Source code for pymatgen.analysis.phase_diagram

# coding: utf-8
# Copyright (c) Pymatgen Development Team.
# Distributed under the terms of the MIT License.

"""
This module defines tools to generate and analyze phase diagrams.
"""

import re
import collections
import itertools
import math
import logging

from monty.json import MSONable, MontyDecoder
from functools import lru_cache

import numpy as np
from scipy.spatial import ConvexHull

from pymatgen.core.composition import Composition
from pymatgen.core.periodic_table import Element, DummySpecie, get_el_sp
from pymatgen.util.coord import Simplex, in_coord_list
from pymatgen.util.string import latexify
from pymatgen.util.plotting import pretty_plot
from pymatgen.analysis.reaction_calculator import Reaction, \
    ReactionError
from pymatgen.entries import Entry

__author__ = "Shyue Ping Ong"
__copyright__ = "Copyright 2011, The Materials Project"
__version__ = "1.0"
__maintainer__ = "Shyue Ping Ong"
__email__ = "shyuep@gmail.com"
__status__ = "Production"
__date__ = "May 16, 2011"

logger = logging.getLogger(__name__)


[docs]class PDEntry(Entry): """ An object encompassing all relevant data for phase diagrams. .. attribute:: composition The composition associated with the PDEntry. .. attribute:: energy The energy associated with the entry. .. 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. .. attribute:: attribute A arbitrary attribute. Can be used to specify that the entry is a newly found compound, or to specify a particular label for the entry, etc. An attribute can be anything but must be MSONable. """ def __init__(self, composition: Composition, energy: float, name: str = None, attribute: object = None): """ Args: composition (Composition): Composition energy (float): Energy for composition. name (str): Optional parameter to name the entry. Defaults to the reduced chemical formula. attribute: Optional attribute of the entry. Must be MSONable. """ super().__init__(composition, energy) self.name = name if name else self.composition.reduced_formula self.attribute = attribute @property def energy(self) -> float: """ :return: the energy of the entry. """ return self._energy def __repr__(self): return "PDEntry : {} with energy = {:.4f}".format(self.composition, self.energy)
[docs] def as_dict(self): """ :return: MSONable dict. """ return_dict = super().as_dict() return_dict.update({"name": self.name, "attribute": self.attribute}) return return_dict
def __eq__(self, other): if isinstance(other, self.__class__): return self.as_dict() == other.as_dict() else: return False def __hash__(self): return id(self)
[docs] @classmethod def from_dict(cls, d): """ :param d: Dict representation :return: PDEntry """ return cls(Composition(d["composition"]), d["energy"], d["name"] if "name" in d else None, d["attribute"] if "attribute" in d else None)
[docs]class GrandPotPDEntry(PDEntry): """ A grand potential pd entry object encompassing all relevant data for phase diagrams. Chemical potentials are given as a element-chemical potential dict. """ def __init__(self, entry, chempots, name=None): """ Args: entry: A PDEntry-like object. chempots: Chemical potential specification as {Element: float}. name: Optional parameter to name the entry. Defaults to the reduced chemical formula of the original entry. """ comp = entry.composition self.original_entry = entry self.original_comp = comp grandpot = entry.energy - sum([comp[el] * pot for el, pot in chempots.items()]) self.chempots = chempots new_comp_map = {el: comp[el] for el in comp.elements if el not in chempots} super().__init__(new_comp_map, grandpot, entry.name) self.name = name if name else entry.name @property def is_element(self): """ True if the entry is an element. """ return self.original_comp.is_element def __repr__(self): chempot_str = " ".join(["mu_%s = %.4f" % (el, mu) for el, mu in self.chempots.items()]) return "GrandPotPDEntry with original composition " + \ "{}, energy = {:.4f}, {}".format(self.original_entry.composition, self.original_entry.energy, chempot_str) def __str__(self): return self.__repr__()
[docs] def as_dict(self): """ :return: MSONAble dict """ return {"@module": self.__class__.__module__, "@class": self.__class__.__name__, "entry": self.original_entry.as_dict(), "chempots": {el.symbol: u for el, u in self.chempots.items()}, "name": self.name}
[docs] @classmethod def from_dict(cls, d): """ :param d: Dict representation :return: PDStructureEntry """ chempots = {Element(symbol): u for symbol, u in d["chempots"].items()} entry = MontyDecoder().process_decoded(d["entry"]) return cls(entry, chempots, d["name"])
def __getattr__(self, a): """ Delegate attribute to original entry if available. """ if hasattr(self.original_entry, a): return getattr(self.original_entry, a) raise AttributeError(a)
[docs]class TransformedPDEntry(PDEntry): """ This class repesents a TransformedPDEntry, which allows for a PDEntry to be transformed to a different composition coordinate space. It is used in the construction of phase diagrams that do not have elements as the terminal compositions. """ def __init__(self, comp, original_entry): """ Args: comp (Composition): Transformed composition as a Composition. original_entry (PDEntry): Original entry that this entry arose from. """ super().__init__(comp, original_entry.energy) self.original_entry = original_entry self.name = original_entry.name def __getattr__(self, a): """ Delegate attribute to original entry if available. """ if hasattr(self.original_entry, a): return getattr(self.original_entry, a) raise AttributeError(a) def __repr__(self): output = ["TransformedPDEntry {}".format(self.composition), " with original composition {}".format(self.original_entry.composition), ", E = {:.4f}".format(self.original_entry.energy)] return "".join(output) def __str__(self): return self.__repr__()
[docs] def as_dict(self): """ :return: MSONable dict """ return {"@module": self.__class__.__module__, "@class": self.__class__.__name__, "entry": self.original_entry.as_dict(), "composition": self.composition}
[docs] @classmethod def from_dict(cls, d): """ :param d: Dict representation :return: TransformedPDEntry """ entry = MontyDecoder().process_decoded(d["entry"]) return cls(d["composition"], entry)
[docs]class PhaseDiagram(MSONable): """ Simple phase diagram class taking in elements and entries as inputs. The algorithm is based on the work in the following papers: 1. S. P. Ong, L. Wang, B. Kang, and G. Ceder, Li-Fe-P-O2 Phase Diagram from First Principles Calculations. Chem. Mater., 2008, 20(5), 1798-1807. doi:10.1021/cm702327g 2. S. P. Ong, A. Jain, G. Hautier, B. Kang, G. Ceder, Thermal stabilities of delithiated olivine MPO4 (M=Fe, Mn) cathodes investigated using first principles calculations. Electrochem. Comm., 2010, 12(3), 427-430. doi:10.1016/j.elecom.2010.01.010 .. attribute: elements: Elements in the phase diagram. ..attribute: all_entries All entries provided for Phase Diagram construction. Note that this does not mean that all these entries are actually used in the phase diagram. For example, this includes the positive formation energy entries that are filtered out before Phase Diagram construction. .. attribute: qhull_data Data used in the convex hull operation. This is essentially a matrix of composition data and energy per atom values created from qhull_entries. .. attribute: qhull_entries: Actual entries used in convex hull. Excludes all positive formation energy entries. .. attribute: dim The dimensionality of the phase diagram. .. attribute: facets Facets of the phase diagram in the form of [[1,2,3],[4,5,6]...]