Elastic Softness of Hybrid Lead Halide Perovskites

Much recent attention has been devoted towards unraveling the microscopic optoelectronic properties of hybrid organic-inorganic perovskites. Here we investigate by coherent inelastic neutron scattering spectroscopy and Brillouin light scattering, low frequency acoustic phonons in four different hybrid perovskite single crystals: ${\mathrm{MAPbBr}}_3$, ${\mathrm{FAPbBr}}_3$, ${\mathrm{MAPbI}}_3$, and $\alpha \text{−}{\mathrm{FAPbI}}_3$ (MA: methylammonium, FA: formamidinium). We report a complete set of elastic constants characterized by a very soft shear modulus $C_{44}$. Further, a tendency towards an incipient ferroelastic transition is observed in ${\mathrm{FAPbBr}}_3$. We observe a systematic lower sound group velocity in the technologically important iodide-based compounds compared to the bromide-based ones. The findings suggest that low thermal conductivity and hot phonon bottleneck phenomena are expected to be enhanced by low elastic stiffness, particularly in the case of the ultrasoft $\alpha \text{−}{\mathrm{FAPbI}}_3$.

Figure 1

Transverse acoustic (TA) phonon spectra measured by inelastic neutron scattering in the cubic phase of (a) ${\mathrm{MAPbBr}}_3$, (b) ${\mathrm{FAPbBr}}_3$, and (c) ${\mathrm{MAPbI}}_3$ for different $Q$ positions going away from the $(002)\equiv (200)$ Bragg peak [i.e., $\mathrm{Q}=(kk2)$]; and of (d) $\alpha \text{−}{\mathrm{FAPbI}}_3$ for different energy values. With the exception of ${\mathrm{MAPbI}}_3$ (340 K), all other compounds were studied at room temperature (RT).

Figure 2

Acoustic phonon dispersion curves of the four HOP (a) TA and (b) LA phonons at around the (002) Bragg reflection, measured by INS. (c) Elastic constants $C_{11}$ and $C_{44}$ as well as the bulk modulus $K$ behavior as a function of the cubic lattice constant of each compound. (d) Sound velocity diagram for ${\mathrm{FAPbBr}}_3$ and ${\mathrm{MAPbBr}}_3$, as determined by Brillouin light scattering. The velocity is given as a function of the angle between the direction of measurement and the [100] direction.

Figure 3

Softening of $C_{44}$ in ${\mathrm{FAPbBr}}_3$ (a) as function of $q$ (at RT) and (b) as a function of temperature (230–300 K), around the (002) Bragg reflection. Also in (b) the Bragg $M$ point intensity (red) across a similar a temperature range. The bare elastic constant, $C_{44}^0$, represents the elastic properties without the influence of the (incipient) phase transition. Note that the $q$ scale is logarithmic to underline the broad $q$ range covered by both experimental techniques.