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Physics and Chemistry of Minerals

, Volume 21, Issue 1–2, pp 67–77 | Cite as

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

  • Dorian M. Hatch
  • Subrata Ghose
  • John L. Bjorkstam
Article

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] (FC). 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.

Keywords

Cristobalite Symmetry Analysis AlPO4 Antiphase Domain Domain Configuration 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Dorian M. Hatch
    • 1
  • Subrata Ghose
    • 2
  • John L. Bjorkstam
    • 3
  1. 1.Department of PhysicsBrigham Young UniversityProvoUSA
  2. 2.Mineral Physics Group, Department of Geological SciencesUniversity of WashingtonSeattleUSA
  3. 3.Department of Electrical EngineeringUniversity of WashingtonSeattleUSA

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