. For a ternary, it is the indices (references to qhull_entries and qhull_data) for the vertices of the phase triangles. Similarly extended to higher D simplices for higher dimensions. .. attribute: el_refs: List of elemental references for the phase diagrams. These are entries corresponding to the lowest energy element entries for simple compositional phase diagrams. .. attribute: simplices: The simplices of the phase diagram as a list of np.ndarray, i.e., the list of stable compositional coordinates in the phase diagram. """ # Tolerance for determining if formation energy is positive. formation_energy_tol = 1e-11 numerical_tol = 1e-8 def __init__(self, entries, elements=None): """ Standard constructor for phase diagram. Args: entries ([PDEntry]): A list of PDEntry-like objects having an energy, energy_per_atom and composition. elements ([Element]): Optional list of elements in the phase diagram. If set to None, the elements are determined from the the entries themselves and are sorted alphabetically. If specified, element ordering (e.g. for pd coordinates) is preserved. """ if elements is None: elements = set() for entry in entries: elements.update(entry.composition.elements) elements = sorted(list(elements)) elements = list(elements) dim = len(elements) entries = sorted(entries, key=lambda e: e.composition.reduced_composition) el_refs = {} min_entries = [] all_entries = [] for c, g in itertools.groupby(entries, key=lambda e: e.composition.reduced_composition): g = list(g) min_entry = min(g, key=lambda e: e.energy_per_atom) if c.is_element: el_refs[c.elements[0]] = min_entry min_entries.append(min_entry) all_entries.extend(g) if len(el_refs) != dim: raise PhaseDiagramError( "There are no entries associated with a terminal element!.") data = np.array([ [e.composition.get_atomic_fraction(el) for el in elements] + [ e.energy_per_atom] for e in min_entries ]) # Use only entries with negative formation energy vec = [el_refs[el].energy_per_atom for el in elements] + [-1] form_e = -np.dot(data, vec) inds = np.where(form_e < -self.formation_energy_tol)[0].tolist() # Add the elemental references inds.extend([min_entries.index(el) for el in el_refs.values()]) qhull_entries = [min_entries[i] for i in inds] qhull_data = data[inds][:, 1:] # Add an extra point to enforce full dimensionality. # This point will be present in all upper hull facets. extra_point = np.zeros(dim) + 1 / dim extra_point[-1] = np.max(qhull_data) + 1 qhull_data = np.concatenate([qhull_data, [extra_point]], axis=0) if dim == 1: self.facets = [qhull_data.argmin(axis=0)] else: facets = get_facets(qhull_data) finalfacets = [] for facet in facets: # Skip facets that include the extra point if max(facet) == len(qhull_data) - 1: continue m = qhull_data[facet] m[:, -1] = 1 if abs(np.linalg.det(m)) > 1e-14: finalfacets.append(facet) self.facets = finalfacets self.simplexes = [Simplex(qhull_data[f, :-1]) for f in self.facets] self.all_entries = all_entries self.qhull_data = qhull_data self.dim = dim self.el_refs = el_refs self.elements = elements self.qhull_entries = qhull_entries self._stable_entries = set(self.qhull_entries[i] for i in set(itertools.chain(*self.facets)))
[docs] def pd_coords(self, comp): """ The phase diagram is generated in a reduced dimensional space (n_elements - 1). This function returns the coordinates in that space. These coordinates are compatible with the stored simplex objects. """ if set(comp.elements).difference(self.elements): raise ValueError('{} has elements not in the phase diagram {}' ''.format(comp, self.elements)) return np.array( [comp.get_atomic_fraction(el) for el in self.elements[1:]])
@property def all_entries_hulldata(self): """ :return: The actual ndarray used to construct the convex hull. """ data = [] for entry in self.all_entries: comp = entry.composition row = [comp.get_atomic_fraction(el) for el in self.elements] row.append(entry.energy_per_atom) data.append(row) return np.array(data)[:, 1:] @property def unstable_entries(self): """ Entries that are unstable in the phase diagram. Includes positive formation energy entries. """ return [e for e in self.all_entries if e not in self.stable_entries] @property def stable_entries(self): """ Returns the stable entries in the phase diagram. """ return self._stable_entries
[docs] def get_form_energy(self, entry): """ Returns the formation energy for an entry (NOT normalized) from the elemental references. Args: entry: A PDEntry-like object. Returns: Formation energy from the elemental references. """ c = entry.composition return entry.energy - sum([c[el] * self.el_refs[el].energy_per_atom for el in c.elements])
[docs] def get_form_energy_per_atom(self, entry): """ Returns the formation energy per atom for an entry from the elemental references. Args: entry: An PDEntry-like object Returns: Formation energy **per atom** from the elemental references. """ return self.get_form_energy(entry) / entry.composition.num_atoms
def __repr__(self): return self.__str__() def __str__(self): symbols = [el.symbol for el in self.elements] output = ["{} phase diagram".format("-".join(symbols)), "{} stable phases: ".format(len(self.stable_entries)), ", ".join([entry.name for entry in self.stable_entries])] return "\n".join(output)
[docs] def as_dict(self): """ :return: MSONAble dict """ return {"@module": self.__class__.__module__, "@class": self.__class__.__name__, "all_entries": [e.as_dict() for e in self.all_entries], "elements": [e.as_dict() for e in self.elements]}
[docs] @classmethod def from_dict(cls, d): """ :param d: Dict representation :return: PhaseDiagram """ entries = [MontyDecoder().process_decoded(dd) for dd in d["all_entries"]] elements = [Element.from_dict(dd) for dd in d["elements"]] return cls(entries, elements)
@lru_cache(1) def _get_facet_and_simplex(self, comp): """ Get any facet that a composition falls into. Cached so successive calls at same composition are fast. """ c = self.pd_coords(comp) for f, s in zip(self.facets, self.simplexes): if s.in_simplex(c, PhaseDiagram.numerical_tol / 10): return f, s raise RuntimeError("No facet found for comp = {}".format(comp)) def _get_facet_chempots(self, facet): """ Calculates the chemical potentials for each element within a facet. Args: facet: Facet of the phase diagram. Returns: { element: chempot } for all elements in the phase diagram. """ complist = [self.qhull_entries[i].composition for i in facet] energylist = [self.qhull_entries[i].energy_per_atom for i in facet] m = [[c.get_atomic_fraction(e) for e in self.elements] for c in complist] chempots = np.linalg.solve(m, energylist) return dict(zip(self.elements, chempots))
[docs] def get_decomposition(self, comp): """ Provides the decomposition at a particular composition. Args: comp: A composition Returns: Decomposition as a dict of {Entry: amount} """ facet, simplex = self._get_facet_and_simplex(comp) decomp_amts = simplex.bary_coords(self.pd_coords(comp)) return {self.qhull_entries[f]: amt for f, amt in zip(facet, decomp_amts) if abs(amt) > PhaseDiagram.numerical_tol}
[docs] def get_hull_energy(self, comp): """ Args: comp (Composition): Input composition Returns: Energy of lowest energy equilibrium at desired composition. Not normalized by atoms, i.e. E(Li4O2) = 2 * E(Li2O) """ e = 0 for k, v in self.get_decomposition(comp).items(): e += k.energy_per_atom * v return e * comp.num_atoms
[docs] def get_decomp_and_e_above_hull(self, entry, allow_negative=False): """ Provides the decomposition and energy above convex hull for an entry. Due to caching, can be much faster if entries with the same composition are processed together. Args: entry: A PDEntry like object allow_negative: Whether to allow negative e_above_hulls. Used to calculate equilibrium reaction energies. Defaults to False. Returns: (decomp, energy above convex hull) Stable entries should have energy above hull of 0. The decomposition is provided as a dict of {Entry: amount}. """ if entry in self.stable_entries: return {entry: 1}, 0 comp = entry.composition facet, simplex = self._get_facet_and_simplex(comp) decomp_amts = simplex.bary_coords(self.pd_coords(comp)) decomp = {self.qhull_entries[f]: amt for f, amt in zip(facet, decomp_amts) if abs(amt) > PhaseDiagram.numerical_tol} energies = [self.qhull_entries[i].energy_per_atom for i in facet] ehull = entry.energy_per_atom - np.dot(decomp_amts, energies) if allow_negative or ehull >= -PhaseDiagram.numerical_tol: return decomp, ehull raise ValueError("No valid decomp found!")
