Discovery of novel low modulus Nb-Ti-Zr biomedical alloys via combined machine learning and first principles approach

The beta-phase stabilized ternary Nb-Ti-Zr alloys with low Young's modulus similar to that of the human bones (30 GPa similar to 40 GPa) are highly desirable for biomedical application. However, owing to the extensive compositions and available solute contents, searching low-modulus ternary Nb-Ti-Zr alloys is still challenging and has attracted intense attention recently. Herein, based on first principles calculations and artificial neural networks (ANN) model, we discover a potential region of interest in the compositional map with a small dataset containing merely 85 data. The results obtained by the first principles calculations and machine learning (ML) approaches are extremely close, suggesting high predictive accuracy and good feature validity of the well-trained ANN model. The random forest classifier is also applied to search the features which have more significant influence on mechanical stability. The valence electron concentration, niobium content and average bulk modulus are the three key features strongly correlated with the elastic properties of Nb-Ti-Zr random solid solution. Then the feature importance was analyzed, which can help to deepen our understanding of the relationship between the solute effects and mechanical properties. Finally, the electronic structure was computed to investigate the bonding behavior, and the bonding force can account for the difference of the modulus.