A symmetry‐mode description of rigid‐body rotations in crystalline solids: a case study of Mg(H2O)6RbBr3

The application of rotational symmetry modes to quantitative rigid-body analysis is demonstrated for octahedral rotations in Mg(H2O)6RbBr3. Rigid-body rotations are treated as axial-vector order parameters and projected using group-theoretical methods. The high-temperature crystal structure of the Mg(H2O)6RbBr3 double salt consists of a cubic perovskite-like corner-sharing network of RbBr6 octahedra with isolated MgO6 octahedra at the perovskite A sites. A phase transition occurs at 411 K upon cooling, whereupon the MgO6 octahedra experience a substantial rigid-body rotation, the RbBr6 octahedra are translated but not rotated, and both types of octahedra become slightly distorted. The MgO6 rotation has three orthogonal components associated with the X5−, Γ4+ and X1− irreducible representations of the parent Pm{\overline 3}m space-group symmetry which, given the weakly first-order character of the transition, appear to be strongly coupled. Parametric and sequential refinements of the temperature-dependent structure were conducted using four model types: (1) traditional atomic xyz coordinates for each atom, (2) traditional rigid-body parameters, (3) purely displacive symmetry modes and (4) rigid-body rotational symmetry modes. We demonstrate that rigid-body rotational symmetry modes are an especially effective parameter set for the Rietveld characterization of phase transitions involving polyhedral rotations.