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Abstract Hybrid organic–inorganic perovskites (HOIPs) such as methylammonium lead iodide (MAPbI₃) are promising candidates for use in photovoltaic cells and other semiconductor applications, but their limited chemical stability poses obstacles to their widespread use.Ab initiomodeling of finite-temperature and pressure thermodynamic equilibria of HOIPs with their decomposition products can reveal stability limits and help develop mitigation strategies. We here use a previously published experimental temperature-pressure equilibrium to benchmark and demonstrate the applicability of the harmonic and quasiharmonic approximations, combined with a simple entropy correction for the configurational freedom of methylammonium cations in solid MAPbI₃and for several density functional approximations, to the thermodynamics of MAPbI₃decomposition. We find that these approximations, together with the dispersion-corrected hybrid density functional HSE06, yield remarkably good agreement with the experimentally assessed equilibrium betweenT= 326 K andT= 407 K, providing a solid foundation for future broad thermodynamic assessments of HOIP stability. 

Abstract We study viscosity solutions to the classical one-phase problem and its thin counterpart. In low dimensions, we show that when the free boundary is the graph of a continuous function, the solution is the half-plane solution. This answers, in the salient dimensions, a one-phase free boundary analogue of Bernstein’s problem for minimal surfaces.As an application, we also classify monotone solutions of semilinear equations with a bump-type nonlinearity. 

Abstract We study the regularity of free boundaries in the multiple elastic membrane problem in the plane. We prove the uniqueness of blow-ups, and that the free boundaries are $C^{1,\log }${C^{1,\log}}-curves near a regular intersection point.