The α-β phase transition in AlPO₄ cristobalite: Symmetry analysis, domain structure and transition dynamics

Abstract

Despite their crystallographic differences, the mechanisms of the α-β phase transitions in the cristobalite phases of SiO₂ and AlPO₄ are very similar. The β→α transition in AlPO₄ cristobalite is from cubic ($\left( {F\bar 43m} \right)$) to orthorhombic (C222₁), whereas that in SiO₂ cristobalite is from cubic ($\left( {Fd\bar 3m} \right)$) to tetragonal (P4₃2₁2 or P4₁2₁2). These crystallographic differences stem from the fact that there are two distinct cation positions in AlPO₄ cristobalite as opposed to one in SiO₂ cristobalite and the ordered (Al,P) distribution is retained through the phase transition. As a result, there are significant differences in their crystal structures, domain configurations resulting from the phase transition and Landau free energy expressions. A symmetry analysis of the “improper ferroelastic” transition from $F\bar 43m \to C222_1$in AlPO₄ cristobalite has been carried out based on the Landau formalism and the projection operator methods. The six-component order parameter, η driving the phase transition transforms as the X₅ representation of $F\bar 43m$and corresponds to the simultaneous translation and rotation of the [AlO₄] and [PO₄] tetrahedra coupled along 110. The Landau free energy expression contains a third order invariant, the minimization of which requires a first-order transition, consistent with experimental results. The tetrahedral configurations of twelve α phase domains resulting from the β→α transition in AlPO₄ cristobalite are of two types: (1) transformation twins from a loss of the 3-fold axis, and (2) antiphase domains from the loss of the translation vectors 1/2[101] and 1/2[011] (F→C). In contrast to α-SiO₂ cristobalite, the α-AlPO₄ cristobalite (C222₁) does not have chiral elements (4₃, 4₁) and hence, enantiomorphous domains are absent. These transformation domains are essentially macroscopic and static in the α phase and microscopic and dynamic in the β phase. The order parameter, η couples with the strain components, which initiates the structural fluctuations causing the domain configurations to dynamically interchange in the β phase. An analysis of the MAS NMR data (²⁹Si, ¹⁷O, ²⁷Al) on the α α-β transitions in SiO₂ and AlPO₄ cristobalites (Spearing et al. 1992, Phillips et al. 1993) essentially confirms the dynamical model proposed earlier for SiO₂ cristobalite (Hatch and Ghose 1991) and yields a detailed picture of the transition dynamics. In both cases, small atomic clusters with the configuration of the low temperature α phase persist considerably above the transition temperature, T₀. The NMR data on the β phases above T₀ cannot be explained by a softening of the tetrahedral rotational and translational modes alone, but require the onset of an order-disorder mechanism resulting in a dynamic averaging due to rapidly changing domain configurations considerably below T₀.