Ferroelastic phase transition in cryolite,Na3AlF6, a mixed fluoride perovskite: High temperature single crystal X-ray diffraction study and symmetry analysis of the transition mechanism

Cryolite, Na₃AlF₆[ = 2Na⁺(Na_0.5 ⁺Al_0.5 ³⁺)F₃] is a mixed fluoride perovskite, in which the corner-sharing octahedral framework is formed by alternating [NaF₆] and [AlF₆] octahedra and the cavities are occupied by Na⁺ ions. At 295 K, it is monoclinic (α phase), space group P2 ₁/n with a = 5.4139 (7), b = 5.6012 (5) and c = 7.7769 (8) Å and β = 90.183 (3)°, Z = 2. A high temperature single crystal X-ray diffraction study in the range 295–900 K indicates a fluctuation-induced first-order phase transition from monoclinic to orthorhombic symmetry at T ₀ ～ 885 K, in contrast to a previous report that it becomes cubic at ～823 K. The space group of the high temperature β phase is Immm with a = 5.632 (4), b = 5.627 (3) and c = 7.958 (4) Å, Z = 2 at 890 K. Above T ₀, the coordination number of the Na⁺ ion in the cavity increases from eight to twelve and the zigzag Na1 — Al octahedral chains parallel to c become straight with the Na1-F-Al angle = 180 °. The phase transition is driven by two coupled primary order parameters. The first corresponds to the rotation of the nearly rigid [AlF₆] group and transforms according to the Γ ₄ ⁺ irreducible representation of Immm. Coupled to the [AlF₆] rotation is a second primary order parameter corresponding to the displacement of the Na2⁺ ion in the cavity from its equilibrium position. This order parameter transforms according to the X ₃ ⁺ irreducible representation of Immm. Following Immm → P2 ₁ /n phase transition, four equivalent domains of P2 ₁/n are determined relative to Immm, which are in an antiphase and/or twin relationship. The abrupt shortening of the octahedral Al-F and Na-F bonds and a sudden change in orientations of the atomic thermal vibration ellipsoids above T ₀ indicate a crossover from displacive to an order-disorder mechanism near the transition temperature. The β phase is interpreted as a dynamic average of four micro-twin and -antiphase domains of the a phase. This view is consistent with the entropy of phase transition, ΔS_trans (11.43 JK^?1 mol^?1) calculated from heat capacity measurements (Anovitz et al. 1987), which corresponds closely to R ln4 (11.53 JK^?1 mol^?1), where 4 is the number of domains formed during the phase transition. The dynamic nature of the β phase is independently confirmed from a considerable narrowing of the ²⁷Al nuclear magnetic resonance (NMR) line-shape above T ₀ (Stebbins et al. 1992).