Mapping temperature-dependent energy–structure–property relationships for solid solutions of inorganic halide perovskites

Abstract

Formation of solid solutions with complex compositions has been exhaustively adopted in materials research for improving the chemical and physical properties. This is also true for halide perovskites, with 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-principles dynamic and electronic structure calculations are performed across 51 different compositions of cubic Cs(Pb_xSn_1−x)X₃ (X = Cl, Br and I), to systematically reveal the composition 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. Benchmarking the 300 K-anharmonicity scores to those of the undoped iodides provides a convincing proof that lead-tin intermixing, however, is still insufficient to vibrationally stabilise the cubic iodides at room temperature. Further combination with unsupervised machine-learning enables us to produce an ESP map for visually correlating 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 a data-driven approach to establish ESP relationships for guiding the future designs of functional perovskites.