursor: chempot_cursor = sorted([doc for doc in self.cursor if doc['stoichiometry'] in species_stoich], key=lambda doc: recursive_get(doc, energy_key)) for species in species_stoich: for doc in chempot_cursor: if doc['stoichiometry'] == species: self.chempot_cursor.append(doc) break if len(self.chempot_cursor) != len(self.species): raise RuntimeError('Found {} of {} required chemical potentials' .format(len(self.chempot_cursor), len(self.species))) if self.args.get('debug'): print([mu['stoichiometry'] for mu in self.chempot_cursor]) else: print(60 * '─') self.chempot_cursor = len(self.species) * [None] # scan for suitable chem pots in database for ind, elem in enumerate(self.species): print('Scanning for suitable', elem, 'chemical potential...') query_dict['$and'] = deepcopy(list(query.calc_dict['$and'])) if not self.args.get('ignore_warnings'): query_dict['$and'].append(query.query_quality()) if len(species_stoich[ind]) == 1: query_dict['$and'].append(query.query_composition(custom_elem=[elem])) else: query_dict['$and'].append(query.query_stoichiometry(custom_stoich=[elem])) # if oqmd, only query composition, not parameters if query.args.get('tags') is not None: query_dict['$and'].append(query.query_tags()) mu_cursor = query.repo.find(SON(query_dict)).sort(energy_key, pm.ASCENDING) if mu_cursor.count() == 0: print_notify('Failed... searching without spin polarization field...') scanned = False while not scanned: for idx, dicts in enumerate(query_dict['$and']): for key in dicts: if key == 'spin_polarized': del query_dict['$and'][idx][key] break if idx == len(query_dict['$and']) - 1: scanned = True mu_cursor = query.repo.find(SON(query_dict)).sort(energy_key, pm.ASCENDING) if mu_cursor.count() == 0: raise RuntimeError('No chemical potentials found for {}...'.format(elem)) self.chempot_cursor[ind] = mu_cursor[0] if self.chempot_cursor[ind] is not None: print('Using', ''.join([self.chempot_cursor[ind]['text_id'][0], ' ', self.chempot_cursor[ind]['text_id'][1]]), 'as chem pot for', elem) print(60 * '─') else: raise RuntimeError('No possible chem pots available for {}.'.format(elem)) for i, mu in enumerate(self.chempot_cursor): self.chempot_cursor[i][self._extensive_energy_key + '_per_b'] = mu[energy_key] self.chempot_cursor[i]['num_a'] = 0 self.chempot_cursor[0]['num_a'] = float('inf') # don't check for IDs if we're loading from cursor if not self.from_cursor: ids = [doc['_id'] for doc in self.cursor] if self.chempot_cursor[0]['_id'] is None or self.chempot_cursor[0]['_id'] not in ids: self.cursor.insert(0, self.chempot_cursor[0]) for match in self.chempot_cursor[1:]: if match['_id'] is None or match['_id'] not in ids: self.cursor.append(match) # add faked chempots to overall cursor elif self.args.get('chempots') is not None: self.cursor.insert(0, self.chempot_cursor[0]) self.cursor.extend(self.chempot_cursor[1:]) # find all elements present in the chemical potentials elements = [] for mu in self.chempot_cursor: for elem, _ in mu['stoichiometry']: if elem not in elements: elements.append(elem) self.elements = elements self.num_elements = len(elements)
[docs] @staticmethod def filter_cursor_by_chempots(species, cursor): """ For the desired chemical potentials, remove any incompatible structures from cursor. Parameters: species (list): list of chemical potential formulae. cursor (list): list of matador documents to filter. Returns: list: the filtered cursor. """ return filter_cursor_by_chempots(species, cursor)
def _setup_per_b_fields(self): """ Calculate the enthalpy and volume per "B" in A_x B. """ if self._per_b_done: return for ind, doc in enumerate(self.cursor): nums_b = len(self.species[1:]) * [0] for elem in doc['stoichiometry']: for chem_pot_ind, chem_pot in enumerate(self.species[1:]): if elem[0] == chem_pot: nums_b[chem_pot_ind] += elem[1] num_b = sum(nums_b) num_fu = doc['num_fu'] if num_b == 0: self.cursor[ind][self._extensive_energy_key + '_per_b'] = 12345e5 self.cursor[ind]['cell_volume_per_b'] = 12345e5 else: self.cursor[ind][self._extensive_energy_key + '_per_b'] = doc[self._extensive_energy_key] / (num_b * num_fu) if 'cell_volume' in doc: self.cursor[ind]['cell_volume_per_b'] = doc['cell_volume'] / (num_b * num_fu) capacities = np.zeros((len(self.cursor))) for i, doc in enumerate(self.cursor): concs = self.cursor[i]['concentration'] concs = get_padded_composition(doc['stoichiometry'], self.elements) capacities[i] = get_generic_grav_capacity(concs, self.elements) set_cursor_from_array(self.cursor, capacities, 'gravimetric_capacity') self._per_b_done = True
