Efficient Pourbaix diagrams of many-element compounds - Anjli M. Patel et al. 2019

Oct 29, 2026

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Pourbaix diagrams evaluate stability regions of materials under varying potential and pH in aqueous environments, but multidimensional multielement systems become computationally prohibitive. A modified Pourbaix construction approach filters candidate species to those lying on the compositional convex hull, ensuring all stable phase mixtures are included. Axes for H+ and electrons are incorporated to capture electrochemical requirements, reducing construction time by several orders of magnitude. The method is integrated into pymatgen and the Materials Project to enable complex multicomponent Pourbaix stability evaluation.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages5

Reading Time13 min

AccessFree to download

Introduction

Pourbaix diagrams for corrosion and electrochemical stability

Pourbaix algorithm

Computational bottlenecks in multi-element construction

Convex-hull filtering to reduce combinatorics

Pu on 31 October 2019. Downloaded by Lawrence Berkeley National Laboratoryblished on 12/17/2019 4:19:01 AM . PCCP | | | | | | --- | --- | --- | --- | | P | APER | View Article Online | | | | View Journal | View Issue | | | Cite this: Phys. Chem. Chem. Phys., 2019, 21, 25323 Received 29th August 2019, Accepted 30th October 2019 DOI: 10.1039/c9cp04799a[rsc.li/pccp](rsc.li/pccp) Eﬃcient Pourbaix diagrams of many-element compounds† Anjli M. Patel,a Jens K. Nørskov, b Kristin A. Perssonc and Joseph H. Montoya *d Pourbaix diagrams have been used extensively to evaluate stability regions of materials subject to varying potential and pH conditions in aqueous environments. However, both recent advances in highthroughput material exploration and increasing complexity of materials of interest for electrochemical applications pose challenges for performing Pourbaix analysis on multidimensional systems. Specifically, current Pourbaix construction algorithms incur significant computational costs for systems consisting of four or more elemental components. Herein, we propose an alternative Pourbaix construction method that filters all potential combinations of species in a system to only those present on a compositional convex hull. By including axes representing the quantities of H+ and e 􀀂 required to form a given phase, one can ensure every stable phase mixture is included in the Pourbaix diagram and reduce the computational time required to construct the resultant Pourbaix diagram by several orders of magnitude. This new Pourbaix algorithm has been incorporated into the pymatgen code and the Materials Project website, and it extends the ability to evaluate the Pourbaix stability of complex multicomponent systems. 1 Introduction Pourbaix diagrams are an invaluable tool for exploring the corrosion profiles of materials as a function of ambient pH and electrochemical potential.1 In recent years, high-throughput computational materials science eﬀorts, like those from the Materials Project,2,3 have enabled more comprehensive Pourbaix diagrams to be constructed and disseminated from computational data.4,5 These analyses have informed a number of computational studies of materials for electrochemical applications, aqueous electrocatalysis6–9 and photoelectrocatalysis,10–12 non-equilibrium crystallization,13,14 and corrosionresistant alloy design.15,16 Pourbaix analysis of multicomponent systems is particularly valuable for finding elusive materials like acid-stable oxygen evolution catalysts,7 earth-abundant hydrogen evolution catalysts,17 and selective CO2 reduction catalysts,18 which often require exploration in multi-element spaces. However, Pourbaix analysis has been limited to three or fewer elements, largely because computing the electrochemical phase stability of higher composition spaces has proven inefficient with existing methods. a Department of Chemical Engineering, Stanford University, Stanford, CA, USA b Department of Physics, Technical University of Denmark, Lyngby, Denmark c Lawrence Berkeley National Laboratory and Department of Materials Science, University of California, Berkeley, CA, USA d Toyota Research Institute, 4440 El Camino Real, Los Altos, CA, USA. [E-mail: joseph.montoya@tri.global](E-mail: joseph.montoya@tri.global) † Electronic supplementary information (ESI) available. See DOI: 10.1039/c9cp04799a In this report, we provide details of a modified method for Pourbaix diagram construction that enables diagrams to be constructed eﬃciently in much higher compositional spaces. This in turn enables phase stability analysis of similarly complex individual materials. We demonstrate this functionality with an analysis of the phase stability of a complex material for the alkaline oxygen evolution reaction (OER) and highlight our implementation in the open-source pymatgen19 code and on the Materials Project website ([materialsproject.org](materialsproject.org)). 2 Pourbaix algorithm The

FAQs

Why are Pourbaix diagram calculations difficult for systems with four or more elements?

Current Pourbaix construction algorithms iterate over many potential species combinations, and the number of evaluations grows combinatorially with elements, making computation prohibitively expensive beyond about three elements.

What is the core idea behind the proposed efficient Pourbaix construction method?

It filters all potential combinations to only those present on the compositional convex hull, while using axes representing H+ and electrons needed to form each phase so that every stable phase mixture is included.

How is the method implemented and made available for use?

The new algorithm is incorporated into the open-source pymatgen code and integrated with the Materials Project website to extend evaluation of Pourbaix stability for complex multicomponent systems.

Oct 29, 2026

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