Model of structural phase transitions in(CH3NH3)2CdCl4-type compounds

Abstract

A model has been proposed describing the structural phase transitions in ${(\mathrm{C}{\mathrm{H}}_{3}\mathrm{N}{\mathrm{H}}_{3})}_{2}$Cd${\mathrm{Cl}}_{4}$ perovskite layer-type compounds as orientational order-disorder transitions of the C${\mathrm{H}}_{3}$N${\mathrm{H}}_{3}$ groups. Each C${\mathrm{H}}_{3}$N${\mathrm{H}}_{3}$ group has four possible equilibrium orientations in the cavities between the corner-sharing Cd${\mathrm{Cl}}_{6}$ octahedra and interacts with its nearest neighbors via two- and four-particle interactions. The four-particle interactions describe the fact that the energy of a given configuration of four C${\mathrm{H}}_{3}$N${\mathrm{H}}_{3}$ groups surrounding a Cd${\mathrm{Cl}}_{6}$ octahedron depends on the number of N-H\dots{}Cl bonds leading to the axial Cl sites of this octahedron, whereas the two-particle interactions describe the direct coupling between the C${\mathrm{H}}_{3}$ ends of the methylammonium groups as well as the indirect coupling via the N-H\dots{}Cl bonds leading to the equatorial Cl sites. In the absence of lattice distortions, the sequence of phase changes is: $\frac{I4}{\mathrm{mmm}}\ensuremath{\rightarrow}\mathrm{Cmca}\ensuremath{\rightarrow}\frac{P{4}_{2}}{\mathrm{ncm}}\ensuremath{\rightarrow}\mathrm{Cmca}$. Due to nonlinear coupling between the motion of the C${\mathrm{H}}_{3}$N${\mathrm{H}}_{3}$ groups and the rotation of the Cd${\mathrm{Cl}}_{6}$ octahedra, a monoclinic distortion of the lattice sets in as soon as the orthorhombic order parameter exceeds a critical value. For certain reasonable values of the coupling parameters one can thus reproduce the experimentally observed sequence of phase changes: $\frac{I4}{\mathrm{mmm}}\ensuremath{\rightarrow}\mathrm{Cmca}\ensuremath{\rightarrow}\frac{P{4}_{2}}{\mathrm{ncm}}\ensuremath{\rightarrow}\frac{P{2}_{1}}{b}$.