[docs] def voltage_curve(self, cursor=None): """ Take a computed convex hull and calculate voltages for either binary or ternary systems. Sets the self.voltage_data attribute with various fields. Parameters: hull_cursor (list(dict)): list of structures to include in the voltage curve. """ hull_cursor = cursor if hull_cursor is None: hull_cursor = [doc for doc in self.hull_cursor if doc.get("hull_distance", 1e20) < 1e-9] if not self._non_elemental: self._setup_per_b_fields() if self._dimension == 2: self._calculate_binary_voltage_curve(hull_cursor) elif self._dimension == 3: self._calculate_ternary_voltage_curve(hull_cursor) else: raise RuntimeError('Unable to calculate voltage curve for hull of dimension {}'.format(self._dimension)) self._scale_voltages(self.species[0]) for profile in self.voltage_data: print(profile.voltage_summary(csv=self.args.get('csv', False)))
[docs] def volume_curve(self): """ Take stable compositions and volume and calculate volume expansion per "B" in AB binary. """ if not self._non_elemental and not self._per_b_done: self._setup_per_b_fields() if self._dimension == 2: self._calculate_binary_volume_curve() elif self._dimension == 3: # dimension 3 is implemented inside the voltage curve call. pass else: raise NotImplementedError( "Volume curves have only been implemented for binary and ternary phase diagrams." ) self.print_volume_summary()
[docs] def print_volume_summary(self): """ Prints a volume data summary. If self.args['csv'] is True, save the summary to a file. """ for reaction_idx, _ in enumerate(self.volume_data['Q']): data_str = '# Reaction {} \n'.format(reaction_idx+1) data_str += '# ' + ''.join(get_formula_from_stoich(self.volume_data['endstoichs'][reaction_idx])) + '\n' data_str += '# {:>10}\t{:>14} \t{:>14}\n'.format('Q (mAh/g)', 'Volume (A^3)', 'Volume ratio with bulk') for idx, _ in enumerate(self.volume_data['electrode_volume'][reaction_idx]): data_str += ('{:>10.2f} \t{:14.2f} \t{:14.2f}' .format(self.volume_data['Q'][reaction_idx][idx], self.volume_data['electrode_volume'][reaction_idx][idx], self.volume_data['volume_ratio_with_bulk'][reaction_idx][idx])) if idx != len(self.volume_data['Q'][reaction_idx]) - 1: data_str += '\n' if self.args.get('csv'): with open(''.join(self.species) + '_volume.csv', 'w') as f: f.write(data_str) print('\nVolume data:') print('\n' + data_str)
[docs] def get_hull_distances(self, *args, **kwargs): """ Wrapper to PhaseDiagram.get_hull_distances. """ return self.phase_diagram.get_hull_distances(*args, **kwargs)
def _calculate_binary_voltage_curve(self, hull_cursor): """ Generate binary voltage curve, setting the self.voltage_data dictionary. Parameters: hull_cursor (list(dict)): list of structures to include in the voltage curve. """ mu_enthalpy = get_array_from_cursor(self.chempot_cursor, self.energy_key) # take a copy of the cursor so it can be reordered _hull_cursor = deepcopy(hull_cursor) x = get_num_intercalated(_hull_cursor) _x_order = np.argsort(x) capacities = np.asarray([ get_generic_grav_capacity( get_padded_composition(doc['stoichiometry'], self.elements), self.elements) for doc in _hull_cursor ]) set_cursor_from_array(_hull_cursor, x, 'conc_of_active_ion') set_cursor_from_array(_hull_cursor, capacities, 'gravimetric_capacity') _hull_cursor = sorted(_hull_cursor, key=lambda doc: doc['conc_of_active_ion']) capacities = capacities[_x_order] x = np.sort(x) stable_enthalpy_per_b = get_array_from_cursor(_hull_cursor, self._extensive_energy_key + '_per_b') x, uniq_idxs = np.unique(x, return_index=True) stable_enthalpy_per_b = stable_enthalpy_per_b[uniq_idxs] capacities = capacities[uniq_idxs] V = np.zeros_like(x) V[1:] = - np.diff(stable_enthalpy_per_b) / np.diff(x) + mu_enthalpy[0] V[0] = V[1] reactions = [((None, get_formula_from_stoich(doc['stoichiometry'])),) for doc in _hull_cursor[1:]] # make V, Q and x available for plotting, stripping NaNs to re-add later # in the edge case of duplicate chemical potentials capacities, unique_caps = np.unique(capacities, return_index=True) non_nan = np.argwhere(np.isfinite(capacities)) V = (np.asarray(V)[unique_caps])[non_nan].flatten().tolist() x = (np.asarray(x)[unique_caps])[non_nan].flatten().tolist() capacities = capacities[non_nan].flatten().tolist() x.append(np.nan) capacities.append(np.nan) V.append(0.0) average_voltage = Electrode.calculate_average_voltage(capacities, V) profile = VoltageProfile( voltages=V, capacities=capacities, average_voltage=average_voltage, starting_stoichiometry=[[self.species[1], 1.0]], reactions=reactions, active_ion=self.species[0] ) self.voltage_data.append(profile) def _calculate_ternary_voltage_curve(self, hull_cursor): """ Calculate tenary voltage curve, setting self.voltage_data. First pass written by James Darby, jpd47@cam.ac.uk. Parameters: hull_cursor (list(dict)): list of structures to include in the voltage curve. """ # construct working array of concentrations and energies stoichs = get_array_from_cursor(hull_cursor, 'stoichiometry') # do another convex hull on just the known hull points, to allow access to useful indices import scipy.spatial # construct working array of concentrations and energies points = np.hstack(( get_array_from_cursor(hull_cursor, 'concentration'), get_array_from_cursor(hull_cursor, self.energy_key).reshape(len(hull_cursor), 1) )) stoichs = get_array_from_cursor(hull_cursor, 'stoichiometry') # do another convex hull on just the known hull points, to allow access to useful indices convex_hull = scipy.spatial.ConvexHull(points) endpoints, endstoichs = Electrode._find_starting_materials(convex_hull.points, stoichs) print('{} starting point(s) found.'.format(len(endstoichs))) for endstoich in endstoichs: print(get_formula_from_stoich(endstoich), end=' ') print('\n') # iterate over possible delithiated phases for reaction_ind, endpoint in enumerate(endpoints): print(30 * '-') print('Reaction {}, {}:'.format(reaction_ind+1, get_formula_from_stoich(endstoichs[reaction_ind]))) reactions, capacities, voltages, average_voltage, volumes = self._construct_electrode( convex_hull, endpoint, endstoichs[reaction_ind], hull_cursor ) profile = VoltageProfile( starting_stoichiometry=endstoichs[reaction_ind], reactions=reactions, capacities=capacities, voltages=voltages, average_voltage=average_voltage, active_ion=self.species[0] ) self.voltage_data.append(profile) if not self._non_elemental: self.volume_data['x'].append(capacities[:-1]) self.volume_data['Q'].append(capacities[:-1]) self.volume_data['electrode_volume'].append(volumes) self.volume_data['endstoichs'].append(endstoichs[reaction_ind]) self.volume_data['volume_ratio_with_bulk'].append(np.asarray(volumes) / volumes[0]) self.volume_data['volume_expansion_percentage'].append(((np.asarray(volumes) / volumes[0]) - 1) * 100) self.volume_data['hull_distances'].append(np.zeros_like(self.volume_data["x"][-1])) def _calculate_binary_volume_curve(self): """ Take stable compositions and volume and calculate volume expansion per "B" in AB binary. """ stable_comp = get_array_from_cursor(self.hull_cursor, 'concentration') stable_comp, unique_comp_inds = np.unique(stable_comp, return_index=True) for doc in self.hull_cursor: if 'cell_volume_per_b' not in doc: raise RuntimeError("Document missing key `cell_volume_per_b`: {}".format(doc)) stable_stoichs = get_array_from_cursor(self.hull_cursor, 'stoichiometry')[unique_comp_inds] stable_vol = get_array_from_cursor(self.hull_cursor, 'cell_volume_per_b')[unique_comp_inds] stable_cap = get_array_from_cursor(self.hull_cursor, 'gravimetric_capacity')[unique_comp_inds] hull_distances = get_array_from_cursor(self.hull_cursor, 'hull_distance')[unique_comp_inds] with np.errstate(divide='ignore'): stable_x = stable_comp / (1 - stable_comp) non_nans = np.argwhere(np.isfinite(stable_x)) self.volume_data['x'].append(stable_x[non_nans].flatten()) self.volume_data['Q'].append(stable_cap[non_nans].flatten()) self.volume_data['electrode_volume'].append(stable_vol[non_nans].flatten()) self.volume_data['volume_ratio_with_bulk'].append((stable_vol[non_nans] / stable_vol[0]).flatten()) self.volume_data['volume_expansion_percentage'].append(((stable_vol[non_nans] / stable_vol[0]) - 1) * 100) self.volume_data['hull_distances'].append(hull_distances[non_nans].flatten()) self.volume_data['endstoichs'].append(stable_stoichs[non_nans].flatten()[0]) def _get_species(self, species=None, elements=None): """ Try to determine species for phase diagram from arguments or passed data. Sets the `self.species` attribute. Keyword arguments: species (str/list): the species kwarg passed to __init__. elements (str/list): the elements kwarg passed to __init__. """ # try to determine species for phase diagram, from arguments and data species = species or elements if species is None: # handles element list passed by query: should only ever be a list of one entry if self.args.get('composition') is not None: if isinstance(self.args.get('composition'), list): species = self.args.get('composition')[0] else: species = self.args.get('composition') if ':' in species: species = species.split(':') if species is None: if self.from_cursor: species = list({atom for doc in self.cursor for atom in doc['atom_types']}) else: raise RuntimeError("Unable to determine species in hull, please specify with " "e.g. `elements=['Li', 'P']") # handles when species is e.g. ['LiCo2:Sn2S'] if isinstance(species, str): if ':' in species: species = species.split(':') else: species = [spec for spec in re.split(r'([A-Z][a-z]*)', species) if spec] # edge case where user passes e.g. ['KP'], when they mean ['K', 'P']. if isinstance(species, list) and len(species) == 1: tmp_species = [] for spec in species: if ':' in spec: tmp_species.append(spec.split(':')) else: tmp_species.extend([item for item in re.split(r'([A-Z][a-z]*)', spec) if item]) species = tmp_species return species def _construct_electrode(self, hull, endpoint, endstoich, hull_cursor): intersections, crossover = self._find_hull_pathway_intersections( endpoint, endstoich, hull ) return self._compute_voltages_from_intersections( intersections, hull, crossover, endstoich, hull_cursor ) def _compute_voltages_from_intersections( self, intersections, hull, crossover, endstoich, hull_cursor ): """ Traverse the composition pathway and its intersections with hull facets and compute the voltage and volume drops along the way, for a ternary system with N 3-phase regions. Parameters: intersections (np.ndarray): Nx3 array containing the list of face indices crossed by the path. hull (scipy.spatial.ConvexHull): the temporary hull object that is referred to by any indices. crossover (np.ndarray): (N+1)x3 array containing the coordinates at which the composition pathway crosses the hull faces. endstoich (list): a matador stoichiometry that defines the end of the pathway. hull_cursor (list): the actual structures used to create the hull. """ if len(crossover) != len(intersections) + 1: raise RuntimeError("Incompatible number of crossovers ({}) and intersections ({})." .format(np.shape(crossover), np.shape(intersections))) # set up output arrays voltages = np.empty(len(intersections) + 1) volumes = np.empty(len(intersections)) reactions = [] # set up some useful arrays for later points = hull.points mu_enthalpy = get_array_from_cursor(self.chempot_cursor, self.energy_key) if not self._non_elemental: input_volumes = get_array_from_cursor(hull_cursor, 'cell_volume') / get_array_from_cursor(hull_cursor, 'num_atoms') capacities = [get_generic_grav_capacity(point, self.species) for point in crossover] # initial composition of one formula unit of the starting material