Spinel nitride solid solutions: charting properties in the configurational space with explainable machine learning

TL;DR

This paper combines density functional theory and explainable machine learning to efficiently predict properties of spinel nitride solid solutions across their configurational space, revealing structure-property relationships.

Contribution

It introduces a hybrid approach using various descriptors and models to accelerate property predictions and interpret trends in complex solid solutions.

Findings

Machine learning models accurately extrapolate properties from limited configurations.

Explainable ML reveals local structures influencing formation energy and bandgap.

Structure-property maps identify configurations with extremal properties.

Abstract

Ab initio prediction of the variation of properties in the configurational space of solid solutions is computationally very demanding. We present an approach to accelerate these predictions via a combination of density functional theory and machine learning, using the cubic spinel nitride GeSn$_2$N$_4$ as a case study, exploring how formation energy and electronic bandgap are affected by configurational variations. Furthermore, we demonstrate the utility of applying explainable machine learning to understand the crystal chemistry origins of the trends that we observe. Different configuration descriptors (Coulomb matrix eigenspectrum, many-body tensor representation, and cluster correlation function vectors) are combined with different models (linear regression, gradient-boosted decision tree, and multi-layer perceptron) to extrapolate the calculation of ab initio properties from a small set of configurations to the full space with thousands of configurations. We discuss the performance of different descriptors and models. SHAP (SHapley Additive exPlanations) analysis of the machine learning models highlights how values of formation energy are dominated by variations in local crystal structure (single polyhedral environments), while values of electronic bandgap are dominated by variations in more extended structural motifs. Finally, we demonstrate the usefulness of this approach by constructing structure-property maps, identifying important configurations of GeSn$_2$N$_4$ with extremal properties, as well as by calculating accurate equilibrium properties using configurational averaging.