# coding: utf-8
# Copyright (c) Pymatgen Development Team.
# Distributed under the terms of the MIT License.
"""
This module defines tools to analyze surface and adsorption related
quantities as well as related plots. If you use this module, please
consider citing the following works::
R. Tran, Z. Xu, B. Radhakrishnan, D. Winston, W. Sun, K. A. Persson,
S. P. Ong, "Surface Energies of Elemental Crystals", Scientific
Data, 2016, 3:160080, doi: 10.1038/sdata.2016.80.
and
Kang, S., Mo, Y., Ong, S. P., & Ceder, G. (2014). Nanoscale
stabilization of sodium oxides: Implications for Na-O2 batteries.
Nano Letters, 14(2), 1016–1020. https://doi.org/10.1021/nl404557w
and
Montoya, J. H., & Persson, K. A. (2017). A high-throughput framework
for determining adsorption energies on solid surfaces. Npj
Computational Materials, 3(1), 14.
https://doi.org/10.1038/s41524-017-0017-z
TODO:
-Still assumes individual elements have their own chempots
in a molecular adsorbate instead of considering a single
chempot for a single molecular adsorbate. E.g. for an OH
adsorbate, the surface energy is a function of delu_O and
delu_H instead of delu_OH
-Need a method to automatically get chempot range when
dealing with non-stoichiometric slabs
-Simplify the input for SurfaceEnergyPlotter such that the
user does not need to generate a dict
"""
import numpy as np
import itertools
import warnings
import random
import copy
from sympy import Symbol
from sympy.solvers import linsolve, solve
from pymatgen.core.composition import Composition
from pymatgen.core.surface import get_slab_regions
from pymatgen.entries.computed_entries import ComputedStructureEntry
from pymatgen.symmetry.analyzer import SpacegroupAnalyzer
from pymatgen.analysis.wulff import WulffShape
from pymatgen.util.plotting import pretty_plot
from pymatgen.io.vasp.outputs import Outcar, Locpot, Poscar
EV_PER_ANG2_TO_JOULES_PER_M2 = 16.0217656
__author__ = "Richard Tran"
__copyright__ = "Copyright 2017, The Materials Virtual Lab"
__version__ = "0.2"
__maintainer__ = "Richard Tran"
__credits__ = "Joseph Montoya, Xianguo Li"
__email__ = "rit001@eng.ucsd.edu"
__date__ = "8/24/17"
[docs]class SlabEntry(ComputedStructureEntry):
"""
A ComputedStructureEntry object encompassing all data relevant to a
slab for analyzing surface thermodynamics.
.. attribute:: miller_index
Miller index of plane parallel to surface.
.. attribute:: label
Brief description for this slab.
.. attribute:: adsorbates
List of ComputedStructureEntry for the types of adsorbates
..attribute:: clean_entry
SlabEntry for the corresponding clean slab for an adsorbed slab
..attribute:: ads_entries_dict
Dictionary where the key is the reduced composition of the
adsorbate entry and value is the entry itself
"""
def __init__(self, structure, energy, miller_index, correction=0.0,
parameters=None, data=None, entry_id=None, label=None,
adsorbates=None, clean_entry=None, marker=None, color=None):
"""
Make a SlabEntry containing all relevant surface thermodynamics data.
Args:
structure (Slab): The primary slab associated with this entry.
energy (float): Energy from total energy calculation
miller_index (tuple(h, k, l)): Miller index of plane parallel
to surface
correction (float): See ComputedSlabEntry
parameters (dict): See ComputedSlabEntry
data (dict): See ComputedSlabEntry
entry_id (obj): See ComputedSlabEntry
data (dict): See ComputedSlabEntry
entry_id (str): See ComputedSlabEntry
label (str): Any particular label for this slab, e.g. "Tasker 2",
"non-stoichiometric", "reconstructed"
adsorbates ([ComputedStructureEntry]): List of reference entries
for the adsorbates on the slab, can be an isolated molecule
(e.g. O2 for O or O2 adsorption), a bulk structure (eg. fcc
Cu for Cu adsorption) or anything.
clean_entry (ComputedStructureEntry): If the SlabEntry is for an
adsorbed slab, this is the corresponding SlabEntry for the
clean slab
marker (str): Custom marker for gamma plots ("--" and "-" are typical)
color (str or rgba): Custom color for gamma plots
"""
self.miller_index = miller_index
self.label = label
self.adsorbates = [] if not adsorbates else adsorbates
self.clean_entry = clean_entry
self.ads_entries_dict = {str(list(ads.composition.as_dict().keys())[0]): ads for ads in self.adsorbates}
self.mark = marker
self.color = color
super().__init__(
structure, energy, correction=correction,
parameters=parameters, data=data, entry_id=entry_id)
[docs] def as_dict(self):
"""
Returns dict which contains Slab Entry data.
"""
d = {"@module": self.__class__.__module__,
"@class": self.__class__.__name__}
d["structure"] = self.structure
d["energy"] = self.energy
d["miller_index"] = self.miller_index
d["label"] = self.label
d["coverage"] = self.coverage
d["adsorbates"] = self.adsorbates
d["clean_entry"] = self.clean_entry
return d
[docs] def gibbs_binding_energy(self, eads=False):
"""
Returns the adsorption energy or Gibb's binding energy
of an adsorbate on a surface
Args:
eads (bool): Whether to calculate the adsorption energy
(True) or the binding energy (False) which is just
adsorption energy normalized by number of adsorbates.
"""
n = self.get_unit_primitive_area
Nads = self.Nads_in_slab
BE = (self.energy - n * self.clean_entry.energy) / Nads - sum([ads.energy_per_atom for ads in self.adsorbates])
return BE * Nads if eads else BE
[docs] def surface_energy(self, ucell_entry, ref_entries=None):
"""
Calculates the surface energy of this SlabEntry.
Args:
ucell_entry (entry): An entry object for the bulk
ref_entries (list: [entry]): A list of entries for each type
of element to be used as a reservoir for nonstoichiometric
systems. The length of this list MUST be n-1 where n is the
number of different elements in the bulk entry. The chempot
of the element ref_entry that is not in the list will be
treated as a variable.
Returns (Add (Sympy class)): Surface energy
"""
# Set up
ref_entries = [] if not ref_entries else ref_entries
# Check if appropriate ref_entries are present if the slab is non-stoichiometric
# TODO: There should be a way to identify which specific species are
# non-stoichiometric relative to the others in systems with more than 2 species
slab_comp = self.composition.as_dict()
ucell_entry_comp = ucell_entry.composition.reduced_composition.as_dict()
slab_clean_comp = Composition({el: slab_comp[el] for el in ucell_entry_comp.keys()})
if slab_clean_comp.reduced_composition != ucell_entry.composition.reduced_composition:
list_els = [list(entry.composition.as_dict().keys())[0] for entry in ref_entries]
if not any([el in list_els for el in ucell_entry.composition.as_dict().keys()]):
warnings.warn("Elemental references missing for the non-dopant species.")
gamma = (Symbol("E_surf") - Symbol("Ebulk")) / (2 * Symbol("A"))
ucell_comp = ucell_entry.composition
ucell_reduced_comp = ucell_comp.reduced_composition
ref_entries_dict = {str(list(ref.composition.as_dict().keys())[0]): ref for ref in ref_entries}
ref_entries_dict.update(self.ads_entries_dict)
# Calculate Gibbs free energy of the bulk per unit formula
gbulk = ucell_entry.energy / ucell_comp.get_integer_formula_and_factor()[1]
# First we get the contribution to the bulk energy
# from each element with an existing ref_entry.
bulk_energy, gbulk_eqn = 0, 0
for el, ref in ref_entries_dict.items():
N, delu = self.composition.as_dict()[el], Symbol("delu_" + str(el))
if el in ucell_comp.as_dict().keys():
gbulk_eqn += ucell_reduced_comp[el] * (delu + ref.energy_per_atom)
bulk_energy += N * (Symbol("delu_" + el) + ref.energy_per_atom)
# Next, we add the contribution to the bulk energy from
# the variable element (the element without a ref_entry),
# as a function of the other elements
for ref_el in ucell_comp.as_dict().keys():
if str(ref_el) not in ref_entries_dict.keys():
break
refEperA = (gbulk - gbulk_eqn) / ucell_reduced_comp.as_dict()[ref_el]
bulk_energy += self.composition.as_dict()[ref_el] * refEperA
se = gamma.subs({Symbol("E_surf"): self.energy, Symbol("Ebulk"): bulk_energy,
Symbol("A"): self.surface_area})
return float(se) if type(se).__name__ == "Float" else se
@property
def get_unit_primitive_area(self):
"""
Returns the surface area of the adsorbed system per
unit area of the primitive slab system.
