Mapping Temperature-Dependent Energy-Structure-Property Relationships for Solid Solutions of Inorganic Halide Perovskites

Formation of solid solutions with complex compositions has been exhaustively adopted in material research for improving chemical and physical properties. This is also the true for halide perovskites, in the hope of further enhancing their stabilities and reducing the toxicities in lead-containing compounds. Replacement of lead with tin, even partially, is a route to achieve the latter goal. However, this has to be compromised with reduction in band gaps as well as structural stabilities. High-throughput statistical samplings over different configurations for random solid solutions have played pivotal roles in guiding the chemical designs of halide perovskite with better stabilities while retaining high photovoltaic efficiencies, but it remains challenging to intuitively and comprehensively understand the intriguing energy-structure-property (ESP) relationships in solid solutions encompassing multiple degrees-of-freedoms. In this work, first--principle dynamic and electronic structure calculations are performed across 51 different compositions of Cs(Pb$_{x}$Sn$_{1-x}$)X$_{3}$ (X=Cl, Br and I), to systematically reveal the compositional and temperature dependent stabilities, vibrational anharmonicities and band gaps in solid solutions of halide perovskites. This is enabled, in particular, by applying a recently proposed `anharmonicity score' that provides a single numerical metric to characterise the structural dynamics in a multi-atomic system. Further combination with unsupervised machine-learning enable us to produce an ESP map to visually correlate the anharmonicity score with structural distortions and energies. However, temperature-dependent variations in band gap energies, which strongly depend on orbital interactions in metal-halide octrahedra, do not necessarily follow the same trend as anharmonicity scores. This work represents our latest developments in applying data--driven approach to establish ESP relationships for guiding the future designs of functional perovskites.