# pymatgen.analysis.pourbaix_diagram module¶

This module is intended to be used to compute Pourbaix diagrams of arbitrary compositions and formation energies. If you use this module in your work, please consider citing the following:

General formalism for solid-aqueous equilibria from DFT:

Decomposition maps, or Pourbaix hull diagrams

Singh et al., DOI: 10.1021/acs.chemmater.7b03980

Fast computation of many-element Pourbaix diagrams:

Patel et al., https://arxiv.org/abs/1909.00035 (submitted)

class IonEntry(ion, energy, name=None, attribute=None)[source]

Object similar to PDEntry, but contains an Ion object instead of a Composition object.

name[source]

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.

Parameters
• ion – Ion object

• energy – Energy for composition.

• name – Optional parameter to name the entry. Defaults to the chemical formula.

as_dict()[source]

Creates a dict of composition, energy, and ion name

classmethod from_dict(d)[source]

Returns an IonEntry object from a dict.

class MultiEntry(entry_list, weights=None)[source]

PourbaixEntry-like object for constructing multi-elemental Pourbaix diagrams.

Initializes a MultiEntry.

Parameters
• entry_list ([PourbaixEntry]) – List of component PourbaixEntries

• weights ([float]) – Weights associated with each entry. Default is None

as_dict()[source]

Returns: MSONable dict

classmethod from_dict(d)[source]
Parameters

() (d) – Dict representation

Returns

MultiEntry

property name[source]

MultiEntry name, i. e. the name of each entry joined by ‘ + ‘

class PourbaixDiagram(entries, comp_dict=None, conc_dict=None, filter_solids=False, nproc=None)[source]

Bases: monty.json.MSONable

Class to create a Pourbaix diagram from entries

Parameters
• entries ([PourbaixEntry] or [MultiEntry]) – Entries list containing Solids and Ions or a list of MultiEntries

• ({str (conc_dict) – float}): Dictionary of compositions, defaults to equal parts of each elements

• ({str – float}): Dictionary of ion concentrations, defaults to 1e-6 for each element

• filter_solids (bool) – applying this filter to a pourbaix diagram ensures all included phases are filtered by stability on the compositional phase diagram. This breaks some of the functionality of the analysis, though, so use with caution.

• nproc (int) – number of processes to generate multientries with in parallel. Defaults to None (serial processing)

property all_entries[source]

Return all entries used to generate the pourbaix diagram

as_dict(include_unprocessed_entries=False)[source]
Parameters

() (include_unprocessed_entries) – Whether to include unprocessed entries.

Returns

MSONable dict.

find_stable_entry(pH, V)[source]

Finds stable entry at a pH,V condition :param pH: pH to find stable entry :type pH: float :param V: V to find stable entry :type V: float

Returns:

classmethod from_dict(d)[source]
Parameters

() (d) – Dict representation.

Returns

PourbaixDiagram

get_decomposition_energy(entry, pH, V)[source]

Finds decomposition to most stable entries in eV/atom, supports vectorized inputs for pH and V

Parameters
• entry (PourbaixEntry) – PourbaixEntry corresponding to compound to find the decomposition for

• pH (float, [float]) – pH at which to find the decomposition

• V (float, [float]) – voltage at which to find the decomposition

Returns

Decomposition energy for the entry, i. e. the energy above

the “pourbaix hull” in eV/atom at the given conditions

get_hull_energy(pH, V)[source]

Gets the minimum energy of the pourbaix “basin” that is formed from the stable pourbaix planes. Vectorized.

Parameters
• pH (float or [float]) – pH at which to find the hull energy

• V (float or [float]) – V at which to find the hull energy

Returns

(float or [float]) minimum pourbaix energy at conditions

static get_pourbaix_domains(pourbaix_entries, limits=None)[source]

Returns a set of pourbaix stable domains (i. e. polygons) in pH-V space from a list of pourbaix_entries

This function works by using scipy’s HalfspaceIntersection function to construct all of the 2-D polygons that form the boundaries of the planes corresponding to individual entry gibbs free energies as a function of pH and V. Hyperplanes of the form a*pH + b*V + 1 - g(0, 0) are constructed and supplied to HalfspaceIntersection, which then finds the boundaries of each pourbaix region using the intersection points.

Parameters
• pourbaix_entries ([PourbaixEntry]) – Pourbaix entries with which to construct stable pourbaix domains

• limits ([[float]]) – limits in which to do the pourbaix analysis

Returns

[boundary_points]}. The list of boundary points are the sides of the N-1 dim polytope bounding the allowable ph-V range of each entry.

Return type

Returns a dict of the form {entry

get_stable_entry(pH, V)[source]

Gets the stable entry at a given pH, V condition

Parameters
• pH (float) – pH at a given condition

• V (float) – V at a given condition

Returns

pourbaix or multi-entry

corresponding ot the minimum energy entry at a given pH, V condition

Return type
static process_multientry(entry_list, prod_comp, coeff_threshold=0.0001)[source]

Static method for finding a multientry based on a list of entries and a product composition. Essentially checks to see if a valid aqueous reaction exists between the entries and the product composition and returns a MultiEntry with weights according to the coefficients if so.

