Discovery of Low-Modulus Ti-Nb-Zr Alloys Based on Machine Learning and First-Principles Calculations

The discovery of low-modulus Ti alloys for biomedical applications is challenging due to a vast number of compositions and available solute contents. In this work, machine learning (ML) methods are employed for the prediction of the bulk modulus (K) and the shear modulus (G) of optimized ternary alloys. As a starting point, the elasticity data of more than 1800 compounds from the Materials Project fed linear models, random forest regressors, and artificial neural networks (NN), with the aims of training predictive models for K and G based on compositional features. The models were then used to predict the resultant Young modulus (E) for all possible compositions in the Ti-Nb-Zr system, with variations in the composition of 2 at. %. Random forest (RF) predictions of E deviate from the NN predictions by less than 4 GPa, which is within the expected variance from the ML training phase. RF regressors seem to generate the most reliable models, given the selected target variables and descriptors. Optimal compositions identified by the ML models were later investigated with the aid of special quasi-random structures (SQSs) and density functional theory (DFT). According to a combined analysis, alloys with 22 Zr (at. %) are promising structural materials to the biomedical field, given their low elastic modulus and elevated beta-phase stability. In alloys with Nb content higher than 14.8 (at. %), the beta phase has lower energy than omega, which may be enough to avoid the formation of omega, a high-modulus phase, during manufacturing.