Cation reorientation and octahedral tilting in the metal-organic perovskites MAPI and FAPI

The metal-organic halide perovskites are the object of great interest since it has been recently found that they have excellent photovoltaic properties, and can therefore be used to create cheap and efficient solar cells, photodetectors and LEDs with a wide range of colors. Much of the research is focused on two issues: the scarce stability of the materials and the mechanisms that allow the photocarriers to have so long lifetimes. These phenomena are closely connected to the structural transformations and to the dynamics of the reorienting organic cations, both of which can be studied by anelastic measurements [1,2]. The anelastic spectra of MAPbI3 (MAPI, MA = methylammonium = CH3NH3) and FAPbI3 (FAPI, FA = formamidinium = CH(NH2)2) have been measured on samples obtained by pressing the powders and electrostatically excited on their free flexural modes at kHz frequencies. Both perovskites are cubic at and above room temperature (alpha phase), with freely rotating FA and MA cations and undergo two tilt transitions of the PbI6 octahedra into a tetragonal (beta phase and orthorhombic (gamma) phase, accompanied by losses of the orientational degrees of freedom of the MA and FA. All these phenomena are clearly visible in the anelastic spectra (Fig. 1), together with an additional phase transition (I) in FAPI at low temperature. According to the Landau theory of phase transitions with coupling between the rotation angle of the octahedra phi and the ensuing strain e of the form e phi^2, at a tilt transition with order parameter phi the elastic constant associated with e undergoes a steplike softening, as observed at the alpha>beta transitions in Fig. 1. The stiffening at the beta>gamma transitions is unexpected, but actually observed in few oxide perovskites when entering the Pnma phase with a-b+a- tilts (the rotations of the octahedra about the cubic axes are alternately +/-phi along a and c and in-phase along b). It has been suggested that this behaviour is due to a sort of blocking of the tilt degrees of freedom due to the concomitant in-phase and out-of-phase tilts, but this explanation can reasonably account, at most, for a complete loss of the softening associated with the tilted beta phase (up to the horizontal dashed lines in Fig. 1). Instead, FAPI and MAPI restiffen well above the value in the untilted alpha phase. At least this excess restiffening, if not more, has to be attributed to the freezing of the residual rotational degrees of freedom of the FA and MA molecules. In MAPI the stiffening below T_(beta/gamma) is partly due to the modulus defect of an intense thermally activated relaxation, identified with the residual reorientation of the MA major axis with strong antiferroelectric correlations, since their electric dipoles do not cause a concomitant dielectric relaxation [1]. In FAPI, instead, the freezing of the reorientation of the FA major axes must progress together with the order parameter of the transition, since the stiffening, though rather structured, does not show a dependence on frequency of the relaxation type and is accompanied by a drop of Q-1 rather than a peak. This fact points to a coupling between FA orientation and tilt of the surrounding octahedra larger than in MAPI, in agreement with the larger size of FA. As a consequence, the beta/gamma transition in FAPI is not a traditional displacive transition as octahedral tilting normally is, but has a dominant kinetic component due to the FA reorientation. This is evident also from the fact that its temperature and the shape of the elastic anomaly depend on sample and thermal history and may even show an inverted thermal hysteresis.