Paraelectric-antiferroelectric phase transition in titanite,CaTiSiO5

The paraelectric to antiferroelectric phase transition in titanite at ～500 K involves a displacement of the titanium atom from the center of the [TiO₆] octahedron in the paraelectric phase (A2/a) to an off-center position in the antiferroelectric (P2 ₁/a) phase. We have carried out a detailed single crystal high temperature x-ray diffraction study of the phase transition including structure refinements at 294, 350, 400, 430, 440, 450, 500, 600, and 700 K. The unit cell dimensions show a pronounced hysteresis effect in the 450–500 K range on heating and cooling during the first cycle along with a reduction of the transition temperature, T _c from 495 ± 5 K on heating to 445 ± 5 K on cooling. The hysteresis effect disappears on further heating and the superstructure reflections show residual intensities above T _c (445 K). An order parameter treatment of the phase transition is presented in terms of Landau theory and induced representation theory. The Ti-displacements parallel and antiparallel to a are taken as the primary order parameter η, which transforms as the Y ₂ ⁺ representation. A coupling of Y ₂ ⁺ with T ₁ ⁺ results in the linear-quadratic coupling of the spontaneous strain components, ? _ij with η. The Ti-displacements are coupled linearly to the Cadisplacements. Both sets of displacements predicted from induced representation theory are observed experimentally. The phase transition is initially driven by the soft mode at the zone boundary point Y ₂ ⁺ ; near T _c critical fluctuations set in and an order-disorder mechanism finally drives the phase transition, whereby parallel and antiparallel Ti-displacements related by [0, 1/2, 1/2] in adjacent domains are dynamically interchanged. Immediately above T _c , the high temperature (A2/a) phase is a statistical average of small dynamic antiphase domains of the low temperature (P2 ₁/a) phase. Vacancies and defects pinning the domain boundaries may drastically alter the transition behavior and affect the domain mobility.     

Hydrated goethite (α-FeOOH) (1 0 0) interface structure: Ordered water and surface functional groups

Goethite(α-FeOOH), an abundant and highly reactive iron oxyhydroxide mineral, has been the subject of numerous studies of environmental interface reactivity. However, such studies have been hampered by the lack of experimental constraints on aqueous interface structure, and especially of the surface water molecular arrangements. Structural information of this type is crucial because reactivity is dictated by the nature of the surface functional groups and the structure or distribution of water and electrolyte at the solid-solution interface. In this study we have investigated the goethite (1 0 0) surface using surface diffraction techniques, and have determined the relaxed surface structure, the surface functional groups, and the three dimensional nature of two distinct sorbed water layers. The crystal truncation rod (CTR) results show that the interface structure consists of a double hydroxyl, double water terminated interface with significant atom relaxations. Further, the double hydroxyl terminated surface dominates with an 89% contribution having a chiral subdomain structure on the (1 0 0) cleavage faces. The proposed interface stoichiometry is ((H₂O)(H₂O)OH₂OHFeOOFeR) with two types of terminal hydroxyls; a bidentate (B-type) hydroxo group and a monodentate (A-type) aquo group. Using the bond-valence approach the protonation states of the terminal hydroxyls are predicted to be OH type (bidentate hydroxyl with oxygen coupled to two Fe³⁺ ions) and OH₂ type (monodentate hydroxyl with oxygen tied to only one Fe³⁺). A double layer three dimensional ordered water structure at the interface was determined from refinement of fits to the experimental data. Application of bond-valence constraints to the terminal hydroxyls with appropriate rotation of the water dipole moments allowed a plausible dipole orientation model as predicted. The structural results are discussed in terms of protonation and H-bonding at the interface, and the results provide an ideal basis for testing theoretical predictions of characteristic surface properties such as pK_a , sorption equilibria, and surface water permittivity.     

