Aqueous Stability (Pourbaix)

How aqueous stability (Pourbaix) diagrams are calculated and plotted on the Materials Project (MP) website.

If using Pourbaix functionality for scientific research, please make sure to consult the original peer-reviewed publication and the section below.

Introduction

A Pourbaix diagram, also frequently called a potential-pH diagram, or E-pH diagram, is a representation of aqueous phase electrochemical equilibria. It is a two-dimensional representation of a three-dimensional free energy-pH-potential diagram. In other words, it shows water-stable phases as a function of pH and potential, where, potential is defined with respect to the standard hydrogen electrode.

Experimentally determining Pourbaix Diagrams is painstaking work, as we need not only the free energy of aqueous ions, but also that of all solid phases that a system can exist in. The Materials Project offers a very convenient and powerful database of materials properties which has been used to generate Pourbaix diagrams in a high-throughput manner.

This manual outlines the usage of the Pourbaix App to calculate Pourbaix diagrams, and the thermodynamic formalism underlying the app.

Thermodynamic Formalism of Pourbaix Diagrams

To calculate a Pourbaix diagram, free energies of the solid phases, and of the aqueous ions are required. Calculating free energies of ions is tricky, and time-consuming. To overcome this problem, a methodology utilizing experimentally measured free energies of aqueous ions and the calculated DFT energies for solid phases available in the Materials Project was developed.[] Note that the correction scheme described below is applied over and above any compatibilities/corrections which are applied to the species.

Referencing Energies of Aqueous Ions

Briefly, for each ion, a reference solid is chosen, and the correction term is calculated for the ion as the energy difference between the experimental and the DFT calculated energies of the reference solid. The basic idea behind this scheme is that, if we have a reference energy for an aqueous ion which reproduces the correct dissolution for one solid, then accurate DFT solid-solid energy differences ensure that all other solids dissolve accurately with respect to that ion. The better the solid is represented by DFT, the more transferable the reference aqueous energy becomes. We therefore prefer to choose simple chemical systems (primarily binaries with an uncomplicated electronic structure) as representative solids.

For an aqueous ion i at standard state conditions (e.g., room temperature, atmospheric pressure, and 10^−6 M concentration) using a representative solid s, we define the chemical potential as:

Figure 1 shows this schematically.

Correction for Water

In an aqueous environment, many chemical and electrochemical reactions are enabled by the breakdown, formation, or incorporation of water molecules. It is therefore important that the free energy of formation of water is captured accurately. This is known accurately from experiments as −2.46 eV. So, at standard state, the free energy of formation of water is set as follows:

Correction for Elemental Gaseous, and Liquid States, except H2

For all gaseous elements, the experimentally determined entropic contribution at 298 K is added to the DFT/corrected energy of the element as follows:

This is implemented for the following elements: O2, F2, Cl2, Br2, Hg

Correction for H2

In an aqueous environment, O2 and H2 in their gaseous states are in equilibrium with water through the reaction

Hence, the hydrogen energy is corrected such that the experimental free energy of formation of H2O is reproduced.

Electrochemical Stability of Metastable Materials

Using the Computational Pourbaix App

The Pourbaix app is capable of plotting elemental, and multi-element Pourbaix diagrams. To construct an Elemental Pourbaix diagram, enter the element of choice, and click on the Generate button.

To generate a multi-elemental Pourbaix diagram, choose the desired multiple elements from the periodic table, and click the Generate button. Note that oxygen and hydrogen are included by default, since these elements are always "open" in a Pourbaix diagram.

For multi-elemental diagrams, sliders are provided to specify a composition of the elements. Note that for each composition, a new Pourbaix diagram is generated from scratch.

To generate electrochemical stability maps of a specific material go to the material's details page and click on the "Aqueous Stability (Pourbaix)" tab which can be found in the "Generate Phase Diagram" tab. A new tab will open which will show the electrochemical stability map superimposed on a Pourbaix diagram. The ratio of elements used to generate the Pourbaix diagram are same as that of the material in consideration. Electrochemical stability maps are available for materials with up to three non H and O elements. For materials with more than three elements, one can use pymatgen to generate the maps programmatically.

Interfacing With the Data

To ensure a clutter-free diagram, the domains on the Pourbaix diagram are not labeled by default. To view labels on the plot, select the "Domain Labels" check box. Each domain has a mouse-over point located at the center of the domain. Mousing over these points displays the entries corresponding to the domain. Domains which contain a solid in solution are shaded. This helps identify passivation regions, especially in multi-elemental systems, were identifying passivation regions is tricky. Zooming into domains is quite simple! Just drag a selection window using your mouse. To reset zoom, click on the reset zoom button which appears on the upper right corner. Data tables are shown to the right of the Pourbaix diagram. Mousing over rows in the "Stable" column of the table highlights the corresponding entries in the Pourbaix diagram. Some stable entries may not get highlighted. This is because the domains corresponding to these entries lies outside the standard limits of the Pourbaix diagram. The "Unstable" column in the table lists the unstable entries, and their corresponding energies above hull. Links in the data tables lead to more information about the corresponding entries. Unlinked entries are ions. Mousing over the book icon next to the ions shows the reference for the free energy of formation of the aqueous ion.

Demonstration of the Pourbaix App

This section briefly demonstrates an elemental Pourbaix diagram, a multi-elemental Pourbaix diagram, and an electrochemical stability map.

Elemental Pourbaix Diagram

Figure 2 shows the elemental Pourbaix diagram for Fe. The default concentration of ions is 10−8 M, but can be varied using the "Concentration" slider above the diagram.

The two orange lines are the hydrogen reduction line, and the line denoting water oxidation to O2. These are clearly labeled in Figure 3. These lines show the stability region of H2O. For example, water is unstable below the H2 line, and so, hydrogen gas evolves at the cathode at conditions below this line. Similarly, above the O2 line, oxygen gas is evolved at the anode.

Multi-elemental Pourbaix diagram

For an n-element diagram, there are n coexisting phases. Note that these can be any mixture of solid, and aqueous phases. So, for the two-element diagram shown in Figure 4, there are two coexisting phases in each domain. As mentioned above, domains shaded blue indicate purely solid domains. For multi-elemental diagrams, shaded domains indicate those in which purely solid phases coexist.

Electrochemical Stability Map

Figure 5 shows the Gibbs free energy of Fe2O3, as a scatter plot, superimposed over the Pourbaix diagram of Fe. For a material with more than one non H and O elements, the ratio of these elements is fixed to the ratio of elements of the material but the concentration of ions can be varied similar to the single- and multi-element Pourbaix diagrams.

A color bar is shown above the electrochemical stability maps. Note that Gibbs free energies larger than 1 eV/atom are not marked in the map. Stable and unstable phase energies can be found in the table to the right of the electrochemical stability map.

Literature References for Ions

The free energies of ions in the aqueous phase have been taken from standard references/recent publications. The acronyms which show up on the tool-tips associated with the aqueous ions, and their corresponding references are as follows.

Authors

Sai Jayaraman

Arunima K. Singh

Rebecca Stern

Eric Sivonxay

Citations

PreviousDiffraction Patterns NextMagnetic Properties

Last updated 2 years ago

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