"""
A_ads = self.surface_area
A_clean = self.clean_entry.surface_area
n = (A_ads / A_clean)
return n
@property
def get_monolayer(self):
"""
Returns the primitive unit surface area density of the
adsorbate.
"""
unit_a = self.get_unit_primitive_area
Nsurfs = self.Nsurfs_ads_in_slab
Nads = self.Nads_in_slab
return Nads / (unit_a * Nsurfs)
@property
def Nads_in_slab(self):
"""
Returns the TOTAL number of adsorbates in the slab on BOTH sides
"""
return sum([self.composition.as_dict()[a] for a in self.ads_entries_dict.keys()])
@property
def Nsurfs_ads_in_slab(self):
"""
Returns the TOTAL number of adsorbed surfaces in the slab
"""
struct = self.structure
weights = [s.species.weight for s in struct]
center_of_mass = np.average(struct.frac_coords, weights=weights, axis=0)
Nsurfs = 0
# Are there adsorbates on top surface?
if any([site.species_string in self.ads_entries_dict.keys()
for site in struct if site.frac_coords[2] > center_of_mass[2]]):
Nsurfs += 1
# Are there adsorbates on bottom surface?
if any([site.species_string in self.ads_entries_dict.keys()
for site in struct if site.frac_coords[2] < center_of_mass[2]]):
Nsurfs += 1
return Nsurfs
[docs] @classmethod
def from_dict(cls, d):
"""
Returns a SlabEntry by reading in an dictionary
"""
structure = SlabEntry.from_dict(d["structure"])
energy = SlabEntry.from_dict(d["energy"])
miller_index = d["miller_index"]
label = d["label"]
coverage = d["coverage"]
adsorbates = d["adsorbates"]
clean_entry = d["clean_entry"]
return SlabEntry(structure, energy, miller_index, label=label,
coverage=coverage, adsorbates=adsorbates,
clean_entry=clean_entry)
@property
def surface_area(self):
"""
Calculates the surface area of the slab
"""
m = self.structure.lattice.matrix
return np.linalg.norm(np.cross(m[0], m[1]))
@property
def cleaned_up_slab(self):
"""
Returns a slab with the adsorbates removed
"""
ads_strs = list(self.ads_entries_dict.keys())
cleaned = self.structure.copy()
cleaned.remove_species(ads_strs)
return cleaned
@property
def create_slab_label(self):
"""
Returns a label (str) for this particular slab based
on composition, coverage and Miller index.
"""
if "label" in self.data.keys():
return self.data["label"]
label = str(self.miller_index)
ads_strs = list(self.ads_entries_dict.keys())
cleaned = self.cleaned_up_slab
label += " %s" % (cleaned.composition.reduced_composition)
if self.adsorbates:
for ads in ads_strs:
label += r"+%s" % (ads)
label += r", %.3f ML" % (self.get_monolayer)
return label
[docs] @staticmethod
def from_computed_structure_entry(entry, miller_index, label=None,
adsorbates=None, clean_entry=None, **kwargs):
"""
Returns SlabEntry from a ComputedStructureEntry
"""
return SlabEntry(entry.structure, entry.energy, miller_index, label=label,
adsorbates=adsorbates, clean_entry=clean_entry, **kwargs)
[docs]class SurfaceEnergyPlotter:
"""
A class used for generating plots to analyze the thermodynamics of surfaces
of a material. Produces stability maps of different slab configurations,
phases diagrams of two parameters to determine stability of configurations
(future release), and Wulff shapes.
.. attribute:: all_slab_entries
Either a list of SlabEntry objects (note for a list, the SlabEntry must
have the adsorbates and clean_entry parameter pulgged in) or a Nested
dictionary containing a list of entries for slab calculations as
items and the corresponding Miller index of the slab as the key.
To account for adsorption, each value is a sub-dictionary with the
entry of a clean slab calculation as the sub-key and a list of
entries for adsorption calculations as the sub-value. The sub-value
can contain different adsorption configurations such as a different
site or a different coverage, however, ordinarily only the most stable
configuration for a particular coverage will be considered as the
function of the adsorbed surface energy has an intercept dependent on
the adsorption energy (ie an adsorption site with a higher adsorption
energy will always provide a higher surface energy than a site with a
lower adsorption energy). An example parameter is provided:
{(h1,k1,l1): {clean_entry1: [ads_entry1, ads_entry2, ...],
clean_entry2: [...], ...}, (h2,k2,l2): {...}}
where clean_entry1 can be a pristine surface and clean_entry2 can be a
reconstructed surface while ads_entry1 can be adsorption at site 1 with
a 2x2 coverage while ads_entry2 can have a 3x3 coverage. If adsorption
entries are present (i.e. if all_slab_entries[(h,k,l)][clean_entry1]), we
consider adsorption in all plots and analysis for this particular facet.
..attribute:: color_dict
Dictionary of colors (r,g,b,a) when plotting surface energy stability. The
keys are individual surface entries where clean surfaces have a solid
color while the corresponding adsorbed surface will be transparent.
.. attribute:: ucell_entry
ComputedStructureEntry of the bulk reference for this particular material.
.. attribute:: ref_entries
List of ComputedStructureEntries to be used for calculating chemical potential.
.. attribute:: color_dict
Randomly generated dictionary of colors associated with each facet.
"""
def __init__(self, all_slab_entries, ucell_entry, ref_entries=None):
"""
Object for plotting surface energy in different ways for clean and
adsorbed surfaces.
Args:
all_slab_entries (dict or list): Dictionary or list containing
all entries for slab calculations. See attributes.
ucell_entry (ComputedStructureEntry): ComputedStructureEntry
of the bulk reference for this particular material.
ref_entries ([ComputedStructureEntries]): A list of entries for
each type of element to be used as a reservoir for
nonstoichiometric systems. The length of this list MUST be
n-1 where n is the number of different elements in the bulk
entry. The bulk energy term in the grand surface potential can
be defined by a summation of the chemical potentials for each
element in the system. As the bulk energy is already provided,
one can solve for one of the chemical potentials as a function
of the other chemical potetinals and bulk energy. i.e. there
are n-1 variables (chempots). e.g. if your ucell_entry is for
LiFePO4 than your ref_entries should have an entry for Li, Fe,
and P if you want to use the chempot of O as the variable.
"""
self.ucell_entry = ucell_entry
self.ref_entries = ref_entries
self.all_slab_entries = all_slab_entries if \
type(all_slab_entries).__name__ == "dict" else \
entry_dict_from_list(all_slab_entries)
self.color_dict = self.color_palette_dict()
se_dict, as_coeffs_dict = {}, {}
for hkl in self.all_slab_entries.keys():
for clean in self.all_slab_entries[hkl].keys():
se = clean.surface_energy(self.ucell_entry, ref_entries=self.ref_entries)
if type(se).__name__ == "float":
se_dict[clean] = se
as_coeffs_dict[clean] = {1: se}
else:
se_dict[clean] = se
as_coeffs_dict[clean] = se.as_coefficients_dict()
for dope in self.all_slab_entries[hkl][clean]:
se = dope.surface_energy(self.ucell_entry, ref_entries=self.ref_entries)
if type(se).__name__ == "float":
se_dict[dope] = se
as_coeffs_dict[dope] = {1: se}
else:
se_dict[dope] = se
as_coeffs_dict[dope] = se.as_coefficients_dict()
self.surfe_dict = se_dict
self.as_coeffs_dict = as_coeffs_dict
list_of_chempots = []
for k in self.as_coeffs_dict.keys():
if type(self.as_coeffs_dict[k]).__name__ == "float":
continue
for du in self.as_coeffs_dict[k].keys():
if du not in list_of_chempots:
list_of_chempots.append(du)
self.list_of_chempots = list_of_chempots
[docs] def get_stable_entry_at_u(self, miller_index, delu_dict=None, delu_default=0,
no_doped=False, no_clean=False):
"""
Returns the entry corresponding to the most stable slab for a particular
facet at a specific chempot. We assume that surface energy is constant
so all free variables must be set with delu_dict, otherwise they are
assumed to be equal to delu_default.
