Simon A. T. Redfern

Unit cell refinement from powder diffraction data; the use of regression diagnostics

Abstract We discuss the use of regression diagnostics combined with nonlinear least-squares to refine cell parameters from powder diffraction data, presenting a method which minimizes residuals in the experimentallydetermined quantity (usually 2θhkt or energy, Ehkt). Regression diagnostics, particularly deletion diagnostics, are invaluable in detection of outliers and influential data which could be deleterious to the regressed results. The usual practice of simple inspection of calculated residuals alone often fails to detect the seriously deleterious outliers in a dataset, because bare residuals provide no information on the leverage (sensitivity) of the datum concerned. The regression diagnostics which predict the change expected in each cell constant upon deletion of each observation (hkl reflection) are particularly valuable in assessing the sensitivity of the calculated results to individual reflections. A new computer program, implementing nonlinear regression methods and providing the diagnostic output, is described.

Synthesis and Rietveld crystal structures refinement of mackinawaite, tetragonal FeS

Abstract Mackinawite, tetragonal FeS, has been synthesised by reacting iron with Na2S solutions. A Rietveld structure refinement of X-ray powder diffraction data, recorded using X-rays monochromated from synchrotron radiation with a wavelength of 0.6023 A, has been performed. The structure has been refined in the tetragonal space group, P4/nmm, and has the following cell parameters: a = 3.6735(4), c = 5.0328(7) Å, V = 67.914(24) A3. Our refinement shows that the FeS4 tetrahedron in mackinawite is almost perfectly regular, with a much smaller distortion than has been previously reported. An improved X-ray diffraction data set is provided.

Thermodynamics and kinetics of cation ordering in MgAl 2 O 4 spinel up to 1600 degrees C from in situ neutron diffraction

Abstract The temperature dependence of the cation distribution in synthetic spinel (MgAl2O4) was determined using in-situ time-of-flight neutron powder diffraction. Neutron diffraction patterns of stoichiometric MgAl2O4 and slightly non-stoichiometric Mg0.99Al2O4 samples were collected under vacuum on heating from room temperature to 1600 °C, and the cation distribution was determined directly from site occupancies obtained by Rietveld refinement. The equilibrium non-convergent ordering has been analyzed using both the O’Neill-Navrotsky and Landau thermodynamic models, both of which fit the observed behavior well over the temperature range of the measurements. Fitting the data between 560 °C and 1600 °C using the O′Neill and Navrotsky (1983) thermodynamic model yields α = 32.8 ± 0.9 kJ/mol and β = 4.7 ± 2.0 kJ/mol. The fit to the Landau expression for ordering gives values of Tc = 445 ± 109 K and c′ = 1.62 ± 0.21. This confirms suggestions that the sign of the β coefficient in FeAl2O4 and MgAl2O4 is positive, and opposite to that found in other 2-3 oxide spinels. Non-equilibrium order-disorder behavior below 600 °C has been analyzed using the Ginzburg-Landau model, and successfully explains the time-temperature dependent relaxation behavior observed in the inversion parameter. Changing the stoichiometry, even by as little as 1 mol% Mg-deficiency, significantly reduces the degree of order.

Thick lead-free ferroelectric films with high Curie temperatures through nanocomposite-induced strain

Ferroelectric materials are used in applications ranging from energy harvesting to high-power electronic transducers. However, industry-standard ferroelectric materials contain lead, which is toxic and environmentally unfriendly. The preferred alternative, BaTiO(3), is non-toxic and has excellent ferroelectric properties, but its Curie temperature of ∼130 °C is too low to be practical. Strain has been used to enhance the Curie temperature of BaTiO(3) (ref. 4) and SrTiO(3) (ref. 5) films, but only for thicknesses of tens of nanometres, which is not thick enough for many device applications. Here, we increase the Curie temperature of micrometre-thick films of BaTiO(3) to at least 330 °C, and the tetragonal-to-cubic structural transition temperature to beyond 800 °C, by interspersing stiff, self-assembled vertical columns of Sm(2)O(3) throughout the film thickness. The columns, which are 10 nm in diameter, strain the BaTiO(3) matrix by 2.35%, forcing it to maintain its tetragonal structure and resulting in the highest BaTiO(3) transition temperatures so far.