[docs] def get_e_above_hull(self, entry): """ Provides the energy above convex hull for an entry Args: entry: A PDEntry like object Returns: Energy above convex hull of entry. Stable entries should have energy above hull of 0. """ return self.get_decomp_and_e_above_hull(entry)[1]
[docs] def get_equilibrium_reaction_energy(self, entry): """ Provides the reaction energy of a stable entry from the neighboring equilibrium stable entries (also known as the inverse distance to hull). Args: entry: A PDEntry like object Returns: Equilibrium reaction energy of entry. Stable entries should have equilibrium reaction energy <= 0. """ if entry not in self.stable_entries: raise ValueError("Equilibrium reaction energy is available only " "for stable entries.") if entry.is_element: return 0 entries = [e for e in self.stable_entries if e != entry] modpd = PhaseDiagram(entries, self.elements) return modpd.get_decomp_and_e_above_hull(entry, allow_negative=True)[1]
[docs] def get_composition_chempots(self, comp): """ Get the chemical potentials for all elements at a given composition. :param comp: Composition :return: Dict of chemical potentials. """ facet = self._get_facet_and_simplex(comp)[0] return self._get_facet_chempots(facet)
[docs] def get_all_chempots(self, comp): """ Get chemical potentials at a given compositon. :param comp: Composition :return: Chemical potentials. """ # note the top part takes from format of _get_facet_and_simplex, # but wants to return all facets rather than the first one that meets this criteria c = self.pd_coords(comp) allfacets = [] for f, s in zip(self.facets, self.simplexes): if s.in_simplex(c, PhaseDiagram.numerical_tol / 10): allfacets.append(f) if not len(allfacets): raise RuntimeError("No facets found for comp = {}".format(comp)) else: chempots = {} for facet in allfacets: facet_elt_list = [self.qhull_entries[j].name for j in facet] facet_name = '-'.join(facet_elt_list) chempots[facet_name] = self._get_facet_chempots(facet) return chempots
[docs] def get_transition_chempots(self, element): """ Get the critical chemical potentials for an element in the Phase Diagram. Args: element: An element. Has to be in the PD in the first place. Returns: A sorted sequence of critical chemical potentials, from less negative to more negative. """ if element not in self.elements: raise ValueError("get_transition_chempots can only be called with " "elements in the phase diagram.") critical_chempots = [] for facet in self.facets: chempots = self._get_facet_chempots(facet) critical_chempots.append(chempots[element]) clean_pots = [] for c in sorted(critical_chempots): if len(clean_pots) == 0: clean_pots.append(c) else: if abs(c - clean_pots[-1]) > PhaseDiagram.numerical_tol: clean_pots.append(c) clean_pots.reverse() return tuple(clean_pots)
[docs] def get_critical_compositions(self, comp1, comp2): """ Get the critical compositions along the tieline between two compositions. I.e. where the decomposition products change. The endpoints are also returned. Args: comp1, comp2 (Composition): compositions that define the tieline Returns: [(Composition)]: list of critical compositions. All are of the form x * comp1 + (1-x) * comp2 """ n1 = comp1.num_atoms n2 = comp2.num_atoms pd_els = self.elements # the reduced dimensionality Simplexes don't use the # first element in the PD c1 = self.pd_coords(comp1) c2 = self.pd_coords(comp2) # none of the projections work if c1 == c2, so just return *copies* # of the inputs if np.all(c1 == c2): return [comp1.copy(), comp2.copy()] intersections = [c1, c2] for sc in self.simplexes: intersections.extend(sc.line_intersection(c1, c2)) intersections = np.array(intersections) # find position along line l = (c2 - c1) l /= np.sum(l ** 2) ** 0.5 proj = np.dot(intersections - c1, l) # only take compositions between endpoints proj = proj[np.logical_and(proj > -self.numerical_tol, proj < proj[1] + self.numerical_tol)] proj.sort() # only unique compositions valid = np.ones(len(proj), dtype=np.bool) valid[1:] = proj[1:] > proj[:-1] + self.numerical_tol proj = proj[valid] ints = c1 + l * proj[:, None] # reconstruct full-dimensional composition array cs = np.concatenate([np.array([1 - np.sum(ints, axis=-1)]).T, ints], axis=-1) # mixing fraction when compositions are normalized x = proj / np.dot(c2 - c1, l) # mixing fraction when compositions are not normalized x_unnormalized = x * n1 / (n2 + x * (n1 - n2)) num_atoms = n1 + (n2 - n1) * x_unnormalized cs *= num_atoms[:, None] return [Composition((c, v) for c, v in zip(pd_els, m)) for m in cs]
[docs] def get_element_profile(self, element, comp, comp_tol=1e-5): """ Provides the element evolution data for a composition. For example, can be used to analyze Li conversion voltages by varying uLi and looking at the phases formed. Also can be used to analyze O2 evolution by varying uO2. Args: element: An element. Must be in the phase diagram. comp: A Composition comp_tol: The tolerance to use when calculating decompositions. Phases with amounts less than this tolerance are excluded. Defaults to 1e-5. Returns: Evolution data as a list of dictionaries of the following format: [ {'chempot': -10.487582010000001, 'evolution': -2.0, 'reaction': Reaction Object], ...] """ element = get_el_sp(element) if element not in self.elements: raise ValueError("get_transition_chempots can only be called with" " elements in the phase diagram.") gccomp = Composition({el: amt for el, amt in comp.items() if el != element}) elref = self.el_refs[element] elcomp = Composition(element.symbol) evolution = [] for cc in self.get_critical_compositions(elcomp, gccomp)[1:]: decomp_entries = self.get_decomposition(cc).keys() decomp = [k.composition for k in decomp_entries] rxn = Reaction([comp], decomp + [elcomp]) rxn.normalize_to(comp) c = self.get_composition_chempots(cc + elcomp * 1e-5)[element] amt = -rxn.coeffs[rxn.all_comp.index(elcomp)] evolution.append({'chempot': c, 'evolution': amt, 'element_reference': elref, 'reaction': rxn, 'entries': decomp_entries}) return evolution
[docs] def get_chempot_range_map(self, elements, referenced=True, joggle=True): """ Returns a chemical potential range map for each stable entry. Args: elements: Sequence of elements to be considered as independent variables. E.g., if you want to show the stability ranges of all Li-Co-O phases wrt to uLi and uO, you will supply [Element("Li"), Element("O")] referenced: If True, gives the results with a reference being the energy of the elemental phase. If False, gives absolute values. joggle (boolean): Whether to joggle the input to avoid precision errors. Returns: Returns a dict of the form {entry: [simplices]}. The list of simplices are the sides of the N-1 dim polytope bounding the allowable chemical potential range of each entry. """ all_chempots = [] pd = self facets = pd.facets for facet in facets: chempots = self._get_facet_chempots(facet) all_chempots.append([chempots[el] for el in pd.elements]) inds = [pd.elements.index(el) for el in elements] el_energies = {el: 0.0 for el in elements} if referenced: el_energies = {el: pd.el_refs[el].energy_per_atom for el in elements} chempot_ranges = collections.defaultdict(list) vertices = [list(range(len(self.elements)))] if len(all_chempots) > len(self.elements): vertices = get_facets(all_chempots, joggle=joggle) for ufacet in vertices: for combi in itertools.combinations(ufacet, 2): data1 = facets[combi[0]] data2 = facets[combi[1]] common_ent_ind = set(data1).intersection(set(data2)) if len(common_ent_ind) == len(elements): common_entries = [pd.qhull_entries[i] for i in common_ent_ind] data = np.array([[all_chempots[i][j] - el_energies[pd.elements[j]] for j in inds] for i in combi]) sim = Simplex(data) for entry in common_entries: chempot_ranges[entry].append(sim) return chempot_ranges
