Microscopic origin of entropy-driven polymorphism in hybrid organic-inorganic perovskite materials

Entropy is a critical, but often overlooked, factor in determining the relative stabilities of crystal phases. The importance of entropy is most pronounced in softer materials, where small changes in free energy can drive phase transitions, which has recently been demonstrated in the case of organic-inorganic hybrid-formate perovskites. In this study we demonstrate the interplay between composition and crystal-structure that is responsible for the particularly pronounced role of entropy in determining polymorphism in hybrid organic-inorganic materials. Using ab initio based lattice dynamics we probe the origins and effects of vibrational entropy of four archetype perovskite (ABX$_3$) structures. We consider a fully inorganic material (SrTiO$_3$), an A-site hybrid halide material (CH$_3$NH$_3$PbI$_3$), an X-site hybrid material (KSr(BH$_4$)$_3$) and a mixed A- and X-site hybrid-formate material (N$_2$H$_5$Zn(HCO$_2$)$_3$), comparing the differences in entropy between two common polymorphs. The results demonstrate the importance of low-frequency inter-molecular modes in determining phase stability in these materials. The understanding gained allows us to propose a general principle for the relative stability of different polymorphs of hybrid materials as temperature is increased.