Args:
miller_index ((h,k,l)): The facet to find the most stable slab in
delu_dict (Dict): Dictionary of the chemical potentials to be set as
constant. Note the key should be a sympy Symbol object of the
format: Symbol("delu_el") where el is the name of the element.
delu_default (float): Default value for all unset chemical potentials
no_doped (bool): Consider stability of clean slabs only.
no_clean (bool): Consider stability of doped slabs only.
Returns:
SlabEntry, surface_energy (float)
"""
all_delu_dict = self.set_all_variables(delu_dict, delu_default)
def get_coeffs(e):
coeffs = []
for du in all_delu_dict.keys():
if type(self.as_coeffs_dict[e]).__name__ == 'float':
coeffs.append(self.as_coeffs_dict[e])
elif du in self.as_coeffs_dict[e].keys():
coeffs.append(self.as_coeffs_dict[e][du])
else:
coeffs.append(0)
return np.array(coeffs)
all_entries, all_coeffs = [], []
for entry in self.all_slab_entries[miller_index].keys():
if not no_clean:
all_entries.append(entry)
all_coeffs.append(get_coeffs(entry))
if not no_doped:
for ads_entry in self.all_slab_entries[miller_index][entry]:
all_entries.append(ads_entry)
all_coeffs.append(get_coeffs(ads_entry))
du_vals = np.array(list(all_delu_dict.values()))
all_gamma = list(np.dot(all_coeffs, du_vals.T))
return all_entries[all_gamma.index(min(all_gamma))], float(min(all_gamma))
[docs] def wulff_from_chempot(self, delu_dict=None, delu_default=0, symprec=1e-5,
no_clean=False, no_doped=False):
"""
Method to get the Wulff shape at a specific chemical potential.
Args:
delu_dict (Dict): Dictionary of the chemical potentials to be set as
constant. Note the key should be a sympy Symbol object of the
format: Symbol("delu_el") where el is the name of the element.
delu_default (float): Default value for all unset chemical potentials
symprec (float): See WulffShape.
no_doped (bool): Consider stability of clean slabs only.
no_clean (bool): Consider stability of doped slabs only.
Returns:
(WulffShape): The WulffShape at u_ref and u_ads.
"""
latt = SpacegroupAnalyzer(self.ucell_entry.structure). \
get_conventional_standard_structure().lattice
miller_list = self.all_slab_entries.keys()
e_surf_list = []
for hkl in miller_list:
# For all configurations, calculate surface energy as a
# function of u. Use the lowest surface energy (corresponds
# to the most stable slab termination at that particular u)
gamma = self.get_stable_entry_at_u(hkl, delu_dict=delu_dict,
delu_default=delu_default,
no_clean=no_clean,
no_doped=no_doped)[1]
e_surf_list.append(gamma)
return WulffShape(latt, miller_list, e_surf_list, symprec=symprec)
[docs] def area_frac_vs_chempot_plot(self, ref_delu, chempot_range, delu_dict=None,
delu_default=0, increments=10, no_clean=False, no_doped=False):
"""
1D plot. Plots the change in the area contribution
of each facet as a function of chemical potential.
Args:
ref_delu (sympy Symbol): The free variable chempot with the format:
Symbol("delu_el") where el is the name of the element.
chempot_range (list): Min/max range of chemical potential to plot along
delu_dict (Dict): Dictionary of the chemical potentials to be set as
constant. Note the key should be a sympy Symbol object of the
format: Symbol("delu_el") where el is the name of the element.
delu_default (float): Default value for all unset chemical potentials
increments (int): Number of data points between min/max or point
of intersection. Defaults to 10 points.
Returns:
(Pylab): Plot of area frac on the Wulff shape
for each facet vs chemical potential.
"""
delu_dict = delu_dict if delu_dict else {}
chempot_range = sorted(chempot_range)
all_chempots = np.linspace(min(chempot_range), max(chempot_range),
increments)
# initialize a dictionary of lists of fractional areas for each hkl
hkl_area_dict = {}
for hkl in self.all_slab_entries.keys():
hkl_area_dict[hkl] = []
# Get plot points for each Miller index
for u in all_chempots:
delu_dict[ref_delu] = u
wulffshape = self.wulff_from_chempot(delu_dict=delu_dict, no_clean=no_clean,
no_doped=no_doped, delu_default=delu_default)
for hkl in wulffshape.area_fraction_dict.keys():
hkl_area_dict[hkl].append(wulffshape.area_fraction_dict[hkl])
# Plot the area fraction vs chemical potential for each facet
plt = pretty_plot(width=8, height=7)
axes = plt.gca()
for hkl in self.all_slab_entries.keys():
clean_entry = list(self.all_slab_entries[hkl].keys())[0]
# Ignore any facets that never show up on the
# Wulff shape regardless of chemical potential
if all([a == 0 for a in hkl_area_dict[hkl]]):
continue
else:
plt.plot(all_chempots, hkl_area_dict[hkl],
'--', color=self.color_dict[clean_entry],
label=str(hkl))
# Make the figure look nice
plt.ylabel(r"Fractional area $A^{Wulff}_{hkl}/A^{Wulff}$")
self.chempot_plot_addons(plt, chempot_range, str(ref_delu).split("_")[1],
axes, rect=[-0.0, 0, 0.95, 1], pad=5, ylim=[0, 1])
return plt
[docs] def get_surface_equilibrium(self, slab_entries, delu_dict=None):
"""
Takes in a list of SlabEntries and calculates the chemical potentials
at which all slabs in the list coexists simultaneously. Useful for
building surface phase diagrams. Note that to solve for x equations
(x slab_entries), there must be x free variables (chemical potentials).
Adjust delu_dict as need be to get the correct number of free variables.
Args:
slab_entries (array): The coefficients of the first equation
delu_dict (Dict): Dictionary of the chemical potentials to be set as
constant. Note the key should be a sympy Symbol object of the
format: Symbol("delu_el") where el is the name of the element.
Returns:
(array): Array containing a solution to x equations with x
variables (x-1 chemical potential and 1 surface energy)
"""
# Generate all possible coefficients
all_parameters = []
all_eqns = []
for slab_entry in slab_entries:
se = self.surfe_dict[slab_entry]
# remove the free chempots we wish to keep constant and
# set the equation to 0 (subtract gamma from both sides)
if type(se).__name__ == "float":
all_eqns.append(se - Symbol("gamma"))
else:
se = sub_chempots(se, delu_dict) if delu_dict else se
all_eqns.append(se - Symbol("gamma"))
all_parameters.extend([p for p in list(se.free_symbols)
if p not in all_parameters])
all_parameters.append(Symbol("gamma"))
# Now solve the system of linear eqns to find the chempot
# where the slabs are at equilibrium with each other
soln = linsolve(all_eqns, all_parameters)
if not soln:
warnings.warn("No solution")
return soln
return {p: list(soln)[0][i] for i, p in enumerate(all_parameters)}
[docs] def stable_u_range_dict(self, chempot_range, ref_delu, no_doped=True,
no_clean=False, delu_dict={}, miller_index=(),
dmu_at_0=False, return_se_dict=False):
"""
Creates a dictionary where each entry is a key pointing to a
chemical potential range where the surface of that entry is stable.
Does so by enumerating through all possible solutions (intersect)
for surface energies of a specific facet.