[docs] def getmu_vertices_stability_phase(self, target_comp, dep_elt, tol_en=1e-2): """ returns a set of chemical potentials corresponding to the vertices of the simplex in the chemical potential phase diagram. The simplex is built using all elements in the target_composition except dep_elt. The chemical potential of dep_elt is computed from the target composition energy. This method is useful to get the limiting conditions for defects computations for instance. Args: target_comp: A Composition object dep_elt: the element for which the chemical potential is computed from the energy of the stable phase at the target composition tol_en: a tolerance on the energy to set Returns: [{Element:mu}]: An array of conditions on simplex vertices for which each element has a chemical potential set to a given value. "absolute" values (i.e., not referenced to element energies) """ muref = np.array([self.el_refs[e].energy_per_atom for e in self.elements if e != dep_elt]) chempot_ranges = self.get_chempot_range_map( [e for e in self.elements if e != dep_elt]) for e in self.elements: if e not in target_comp.elements: target_comp = target_comp + Composition({e: 0.0}) coeff = [-target_comp[e] for e in self.elements if e != dep_elt] for e in chempot_ranges.keys(): if e.composition.reduced_composition == \ target_comp.reduced_composition: multiplicator = e.composition[dep_elt] / target_comp[dep_elt] ef = e.energy / multiplicator all_coords = [] for s in chempot_ranges[e]: for v in s._coords: elts = [e for e in self.elements if e != dep_elt] res = {} for i in range(len(elts)): res[elts[i]] = v[i] + muref[i] res[dep_elt] = (np.dot(v + muref, coeff) + ef) / target_comp[dep_elt] already_in = False for di in all_coords: dict_equals = True for k in di: if abs(di[k] - res[k]) > tol_en: dict_equals = False break if dict_equals: already_in = True break if not already_in: all_coords.append(res) return all_coords
[docs] def get_chempot_range_stability_phase(self, target_comp, open_elt): """ returns a set of chemical potentials corresponding to the max and min chemical potential of the open element for a given composition. It is quite common to have for instance a ternary oxide (e.g., ABO3) for which you want to know what are the A and B chemical potential leading to the highest and lowest oxygen chemical potential (reducing and oxidizing conditions). This is useful for defect computations. Args: target_comp: A Composition object open_elt: Element that you want to constrain to be max or min Returns: {Element:(mu_min,mu_max)}: Chemical potentials are given in "absolute" values (i.e., not referenced to 0) """ muref = np.array([self.el_refs[e].energy_per_atom for e in self.elements if e != open_elt]) chempot_ranges = self.get_chempot_range_map( [e for e in self.elements if e != open_elt]) for e in self.elements: if e not in target_comp.elements: target_comp = target_comp + Composition({e: 0.0}) coeff = [-target_comp[e] for e in self.elements if e != open_elt] max_open = -float('inf') min_open = float('inf') max_mus = None min_mus = None for e in chempot_ranges.keys(): if e.composition.reduced_composition == \ target_comp.reduced_composition: multiplicator = e.composition[open_elt] / target_comp[open_elt] ef = e.energy / multiplicator all_coords = [] for s in chempot_ranges[e]: for v in s._coords: all_coords.append(v) if (np.dot(v + muref, coeff) + ef) / target_comp[open_elt] > max_open: max_open = (np.dot(v + muref, coeff) + ef) / target_comp[open_elt] max_mus = v if (np.dot(v + muref, coeff) + ef) / target_comp[open_elt] < min_open: min_open = (np.dot(v + muref, coeff) + ef) / target_comp[open_elt] min_mus = v elts = [e for e in self.elements if e != open_elt] res = {} for i in range(len(elts)): res[elts[i]] = (min_mus[i] + muref[i], max_mus[i] + muref[i]) res[open_elt] = (min_open, max_open) return res
[docs]class GrandPotentialPhaseDiagram(PhaseDiagram): """ A class representing a Grand potential phase diagram. Grand potential phase diagrams are essentially phase diagrams that are open to one or more components. To construct such phase diagrams, the relevant free energy is the grand potential, which can be written as the Legendre transform of the Gibbs free energy as follows Grand potential = G - u_X N_X The algorithm is based on the work in the following papers: 1. S. P. Ong, L. Wang, B. Kang, and G. Ceder, Li-Fe-P-O2 Phase Diagram from First Principles Calculations. Chem. Mater., 2008, 20(5), 1798-1807. doi:10.1021/cm702327g 2. S. P. Ong, A. Jain, G. Hautier, B. Kang, G. Ceder, Thermal stabilities of delithiated olivine MPO4 (M=Fe, Mn) cathodes investigated using first principles calculations. Electrochem. Comm., 2010, 12(3), 427-430. doi:10.1016/j.elecom.2010.01.010 """ def __init__(self, entries, chempots, elements=None): """ Standard constructor for grand potential phase diagram. Args: entries ([PDEntry]): A list of PDEntry-like objects having an energy, energy_per_atom and composition. chempots {Element: float}: Specify the chemical potentials of the open elements. elements ([Element]): Optional list of elements in the phase diagram. If set to None, the elements are determined from the the entries themselves. """ if elements is None: elements = set() for entry in entries: elements.update(entry.composition.elements) self.chempots = {get_el_sp(el): u for el, u in chempots.items()} elements = set(elements).difference(self.chempots.keys()) all_entries = [] for e in entries: if len(set(e.composition.elements).intersection(set(elements))) > 0: all_entries.append(GrandPotPDEntry(e, self.chempots)) super().__init__(all_entries, elements) def __str__(self): output = [] chemsys = "-".join([el.symbol for el in self.elements]) output.append("{} grand potential phase diagram with ".format(chemsys)) output[-1] += ", ".join(["u{}={}".format(el, v) for el, v in self.chempots.items()]) output.append("{} stable phases: ".format(len(self.stable_entries))) output.append(", ".join([entry.name for entry in self.stable_entries])) return "\n".join(output)
[docs] def as_dict(self): """ :return: MSONable dict """ return {"@module": self.__class__.__module__, "@class": self.__class__.__name__, "all_entries": [e.as_dict() for e in self.all_entries], "chempots": self.chempots, "elements": [e.as_dict() for e in self.elements]}
[docs] @classmethod def from_dict(cls, d): """ :param d: Dict representation :return: GrandPotentialPhaseDiagram """ entries = MontyDecoder().process_decoded(d["all_entries"]) elements = MontyDecoder().process_decoded(d["elements"]) return cls(entries, d["chempots"], elements)
[docs]class CompoundPhaseDiagram(PhaseDiagram): """ Generates phase diagrams from compounds as terminations instead of elements. """ # Tolerance for determining if amount of a composition is positive. amount_tol = 1e-5 def __init__(self, entries, terminal_compositions, normalize_terminal_compositions=True): """ Initializes a CompoundPhaseDiagram. Args: entries ([PDEntry]): Sequence of input entries. For example, if you want a Li2O-P2O5 phase diagram, you might have all Li-P-O entries as an input. terminal_compositions ([Composition]): Terminal compositions of phase space. In the Li2O-P2O5 example, these will be the Li2O and P2O5 compositions. normalize_terminal_compositions (bool): Whether to normalize the terminal compositions to a per atom basis. If normalized, the energy above hulls will be consistent for comparison across systems. Non-normalized terminals are more intuitive in terms of compositional breakdowns. """ self.original_entries = entries self.terminal_compositions = terminal_compositions self.normalize_terminals = normalize_terminal_compositions (pentries, species_mapping) = \ self.transform_entries(entries, terminal_compositions) self.species_mapping = species_mapping super().__init__( pentries, elements=species_mapping.values())
