Materials which undergo structural phase transitions with bilinear coupling between the spontaneous strain (e(i)(sp)) and the thermodynamic order parameter (Q) of the type lambda(i)e(i)(sp)Q show characteristic fluctuation pattern at T greater than or similar to T-c. Snapshots of such pattern show tweed-like structures with butterfly shaped structure factors. Some experimental fluctuation patterns are reviewed and compared with the theoretical predictions.At T less than or similar to T-c, characteristic microstructures often include structural twinning. The relevant energy expressions for order/disorder systems are recalled and their contribution to thermodynamic fluctuations are described. It is anticipated that some of the physical mechanisms may play a role also in improper ferroelastics with coupling of the type lambda(ik)e(i)(sp)Q(k)(2) where Q(k) is a component of a degenerate order parameter Q = {Q(k)}.

The transition from highly defective (metamict) to crystalline zircon is characterized by short‐range structural order, which follows a different kinetic behavior than the corresponding long‐range order. Experimental results from in situ powder X‐ray diffraction experiments are analyzed using Rietveld refinement and direct Fourier analysis. The Rietveld refinement leads to a detailed assessment of the structural contraction of the crystalline portion of the same during thermal annealing. The Fourier analysis shows a highly heterogeneous distribution of interatomic bond distances. The main effect of structural annealing is a change of the distances between Si and O atoms and the average Si–Zr distance. The Zr–Zr distance seems to be less affected by this thermal treatment. Short‐range order is recovered at lower temperatures than that of long‐range order. Crystallinity is recovered anisotropically with slower annealing along the crystallographic c‐direction than along the a‐direction.

Single crystal X-ray diffraction was applied in order to investigate defect-induced microstructures in radiation damaged zircon. The formation of domains with different degrees of order was observed and in particular, it was possible to distinguish two types of defects: isolated lattice defects and dislocations. These lattice deformations have a great influence on the structural and physical properties of the materials.

The role of SiO4 groups in a thermally annealed zircon has been investigated. The lattice parameters suggest that at 1,343 K recrystallized zircon is in the high temperature structural modification. The observed changes in the IR spectra of annealed zircon can be explained with a two stage process: (i) a relaxation of the tetrahedra as a function of time, indicating that in the metamict zircon there is a further deformation of the tetrahedra with respect to the one related to the high-temperature structural change and (ii) new absorption bands appear and they can be identified as cristobalite. This latter observation helps the modelling of the recrystallization process based upon diffusion rates.

Ferroelastic twin structures may be tailored and used for chemical reactions in the confined space of twin walls. As an example, superconducting twin walls are described in an isolating matrix of WO3. The crucial role of the wall energy and the wall thickness for compositional changes are discussed. Wall patterns include the bending of twin walls and the formation of needle domains as steps in the construction of hierarchical wall structures. Emphasis is given to the structural features at the intersection of twin walls with the sample surface.

Twin wall related diffuse scattering intensities from a single crystal of LaAlO3 were determined using high-resolution x-ray diffraction methods. Rocking curves were measured for sample temperatures between 295 and 900 K. The wall thickness W was determined by comparing the observed diffraction profiles with structure factor calculations for a tanh(x/W) wall profile. It is shown that W≈20 Å at low temperatures and increases slowly with temperature reaching values in excess of 200 Å near Tc≈850 K with W∝|T−Tc|−1.

Abstract Diffuse X-ray scattering from single crystals of metamict zircon reveals residual crystallinity even at high fluences (up to 7.2 × 1018 α-decay events/g). The experimental evidence does not suggest that radiation-induced amorphization is a “phase transition.” The observations are in good agreement with a nonconvergent, heterogeneous model of amorphization in which damage production is a random process of cascade formation and overlap at increasing fluence. Instead of an amorphization transition, the existence of a percolation transition is postulated. At the level of radiation damage near the percolation point, the heterogeneous strain broadening of Xray diffraction profiles is reduced whereas the particle-size broadening increases. Simultaneously, the macroscopic swelling of the zircon becomes larger than the maximum expansion of the unit-cell parameters. A suitable empirical parameter that characterizes this transition is the flux, Ds, at which the macroscopic expansion is identical to the maximum expansion of the crystallographic unit cell. In zircon, Ds = 3.5·1018 α-decay events/g.

