A dynamical model for the I\bar 1 - P\bar 1 phase transition in anorthite,CaAl2Si2O8

The non-ferroic triclinic to triclinic \(I\bar 1 - P\bar 1\) phase transition in anorthite is described in terms of the spontaneous onset of an order parameter η. A triclinic to triclinic phase transition can be driven by order parameters (representations) arising from the Γ, Z, X, U, V, R, Y, and T points of symmetry of the Brillouin zone. Each point leads to a set of two inequivalent representations and thus there is a total of sixteen inequivalent order parameters. However, only the R ₁ ⁺ representation is consistent with the change from the body-centered to primitive cell (increase of primitive cell size of two) and also with the origin of the two space groups (inversion center) being at the same position. The R ₁ ⁺ order parameter of the high symmetry triclinic phase \(P\bar 1_0\) (or equivalently \(I\bar 1\) ) causes a reciprocal lattice change and, in terms of the lower symmetry reciprocal lattice, the order parameter corresponds to the b^* point. This is consistent with experimentally observed x-ray diffuse scattering. Using induced representation theory, microscopic distortions compatible with the R ₁ ⁺ order parameter are obtained. Assuming a distortion in an arbitrary direction at the general 2(i) Wyckoff position (x₀,y₀,z₀) of \(P\bar 1_0\) (the higher symmetry phase) induced representation theory demands an opposite displacement at the position (x₀, y₀, z₀), an opposite displacement at (x₀+1,y₀+1,z₀+1), and the same displacement at ( \(\bar x\) ₀+1, \(\bar y\) ₀+1, \(\bar z\) ₀+1) of \(P\bar 1_0\) . This is also consistent with experiment. The presence of the weak c-type reflections above the transition is attributed to the fluctuating lower symmetry antiphase domains related by the translation (1/2, 1/2, 1/2).     

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

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.     

Returns from a speculation

A reply to a recent paper by Setten.     

Reply to discussion of Jamaican cenozoic ichnology: review and prospectus: (v. 50, p. 364–382)

Mitchell and Ramsook comment on the lithostratigraphic assignment of Jamaican Cenozoic ichnofossils discussed in Donovan et al. They argue that the Paleogene Richmond Formation should be subdivided to produce a ‘Moore Town formation’ in eastern Jamaica, but the latter remains undefined as a lithostratigraphic unit and no new lithostratigraphic evidence is produced to support their supposition. Further, their use of a flawed table of trace fossil distributions does not support their thesis. The distribution of trace fossils in the White Limestone Group presented by Donovan et al. follows the lithostratigraphic scheme that was current at the time that the research was originally undertaken in the early 2000s. Yet, whatever lithostratigraphic scheme is utilised for the island, it is apparent that the more accurate data is provided by the biostratigraphy of the larger benthic foraminifers. Copyright © 2015 John Wiley & Sons, Ltd.     

A case study in catchment hydrochemistry: Conflicting interpretations from hydrological and chemical observations

Soil water, stream water, groundwater and rain water were sampled through a storm event in a moorland catchment. Samples were analysed for major ions and deuterium. Chloride and deuterium are used as tracers to enable separation of the stream runoff hydrograph into three components: rain, soil and groundwater. The results indicate that rain water arrives in the stream quickly during the event and contributes a significant volume to the runoff peak. The chemical signal in the rain water is, however, significantly damped, apparently due to mixing with soil water held in the catchment before the event. This is further modified before reaching the stream, apparently through mixing with a deeper groundwater component. Interpretation of tracer, chemistry and hydrological data to present an integrated picture of catchment hydrochemical response is difficult due to problems in the chemical and conceptual definition of the flow components.