initial_comp = get_padded_composition(endstoich, self.species) # loop over intersected faces and compute the voltage and volume at the # crossover with that face for ind, face in enumerate(intersections): simplex_index = int(face[0]) final_stoichs = [hull_cursor[idx]['stoichiometry'] for idx in hull.simplices[simplex_index]] atoms_per_fu = [sum([elem[1] for elem in stoich]) for stoich in final_stoichs] energy_vec = points[hull.simplices[simplex_index], 2] comp = points[hull.simplices[simplex_index], :] comp[:, 2] = 1 - comp[:, 0] - comp[:, 1] # normalize the crossover composition to one formula unit of the starting electrode norm = np.asarray(crossover[ind][1:]) / np.asarray(initial_comp[1:]) ratios_of_phases = np.linalg.solve(comp.T, crossover[ind] / norm[0]) # remove small numerical noise ratios_of_phases[np.where(ratios_of_phases < EPS)] = 0 # create a list containing the sections of the balanced reaction for printing balanced_reaction = [] for i, ratio in enumerate(ratios_of_phases): if ratio < EPS: continue else: formula = get_formula_from_stoich(final_stoichs[i]) balanced_reaction.append((ratio / atoms_per_fu[i], formula)) reactions.append(balanced_reaction) # compute the voltage as the difference between the projection of the gradient down to pure active ion, # and the reference chemical potential comp_inv = np.linalg.inv(comp.T) V = -(comp_inv.dot([1, 0, 0])).dot(energy_vec) V = V + mu_enthalpy[0] # compute the volume of the final electrode if not self._non_elemental: if ind <= len(intersections) - 1: volume_vec = input_volumes[hull.simplices[simplex_index]] volumes[ind] = np.dot(ratios_of_phases, volume_vec) # double up on first voltage if ind == 0: voltages[0] = V voltages[ind+1] = V average_voltage = Electrode.calculate_average_voltage(capacities, voltages) # print the reaction over a few lines, remove 1s and rounded ratios print( ' ---> '.join( [' + '.join( ["{}{}".format( str(round(chem[0], 3)) + ' ' if abs(chem[0] - 1) > EPS else '', chem[1]) for chem in region]) for region in reactions]) ) return reactions, capacities, voltages, average_voltage, volumes def _find_hull_pathway_intersections(self, endpoint, endstoich, hull): """ This function traverses a ternary phase diagram on a path from `endpoint` towards [1, 0, 0], i.e. a pure phase of the active ion. The aim is to find all of the faces and intersections along this pathway, making sure to only add unique intersections, and making appropriate (symmetry-breaking) choices of which face to use. We proceed as follows: 1. Filter out any vertices that contain only binary phases, or that contain only the chemical potentials. 2. Loop over all faces of the convex hull and test if the pathway touches/intersects that face. If it does, ascertain where the intersection occurs, and whether it is at one, two or none of the vertices of the face. Create an array of unique intersections for this face and save them for later. 3. Loop over the zeros found between for each face. If the pathway only grazes a single point on this face, ignore it. If one of the edges is parallel to the pathway, make sure to include this face and the faces either side of it. Parameters: endpoint (np.ndarray): array containing composition (2D) and energy of start point. """ import scipy.spatial.distance import itertools endpoint = endpoint[:-1] compositions = np.zeros_like(hull.points) compositions[:, 0] = hull.points[:, 0] compositions[:, 1] = hull.points[:, 1] compositions[:, 2] = 1 - hull.points[:, 0] - hull.points[:, 1] # define the composition pathway through ternary space gradient = endpoint[1] / (endpoint[0] - 1) # has to intersect [1, 0] so c = y0 - m*x0 = -m y0 = -gradient # filter the vertices we're going to consider skip_inds = set() for simp_ind, simplex in enumerate(hull.simplices): vertices = np.asarray([compositions[i] for i in simplex]) # skip all simplices that contain only binary phases for i in range(3): if np.max(vertices[:, i]) < BOUNDARY_EPS: skip_inds.add(simp_ind) continue # skip the outer triangle formed by the chemical