Args:
chempot_range ([max_chempot, min_chempot]): Range to consider the
stability of the slabs.
ref_delu (sympy Symbol): The range stability of each slab is based
on the chempot range of this chempot. Should be a sympy Symbol
object of the format: Symbol("delu_el") where el is the name of
the element
no_doped (bool): Consider stability of clean slabs only.
no_clean (bool): Consider stability of doped slabs only.
delu_dict (Dict): Dictionary of the chemical potentials to be set as
constant. Note the key should be a sympy Symbol object of the
format: Symbol("delu_el") where el is the name of the element.
miller_index (list): Miller index for a specific facet to get a
dictionary for.
dmu_at_0 (bool): If True, if the surface energies corresponding to
the chemical potential range is between a negative and positive
value, the value is a list of three chemical potentials with the
one in the center corresponding a surface energy of 0. Uselful
in identifying unphysical ranges of surface energies and their
chemical potential range.
return_se_dict (bool): Whether or not to return the corresponding
dictionary of surface energies
"""
chempot_range = sorted(chempot_range)
stable_urange_dict, se_dict = {}, {}
# Get all entries for a specific facet
for hkl in self.all_slab_entries.keys():
entries_in_hkl = []
# Skip this facet if this is not the facet we want
if miller_index and hkl != tuple(miller_index):
continue
if not no_clean:
entries_in_hkl.extend([clean for clean in self.all_slab_entries[hkl]])
if not no_doped:
for entry in self.all_slab_entries[hkl]:
entries_in_hkl.extend([ads_entry for ads_entry in
self.all_slab_entries[hkl][entry]])
for entry in entries_in_hkl:
stable_urange_dict[entry] = []
se_dict[entry] = []
# if there is only one entry for this facet, then just give it the
# default urange, you can't make combinations with just 1 item
if len(entries_in_hkl) == 1:
stable_urange_dict[entries_in_hkl[0]] = chempot_range
u1, u2 = delu_dict.copy(), delu_dict.copy()
u1[ref_delu], u2[ref_delu] = chempot_range[0], chempot_range[1]
se = self.as_coeffs_dict[entries_in_hkl[0]]
se_dict[entries_in_hkl[0]] = [sub_chempots(se, u1), sub_chempots(se, u2)]
continue
for pair in itertools.combinations(entries_in_hkl, 2):
# I'm assuming ref_delu was not set in delu_dict,
# so the solution should be for ref_delu
solution = self.get_surface_equilibrium(pair, delu_dict=delu_dict)
# Check if this solution is stable
if not solution:
continue
new_delu_dict = delu_dict.copy()
new_delu_dict[ref_delu] = solution[ref_delu]
stable_entry, gamma = self.get_stable_entry_at_u(hkl, new_delu_dict,
no_doped=no_doped,
no_clean=no_clean)
if stable_entry not in pair:
continue
# Now check if the solution is within the chempot range
if not (chempot_range[0] <= solution[ref_delu] <= chempot_range[1]):
continue
for entry in pair:
stable_urange_dict[entry].append(solution[ref_delu])
se_dict[entry].append(gamma)
# Now check if all entries have 2 chempot values. If only
# one, we need to set the other value as either the upper
# limit or lower limit of the user provided chempot_range
new_delu_dict = delu_dict.copy()
for u in chempot_range:
new_delu_dict[ref_delu] = u
entry, gamma = self.get_stable_entry_at_u(hkl, delu_dict=new_delu_dict,
no_doped=no_doped,
no_clean=no_clean)
stable_urange_dict[entry].append(u)
se_dict[entry].append(gamma)
if dmu_at_0:
for entry in se_dict.keys():
# if se are of opposite sign, determine chempot when se=0.
# Useful for finding a chempot range where se is unphysical
if not stable_urange_dict[entry]:
continue
if se_dict[entry][0] * se_dict[entry][1] < 0:
# solve for gamma=0
se = self.as_coeffs_dict[entry]
se_dict[entry].append(0)
stable_urange_dict[entry].append(solve(sub_chempots(se, delu_dict),
ref_delu)[0])
# sort the chempot ranges for each facet
for entry in stable_urange_dict.keys():
se_dict[entry] = [se for i, se in sorted(zip(stable_urange_dict[entry],
se_dict[entry]))]
stable_urange_dict[entry] = sorted(stable_urange_dict[entry])
if return_se_dict:
return stable_urange_dict, se_dict
else:
return stable_urange_dict
[docs] def color_palette_dict(self, alpha=0.35):
"""
Helper function to assign each facet a unique color using a dictionary.
Args:
alpha (float): Degree of transparency
return (dict): Dictionary of colors (r,g,b,a) when plotting surface
energy stability. The keys are individual surface entries where
clean surfaces have a solid color while the corresponding adsorbed
surface will be transparent.
"""
color_dict = {}
for hkl in self.all_slab_entries.keys():
rgb_indices = [0, 1, 2]
color = [0, 0, 0, 1]
random.shuffle(rgb_indices)
for i, ind in enumerate(rgb_indices):
if i == 2:
break
color[ind] = np.random.uniform(0, 1)
# Get the clean (solid) colors first
clean_list = np.linspace(0, 1, len(self.all_slab_entries[hkl]))
for i, clean in enumerate(self.all_slab_entries[hkl].keys()):
c = copy.copy(color)
c[rgb_indices[2]] = clean_list[i]
color_dict[clean] = c
# Now get the adsorbed (transparent) colors
for ads_entry in self.all_slab_entries[hkl][clean]:
c_ads = copy.copy(c)
c_ads[3] = alpha
color_dict[ads_entry] = c_ads
return color_dict
[docs] def chempot_vs_gamma_plot_one(self, plt, entry, ref_delu, chempot_range,
delu_dict={}, delu_default=0, label='', JPERM2=False):
"""
Helper function to help plot the surface energy of a
single SlabEntry as a function of chemical potential.
Args:
plt (Plot): A plot.
entry (SlabEntry): Entry of the slab whose surface energy we want
to plot
ref_delu (sympy Symbol): The range stability of each slab is based
on the chempot range of this chempot. Should be a sympy Symbol
object of the format: Symbol("delu_el") where el is the name of
the element
chempot_range ([max_chempot, min_chempot]): Range to consider the
stability of the slabs.
delu_dict (Dict): Dictionary of the chemical potentials to be set as
constant. Note the key should be a sympy Symbol object of the
format: Symbol("delu_el") where el is the name of the element.
delu_default (float): Default value for all unset chemical potentials
label (str): Label of the slab for the legend.
JPERM2 (bool): Whether to plot surface energy in /m^2 (True) or
eV/A^2 (False)
Returns:
(Plot): Plot of surface energy vs chemical potential for one entry.
"""
chempot_range = sorted(chempot_range)
# use dashed lines for slabs that are not stoichiometric
# wrt bulk. Label with formula if nonstoichiometric
ucell_comp = self.ucell_entry.composition.reduced_composition
if entry.adsorbates:
s = entry.cleaned_up_slab
clean_comp = s.composition.reduced_composition
else:
clean_comp = entry.composition.reduced_composition
mark = '--' if ucell_comp != clean_comp else '-'
delu_dict = self.set_all_variables(delu_dict, delu_default)
delu_dict[ref_delu] = chempot_range[0]
gamma_min = self.as_coeffs_dict[entry]
gamma_min = gamma_min if type(gamma_min).__name__ == "float" else sub_chempots(gamma_min, delu_dict)
delu_dict[ref_delu] = chempot_range[1]
gamma_max = self.as_coeffs_dict[entry]
gamma_max = gamma_max if type(gamma_max).__name__ == "float" else sub_chempots(gamma_max, delu_dict)
gamma_range = [gamma_min, gamma_max]
se_range = np.array(gamma_range) * EV_PER_ANG2_TO_JOULES_PER_M2 \
if JPERM2 else gamma_range
mark = entry.mark if entry.mark else mark
c = entry.color if entry.color else self.color_dict[entry]
plt.plot(chempot_range, se_range, mark, color=c, label=label)
return plt
[docs] def chempot_vs_gamma(self, ref_delu, chempot_range, miller_index=(),
delu_dict={}, delu_default=0, JPERM2=False,
show_unstable=False, ylim=[], plt=None,
no_clean=False, no_doped=False,
use_entry_labels=False, no_label=False):
"""
Plots the surface energy as a function of chemical potential.
Each facet will be associated with its own distinct colors.
Dashed lines will represent stoichiometries different from that
of the mpid's compound. Transparent lines indicates adsorption.