[docs] def transform_entries(self, entries, terminal_compositions): """ Method to transform all entries to the composition coordinate in the terminal compositions. If the entry does not fall within the space defined by the terminal compositions, they are excluded. For example, Li3PO4 is mapped into a Li2O:1.5, P2O5:0.5 composition. The terminal compositions are represented by DummySpecies. Args: entries: Sequence of all input entries terminal_compositions: Terminal compositions of phase space. Returns: Sequence of TransformedPDEntries falling within the phase space. """ new_entries = [] if self.normalize_terminals: fractional_comp = [c.fractional_composition for c in terminal_compositions] else: fractional_comp = terminal_compositions # Map terminal compositions to unique dummy species. sp_mapping = collections.OrderedDict() for i, comp in enumerate(fractional_comp): sp_mapping[comp] = DummySpecie("X" + chr(102 + i)) for entry in entries: try: rxn = Reaction(fractional_comp, [entry.composition]) rxn.normalize_to(entry.composition) # We only allow reactions that have positive amounts of # reactants. if all([rxn.get_coeff(comp) <= CompoundPhaseDiagram.amount_tol for comp in fractional_comp]): newcomp = {sp_mapping[comp]: -rxn.get_coeff(comp) for comp in fractional_comp} newcomp = {k: v for k, v in newcomp.items() if v > CompoundPhaseDiagram.amount_tol} transformed_entry = \ TransformedPDEntry(Composition(newcomp), entry) new_entries.append(transformed_entry) except ReactionError: # If the reaction can't be balanced, the entry does not fall # into the phase space. We ignore them. pass return new_entries, sp_mapping
[docs] def as_dict(self): """ :return: MSONable dict """ return { "@module": self.__class__.__module__, "@class": self.__class__.__name__, "original_entries": [e.as_dict() for e in self.original_entries], "terminal_compositions": [c.as_dict() for c in self.terminal_compositions], "normalize_terminal_compositions": self.normalize_terminals}
[docs] @classmethod def from_dict(cls, d): """ :param d: Dict Representation :return: CompoundPhaseDiagram """ dec = MontyDecoder() entries = dec.process_decoded(d["original_entries"]) terminal_compositions = dec.process_decoded(d["terminal_compositions"]) return cls(entries, terminal_compositions, d["normalize_terminal_compositions"])
[docs]class ReactionDiagram: """ Analyzes the possible reactions between a pair of compounds, e.g., an electrolyte and an electrode. """ def __init__(self, entry1, entry2, all_entries, tol=1e-4, float_fmt="%.4f"): """ Args: entry1 (ComputedEntry): Entry for 1st component. Note that corrections, if any, must already be pre-applied. This is to give flexibility for different kinds of corrections, e.g., if a particular entry is fitted to an experimental data (such as EC molecule). entry2 (ComputedEntry): Entry for 2nd component. Note that corrections must already be pre-applied. This is to give flexibility for different kinds of corrections, e.g., if a particular entry is fitted to an experimental data (such as EC molecule). all_entries ([ComputedEntry]): All other entries to be considered in the analysis. Note that corrections, if any, must already be pre-applied. tol (float): Tolerance to be used to determine validity of reaction. float_fmt (str): Formatting string to be applied to all floats. Determines number of decimal places in reaction string. """ elements = set() for e in [entry1, entry2]: elements.update([el.symbol for el in e.composition.elements]) elements = tuple(elements) # Fix elements to ensure order. comp_vec1 = np.array([entry1.composition.get_atomic_fraction(el) for el in elements]) comp_vec2 = np.array([entry2.composition.get_atomic_fraction(el) for el in elements]) r1 = entry1.composition.reduced_composition r2 = entry2.composition.reduced_composition logger.debug("%d total entries." % len(all_entries)) pd = PhaseDiagram(all_entries + [entry1, entry2]) terminal_formulas = [entry1.composition.reduced_formula, entry2.composition.reduced_formula] logger.debug("%d stable entries" % len(pd.stable_entries)) logger.debug("%d facets" % len(pd.facets)) logger.debug("%d qhull_entries" % len(pd.qhull_entries)) rxn_entries = [] done = [] def fmt(fl): return float_fmt % fl for facet in pd.facets: for face in itertools.combinations(facet, len(facet) - 1): face_entries = [pd.qhull_entries[i] for i in face] if any([e.composition.reduced_formula in terminal_formulas for e in face_entries]): continue try: m = [] for e in face_entries: m.append([e.composition.get_atomic_fraction(el) for el in elements]) m.append(comp_vec2 - comp_vec1) m = np.array(m).T coeffs = np.linalg.solve(m, comp_vec2) x = coeffs[-1] if all([c >= -tol for c in coeffs]) and \ (abs(sum(coeffs[:-1]) - 1) < tol) and \ (tol < x < 1 - tol): c1 = x / r1.num_atoms c2 = (1 - x) / r2.num_atoms factor = 1 / (c1 + c2) c1 *= factor c2 *= factor # Avoid duplicate reactions. if any([np.allclose([c1, c2], cc) for cc in done]): continue done.append((c1, c2)) rxn_str = "%s %s + %s %s -> " % ( fmt(c1), r1.reduced_formula, fmt(c2), r2.reduced_formula) products = [] product_entries = [] energy = - (x * entry1.energy_per_atom + (1 - x) * entry2.energy_per_atom) for c, e in zip(coeffs[:-1], face_entries): if c > tol: r = e.composition.reduced_composition products.append("%s %s" % ( fmt(c / r.num_atoms * factor), r.reduced_formula)) product_entries.append((c, e)) energy += c * e.energy_per_atom rxn_str += " + ".join(products) comp = x * comp_vec1 + (1 - x) * comp_vec2 entry = PDEntry( Composition(dict(zip(elements, comp))), energy=energy, attribute=rxn_str) entry.decomposition = product_entries rxn_entries.append(entry) except np.linalg.LinAlgError: logger.debug("Reactants = %s" % (", ".join([ entry1.composition.reduced_formula, entry2.composition.reduced_formula]))) logger.debug("Products = %s" % ( ", ".join([e.composition.reduced_formula for e in face_entries]))) rxn_entries = sorted(rxn_entries, key=lambda e: e.name, reverse=True) self.entry1 = entry1 self.entry2 = entry2 self.rxn_entries = rxn_entries self.labels = collections.OrderedDict() for i, e in enumerate(rxn_entries): self.labels[str(i + 1)] = e.attribute e.name = str(i + 1) self.all_entries = all_entries self.pd = pd
[docs] def get_compound_pd(self): """ Get the CompoundPhaseDiagram object, which can then be used for plotting. Returns: (CompoundPhaseDiagram) """ # For this plot, since the reactions are reported in formation # energies, we need to set the energies of the terminal compositions # to 0. So we make create copies with 0 energy. entry1 = PDEntry(self.entry1.composition, 0) entry2 = PDEntry(self.entry2.composition, 0) cpd = CompoundPhaseDiagram( self.rxn_entries + [entry1, entry2], [Composition(entry1.composition.reduced_formula), Composition(entry2.composition.reduced_formula)], normalize_terminal_compositions=False) return cpd
[docs]class PhaseDiagramError(Exception): """ An exception class for Phase Diagram generation. """ pass
[docs]def get_facets(qhull_data, joggle=False): """ Get the simplex facets for the Convex hull. Args: qhull_data (np.ndarray): The data from which to construct the convex hull as a Nxd array (N being number of data points and d being the dimension) joggle (boolean): Whether to joggle the input to avoid precision errors. Returns: List of simplices of the Convex Hull. """ if joggle: return ConvexHull(qhull_data, qhull_options="QJ i").simplices else: return ConvexHull(qhull_data, qhull_options="Qt i").simplices