potentials if all(np.max(vertices, axis=-1) > 1 - BOUNDARY_EPS): skip_inds.add(simp_ind) continue two_phase_crossover = [] three_phase_crossover = [] for simp_ind, simplex in enumerate(hull.simplices): if simp_ind in skip_inds: continue vertices = np.asarray([compositions[i] for i in simplex]) # put each vertex of triangle into line equation and test their signs test = vertices[:, 0] * gradient + y0 - vertices[:, 1] test[np.abs(test) < BOUNDARY_EPS] = 0.0 test = np.sign(test) # if there are two different signs in the test array, then the line intersects/grazes this face triangle if len(np.unique(test)) > 1: # now find intersection points and split them into one, two and three-phase crossover regions zeros = [val for zero in np.where(test == 0) for val in zero.tolist()] num_zeros = len(zeros) zero_points = [] # skip_vertex = None for zero in zeros: zero_pos = compositions[simplex[zero]] if num_zeros == 2: zero_points.append(zero_pos) two_phase_crossover.append((zero_pos, simp_ind)) # if we have already found both crossovers, skip to next face if num_zeros == 2: continue # now find the non-trivial intersections for i, j in itertools.combinations(simplex, r=2): # if skip_vertex in [i, j]: # continue A = compositions[i] B = compositions[j] C = endpoint D = [1, 0] def coeffs(X, Y): # find line equation for edge AB # a x + b y = c return (Y[1] - X[1], X[0] - Y[0]) a1, b1 = coeffs(A, B) c1 = a1 * A[0] + b1 * A[1] a2, b2 = coeffs(C, D) c2 = a2 * C[0] + b2 * C[1] det = a1 * b2 - a2 * b1 if det == 0: continue x = (b2 * c1 - b1 * c2) / det y = (a1 * c2 - a2 * c1) / det intersection_point = np.asarray([x, y, 1-x-y]) # now have to test whether that intersection point is inside the triangle # which we can do by testing that is inside the rectangle spanned by AB x_bound = sorted([A[0], B[0]]) y_bound = sorted([A[1], B[1]]) if ( x_bound[0] - BOUNDARY_EPS/2 <= intersection_point[0] <= x_bound[1] + BOUNDARY_EPS/2 and y_bound[0] - BOUNDARY_EPS/2 <= intersection_point[1] <= y_bound[1] + BOUNDARY_EPS/2 ): # three_phase_crossover.append((intersection_point, simp_ind)) zero_points.append(intersection_point) unique_zeros = [] for zero in zero_points: if (len(unique_zeros) >= 1 and np.any(scipy.spatial.distance.cdist(unique_zeros, zero.reshape(1, 3)) < BOUNDARY_EPS)): pass else: unique_zeros.append(zero) num_zeros = len(unique_zeros) if num_zeros == 1: # we never need to use faces which just touch the triangle continue elif num_zeros == 2: three_phase_crossover.append((unique_zeros[0], simp_ind)) three_phase_crossover.append((unique_zeros[1], simp_ind)) # loop over points and only add the unique ones to the crossover array # if a point exists as a two-phase region, then always add that simplex crossover = [[1, 0, 0]] simplices = {} zeros = sorted(two_phase_crossover + three_phase_crossover, key=lambda x: x[0][0]) # for multiplicity, zeros in enumerate([one_phase_crossover, two_phase_crossover, three_phase_crossover]): for zero, simp_ind in zeros: if len(crossover) >= 1 and np.any(scipy.spatial.distance.cdist(crossover, zero.reshape(1, 3)) < BOUNDARY_EPS): pass else: if simp_ind not in simplices: crossover.append(zero) # if multiplicity > 0: simplices[simp_ind] = zero[0] intersections = sorted(simplices.items(), key=lambda x: x[1]) if len(intersections) == 0: raise RuntimeError( 'No intermediate structures found for starting point {}.' .format(get_formula_from_stoich(endstoich)) ) return intersections, sorted(crossover, key=lambda x: x[0]) def _scale_voltages(self, species): """ Rescale voltages to account for the valence of the active ion, as stored in the Electrode class. """ valence_factor = Electrode.valence_data.get(species, None) if valence_factor is None: warnings.warn("Unable to find valence of species {}, treating it as 1.".format(species)) return if valence_factor != 1: for ind, start_point in enumerate(self.voltage_data): for j in range(len(self.voltage_data[ind].voltages)): self.voltage_data[ind].voltages[j] *= valence_factor self.voltage_data[ind].average_voltage *= valence_factor