Args:
ref_delu (sympy Symbol): The range stability of each slab is based
on the chempot range of this chempot. Should be a sympy Symbol
object of the format: Symbol("delu_el") where el is the name of
the element
chempot_range ([max_chempot, min_chempot]): Range to consider the
stability of the slabs.
miller_index (list): Miller index for a specific facet to get a
dictionary for.
delu_dict (Dict): Dictionary of the chemical potentials to be set as
constant. Note the key should be a sympy Symbol object of the
format: Symbol("delu_el") where el is the name of the element.
delu_default (float): Default value for all unset chemical potentials
JPERM2 (bool): Whether to plot surface energy in /m^2 (True) or
eV/A^2 (False)
show_unstable (bool): Whether or not to show parts of the surface
energy plot outside the region of stability.
ylim ([ymax, ymin]): Range of y axis
no_doped (bool): Whether to plot for the clean slabs only.
no_clean (bool): Whether to plot for the doped slabs only.
use_entry_labels (bool): If True, will label each slab configuration
according to their given label in the SlabEntry object.
no_label (bool): Option to turn off labels.
Returns:
(Plot): Plot of surface energy vs chempot for all entries.
"""
chempot_range = sorted(chempot_range)
plt = pretty_plot(width=8, height=7) if not plt else plt
axes = plt.gca()
for hkl in self.all_slab_entries.keys():
if miller_index and hkl != tuple(miller_index):
continue
# Get the chempot range of each surface if we only
# want to show the region where each slab is stable
if not show_unstable:
stable_u_range_dict = self.stable_u_range_dict(chempot_range, ref_delu,
no_doped=no_doped,
delu_dict=delu_dict,
miller_index=hkl)
already_labelled = []
label = ''
for clean_entry in self.all_slab_entries[hkl]:
urange = stable_u_range_dict[clean_entry] if \
not show_unstable else chempot_range
# Don't plot if the slab is unstable, plot if it is.
if urange != []:
label = clean_entry.label
if label in already_labelled:
label = None
else:
already_labelled.append(label)
if not no_clean:
if use_entry_labels:
label = clean_entry.label
if no_label:
label = ""
plt = self.chempot_vs_gamma_plot_one(plt, clean_entry, ref_delu,
urange, delu_dict=delu_dict,
delu_default=delu_default,
label=label, JPERM2=JPERM2)
if not no_doped:
for ads_entry in self.all_slab_entries[hkl][clean_entry]:
# Plot the adsorbed slabs
# Generate a label for the type of slab
urange = stable_u_range_dict[ads_entry] \
if not show_unstable else chempot_range
if urange != []:
if use_entry_labels:
label = ads_entry.label
if no_label:
label = ""
plt = self.chempot_vs_gamma_plot_one(plt, ads_entry,
ref_delu, urange,
delu_dict=delu_dict,
delu_default=delu_default,
label=label,
JPERM2=JPERM2)
# Make the figure look nice
plt.ylabel(r"Surface energy (J/$m^{2}$)") if JPERM2 \
else plt.ylabel(r"Surface energy (eV/$\AA^{2}$)")
plt = self.chempot_plot_addons(plt, chempot_range, str(ref_delu).split("_")[1],
axes, ylim=ylim)
return plt
[docs] def monolayer_vs_BE(self, plot_eads=False):
"""
Plots the binding energy energy as a function of monolayers (ML), i.e.
the fractional area adsorbate density for all facets. For each
facet at a specific monlayer, only plot the lowest binding energy.
Args:
plot_eads (bool): Option to plot the adsorption energy (binding
energy multiplied by number of adsorbates) instead.
Returns:
(Plot): Plot of binding energy vs monolayer for all facets.
"""
plt = pretty_plot(width=8, height=7)
for hkl in self.all_slab_entries.keys():
ml_be_dict = {}
for clean_entry in self.all_slab_entries[hkl].keys():
if self.all_slab_entries[hkl][clean_entry]:
for ads_entry in self.all_slab_entries[hkl][clean_entry]:
if ads_entry.get_monolayer not in ml_be_dict.keys():
ml_be_dict[ads_entry.get_monolayer] = 1000
be = ads_entry.gibbs_binding_energy(eads=plot_eads)
if be < ml_be_dict[ads_entry.get_monolayer]:
ml_be_dict[ads_entry.get_monolayer] = be
# sort the binding energies and monolayers
# in order to properly draw a line plot
vals = sorted(ml_be_dict.items())
monolayers, BEs = zip(*vals)
plt.plot(monolayers, BEs, '-o',
c=self.color_dict[clean_entry], label=hkl)
adsorbates = tuple(ads_entry.ads_entries_dict.keys())
plt.xlabel(" %s" * len(adsorbates) % adsorbates + " Coverage (ML)")
plt.ylabel("Adsorption Energy (eV)") if plot_eads \
else plt.ylabel("Binding Energy (eV)")
plt.legend()
plt.tight_layout()
return plt
[docs] def chempot_plot_addons(self, plt, xrange, ref_el, axes, pad=2.4,
rect=[-0.047, 0, 0.84, 1], ylim=[]):
"""
Helper function to a chempot plot look nicer.
Args:
plt (Plot) Plot to add things to.
xrange (list): xlim parameter
ref_el (str): Element of the referenced chempot.
axes(axes) Axes object from matplotlib
pad (float) For tight layout
rect (list): For tight layout
ylim (ylim parameter):
return (Plot): Modified plot with addons.
return (Plot): Modified plot with addons.
"""
# Make the figure look nice
plt.legend(bbox_to_anchor=(1.01, 1), loc=2, borderaxespad=0.)
axes.set_xlabel(r"Chemical potential $\Delta\mu_{%s}$ (eV)" % (ref_el))
ylim = ylim if ylim else axes.get_ylim()
plt.xticks(rotation=60)
plt.ylim(ylim)
xlim = axes.get_xlim()
plt.xlim(xlim)
plt.tight_layout(pad=pad, rect=rect)
plt.plot([xrange[0], xrange[0]], ylim, '--k')
plt.plot([xrange[1], xrange[1]], ylim, '--k')
xy = [np.mean([xrange[1]]), np.mean(ylim)]
plt.annotate("%s-rich" % (ref_el), xy=xy,
xytext=xy, rotation=90, fontsize=17)
xy = [np.mean([xlim[0]]), np.mean(ylim)]
plt.annotate("%s-poor" % (ref_el), xy=xy,
xytext=xy, rotation=90, fontsize=17)
return plt
[docs] def BE_vs_clean_SE(self, delu_dict, delu_default=0, plot_eads=False,
annotate_monolayer=True, JPERM2=False):
"""
For each facet, plot the clean surface energy against the most
stable binding energy.
Args:
delu_dict (Dict): Dictionary of the chemical potentials to be set as
constant. Note the key should be a sympy Symbol object of the
format: Symbol("delu_el") where el is the name of the element.
delu_default (float): Default value for all unset chemical potentials
plot_eads (bool): Option to plot the adsorption energy (binding
energy multiplied by number of adsorbates) instead.
annotate_monolayer (bool): Whether or not to label each data point
with its monolayer (adsorbate density per unit primiitve area)
JPERM2 (bool): Whether to plot surface energy in /m^2 (True) or
eV/A^2 (False)
Returns:
(Plot): Plot of clean surface energy vs binding energy for
all facets.
"""
plt = pretty_plot(width=8, height=7)
for hkl in self.all_slab_entries.keys():
for clean_entry in self.all_slab_entries[hkl].keys():
all_delu_dict = self.set_all_variables(delu_dict, delu_default)
if self.all_slab_entries[hkl][clean_entry]:
clean_se = self.as_coeffs_dict[clean_entry]
se = sub_chempots(clean_se, all_delu_dict)
for ads_entry in self.all_slab_entries[hkl][clean_entry]:
ml = ads_entry.get_monolayer
be = ads_entry.gibbs_binding_energy(eads=plot_eads)
# Now plot the surface energy vs binding energy
plt.scatter(se, be)
if annotate_monolayer:
plt.annotate("%.2f" % (ml), xy=[se, be],
xytext=[se, be])
plt.xlabel(r"Surface energy ($J/m^2$)") if JPERM2 \
else plt.xlabel(r"Surface energy ($eV/\AA^2$)")
plt.ylabel("Adsorption Energy (eV)") if plot_eads \
else plt.ylabel("Binding Energy (eV)")
plt.tight_layout()
plt.xticks(rotation=60)
return plt
[docs] def surface_chempot_range_map(self, elements, miller_index, ranges,
incr=50, no_doped=False, no_clean=False,
delu_dict=None, plt=None, annotate=True,
show_unphyiscal_only=False, fontsize=10):
"""
Adapted from the get_chempot_range_map() method in the PhaseDiagram
class. Plot the chemical potential range map based on surface
energy stability. Currently works only for 2-component PDs. At
the moment uses a brute force method by enumerating through the
range of the first element chempot with a specified increment
and determines the chempot rangeo fht e second element for each
SlabEntry. Future implementation will determine the chempot range
map first by solving systems of equations up to 3 instead of 2.
