Frequency estimate for multicomponent crystalline compounds

TL;DR

This paper investigates why high-component crystalline compounds are rare despite the large number of possible combinations, proposing that their actual numbers are much higher than known, based on geometric and energetic considerations.

Contribution

It introduces a method to estimate the number of multicomponent crystalline compounds using the empirical Miedema enthalpy model and geometric analysis.

Findings

High-dimensional composition space reduces the number of stable compounds.

Surface effects favor compounds with fewer components.

Estimated number of 4- and 5-component alloys exceeds known examples.

Abstract

Among crystal structures of N-component metal alloys, far fewer examples are known with N>=4 than with N=2 or 3, in apparent contradiction to the exponentially growing number of possible combinations of elements. Two effects contribute to this shortfall. Since the N-component composition space resides within a d-dimensional simplex with d=N-1, the vanishing volume in high dimensions reduces the distinct N-component compositions. Additionally, the increasing surface area makes it more probable that stable structures reside on the surface of the simplex (containing fewer than N components) as opposed to its interior. Despite their rarity, we propose that the actual number of N=4- and 5-component alloys greatly exceeds the number that are currently known. Specific estimates are developed through application of the empirical Miedema enthalpy model.