Data-efficient machine-learning of complex Fe-Mo intermetallics using domain knowledge of chemistry and crystallography

TL;DR

This paper develops data-efficient machine learning models that leverage domain knowledge of chemistry and crystallography to accurately predict complex Fe-Mo intermetallic phases with minimal training data, validated by experiments.

Contribution

It introduces ML models that incorporate domain knowledge to efficiently predict complex TCP phases in Fe-Mo with limited data, outperforming traditional approaches.

Findings

ML models achieve accurate phase predictions with less than 300 DFT calculations.

Predicted phase convex hulls agree well with DFT results, with uncertainties of 20-25 meV/atom.

Experimental X-ray analysis confirms ML predictions of WS occupancy in Fe-Mo R-phase.

Abstract

Atomistic simulations of multi-component systems require accurate descriptions of interatomic interactions to resolve details in the energy of competing phases. A particularly challenging case are topologically close-packed (TCP) phases with close energetic competition of numerous different site occupations even in binary systems like Fe-Mo. In this work, machine learning (ML) models are presented that overcome this challenge by using features with domain knowledge of chemistry and crystallography. The resulting data-efficient ML models need only a small set of training data of simple TCP phases $A$15, $\sigma$, $\chi$, $\mu$, $C$14, $C$15, $C$36 with 2-5 WS to reach robust and accurate predictions for the complex TCP phases $R$, $M$, $P$, $\delta$ with 11-14 WS. Several ML models with kernel-ridge regression, multi-layer perceptrons, and random forests, are trained on less than 300 DFT calculations for the simple TCP phases in Fe-Mo. The performance of these ML models is shown to improve systematically with increased utilization of domain knowledge. The convex hulls of the $R$, $M$, $P$ and $\delta$ phase in the Fe-Mo system are predicted with uncertainties of 20-25 meV/atom and show very good agreement with DFT verification. Complementary X-ray diffraction experiments and Rietveld analysis are carried out for an Fe-Mo R-phase sample. The measured WS occupancy is in excellent agreement with the predictions of our ML model using the Bragg Williams approximation at the same temperature.