Args:
elements (list): 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 duLi and duO, you will supply
[Element("Li"), Element("O")]
miller_index ([h, k, l]): Miller index of the surface we are interested in
ranges ([[range1], [range2]]): List of chempot ranges (max and min values)
for the first and second element.
incr (int): Number of points to sample along the range of the first chempot
no_doped (bool): Whether or not to include doped systems.
no_clean (bool): Whether or not to include clean systems.
delu_dict (Dict): Dictionary of the chemical potentials to be set as
constant. Note the key should be a sympy Symbol object of the
format: Symbol("delu_el") where el is the name of the element.
annotate (bool): Whether to annotate each "phase" with the label of
the entry. If no label, uses the reduced formula
show_unphyiscal_only (bool): Whether to only show the shaded region where
surface energy is negative. Useful for drawing other chempot range maps.
"""
# Set up
delu_dict = delu_dict if delu_dict else {}
plt = pretty_plot(12, 8) if not plt else plt
el1, el2 = str(elements[0]), str(elements[1])
delu1 = Symbol("delu_%s" % (str(elements[0])))
delu2 = Symbol("delu_%s" % (str(elements[1])))
range1 = ranges[0]
range2 = ranges[1]
# Find a range map for each entry (surface). This part is very slow, will
# need to implement a more sophisticated method of getting the range map
vertices_dict = {}
for dmu1 in np.linspace(range1[0], range1[1], incr):
# Get chemical potential range of dmu2 for each increment of dmu1
new_delu_dict = delu_dict.copy()
new_delu_dict[delu1] = dmu1
range_dict, se_dict = self.stable_u_range_dict(range2, delu2, dmu_at_0=True,
miller_index=miller_index,
no_doped=no_doped,
no_clean=no_clean,
delu_dict=new_delu_dict,
return_se_dict=True)
# Save the chempot range for dmu1 and dmu2
for entry in range_dict.keys():
if not range_dict[entry]:
continue
if entry not in vertices_dict.keys():
vertices_dict[entry] = []
selist = se_dict[entry]
vertices_dict[entry].append({delu1: dmu1, delu2: [range_dict[entry], selist]})
# Plot the edges of the phases
for entry in vertices_dict.keys():
xvals, yvals = [], []
# Plot each edge of a phase within the borders
for ii, pt1 in enumerate(vertices_dict[entry]):
# Determine if the surface energy at this lower range
# of dmu2 is negative. If so, shade this region.
if len(pt1[delu2][1]) == 3:
if pt1[delu2][1][0] < 0:
neg_dmu_range = [pt1[delu2][0][0], pt1[delu2][0][1]]
else:
neg_dmu_range = [pt1[delu2][0][1], pt1[delu2][0][2]]
# Shade the threshold and region at which se<=0
plt.plot([pt1[delu1], pt1[delu1]], neg_dmu_range, 'k--')
elif pt1[delu2][1][0] < 0 and pt1[delu2][1][1] < 0:
# Any chempot at at this point will result
# in se<0, shade the entire y range
if not show_unphyiscal_only:
plt.plot([pt1[delu1], pt1[delu1]], range2, 'k--')
if ii == len(vertices_dict[entry]) - 1:
break
pt2 = vertices_dict[entry][ii + 1]
if not show_unphyiscal_only:
plt.plot([pt1[delu1], pt2[delu1]], [pt1[delu2][0][0], pt2[delu2][0][0]], 'k')
# Need these values to get a good position for labelling phases
xvals.extend([pt1[delu1], pt2[delu1]])
yvals.extend([pt1[delu2][0][0], pt2[delu2][0][0]])
# Plot the edge along the max x value
pt = vertices_dict[entry][-1]
delu1, delu2 = pt.keys()
xvals.extend([pt[delu1], pt[delu1]])
yvals.extend(pt[delu2][0])
if not show_unphyiscal_only:
plt.plot([pt[delu1], pt[delu1]], [pt[delu2][0][0], pt[delu2][0][-1]], 'k')
if annotate:
# Label the phases
x = np.mean([max(xvals), min(xvals)])
y = np.mean([max(yvals), min(yvals)])
label = entry.label if entry.label else entry.composition.reduced_formula
plt.annotate(label, xy=[x, y], xytext=[x, y], fontsize=fontsize)
# Label plot
plt.xlim(range1)
plt.ylim(range2)
plt.xlabel(r"$\Delta\mu_{%s} (eV)$" % (el1), fontsize=25)
plt.ylabel(r"$\Delta\mu_{%s} (eV)$" % (el2), fontsize=25)
plt.xticks(rotation=60)
return plt
[docs] def set_all_variables(self, delu_dict, delu_default):
"""
Sets all chemical potential values and returns a dictionary where
the key is a sympy Symbol and the value is a float (chempot).
Args:
entry (SlabEntry): Computed structure entry of the slab
delu_dict (Dict): Dictionary of the chemical potentials to be set as
constant. Note the key should be a sympy Symbol object of the
format: Symbol("delu_el") where el is the name of the element.
delu_default (float): Default value for all unset chemical potentials
Returns:
Dictionary of set chemical potential values
"""
# Set up the variables
all_delu_dict = {}
for du in self.list_of_chempots:
if delu_dict and du in delu_dict.keys():
all_delu_dict[du] = delu_dict[du]
elif du == 1:
all_delu_dict[du] = du
else:
all_delu_dict[du] = delu_default
return all_delu_dict
# def surface_phase_diagram(self, y_param, x_param, miller_index):
# return
#
# def wulff_shape_extrapolated_model(self):
# return
#
# def surface_pourbaix_diagram(self):
#
# return
#
# def surface_p_vs_t_phase_diagram(self):
#
# return
#
# def broken_bond_vs_gamma(self):
#
# return
[docs]def entry_dict_from_list(all_slab_entries):
"""
Converts a list of SlabEntry to an appropriate dictionary. It is
assumed that if there is no adsorbate, then it is a clean SlabEntry
and that adsorbed SlabEntry has the clean_entry parameter set.
Args:
all_slab_entries (list): List of SlabEntry objects
Returns:
(dict): Dictionary of SlabEntry with the Miller index as the main
key to a dictionary with a clean SlabEntry as the key to a
list of adsorbed SlabEntry.
"""
entry_dict = {}
for entry in all_slab_entries:
hkl = tuple(entry.miller_index)
if hkl not in entry_dict.keys():
entry_dict[hkl] = {}
if entry.clean_entry:
clean = entry.clean_entry
else:
clean = entry
if clean not in entry_dict[hkl].keys():
entry_dict[hkl][clean] = []
if entry.adsorbates:
entry_dict[hkl][clean].append(entry)
return entry_dict
[docs]class WorkFunctionAnalyzer:
"""
A class used for calculating the work function
from a slab model and visualizing the behavior
of the local potential along the slab.
.. attribute:: efermi
The Fermi energy
.. attribute:: locpot_along_c
Local potential in eV along points along the axis
.. attribute:: vacuum_locpot
The maximum local potential along the c direction for
the slab model, ie the potential at the vacuum
.. attribute:: work_function
The minimum energy needed to move an electron from the
surface to infinity. Defined as the difference between
the potential at the vacuum and the Fermi energy.
.. attribute:: slab
The slab structure model
.. attribute:: along_c
Points along the c direction with same
increments as the locpot in the c axis
.. attribute:: ave_locpot
Mean of the minimum and maximmum (vacuum) locpot along c
.. attribute:: sorted_sites
List of sites from the slab sorted along the c direction
.. attribute:: ave_bulk_p
The average locpot of the slab region along the c direction
"""
def __init__(self, structure, locpot_along_c, efermi, shift=0, blength=3.5):
"""
Initializes the WorkFunctionAnalyzer class.
Args:
structure (Structure): Structure object modelling the surface
locpot_along_c (list): Local potential along the c direction
outcar (MSONable): Outcar vasp output object
shift (float): Parameter to translate the slab (and
therefore the vacuum) of the slab structure, thereby
translating the plot along the x axis.
blength (float (Ang)): The longest bond length in the material.
