Machine-learning prediction of Vegard's law factor and volume size factor for binary substitutional metallic solid solutions

Vegard`s law factor (VLF) and volume size factor (SF) of binary substitutional metallic solid solutions (BSMSS) are crucial in alloy design. However, general models for accurately predicting these structure parameters are still undeveloped. In this work, a kernel ridge regression (KRR) model was developed to predict VLF and SF of BSMSS based on 409 published entries and elemental descriptors. The KRR model achieves an average R ² score of 0.67, an average Pearson coefficient of 0.82 for VLF and an average R ² of 0.80, an average Pearson coefficient of 0.90 for SF among 100 random splits of training/testing dataset. The performances of this KRR model based on training sets without certain solvent/solute elements were also investigated. In addition, an explicit expression was learned by the symbolic transformer, which exhibits prediction efficiency with R ² of 0.8 for VLF and 0.9 for SF. The expression can be interpreted as a physically meaningful 2D descriptor with one component containing size difference between solute and solvent atoms in the pure state while the other one does not. This is helpful to clarify the electronic coupling effect referred in previous studies. The predictions of both ML models are compared with those of density functional theory (DFT) for 37 Fe-based BSMSS (Fe-X). The results show that ML models exhibit higher R ² than that of DFT for the 20 Fe-X with experimental data available, and provide reasonable results for the 17 Fe-X without experimental data.