[docs]class PDPlotter: """ A plotter class for phase diagrams. """ def __init__(self, phasediagram, show_unstable=0, **plotkwargs): r""" Args: phasediagram: PhaseDiagram object. show_unstable (float): Whether unstable phases will be plotted as well as red crosses. If a number > 0 is entered, all phases with ehull < show_unstable will be shown. **plotkwargs: Keyword args passed to matplotlib.pyplot.plot. Can be used to customize markers etc. If not set, the default is { "markerfacecolor": (0.2157, 0.4941, 0.7216), "markersize": 10, "linewidth": 3 } """ # note: palettable imports matplotlib from palettable.colorbrewer.qualitative import Set1_3 self._pd = phasediagram self._dim = len(self._pd.elements) if self._dim > 4: raise ValueError("Only 1-4 components supported!") self.lines = uniquelines(self._pd.facets) if self._dim > 1 else \ [[self._pd.facets[0][0], self._pd.facets[0][0]]] self.show_unstable = show_unstable colors = Set1_3.mpl_colors self.plotkwargs = plotkwargs or { "markerfacecolor": colors[2], "markersize": 10, "linewidth": 3 } @property def pd_plot_data(self): """ Plot data for phase diagram. 2-comp - Full hull with energies 3/4-comp - Projection into 2D or 3D Gibbs triangle. Returns: (lines, stable_entries, unstable_entries): - lines is a list of list of coordinates for lines in the PD. - stable_entries is a {coordinate : entry} for each stable node in the phase diagram. (Each coordinate can only have one stable phase) - unstable_entries is a {entry: coordinates} for all unstable nodes in the phase diagram. """ pd = self._pd entries = pd.qhull_entries data = np.array(pd.qhull_data) lines = [] stable_entries = {} for line in self.lines: entry1 = entries[line[0]] entry2 = entries[line[1]] if self._dim < 3: x = [data[line[0]][0], data[line[1]][0]] y = [pd.get_form_energy_per_atom(entry1), pd.get_form_energy_per_atom(entry2)] coord = [x, y] elif self._dim == 3: coord = triangular_coord(data[line, 0:2]) else: coord = tet_coord(data[line, 0:3]) lines.append(coord) labelcoord = list(zip(*coord)) stable_entries[labelcoord[0]] = entry1 stable_entries[labelcoord[1]] = entry2 all_entries = pd.all_entries all_data = np.array(pd.all_entries_hulldata) unstable_entries = dict() stable = pd.stable_entries for i in range(0, len(all_entries)): entry = all_entries[i] if entry not in stable: if self._dim < 3: x = [all_data[i][0], all_data[i][0]] y = [pd.get_form_energy_per_atom(entry), pd.get_form_energy_per_atom(entry)] coord = [x, y] elif self._dim == 3: coord = triangular_coord([all_data[i, 0:2], all_data[i, 0:2]]) else: coord = tet_coord([all_data[i, 0:3], all_data[i, 0:3], all_data[i, 0:3]]) labelcoord = list(zip(*coord)) unstable_entries[entry] = labelcoord[0] return lines, stable_entries, unstable_entries
[docs] def get_plot(self, label_stable=True, label_unstable=True, ordering=None, energy_colormap=None, process_attributes=False, plt=None): """ :param label_stable: Whether to label stable compounds. :param label_unstable: Whether to label unstable compounds. :param ordering: Ordering of vertices. :param energy_colormap: Colormap for coloring energy. :param process_attributes: Whether to process the attributes. :param plt: Existing plt object if plotting multiple phase diagrams. :return: matplotlib.pyplot. """ if self._dim < 4: plt = self._get_2d_plot(label_stable, label_unstable, ordering, energy_colormap, plt=plt, process_attributes=process_attributes) elif self._dim == 4: plt = self._get_3d_plot(label_stable) return plt
[docs] def plot_element_profile(self, element, comp, show_label_index=None, xlim=5): """ Draw the element profile plot for a composition varying different chemical potential of an element. X value is the negative value of the chemical potential reference to elemental chemical potential. For example, if choose Element("Li"), X= -(µLi-µLi0), which corresponds to the voltage versus metal anode. Y values represent for the number of element uptake in this composition (unit: per atom). All reactions are printed to help choosing the profile steps you want to show label in the plot. Args: element (Element): An element of which the chemical potential is considered. It also must be in the phase diagram. comp (Composition): A composition. show_label_index (list of integers): The labels for reaction products you want to show in the plot. Default to None (not showing any annotation for reaction products). For the profile steps you want to show the labels, just add it to the show_label_index. The profile step counts from zero. For example, you can set show_label_index=[0, 2, 5] to label profile step 0,2,5. xlim (float): The max x value. x value is from 0 to xlim. Default to 5 eV. Returns: Plot of element profile evolution by varying the chemical potential of an element. """ plt = pretty_plot(12, 8) pd = self._pd evolution = pd.get_element_profile(element, comp) num_atoms = evolution[0]["reaction"].reactants[0].num_atoms element_energy = evolution[0]['chempot'] x1, x2, y1 = None, None, None for i, d in enumerate(evolution): v = -(d["chempot"] - element_energy) if i != 0: plt.plot([x2, x2], [y1, d["evolution"] / num_atoms], 'k', linewidth=2.5) x1 = v y1 = d["evolution"] / num_atoms if i != len(evolution) - 1: x2 = - (evolution[i + 1]["chempot"] - element_energy) else: x2 = 5.0 if show_label_index is not None and i in show_label_index: products = [re.sub(r"(\d+)", r"$_{\1}$", p.reduced_formula) for p in d["reaction"].products if p.reduced_formula != element.symbol] plt.annotate(", ".join(products), xy=(v + 0.05, y1 + 0.05), fontsize=24, color='r') plt.plot([x1, x2], [y1, y1], 'r', linewidth=3) else: plt.plot([x1, x2], [y1, y1], 'k', linewidth=2.5) plt.xlim((0, xlim)) plt.xlabel("-$\\Delta{\\mu}$ (eV)") plt.ylabel("Uptake per atom") return plt
[docs] def show(self, *args, **kwargs): r""" Draws the phase diagram using Matplotlib and show it. Args: *args: Passed to get_plot. **kwargs: Passed to get_plot. """ self.get_plot(*args, **kwargs).show()
def _get_2d_plot(self, label_stable=True, label_unstable=True, ordering=None, energy_colormap=None, vmin_mev=-60.0, vmax_mev=60.0, show_colorbar=True, process_attributes=False, plt=None): """ Shows the plot using pylab. Usually I won't do imports in methods, but since plotting is a fairly expensive library to load and not all machines have matplotlib installed, I have done it this way. """ if plt is None: plt = pretty_plot(8, 6) from matplotlib.font_manager import FontProperties if ordering is None: (lines, labels, unstable) = self.pd_plot_data else: (_lines, _labels, _unstable) = self.pd_plot_data (lines, labels, unstable) = order_phase_diagram( _lines, _labels, _unstable, ordering) if energy_colormap is None: if process_attributes: for x, y in lines: plt.plot(x, y, "k-", linewidth=3, markeredgecolor="k") # One should think about a clever way to have "complex" # attributes with complex processing options but with a clear # logic. At this moment, I just use the attributes to know # whether an entry is a new compound or an existing (from the # ICSD or from the MP) one. for x, y in labels.keys(): if labels[(x, y)].attribute is None or \ labels[(x, y)].attribute == "existing": plt.plot(x, y, "ko", **self.plotkwargs) else: plt.plot(x, y, "k*", **self.plotkwargs) else: for x, y in lines: plt.plot(x, y, "ko-", **self.plotkwargs) else: from matplotlib.colors import Normalize, LinearSegmentedColormap from matplotlib.cm import ScalarMappable for x, y in lines: plt.plot(x, y, "k-", markeredgecolor="k") vmin = vmin_mev / 1000.0 vmax = vmax_mev / 1000.0 if energy_colormap == 'default': mid = - vmin / (vmax - vmin) cmap = LinearSegmentedColormap.from_list( 'my_colormap', [(0.0, '#005500'), (mid, '#55FF55'), (mid, '#FFAAAA'), (1.0, '#FF0000')]) else: cmap = energy_colormap norm = Normalize(vmin=vmin, vmax=vmax) _map = ScalarMappable(norm=norm, cmap=cmap) _energies = [self._pd.get_equilibrium_reaction_energy(entry) for coord, entry in labels.items()] energies = [en if en < 0.0 else -0.00000001 for en in _energies] vals_stable = _map.to_rgba(energies) ii = 0 if process_attributes: for x, y in labels.keys(): if labels[(x, y)].attribute