Used to handle pbc for noncontiguous slab layers
"""
# ensure shift between 0 and 1
if shift < 0:
shift += -1 * int(shift) + 1
elif shift >= 1:
shift -= int(shift)
self.shift = shift
# properties that can be shifted
slab = structure.copy()
slab.translate_sites([i for i, site in enumerate(slab)], [0, 0, self.shift])
self.slab = slab
self.sorted_sites = sorted(self.slab, key=lambda site: site.frac_coords[2])
# Get the plot points between 0 and c
# increments of the number of locpot points
self.along_c = np.linspace(0, 1, num=len(locpot_along_c))
# Get the plot points between 0 and c
# increments of the number of locpot points
locpot_along_c_mid, locpot_end, locpot_start = [], [], []
for i, s in enumerate(self.along_c):
j = s + self.shift
if j > 1:
locpot_start.append(locpot_along_c[i])
elif j < 0:
locpot_end.append(locpot_along_c[i])
else:
locpot_along_c_mid.append(locpot_along_c[i])
self.locpot_along_c = locpot_start + locpot_along_c_mid + locpot_end
# identify slab region
self.slab_regions = get_slab_regions(self.slab, blength=blength)
# get the average of the signal in the bulk-like region of the
# slab, i.e. the average of the oscillating region. This gives
# a rough appr. of the potential in the interior of the slab
bulk_p = []
for r in self.slab_regions:
bulk_p.extend([p for i, p in enumerate(self.locpot_along_c) if r[1] >= self.along_c[i] > r[0]])
if len(self.slab_regions) > 1:
bulk_p.extend([p for i, p in enumerate(self.locpot_along_c) if self.slab_regions[1][1] <= self.along_c[i]])
bulk_p.extend([p for i, p in enumerate(self.locpot_along_c) if self.slab_regions[0][0] >= self.along_c[i]])
self.ave_bulk_p = np.mean(bulk_p)
# shift independent quantities
self.efermi = efermi
self.vacuum_locpot = max(self.locpot_along_c)
# get the work function
self.work_function = self.vacuum_locpot - self.efermi
# for setting ylim and annotating
self.ave_locpot = (self.vacuum_locpot - min(self.locpot_along_c)) / 2
[docs] def get_locpot_along_slab_plot(self, label_energies=True,
plt=None, label_fontsize=10):
"""
Returns a plot of the local potential (eV) vs the
position along the c axis of the slab model (Ang)
Args:
label_energies (bool): Whether to label relevant energy
quantities such as the work function, Fermi energy,
vacuum locpot, bulk-like locpot
plt (plt): Matplotlib pylab object
label_fontsize (float): Fontsize of labels
Returns plt of the locpot vs c axis
"""
plt = pretty_plot(width=6, height=4) if not plt else plt
# plot the raw locpot signal along c
plt.plot(self.along_c, self.locpot_along_c, 'b--')
# Get the local averaged signal of the locpot along c
xg, yg = [], []
for i, p in enumerate(self.locpot_along_c):
# average signal is just the bulk-like potential when in the slab region
in_slab = False
for r in self.slab_regions:
if r[0] <= self.along_c[i] <= r[1]:
in_slab = True
if len(self.slab_regions) > 1:
if self.along_c[i] >= self.slab_regions[1][1]:
in_slab = True
if self.along_c[i] <= self.slab_regions[0][0]:
in_slab = True
if in_slab:
yg.append(self.ave_bulk_p)
xg.append(self.along_c[i])
elif p < self.ave_bulk_p:
yg.append(self.ave_bulk_p)
xg.append(self.along_c[i])
else:
yg.append(p)
xg.append(self.along_c[i])
xg, yg = zip(*sorted(zip(xg, yg)))
plt.plot(xg, yg, 'r', linewidth=2.5, zorder=-1)
# make it look nice
if label_energies:
plt = self.get_labels(plt, label_fontsize=label_fontsize)
plt.xlim([0, 1])
plt.ylim([min(self.locpot_along_c),
self.vacuum_locpot + self.ave_locpot * 0.2])
plt.xlabel(r"Fractional coordinates ($\hat{c}$)", fontsize=25)
plt.xticks(fontsize=15, rotation=45)
plt.ylabel(r"Potential (eV)", fontsize=25)
plt.yticks(fontsize=15)
return plt
[docs] def get_labels(self, plt, label_fontsize=10):
"""
Handles the optional labelling of the plot with relevant quantities
Args:
plt (plt): Plot of the locpot vs c axis
label_fontsize (float): Fontsize of labels
Returns Labelled plt
"""
# center of vacuum and bulk region
if len(self.slab_regions) > 1:
label_in_vac = (self.slab_regions[0][1] + self.slab_regions[1][0]) / 2
if abs(self.slab_regions[0][0] - self.slab_regions[0][1]) > \
abs(self.slab_regions[1][0] - self.slab_regions[1][1]):
label_in_bulk = self.slab_regions[0][1] / 2
else:
label_in_bulk = (self.slab_regions[1][1] + self.slab_regions[1][0]) / 2
else:
label_in_bulk = (self.slab_regions[0][0] + self.slab_regions[0][1]) / 2
if self.slab_regions[0][0] > 1 - self.slab_regions[0][1]:
label_in_vac = self.slab_regions[0][0] / 2
else:
label_in_vac = (1 + self.slab_regions[0][1]) / 2
plt.plot([0, 1], [self.vacuum_locpot] * 2, 'b--', zorder=-5, linewidth=1)
xy = [label_in_bulk, self.vacuum_locpot + self.ave_locpot * 0.05]
plt.annotate(r"$V_{vac}=%.2f$" % (self.vacuum_locpot), xy=xy,
xytext=xy, color='b', fontsize=label_fontsize)
# label the fermi energy
plt.plot([0, 1], [self.efermi] * 2, 'g--',
zorder=-5, linewidth=3)
xy = [label_in_bulk, self.efermi + self.ave_locpot * 0.05]
plt.annotate(r"$E_F=%.2f$" % (self.efermi), xytext=xy,
xy=xy, fontsize=label_fontsize, color='g')
# label the bulk-like locpot
plt.plot([0, 1], [self.ave_bulk_p] * 2, 'r--', linewidth=1., zorder=-1)
xy = [label_in_vac, self.ave_bulk_p + self.ave_locpot * 0.05]
plt.annotate(r"$V^{interior}_{slab}=%.2f$" % (self.ave_bulk_p),
xy=xy, xytext=xy, color='r', fontsize=label_fontsize)
# label the work function as a barrier
plt.plot([label_in_vac] * 2, [self.efermi, self.vacuum_locpot],
'k--', zorder=-5, linewidth=2)
xy = [label_in_vac, self.efermi + self.ave_locpot * 0.05]
plt.annotate(r"$\Phi=%.2f$" % (self.work_function),
xy=xy, xytext=xy, fontsize=label_fontsize)
return plt
[docs] def is_converged(self, min_points_frac=0.015, tol=0.0025):
"""
A well converged work function should have a flat electrostatic
potential within some distance (min_point) about where the peak
electrostatic potential is found along the c direction of the
slab. This is dependent on the size of the slab.
Args:
min_point (fractional coordinates): The number of data points
+/- the point of where the electrostatic potential is at
its peak along the c direction.
tol (float): If the electrostatic potential stays the same
within this tolerance, within the min_points, it is converged.
Returns a bool (whether or not the work function is converged)
"""
conv_within = tol * (max(self.locpot_along_c) - min(self.locpot_along_c))
min_points = int(min_points_frac * len(self.locpot_along_c))
peak_i = self.locpot_along_c.index(self.vacuum_locpot)
all_flat = []
for i in range(len(self.along_c)):
if peak_i - min_points < i < peak_i + min_points:
if abs(self.vacuum_locpot - self.locpot_along_c[i]) > conv_within:
all_flat.append(False)
else:
all_flat.append(True)
return all(all_flat)
[docs] @staticmethod
def from_files(poscar_filename, locpot_filename, outcar_filename, shift=0, blength=3.5):
"""
:param poscar_filename: POSCAR file
:param locpot_filename: LOCPOT file
:param outcar_filename: OUTCAR file
:param shift: shift
:param blength: The longest bond length in the material.
