Model of structural phase transitions in ${\left(\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\right)}_2$Cd${\mathrm{Cl}}_4$-type compounds

A model has been proposed describing the structural phase transitions in ${\left(\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\right)}_2$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…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…Cl bonds leading to the equatorial Cl sites. In the absence of lattice distortions, the sequence of phase changes is: $\frac{I4\mathrm{}}{\mathrm{mmm}}\to \mathrm{Cmca}\to \frac{P{4}_2}{\mathrm{ncm}}\to \mathrm{Cmca}$. 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: $\frac{I4\mathrm{}}{\mathrm{mmm}}\to \mathrm{Cmca}\to \frac{P{4}_2}{\mathrm{ncm}}\to \frac{P{2}_1}{b}$.