is None or \ labels[(x, y)].attribute == "existing": plt.plot(x, y, "o", markerfacecolor=vals_stable[ii], markersize=12) else: plt.plot(x, y, "*", markerfacecolor=vals_stable[ii], markersize=18) ii += 1 else: for x, y in labels.keys(): plt.plot(x, y, "o", markerfacecolor=vals_stable[ii], markersize=15) ii += 1 font = FontProperties() font.set_weight("bold") font.set_size(24) # Sets a nice layout depending on the type of PD. Also defines a # "center" for the PD, which then allows the annotations to be spread # out in a nice manner. if len(self._pd.elements) == 3: plt.axis("equal") plt.xlim((-0.1, 1.2)) plt.ylim((-0.1, 1.0)) plt.axis("off") center = (0.5, math.sqrt(3) / 6) else: all_coords = labels.keys() miny = min([c[1] for c in all_coords]) ybuffer = max(abs(miny) * 0.1, 0.1) plt.xlim((-0.1, 1.1)) plt.ylim((miny - ybuffer, ybuffer)) center = (0.5, miny / 2) plt.xlabel("Fraction", fontsize=28, fontweight='bold') plt.ylabel("Formation energy (eV/atom)", fontsize=28, fontweight='bold') for coords in sorted(labels.keys(), key=lambda x: -x[1]): entry = labels[coords] label = entry.name # The follow defines an offset for the annotation text emanating # from the center of the PD. Results in fairly nice layouts for the # most part. vec = (np.array(coords) - center) vec = vec / np.linalg.norm(vec) * 10 if np.linalg.norm(vec) != 0 \ else vec valign = "bottom" if vec[1] > 0 else "top" if vec[0] < -0.01: halign = "right" elif vec[0] > 0.01: halign = "left" else: halign = "center" if label_stable: if process_attributes and entry.attribute == 'new': plt.annotate(latexify(label), coords, xytext=vec, textcoords="offset points", horizontalalignment=halign, verticalalignment=valign, fontproperties=font, color='g') else: plt.annotate(latexify(label), coords, xytext=vec, textcoords="offset points", horizontalalignment=halign, verticalalignment=valign, fontproperties=font) if self.show_unstable: font = FontProperties() font.set_size(16) energies_unstable = [self._pd.get_e_above_hull(entry) for entry, coord in unstable.items()] if energy_colormap is not None: energies.extend(energies_unstable) vals_unstable = _map.to_rgba(energies_unstable) ii = 0 for entry, coords in unstable.items(): ehull = self._pd.get_e_above_hull(entry) if ehull < self.show_unstable: vec = (np.array(coords) - center) vec = vec / np.linalg.norm(vec) * 10 \ if np.linalg.norm(vec) != 0 else vec label = entry.name if energy_colormap is None: plt.plot(coords[0], coords[1], "ks", linewidth=3, markeredgecolor="k", markerfacecolor="r", markersize=8) else: plt.plot(coords[0], coords[1], "s", linewidth=3, markeredgecolor="k", markerfacecolor=vals_unstable[ii], markersize=8) if label_unstable: plt.annotate(latexify(label), coords, xytext=vec, textcoords="offset points", horizontalalignment=halign, color="b", verticalalignment=valign, fontproperties=font) ii += 1 if energy_colormap is not None and show_colorbar: _map.set_array(energies) cbar = plt.colorbar(_map) cbar.set_label( 'Energy [meV/at] above hull (in red)\nInverse energy [' 'meV/at] above hull (in green)', rotation=-90, ha='left', va='center') f = plt.gcf() f.set_size_inches((8, 6)) plt.subplots_adjust(left=0.09, right=0.98, top=0.98, bottom=0.07) return plt def _get_3d_plot(self, label_stable=True): """ Shows the plot using pylab. Usually I won"t do imports in methods, but since plotting is a fairly expensive library to load and not all machines have matplotlib installed, I have done it this way. """ import matplotlib.pyplot as plt import mpl_toolkits.mplot3d.axes3d as p3 from matplotlib.font_manager import FontProperties fig = plt.figure() ax = p3.Axes3D(fig) font = FontProperties() font.set_weight("bold") font.set_size(20) (lines, labels, unstable) = self.pd_plot_data count = 1 newlabels = list() for x, y, z in lines: ax.plot(x, y, z, "bo-", linewidth=3, markeredgecolor="b", markerfacecolor="r", markersize=10) for coords in sorted(labels.keys()): entry = labels[coords] label = entry.name if label_stable: if len(entry.composition.elements) == 1: ax.text(coords[0], coords[1], coords[2], label) else: ax.text(coords[0], coords[1], coords[2], str(count)) newlabels.append("{} : {}".format(count, latexify(label))) count += 1 plt.figtext(0.01, 0.01, "\n".join(newlabels)) ax.axis("off") return plt
[docs] def write_image(self, stream, image_format="svg", **kwargs): r""" Writes the phase diagram to an image in a stream. Args: stream: stream to write to. Can be a file stream or a StringIO stream. image_format format for image. Can be any of matplotlib supported formats. Defaults to svg for best results for vector graphics. **kwargs: Pass through to get_plot functino. """ plt = self.get_plot(**kwargs) f = plt.gcf() f.set_size_inches((12, 10)) plt.savefig(stream, format=image_format)
[docs] def plot_chempot_range_map(self, elements, referenced=True): """ Plot the chemical potential range _map. Currently works only for 3-component PDs. Args: elements: Sequence of elements to be considered as independent variables. E.g., if you want to show the stability ranges of all Li-Co-O phases wrt to uLi and uO, you will supply [Element("Li"), Element("O")] referenced: if True, gives the results with a reference being the energy of the elemental phase. If False, gives absolute values. """ self.get_chempot_range_map_plot(elements, referenced=referenced).show()
[docs] def get_chempot_range_map_plot(self, elements, referenced=True): """ Returns a plot of the chemical potential range _map. Currently works only for 3-component PDs. Args: elements: Sequence of elements to be considered as independent variables. E.g., if you want to show the stability ranges of all Li-Co-O phases wrt to uLi and uO, you will supply [Element("Li"), Element("O")] referenced: if True, gives the results with a reference being the energy of the elemental phase. If False, gives absolute values. Returns: A matplotlib plot object. """ plt = pretty_plot(12, 8) chempot_ranges = self._pd.get_chempot_range_map( elements, referenced=referenced) missing_lines = {} excluded_region = [] for entry, lines in chempot_ranges.items(): comp = entry.composition center_x = 0 center_y = 0 coords = [] contain_zero = any([comp.get_atomic_fraction(el) == 0 for el in elements]) is_boundary = (not contain_zero) and sum([comp.get_atomic_fraction(el) for el in elements]) == 1 for line in lines: (x, y) = line.coords.transpose() plt.plot(x, y, "k-") for coord in line.coords: if not in_coord_list(coords, coord): coords.append(coord.tolist()) center_x += coord[0] center_y += coord[1] if is_boundary: excluded_region.extend(line.coords) if coords and contain_zero: missing_lines[entry] = coords else: xy = (center_x / len(coords), center_y / len(coords)) plt.annotate(latexify(entry.name), xy, fontsize=22) ax = plt.gca() xlim = ax.get_xlim() ylim = ax.get_ylim() # Shade the forbidden chemical potential regions. excluded_region.append([xlim[1], ylim[1]]) excluded_region = sorted(excluded_region, key=lambda c: c[0]) (x, y) = np.transpose(excluded_region) plt.fill(x, y, "0.80") # The hull does not generate the missing horizontal and vertical lines. # The following code fixes this. el0 = elements[0] el1 = elements[1] for entry, coords in missing_lines.items(): center_x = sum([c[0] for c in coords]) center_y = sum([c[1] for c in coords]) comp = entry.composition is_x = comp.get_atomic_fraction(el0) < 0.01 is_y = comp.get_atomic_fraction(el1) < 0.01 n = len(coords) if not (is_x and is_y): if is_x: coords = sorted(coords, key=lambda c: c[1]) for i in [0, -1]: x = [min(xlim), coords[i][0]] y = [coords[i][1], coords[i][1]] plt.plot(x, y, "k") center_x += min(xlim) center_y += coords[i][1] elif is_y: coords = sorted(coords, key=lambda c: c[0]) for i in [0, -1]: x = [coords[i][0], coords[i][0]] y = [coords[i][1], min(ylim)] plt.plot(x, y, "k") center_x += coords[i][0] center_y += min(ylim) xy = (center_x / (n + 2), center_y / (n + 2)) else: center_x = sum(coord[0] for coord in coords) + xlim[0] center_y = sum(coord[1] for coord in coords) + ylim[0] xy = (center_x / (n + 1), center_y / (n + 1)) plt.annotate(latexify(entry.name), xy, horizontalalignment="center", verticalalignment="center", fontsize=22) plt.xlabel("$\\mu_{{{0}}} - \\mu_{{{0}}}^0$ (eV)" .format(el0.symbol)) plt.ylabel("$\\mu_{{{0}}} - \\mu_{{{0}}}^0$ (eV)" .format(el1.symbol)) plt.tight_layout() return plt
