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 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.