Parameters
• entry_list ([Entry]) – list of entries from which to create a MultiEntry

• prod_comp (Composition) – composition constraint for setting weights of MultiEntry

• coeff_threshold (float) – threshold of stoichiometric coefficients to filter, if weights are lower than this value, the entry is not returned

property stable_entries[source]

Returns the stable entries in the Pourbaix diagram.

property unprocessed_entries[source]

Return unprocessed entries

property unstable_entries[source]

Returns all unstable entries in the Pourbaix diagram

class PourbaixEntry(entry, entry_id=None, concentration=1e-06)[source]

Bases: monty.json.MSONable

An object encompassing all data relevant to a solid or ion in a pourbaix diagram. Each bulk solid/ion has an energy g of the form: e = e0 + 0.0591 log10(conc) - nO mu_H2O + (nH - 2nO) pH + phi (-nH + 2nO + q)

Note that the energies corresponding to the input entries should be formation energies with respect to hydrogen and oxygen gas in order for the pourbaix diagram formalism to work. This may be changed to be more flexible in the future.

Parameters
• entry (ComputedEntry/ComputedStructureEntry/PDEntry/IonEntry) – An entry object

• () (concentration) –

• ()

as_dict()[source]

Returns dict which contains Pourbaix Entry data. Note that the pH, voltage, H2O factors are always calculated when constructing a PourbaixEntry object.

property composition[source]

Returns composition

property conc_term[source]

Returns the concentration contribution to the free energy, and should only be present when there are ions in the entry

property energy[source]

returns energy

Returns (float): total energy of the pourbaix

entry (at pH, V = 0 vs. SHE)

energy_at_conditions(pH, V)[source]

Get free energy for a given pH and V

Parameters
• pH (float) – pH at which to evaluate free energy

• V (float) – voltage at which to evaluate free energy

Returns

free energy at conditions

property energy_per_atom[source]

energy per atom of the pourbaix entry

Returns (float): energy per atom

classmethod from_dict(d)[source]

Invokes

get_element_fraction(element)[source]

Gets the elemental fraction of a given non-OH element

Parameters

element (Element or str) – string or element corresponding to element to get from composition

Returns

fraction of element / sum(all non-OH elements)

property nH2O[source]

Number of H2O.

Type

Returns

property nPhi[source]

Number of H2O.

Type

Returns

property name[source]

Name for entry

Type

Returns

property normalization_factor[source]

Sum of number of atoms minus the number of H and O in composition

property normalized_energy[source]

Returns: energy normalized by number of non H or O atoms, e. g. for Zn2O6, energy / 2 or for AgTe3(OH)3, energy / 4

normalized_energy_at_conditions(pH, V)[source]

Energy at an electrochemical condition, compatible with numpy arrays for pH/V input

Parameters
• pH (float) – pH at condition

• V (float) – applied potential at condition

Returns

energy normalized by number of non-O/H atoms at condition

property npH[source]

Returns:

property num_atoms[source]

Return number of atoms in current formula. Useful for normalization

class PourbaixPlotter(pourbaix_diagram)[source]

Bases: object

A plotter class for phase diagrams.

Parameters

pourbaix_diagram (PourbaixDiagram) – A PourbaixDiagram object.

domain_vertices(entry)[source]

Returns the vertices of the Pourbaix domain.

Parameters

entry – Entry for which domain vertices are desired

Returns

list of vertices

get_pourbaix_plot(limits=None, title='', label_domains=True, plt=None)[source]

Plot Pourbaix diagram.

Parameters
• limits – 2D list containing limits of the Pourbaix diagram of the form [[xlo, xhi], [ylo, yhi]]

• title (str) – Title to display on plot

• label_domains (bool) – whether to label pourbaix domains

• plt (pyplot) – Pyplot instance for plotting

Returns

plt (pyplot) - matplotlib plot object with pourbaix diagram

plot_entry_stability(entry, pH_range=None, pH_resolution=100, V_range=None, V_resolution=100, e_hull_max=1, cmap='RdYlBu_r', **kwargs)[source]
Parameters
• () (**kwargs) –

• ()

• ()

• ()

• ()

• ()

• ()

• ()

Returns:

show(*args, **kwargs)[source]

Shows the pourbaix plot

Parameters
• *args – args to get_pourbaix_plot

• **kwargs – kwargs to get_pourbaix_plot

Returns

None

generate_entry_label(entry)[source]

Generates a label for the pourbaix plotter

Parameters

entry (PourbaixEntry or MultiEntry) – entry to get a label for

ion_or_solid_comp_object(formula)[source]

Returns either an ion object or composition object given a formula.

Parameters

formula – String formula. Eg. of ion: NaOH(aq), Na[+]; Eg. of solid: Fe2O3(s), Fe(s), Na2O

Returns

Composition/Ion object

latexify_ion(formula)[source]

Convert a formula to latex format.

Parameters

formula (str) – Formula

Returns

Latex string.