[docs] def get_contour_pd_plot(self): """ Plot a contour phase diagram plot, where phase triangles are colored according to degree of instability by interpolation. Currently only works for 3-component phase diagrams. Returns: A matplotlib plot object. """ from scipy import interpolate from matplotlib import cm pd = self._pd entries = pd.qhull_entries data = np.array(pd.qhull_data) plt = self._get_2d_plot() data[:, 0:2] = triangular_coord(data[:, 0:2]).transpose() for i, e in enumerate(entries): data[i, 2] = self._pd.get_e_above_hull(e) gridsize = 0.005 xnew = np.arange(0, 1., gridsize) ynew = np.arange(0, 1, gridsize) f = interpolate.LinearNDInterpolator(data[:, 0:2], data[:, 2]) znew = np.zeros((len(ynew), len(xnew))) for (i, xval) in enumerate(xnew): for (j, yval) in enumerate(ynew): znew[j, i] = f(xval, yval) plt.contourf(xnew, ynew, znew, 1000, cmap=cm.autumn_r) plt.colorbar() return plt
[docs]def uniquelines(q): """ Given all the facets, convert it into a set of unique lines. Specifically used for converting convex hull facets into line pairs of coordinates. Args: q: A 2-dim sequence, where each row represents a facet. E.g., [[1,2,3],[3,6,7],...] Returns: setoflines: A set of tuple of lines. E.g., ((1,2), (1,3), (2,3), ....) """ setoflines = set() for facets in q: for line in itertools.combinations(facets, 2): setoflines.add(tuple(sorted(line))) return setoflines
[docs]def triangular_coord(coord): """ Convert a 2D coordinate into a triangle-based coordinate system for a prettier phase diagram. Args: coordinate: coordinate used in the convex hull computation. Returns: coordinates in a triangular-based coordinate system. """ unitvec = np.array([[1, 0], [0.5, math.sqrt(3) / 2]]) result = np.dot(np.array(coord), unitvec) return result.transpose()
[docs]def tet_coord(coord): """ Convert a 3D coordinate into a tetrahedron based coordinate system for a prettier phase diagram. Args: coordinate: coordinate used in the convex hull computation. Returns: coordinates in a tetrahedron-based coordinate system. """ unitvec = np.array([[1, 0, 0], [0.5, math.sqrt(3) / 2, 0], [0.5, 1.0 / 3.0 * math.sqrt(3) / 2, math.sqrt(6) / 3]]) result = np.dot(np.array(coord), unitvec) return result.transpose()
[docs]def order_phase_diagram(lines, stable_entries, unstable_entries, ordering): """ Orders the entries (their coordinates) in a phase diagram plot according to the user specified ordering. Ordering should be given as ['Up', 'Left', 'Right'], where Up, Left and Right are the names of the entries in the upper, left and right corners of the triangle respectively. Args: lines: list of list of coordinates for lines in the PD. stable_entries: {coordinate : entry} for each stable node in the phase diagram. (Each coordinate can only have one stable phase) unstable_entries: {entry: coordinates} for all unstable nodes in the phase diagram. ordering: Ordering of the phase diagram, given as a list ['Up', 'Left','Right'] Returns: (newlines, newstable_entries, newunstable_entries): - newlines is a list of list of coordinates for lines in the PD. - newstable_entries is a {coordinate : entry} for each stable node in the phase diagram. (Each coordinate can only have one stable phase) - newunstable_entries is a {entry: coordinates} for all unstable nodes in the phase diagram. """ yup = -1000.0 xleft = 1000.0 xright = -1000.0 for coord in stable_entries: if coord[0] > xright: xright = coord[0] nameright = stable_entries[coord].name if coord[0] < xleft: xleft = coord[0] nameleft = stable_entries[coord].name if coord[1] > yup: yup = coord[1] nameup = stable_entries[coord].name if (nameup not in ordering) or (nameright not in ordering) or (nameleft not in ordering): raise ValueError( 'Error in ordering_phase_diagram : \n"{up}", "{left}" and "{' 'right}"' ' should be in ordering : {ord}'.format(up=nameup, left=nameleft, right=nameright, ord=ordering)) cc = np.array([0.5, np.sqrt(3.0) / 6.0], np.float) if nameup == ordering[0]: if nameleft == ordering[1]: # The coordinates were already in the user ordering return lines, stable_entries, unstable_entries else: newlines = [[np.array(1.0 - x), y] for x, y in lines] newstable_entries = {(1.0 - c[0], c[1]): entry for c, entry in stable_entries.items()} newunstable_entries = {entry: (1.0 - c[0], c[1]) for entry, c in unstable_entries.items()} return newlines, newstable_entries, newunstable_entries elif nameup == ordering[1]: if nameleft == ordering[2]: c120 = np.cos(2.0 * np.pi / 3.0) s120 = np.sin(2.0 * np.pi / 3.0) newlines = [] for x, y in lines: newx = np.zeros_like(x) newy = np.zeros_like(y) for ii, xx in enumerate(x): newx[ii] = c120 * (xx - cc[0]) - s120 * (y[ii] - cc[1]) + cc[0] newy[ii] = s120 * (xx - cc[0]) + c120 * (y[ii] - cc[1]) + cc[1] newlines.append([newx, newy]) newstable_entries = { (c120 * (c[0] - cc[0]) - s120 * (c[1] - cc[1]) + cc[0], s120 * (c[0] - cc[0]) + c120 * (c[1] - cc[1]) + cc[1]): entry for c, entry in stable_entries.items()} newunstable_entries = { entry: (c120 * (c[0] - cc[0]) - s120 * (c[1] - cc[1]) + cc[0], s120 * (c[0] - cc[0]) + c120 * (c[1] - cc[1]) + cc[1]) for entry, c in unstable_entries.items()} return newlines, newstable_entries, newunstable_entries else: c120 = np.cos(2.0 * np.pi / 3.0) s120 = np.sin(2.0 * np.pi / 3.0) newlines = [] for x, y in lines: newx = np.zeros_like(x) newy = np.zeros_like(y) for ii, xx in enumerate(x): newx[ii] = -c120 * (xx - 1.0) - s120 * y[ii] + 1.0 newy[ii] = -s120 * (xx - 1.0) + c120 * y[ii] newlines.append([newx, newy]) newstable_entries = {(-c120 * (c[0] - 1.0) - s120 * c[1] + 1.0, -s120 * (c[0] - 1.0) + c120 * c[1]): entry for c, entry in stable_entries.items()} newunstable_entries = { entry: (-c120 * (c[0] - 1.0) - s120 * c[1] + 1.0, -s120 * (c[0] - 1.0) + c120 * c[1]) for entry, c in unstable_entries.items()} return newlines, newstable_entries, newunstable_entries elif nameup == ordering[2]: if nameleft == ordering[0]: c240 = np.cos(4.0 * np.pi / 3.0) s240 = np.sin(4.0 * np.pi / 3.0) newlines = [] for x, y in lines: newx = np.zeros_like(x) newy = np.zeros_like(y) for ii, xx in enumerate(x): newx[ii] = c240 * (xx - cc[0]) - s240 * (y[ii] - cc[1]) + cc[0] newy[ii] = s240 * (xx - cc[0]) + c240 * (y[ii] - cc[1]) + cc[1] newlines.append([newx, newy]) newstable_entries = { (c240 * (c[0] - cc[0]) - s240 * (c[1] - cc[1]) + cc[0], s240 * (c[0] - cc[0]) + c240 * (c[1] - cc[1]) + cc[1]): entry for c, entry in stable_entries.items()} newunstable_entries = { entry: (c240 * (c[0] - cc[0]) - s240 * (c[1] - cc[1]) + cc[0], s240 * (c[0] - cc[0]) + c240 * (c[1] - cc[1]) + cc[1]) for entry, c in unstable_entries.items()} return newlines, newstable_entries, newunstable_entries else: c240 = np.cos(4.0 * np.pi / 3.0) s240 = np.sin(4.0 * np.pi / 3.0) newlines = [] for x, y in lines: newx = np.zeros_like(x) newy = np.zeros_like(y) for ii, xx in enumerate(x): newx[ii] = -c240 * xx - s240 * y[ii] newy[ii] = -s240 * xx + c240 * y[ii] newlines.append([newx, newy]) newstable_entries = {(-c240 * c[0] - s240 * c[1], -s240 * c[0] + c240 * c[1]): entry for c, entry in stable_entries.items()} newunstable_entries = {entry: (-c240 * c[0] - s240 * c[1], -s240 * c[0] + c240 * c[1]) for entry, c in unstable_entries.items()} return newlines, newstable_entries, newunstable_entries