Free-Energy Assessment of α-δ Phase Stability in FAPbI₃ via Thermodynamic Integration with Machine-Learning Potentials 

    Formamidinium lead iodide (FAPbI₃) is a promising perovskite material for high-efficiency solar cells. However, the photoactive α-phase is thermodynamically metastable at room temperature and spontaneously transforms to the optically inactive δ-phase. Quantifying the free energy difference between these phases is essential for understanding stability and designing stabilization strategies. However, anharmonic behavior of the PbI₆ lattice and FA cation rotation prevent accurate phonon calculations using the quasiharmonic approximation. While first-principles molecular dynamics can track cooperative effects of FA orientations and PbI₆ octahedral distortions, computational costs are prohibitive.

    We performed free energy calculations accounting for FA cation rotation and PbI₆ octahedral anharmonicity by combining machine learning interatomic potentials with thermodynamic integration. This approach enables quantitative determination of the temperature-dependent Gibbs free energy difference between α- and δ-phases, elucidating thermodynamic driving forces for phase transitions. It also supports systematic evaluation of stabilization strategies and accelerates rational design of stable perovskite solar cells.