Transformation of mackinawite to greigite; an in situ X-ray powder diffraction and transmission electron microscope study

Abstract Synthetic mackinawite (tetragonal FeS) has been found to transform rapidly to greigite (Fe3S4) above ∼373 K during heating experiments, as observed by in situ X-ray diffraction. Using monochromatic synchrotron radiation (λ = 0.60233 Å), we measured the unit-cell parameters of both synthetic mackinawite between 293 and 453 K and of greigite formed from this mackinawite between 293 and 593 K. The coefficients of thermal expansion for mackinawite are α1 = α2 = (1.36 ± 6 0.11) × 10-5, α3 = (2.98 ± 0.12) × 10-5, and αvol = (5.67 ± 0.19) × 10-5 between 293 and 453 K. The coefficients of thermal expansion for greigite are α1 = α2 = α3 = (1.63 ± 0.15) × 10-5, and αvol = (4.86 ± 0.25) x 10-5 between 293 and 593 K. On further heating in situ, we observed the reaction greigite → pyrrhotite + magnetite. Partial transformation of mackinawite to greigite was also observed using transmission electron microscopy (TEM) following in situ heating. Electron diffraction patterns show that (001) of mackinawite is parallel to (001) of greigite, and [110] of mackinawite is parallel to [100] of greigite. This orientation relationship confirms that the cubic closepacked S array in mackinawite is retained in greigite and implies that oxidation of some Fe2+ in mackinawite drives rearrangement of Fe to form the new phase. Small regions of the crystallites show Moiré fringes resulting from the lattice mismatch between mackinawite and greigite. Electron diffraction patterns of mackinawite subjected to prolonged exposure to the atmosphere also show faint spots corresponding to greigite. We propose that in these experiments surplus Fe is accommodated by reaction with either adsorbed O2 or H2O to form amorphous nanophase Fe-O(H). Because greigite is so easily formed by oxidation from mackinawite, greigite should be an important precursor for pyrite nucleation, although any orientation relationship between greigite and pyrite remains to be determined.

High-temperature structural phase transitions in perovskite

High-temperature powder x-ray diffraction data are presented for perovskite between 293 and 1523 K. The temperature-dependence of superlattice intensities and cell parameters suggests a sequence of phase transitions from the room temperature orthorhombic (Pbnm) structure to a tetragonal (I4/mcm) polymorph at temperatures in the range 1373 - 1423 K, followed by transformation to the cubic aristotype at . The intensity of the diffuse background increases on transformation to the cubic structure and is associated with disorder (and anionic mobility) of the oxygen sub-lattice. The I4/mcm - Pbnm transition induces a large spontaneous strain, but the tetragonal spontaneous strain in the I4/mcm phase due to the - I4/mcm transition is small, below the resolution of this experiment. These results add weight to suggestions from recent computer simulations that orthorhombic may transform to a tetragonal (rather than a cubic) polymorph under the conditions of the Earths mantle, in which case the effects on electrical conductivity would not be expected to be as great as for a transition to a cubic polymorph, although the consequences for elastic properties may be more significant.

The temperature dependence of the cation distribution in synthetic hercynite (FeAl 2 O 4 ) from in-situ neutron structure refinements

Abstract The temperature dependence of the cation distribution in synthetic hercynite (FeAl2O4) has been determined using in-situ time-of-flight neutron powder diffraction. The sample was synthesized from the oxides under controlled oxygen fugacity and then quenched in air. Neutron diffraction patterns were then collected under vacuum on heating from room temperature to 1150 °C, and the cation distribution was determined directly from site occupancies obtained by Rietveld refinement. The degree of inversion, x, decreased from 0.135(4) at room temperature to 0.112(4) at 600 °C. Thereafter the degree of inversion increases smoothly with increasing temperature, reaching a value of 0.219(5) at 1150 °C. The decrease in x on heating to 600 °C is a kinetic phenomenon caused by the system moving toward its equilibrium degree of order from the relatively disordered state maintained after quenching from the synthesis temperature. The equilibrium ordering behavior between 600 and 1150 °C has been analyzed using both the O’Neill-Navrotsky and Landau thermodynamic models. Although the data could be fitted with both models over the temperature range of the measurements, Landau theory predicts the incorrect curvature of the equilibrium x-T curve, leading to a significant discrepancy in the calculated behavior when the model is extrapolated outside the calibrated temperature range. The correct x-T curvature is predicted by the O’Neill-Navrotsky model, and values of the model coefficients α = 31.3 ± 1.1 kJ/mol and β = 19.7 ± 3.4 kJ/mol were obtained by least-squares fitting to the equilibrium data. This confirms the results of a previous study using quenched material, which suggested that the sign of the β coefficient in FeAl2O4 is opposite to that found in other 2-3 oxide spinels.

