Backward Elimination: A Strategy for High-Entropy Alloy Catalyst Discovery

Abstract

A promising opportunity and major challenge in the field of High-Entropy Alloy (HEA) catalysis is the abundance of possible compositions. The number of possible compositions makes it impossible to study all of them. Therefore, sophisticated methods are required to intelligently select interesting compositions. On one hand, adding an element to a composition space increases the dimensionality of that space and the number of compositions within it combinatorially. However, it also increases the number of sub-spaces that are part of this larger composition space. Assuming a constant sampling density, the number of experiments required to study a large, combined composition space of sufficient dimensionality can be less than studying all of its individual sub-spaces. This hypothesis is investigated using experimental work in which 200 compositions in an 8-element composition space composed of Au, Ir, Os, Pd, Pt, Re, Rh, and Ru were synthesized as nanoparticles. Each composition was experimentally tested for the electrocatalytic activity towards the oxygen reduction reaction. The model that was constructed using this data turned out to adequately predict data in three of its 5-element composition sub-spaces. This observation paves way for a backward elimination strategy in HEA discovery. According to this strategy all elements of interest are studied in a single composition space from which knowledge of all subspaces can be learnt. Subsequently, elements that do not show a positive influence towards the studied reaction can be removed from the search space. Ultimately, this backward elimination search produces an alloy space which has a high probability of containing the most active catalyst composition.

Discovering High Entropy Alloy Electrocatalysts in Vast Composition Spaces with Multiobjective Optimization

“…For ease of illustration, we choose five different 5-element HEA spaces: AgIrPdPtRu, AuOsPdPtRu, AgCuIrPdRe, IrOsPdPtRh, and IrPdReRhRu, where the first two have been synthesized and studied in recent publications. ,,, Figure a shows the resulting Pareto front of biobjective BO for catalytic activity and relative cost. The Pareto front is defined as the set of nondominated solutions that provide a suitable compromise between all objectives. , It is intriguing that, in general, activity and relative cost are conflicting properties, and different 5-element compositions exhibit varied relationships between these two objectives.…”

“…Besides its focus on a sole target property, the single-objective BO in these studies also places excessive emphasis on a single global optimum within the explored 5-element space, ,,, which is not directly applicable to higher-dimensional scenarios. A recent experiment conducted in a 6-element HEA space has demonstrated the existence of multiple optimal solutions .…”

High entropy alloy nanoparticle formation at low temperatures

“…Extending this to other syntheses with similar solid, mixed precursors can provide a way to design new low-temperature approaches for small high entropy alloy nanoparticles. It can further be argued that starting with a high number of different elements favors the exploration of high-entropy material spaces 34 . Structural characterization of the particles reveals that the lattices are very strained and the HEA nanoparticles contain a high number of defects.…”

Exploring the High-Entropy Oxide Composition Space: Insights through Comparing Experimental with Theoretical Models for the Oxygen Evolution Reaction

“…26,27 Furthermore, we demonstrated that the search for HEA catalysts can be accelerated by including a larger number of elements in the initial composition search space. 28 Finally, a strategy based on density functional theory (DFT) calculations has been developed to enable computational screening of HEA and HEO catalysts. 29,30 Both experimental and theoretical screening methods procure information about the catalyst from different angles.…”

“…The number of experiments that can be performed manually is limited, and the number of samples required for grid searches thus calls for a partly automated experimental setup. , Alternatively, the combination of laboratory experiments with computational and statistical methods can be used to reduce the number of samples that are needed. Presently, Bayesian optimization has been demonstrated to effectively optimize 5-element high-entropy alloy (HEA) catalyst compositions with less than 50 experiments. , Furthermore, we demonstrated that the search for HEA catalysts can be accelerated by including a larger number of elements in the initial composition search space . Finally, a strategy based on density functional theory (DFT) calculations has been developed to enable computational screening of HEA and HEO catalysts. , Both experimental and theoretical screening methods procure information about the catalyst from different angles.…”