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.