In-situ temperature-dependent X-ray powder diffraction is used to study the annealing behaviour of a natural U-thorite which is characterized by some degree of radiation damage. While the lattice parameters and the line widths are independent of the annealing conditions, the thermal variation of the intensities is hkl dependent at lower temperatures indicating a multistage annealing process. Impurities such as U and Fe are believed to play a major role during cation diffusion and therefore in the annealing process.

The diffuse scattering in WO3 has been investigated using high-resolution X-ray methods. The structure of the (040)/(400) diffraction profiles in a densely twinned orthorhombic crystal has been mapped. The scattering is characterised by strong, well defined Bragg peaks with a diffuse streak between these of intensity three orders of magnitude lower, arising from the domain walls. Comparison with a simple analytical model for the scattering from such a microstructure suggests an effective domain wall width of around 4 unit cells.

Abstract Radiogenic impurities of 400 to 800 ppm U and Th in titanite, CaTiSiO5, lead to moderate radiation damage (≈1.5 × 1018 α-decay events/g) and therefore to partial amorphization (≈30%). Powder X-ray diffraction on such damaged titanite from the Cardiff locality in Canada shows that two modifications of the crystalline material coexist. Both modifications are structurally β phase but differ systematically in their lattice parameters and also in their chemical composition. One modification exhibits strong particle size broadening in X-ray diffraction patterns, whereas it is almost unstrained with respect to fully annealed titanite. The other modification shows large strain broadening and increased specific volume (about 3%) due to a high concentration of defects. The unstrained modification consists of small nucleation centers in the damaged material, and it grows when the sample is annealed. At annealing temperatures above 823 K, this modification dominates rapidly and replaces the strained titanite. The results of Rietveld refinement of the annealed samples and of the time evolution of isothermal annealing studies are discussed. The analysis of volume strain and of structural strain resulting from the peak profiles suggests a temperature-dependent activation energy for the recrystallization process, with EA ≈ 380 kJ/mol at T > 873 K and EA ≈ 500 kJ/mol at temperatures 773 K < T < 873 K.

AbstractAt any set of thermodynamic conditions a mineral will have some well defined equilibrium crystal structure. However, this structure can be locally disturbed by crystal defects, such as domain walls or solute atoms. This distorted structure will only affect a finite volume within the crystal, but the need to retain continuity within the crystal means that this volume must be non-zero. This means, for example, that the boundary between two domains will include a transition zone from one domain's crystal structure to that of the other domain. Thick twin domain walls can be studied quantitatively, by measuring the intensity of diffuse diffraction between pairs of twin-related Bragg peaks. In alkali feldspar (Or30) at room temperature, these walls are approximately 25 Å thick. Similarly, a single solute atom in a mineral will only affect a small region within a crystal. As a result, chemical mixing will only occur in a substitutional solid solution once there is significant overlap between the strain fields around individual solute atoms. This causes the ‘plateau effect’, where the properties of a phase transition are independent of composition. In alkali feldspar, this plateau extends from albite to 2% Or, which corresponds to a strain field radius of 10 Å.These phenomena can be modelled using Ginzburg-Landau theory, which predicts that the range of these strain fields will increase as the temperature is raised to Tc. This has been confirmed by measuring the thickness of twin walls as a function of temperature.

An easy approach to the quantitative analysis of non-crystalline phases in ceramic materials is proposed for XRD data. The Foul icr transform of the total intensity of a powder diffraction spectrum yields structural information for both crystalline and amorphous components. In addition, it allows the characterisation of the nature of defective structures in those cases where compositional fluctuations are present. (C) 1998 The Institute of Materials.

In situ time-dependent high-temperature X-ray powder diffraction was used to study the amorphous to crystalline transition in natural zircons which are characterized by a high degree of radiation damage. It was possible to distinguish two stages of the annealing process: (i) the recovery of the heavily disturbed but still crystalline domains and (ii) the recrystallization of the amorphous regions. The first stage is very fast under the chosen experimental conditions and, at least apparently, is not thermally activated. The second stage is a diffusion-controlled process, whose products (zircon or zircon and zirconia phases) are strongly correlated to the annealing temperature.