Used to handle pbc for noncontiguous slab layers
:return: WorkFunctionAnalyzer
"""
p = Poscar.from_file(poscar_filename)
l = Locpot.from_file(locpot_filename)
o = Outcar(outcar_filename)
return WorkFunctionAnalyzer(p.structure, l.get_average_along_axis(2),
o.efermi, shift=shift, blength=blength)
[docs]class NanoscaleStability:
"""
A class for analyzing the stability of nanoparticles of different
polymorphs with respect to size. The Wulff shape will be the
model for the nanoparticle. Stability will be determined by
an energetic competition between the weighted surface energy
(surface energy of the Wulff shape) and the bulk energy. A
future release will include a 2D phase diagram (e.g. wrt size
vs chempot for adsorbed or nonstoichiometric surfaces). Based
on the following work:
Kang, S., Mo, Y., Ong, S. P., & Ceder, G. (2014). Nanoscale
stabilization of sodium oxides: Implications for Na-O2
batteries. Nano Letters, 14(2), 1016–1020.
https://doi.org/10.1021/nl404557w
.. attribute:: se_analyzers
List of SurfaceEnergyPlotter objects. Each item corresponds to a
different polymorph.
.. attribute:: symprec
See WulffShape.
"""
def __init__(self, se_analyzers, symprec=1e-5):
"""
Analyzes the nanoscale stability of different polymorphs.
"""
self.se_analyzers = se_analyzers
self.symprec = symprec
[docs] def solve_equilibrium_point(self, analyzer1, analyzer2,
delu_dict={}, delu_default=0, units="nanometers"):
"""
Gives the radial size of two particles where equilibrium is reached
between both particles. NOTE: the solution here is not the same
as the solution visualized in the plot because solving for r
requires that both the total surface area and volume of the
particles are functions of r.
Args:
analyzer1 (SurfaceEnergyPlotter): Analyzer associated with the
first polymorph
analyzer2 (SurfaceEnergyPlotter): Analyzer associated with the
second polymorph
delu_dict (Dict): Dictionary of the chemical potentials to be set as
constant. Note the key should be a sympy Symbol object of the
format: Symbol("delu_el") where el is the name of the element.
delu_default (float): Default value for all unset chemical potentials
units (str): Can be nanometers or Angstrom
Returns:
Particle radius in nm
"""
# Set up
wulff1 = analyzer1.wulff_from_chempot(delu_dict=delu_dict,
delu_default=delu_default,
symprec=self.symprec)
wulff2 = analyzer2.wulff_from_chempot(delu_dict=delu_dict,
delu_default=delu_default,
symprec=self.symprec)
# Now calculate r
delta_gamma = wulff1.weighted_surface_energy - wulff2.weighted_surface_energy
delta_E = self.bulk_gform(analyzer1.ucell_entry) - self.bulk_gform(analyzer2.ucell_entry)
r = ((-3 * delta_gamma) / (delta_E))
return r / 10 if units == "nanometers" else r
[docs] def scaled_wulff(self, wulffshape, r):
"""
Scales the Wulff shape with an effective radius r. Note that the resulting
Wulff does not neccesarily have the same effective radius as the one
provided. The Wulff shape is scaled by its surface energies where first
the surface energies are scale by the minimum surface energy and then
multiplied by the given effective radius.
Args:
wulffshape (WulffShape): Initial, unscaled WulffShape
r (float): Arbitrary effective radius of the WulffShape
Returns:
WulffShape (scaled by r)
"""
# get the scaling ratio for the energies
r_ratio = r / wulffshape.effective_radius
miller_list = wulffshape.miller_energy_dict.keys()
# Normalize the magnitude of the facet normal vectors
# of the Wulff shape by the minimum surface energy.
se_list = np.array(list(wulffshape.miller_energy_dict.values()))
# Scale the magnitudes by r_ratio
scaled_se = se_list * r_ratio
return WulffShape(wulffshape.lattice, miller_list,
scaled_se, symprec=self.symprec)
[docs] def plot_one_stability_map(self, analyzer, max_r, delu_dict=None, label="",
increments=50, delu_default=0, plt=None,
from_sphere_area=False, e_units="keV",
r_units="nanometers", normalize=False,
scale_per_atom=False):
"""
Returns the plot of the formation energy of a particle against its
effect radius
Args:
analyzer (SurfaceEnergyPlotter): Analyzer associated with the
first polymorph
max_r (float): The maximum radius of the particle to plot up to.
delu_dict (Dict): Dictionary of the chemical potentials to be set as
constant. Note the key should be a sympy Symbol object of the
format: Symbol("delu_el") where el is the name of the element.
label (str): Label of the plot for legend
increments (int): Number of plot points
delu_default (float): Default value for all unset chemical potentials
plt (pylab): Plot
from_sphere_area (bool): There are two ways to calculate the bulk
formation energy. Either by treating the volume and thus surface
area of the particle as a perfect sphere, or as a Wulff shape.
r_units (str): Can be nanometers or Angstrom
e_units (str): Can be keV or eV
normalize (str): Whether or not to normalize energy by volume
"""
plt = plt if plt else pretty_plot(width=8, height=7)
wulffshape = analyzer.wulff_from_chempot(delu_dict=delu_dict,
delu_default=delu_default,
symprec=self.symprec)
gform_list, r_list = [], []
for r in np.linspace(1e-6, max_r, increments):
gform, r = self.wulff_gform_and_r(wulffshape, analyzer.ucell_entry,
r, from_sphere_area=from_sphere_area,
r_units=r_units, e_units=e_units,
normalize=normalize,
scale_per_atom=scale_per_atom)
gform_list.append(gform)
r_list.append(r)
ru = "nm" if r_units == "nanometers" else r"\AA"
plt.xlabel(r"Particle radius ($%s$)" % (ru))
eu = "$%s/%s^3$" % (e_units, ru)
plt.ylabel(r"$G_{form}$ (%s)" % (eu))
plt.plot(r_list, gform_list, label=label)
return plt
[docs] def plot_all_stability_map(self, max_r, increments=50, delu_dict=None,
delu_default=0, plt=None, labels=None,
from_sphere_area=False, e_units="keV",
r_units="nanometers", normalize=False,
scale_per_atom=False):
"""
Returns the plot of the formation energy of a particles
of different polymorphs against its effect radius
Args:
max_r (float): The maximum radius of the particle to plot up to.
increments (int): Number of plot points
delu_dict (Dict): Dictionary of the chemical potentials to be set as
constant. Note the key should be a sympy Symbol object of the
format: Symbol("delu_el") where el is the name of the element.
delu_default (float): Default value for all unset chemical potentials
plt (pylab): Plot
labels (list): List of labels for each plot, corresponds to the
list of se_analyzers
from_sphere_area (bool): There are two ways to calculate the bulk
formation energy. Either by treating the volume and thus surface
area of the particle as a perfect sphere, or as a Wulff shape.
"""
plt = plt if plt else pretty_plot(width=8, height=7)
for i, analyzer in enumerate(self.se_analyzers):
label = labels[i] if labels else ""
plt = self.plot_one_stability_map(analyzer, max_r, delu_dict,
label=label, plt=plt,
increments=increments,
delu_default=delu_default,
from_sphere_area=from_sphere_area,
e_units=e_units, r_units=r_units,
normalize=normalize,
scale_per_atom=scale_per_atom)
return plt
# class GetChempotRange:
# def __init__(self, entry):
# self.entry = entry
#
#
# class SlabEntryGenerator:
# def __init__(self, entry):
# self.entry = entry
[docs]def sub_chempots(gamma_dict, chempots):
"""
Uses dot product of numpy array to sub chemical potentials
into the surface grand potential. This is much faster
than using the subs function in sympy.
Args:
gamma_dict (dict): Surface grand potential equation
as a coefficient dictionary
chempots (dict): Dictionary assigning each chemical
potential (key) in gamma a value
Returns:
Surface energy as a float
"""
coeffs = [gamma_dict[k] for k in gamma_dict.keys()]
chempot_vals = []
for k in gamma_dict.keys():
if k not in chempots.keys():
chempot_vals.append(k)
elif k == 1:
chempot_vals.append(1)
else:
chempot_vals.append(chempots[k])
return np.dot(coeffs, chempot_vals)