Structural States of Mg-Cordierite I: Order Parameters from Synchrotron X-Ray and NMR Data

The hexagonal to orthorhombic phase transition in synthetic Mg-cordierite has been studied by (i) measuring the spontaneous strain associated with the transition using Synchrotron X-ray powder diffraction and (ii) measuring the degree of Al, Si order in terms of the number of Al-O-Al bonds per formula unit using solid state NMR spectroscopy. This defines the two order parametersQ andQodrespectively, and their relationship as a function of annealing temperature and time is used to define the structural states of cordierite during the ordering sequence. The formation of modulated hexagonal cordierite within which a high degree of Al, Si order can be attained, results in a strongly non-linear relationship betweenQ andQod.The transition from modulated to orthorhombic cordierite is strongly first-order under all temperature conditions studied and involves a large step inQ, whileQodchanges continuously throughout the ordering sequence with no marked discontinuity at the phase transition. The lattice distortion, traditionally defined in cordierite by the Δ index provides no full information on the degree of Al, Si order in anhydrous Mg-cordierite, and both order parameters must be used to define its structural state. Transmission electron microscopy has been used to study the mechanism of the transformation from hexagonal to modulated to orthorhombic cordierite.

Computational methods for the study of energies of cation distributions: applications to cation-ordering phase transitions and solid solutions

Abstract The structural and thermodynamic properties of minerals are strongly affected by cation site-ordering processes. We describe methods to determine the main interatomic interactions that drive the ordering process, which are based on parameterizing model Hamiltonians using empirical interatomic potentials and/or ab initio quantum mechanics methods. The methods are illustrated by a number of case study examples, including Al/Si ordering in aluminosilicates, Mg/Ca ordering in garnets, simultaneous Al/Si and Mg/Al ordering in pyroxenes, micas and amphiboles, and Mg/Al non-convergent ordering in spinel using only quantum mechanical methods.

The influence of transformation twins on the seismic-frequency elastic and anelastic properties of perovskite: dynamical mechanical analysis of single crystal LaAlO3

The low-frequency mechanical properties of single crystal LaAlO3 have been investigated as a function of temperature, frequency and applied force using the technique of dynamical mechanical analysis (DMA) in three-point bend geometry. LaAlO3 undergoes a cubic to rhombohedral phase transition below 550 ◦ C. The mechanical response in the low-temperature rhombohedral phase is shown to be dominated by the viscous motion of transformation twin domain walls, resulting in a factor of 10 decrease in the storage modulus relative to the high-temperature cubic phase (super-elastic softening) and a significant increase in attenuation. Super-elastic softening is observed down to 200 ◦ C, below which the mobility of the domain walls decreases markedly, causing a rapid increase in storage modulus and a pronounced peak in attenuation (domain wall freezing). The frequency dependence of the storage modulus close to the freezing temperature is accurately described by a modified Burgers model with a Gaussian distribution of activation energies with mean value 84.1(1) kJ/mol and S.D. 10.3(1) kJ/mol. This activation energy suggests that domain walls are pinned predominantly by oxygen vacancies. Detailed analysis of the dynamic force-deflection curves reveals three distinct regimes of mechanical response. In the elastic regime, the domain walls are pinned and unable to move. The elastic response is linear with a slope determined by the intrinsic stiffness of the lattice, the initial susceptibility of the pinning potential and the bending of twin walls between the pinning sites. In the super-elastic regime, the domain walls unpin and displace by an amount determined by the balance between the applied and restoring forces. The value of the apparent super-elastic modulus is shown to be independent of the spontaneous strain and hence independent of temperature. At high values of the applied force, adjacent domain walls come into contact with each other and prevent further super-elastic deformation (saturation). The strain in the saturation regime scales with the spontaneous strain and the resulting modulus is strongly temperature dependent. The possible effects of domain wall motion on the seismic properties of minerals are discussed. It is concluded that, if these results are directly transferred to mantle-forming (Mg, Fe)(Si, Al)O 3 perovskite, the strain amplitude of a typical seismic wave would be sufficient to cause super-elastic softening. However, pinning of domain walls by oxygen vacancies leads to very short relaxation times at mantle temperatures. If translated to (Mg, Fe)(Si, Al)O 3, these would be too short to amount to significant seismic attenuation. Increased pinning of ferroelastic domain walls by defects, impurities and grain boundaries