Weak uniaxial stress (< 1 kPa) along the cubic [100] and [110] directions of modifies significantly the domain structure near the crystal surface on cooling to the tetragonal phase. High-resolution x-ray rocking curves show that oriented slabs have a preference of `c' domains perpendicular to a small (001) surface. On heating from 10 K the domain population increasingly randomizes when the transition point is approached. In oriented slabs the domain population is more random with little temperature dependence for nominally stress-free samples. Uniaxial stress along increases the population of `a' domains for . The `c' domains have characteristically shorter length scales perpendicular to the surface than the larger `a' domains. The rocking angle of `c' domains has a much larger angular spread (ca ) than those of `a' domains.

X-ray diffraction rocking curves of titanite, CaTiSiO5, were measured using a novel high-resolution diffractometer. Three Bragg reflections were recorded as a function of temperature and their profiles analyzed in terms of a Gaussian Bragg peak and a diffuse scattering component with an overall Lorentzian shape. The temperature dependence of the Gaussian intensities of the rocking peaks of superstructure reflections, hkl with k + l odd, scale with the long-range order parameter as I alpha Q(2) alpha \T - T-c\(2 beta), where beta = 0.14(1) is the effective order parameter exponent.The diffuse scattering intensity changes little with temperature at T < T-c - 20 K. Strong diffuse scattering is found at T > T-c with centers of their Lorentzian diffraction profiles shifted by Delta omega approximate to 0.5 degrees with respect to the position of the equivalent Bragg peak. A second phase transition at 825 K is confirmed and the possibility of a third transition at similar to 1150 K is discussed.

We present the first systematic study of the microstructures and properties of a series of epitaxial YBa2(Cu1−xAlx)3O7−δ thin films of various Al concentrations deposited on (001) MgO by pulsed laser ablation. The samples have been characterized using optical microscopy, scanning tunneling microscopy, transmission electron microscopy and X-ray diffractometry. We report a transition from a twin to a tweed contrast in the electron microscope and a decrease in the orthorhombicity of the films on doping with Al. The length scale of the twin microstructures observed by TEM correlate well with that of a characteristic contrast in the polarized light microscope. From our experiments we have been able to estimate the critical dopant concentration to form a macroscopically tetragonal YBa2(Cu1−xAlx)3O7−δ film at room temperature to be x = 0.055.

Novel high-resolution X-ray diffractometers have been used to investigate a variety of microstructures such as twins, tweed, and domain boundaries in ferroelastic materials. It is shown that copious information can be extracted using our experimental methods. The instruments are equipped with 1D and 2D detectors, where the distance to the sample can be varied to enhance the intrinsic resolution. Both the specimen and the detectors possess several degrees of freedom which include sample tilts and rotations as well as translations. In our contribution we introduce briefly the experimental and theoretical methods connected with this special equipment and describe its application to the characterization of a wide variety of specimens such as single crystals, ceramic materials and thin films.

Using a 5 GHz parallel plate resonator, several Gd123 thin films have been studied. The low RF power dependence, the DC field dependence and the power dependence in the presence of DC fields have been measured. Two films were modified by introducing intragranular defects by high energy irradiation of either Kr ions or /spl alpha/ particles. By using a simple model, values for high frequency pinning constant /spl kappa//sub p/ were extracted. The DC screening current density J, was also measured. We examine whether the irradiation has improved the DC and high frequency pinning properties and the impact this has on the power dependence of the surface resistance. Comparison between the DC and the power dependence losses are made.

A new high-resolution X-ray diffractometer is described which combines and enhances the flexibility of a 4-circle diffractometer with the possibility to use it as a bond camera and as grazing incidence surface diffractometer. The X-ray beam is strictly monochromatic (CuK alpha(1)) and focused with a long focal length on the sample. The beam diameter is adjustable between 0.05 mm and 5 mm. The sample goniometer can be rotated around three perpendicular axes with two rotation axes perpendicular to the direction of the incoming beam. The instruments are equipped with 1D and 2D detectors, their distance to the sample can be varied between 10 and 30 cm. The detectors themselves have additional degrees of freedom so that out-of-plane reflections can be measured. In our contribution we describe mainly the experimental methods connected with this special equipment which allows the characterisation of a wide variety of specimens (single crystals, thin films, and ceramic or powder materials).