# Journal of Applied Crystallography

### Volume 47, Part 2 (April 2014)

## research papers

*J. Appl. Cryst.* (2014). **47**, 532-538 [ doi:10.1107/S1600576713034560 ]

### A symmetry-mode description of rigid-body rotations in crystalline solids: a case study of Mg(H_{2}O)_{6}RbBr_{3}

**Abstract:** The application of rotational symmetry modes to quantitative rigid-body analysis is demonstrated for octahedral rotations in Mg(H_{2}O)_{6}RbBr_{3}. Rigid-body rotations are treated as axial-vector order parameters and projected using group-theoretical methods. The high-temperature crystal structure of the Mg(H_{2}O)_{6}RbBr_{3} double salt consists of a cubic perovskite-like corner-sharing network of RbBr_{6} octahedra with isolated MgO_{6} octahedra at the perovskite *A* sites. A phase transition occurs at 411 K upon cooling, whereupon the MgO_{6} octahedra experience a substantial rigid-body rotation, the RbBr_{6} octahedra are translated but not rotated, and both types of octahedra become slightly distorted. The MgO_{6} rotation has three orthogonal components associated with the *X*_{5}^{-}, _{4}^{+} and *X*_{1}^{-} 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.

**Keywords: rigid-body rotation; symmetry mode; irreducible representation; parametric refinement; phase transition.**

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