Analbite → monalbite transition in a heat treated twinned amelia albite

Amelia albite annealed at > 1080 °C for 3200 hrs by Duba and Piwinskii (1974) shows very fine twin lamellae (～1 μm) after the albite law, suggesting that it once underwent transformation into monalbite. A fragment of this specimen was investigated at 27 °C, 300 °C, 550 °C, 800 °C and 930 °C using the high-temperature precession technique. As the temperature increases, the splitting angle of c ^*-axes (likewise c ^*-axes) of two twin individuals continues to decrease. The photographs taken at 930 °C show that these two splitting angles have converged to 0^o, indicating completion of the transformation into monalbite. The transition point we observe supports the results of MacKenzie (1952) (920±20 °C) and Grundy et al. (1967) (930 °C) rather than those of Sueno et al. (1973) and Prewitt et al. (1974) (> 1080 °C); the discrepancy is most likely due to the differences in the degree of Al-Si disorder of the samples used in the experiments.     

Lattice dynamics and inelastic neutron scattering from forsterite,Mg2SiO4: Phonon dispersion relation,density of states and specific heat

Magnesium-rich olivine (Mg_0.9Fe_0.1)₂SiO₄ is considered to be a major constituent of the Earth's upper mantle. Because of its major geophysical importance, the temperature and pressure dependence of its crystal structure, elastic and dielectric constants, long-wavelength phonon modes and specific heat have been measured using a variety of experimental techniques. Theoretical study of lattice dynamics provides a means of analyzing and understanding a host of such experimental data in a unified manner. A detailed study of the lattice dynamics of forsterite, Mg₂SiO₄, has been made using a crystal potential function consisting of Coulombic and short-range terms. Quasiharmonic lattice dynamical calculations based on a rigid molecular-ion model have provided theoretical estimates of elastic constants, long-wavelength modes, phonon dispersion relation for external modes along the three high symmetry directions in the Brillouin zone, total and partial density of states and inelastic neutron scattering cross-sections. The neutron cross-sections were used as guides for the coherent inelastic neutron scattering experiment on a large single crystal using a triple axis spectrometer in the constant Q mode. The observed and predicted phonon dispersion relation show excellent agreement. The inelastically scattered neutron spectra from a powder sample have been analyzed on the basis of a phonon density of states calculated from a rigid-ion model, which includes both external and internal modes. The experimental data from a powder sample show good agreement with the calculated spectra, which include a multiphonon contribution in the incoherent approximation. The computed phonon densities of states are used to calculate the specific heat as a function of temperature using both the rigid molecular-ion and rigid ion models. These results are in very good agreement with the calorimetric measurement of the specific heat. The interatomic potential developed here can be used with some confidence to study physical properties of forsterite as a function of pressure and temperature.     

Electron delocalization and magnetic behavior in a single crystal of ilvaite,a mixed valence iron silicate

Ilvaite, Ca(Fe²⁺, Fe³⁺)Fe²⁺Si₂O₈(OH), a black mixed valence iron silicate shows considerable Fe²⁺?Fe³⁺ electron delocalization above 400 K, reminiscent of magnetite. A crystallographic phase transition from orthorhombic (Pnam) to monoclinic (P2 ₁/a) symmetry takes place on cooling at 343 K induced by electron ordering. In both phases, Fe²⁺ and Fe³⁺ occur in double octahedral chains parallel to the c axis. The thermal characteristics of the magnetic susceptibilities and their anisotropies in different crystallographic planes have been measured in the temperature range 400?21 K. Below 343±1K, a continuous rotation of the molar susceptibility K _∥ in the ab plane down to 90±2 K is observed, where the symmetry of the magnetic ellipsoid remains unchanged. X _a, X _b and X _c increase abruptly below 123±0.5 K, although antiferromagnetic ordering of Fe²⁺ and Fe³⁺ spins on A sites was suggested in previous Mössbauer and neutron powder diffraction studies. In addition, 1/X _a shows an antiferromagnetic maximum at 50±3 K, whereas 1/X _b and 1/X _c at first increase sharply below 123 K, followed by antiferromagnetic curvatures in the lowest temperature region. This behavior is consistent with the antiferromagnetic ordering of Fe²⁺ spins in the B sites. The observed magnetic phenomena suggest charge delocatization effects between adjacent Fe²⁺(A)-Fe³⁺(A) pairs not only along c, but also along a and b directions. The negative sign of the molar anisotropy (K _∥-K_⊥) suggests a singlet ground State ⁵A₁ for the Fe²⁺ ions, in agreement with previous Mössbauer studies.     

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.