Phase Stability in Rare-Earth-Doped Apatites: A Machine Learning Approach

The study examines thermal behavior and phase stability of rare-earth-doped apatites (cerium, samarium, and holmium ions) between 25 °C and 1200 °C. Decomposition and thermal-induced phase transitions are analyzed by in situ high-temperature X-ray diffraction (HT-XRD) and thermogravimetric analysis (TGA). Decision tree machine learning (ML) model is developed to predict phase stability and decomposition products as a function of composition and temperature. The feature importance analysis identifies temperature as the determining factor for phase stability. The correlation heatmap shows strong correlation between temperatures above 600 °C and phase instability. The model achieves an accuracy of ≈86%, classified into three thermal regimes: 1) single-phase stable behavior below 500 °C, 2) partial decomposition between 500 °C and 800 °C with formation of β-tricalcium phosphate (β-TCP) and oxyapatite, and 3) complete transformation above 800 °C into α-TCP and Sr/Ca-apatite phases. Cerium and samarium ion doping improve stability up to 600 °C by reducing vacancy formation, whereas co-doping with holmium ion triggers earlier decomposition (≈500 °C) due to increased lattice strain. ML-based framework reduces need for large-scale experimental screening, enhances research efficiency and offers predictive in silico tool to design thermally stable apatite-based materials for biomedical and catalytic applications.