Four-dimensional description of the structure and phase transitions of KFeF₄ (phase II and superstructure phase III)

The structural phase transitions of KFeF₄ have been investigated by x-ray powder and monocrystal techniques. Dilatometric experiments have allowed us to characterize the transition between the so-called phase II and the twofold superstructure phase III. It is accompanied by a contraction of the a and b parameters, which is compatible with a rotation of the FeF₆ octahedra around the c axis, and by an anomaly along the c direction, 10 K above the previous transition temperature. To investigate the phase transition II→III, structural characterization of the two phases II and III has been achieved. Preliminary classical studies had shown that the related symmetry space groups were, respectively, Amma and Pmcn. A new structural four-dimensional investigation, which considers phase III as a modulated structure of the average of phase II, has confirmed these first results.

The superspace group is P_11^Am¯s^ma and the real structure corresponds to the section t=(1/8 of the supercrystal. The structural refinement of the structure leads to an R factor of 0.046 for 31 refinement parameters. The atomic displacements are consistent with a rigid-body rotation of the FeF₆ octahedra in agreement with the dilatometric-powder study. Moreover, the four-dimensional method has proved to be more rigorous to take into account the real symmetry of phase III, to describe more correctly the diffraction pattern, and to be more efficient in refining the structure with fewer refinement parameters. We have shown that the phase transition II→III is also compatible with the Landau theory for structural, continuous phase transitions, which allowed us to derive the symmetry of the modulated structure of phase III. KFeF₄ is proved to be a good example first to prove the usefulness of the four-dimensional analysis for a superstructure considered as a commensurate modulated structure, and second, to make a useful comparison between the superspace theory and the Landau theory of the invariance of the free-energy expansion.