F.L. Cumbrera

On the transformation toughening of Y–ZrO2 ceramics with mixed Y–TZP/PSZ microstructures

Abstract Heat treatment of Y–TZP at high temperatures produces materials with a mixed Y–TZP/PSZ phase assemblage, which exhibit a unique combination of high mechanical strength and fracture toughness, uncommon in zirconia ceramics. The microstructure and crack growth resistance of the Y–TZP/PSZ materials developed by treating at 1650°C in air a fine-grained Y–TZP was studied. XRD as well as Raman spectroscopy results indicate that the obtained microstructure allow the retention of large tetragonal grains (up to ∼4 μm), resulting in both phase transformability enhancement and pronounced R-curve behavior. The large transformation zone, discerned from accurate measurements with Raman microprobe spectroscopy, sustains the above assessment and points out tetragonal to monoclinic phase transformation as the main toughening mechanism in the investigated Y–TZP/PSZ microstructures. This was confirmed by satisfactory agreement between the transformation toughening estimated from numerical analysis and the crack shielding experimentally determined from the R-curve measurements.

Contact fracture of brittle bilayer coatings on soft substrates

Contact-induced fracture modes in trilayers consisting of a brittle bilayer coating on a soft substrate were investigated. Experiments were performed on model transparent glass/sapphire/polycarbonate structures bonded with epoxy adhesive, to enable in situ observation during the contact. Individual layer surfaces were preferentially abraded to introduce uniform flaw states and so allowed each crack type to be studied separately and controllably. Fracture occurred by cone cracking at the glass top surface or by radial cracking at the glass or sapphire bottom surfaces. Critical loads for each crack type were measured, for fixed glass thickness and several specified sapphire thicknesses. Finite element modeling (FEM) was used to evaluate the critical load data for radial cracking, using as essential input material parameters evaluated from characterization tests on constituent materials and supplemental glass/polymer and sapphirse/polymer bilayer structures. The FEM calculations demonstrated pronounced stress transfer from the applied contact to the underlying sapphire layer, explaining a tendency for preferred fracture of this relatively stiff component. Factors affecting the design of optimal trilayer structures for maximum fracture resistance of practical layer systems were considered.

The use of the JMAYK kinetic equation for the analysis of solid-state reactions: critical considerations and recent interpretations

The present work is concerned with the classical Johnson-Mehl-Avrami-Yerofeev-Kolmogorov (JMAYK) equation. Some critical points are presented because this kinetic relation has been extensively misused. Various aspects regarding its failure when it is applied to recrystallization of plastically deformed metals are also considered. Recent conceptual improvements, such as the new approach where the transformation is described by the superposition of single JMAYK processes, have resulted in the resurgence of this approach.

Role of flaw statistics in contact fracture of brittle coatings

Abstract A flaw statistics analysis is here developed to account for systematic differences between experimentally observed and theoretically predicted critical loads for the initiation of contact-induced radial cracks in brittle coatings on compliant substrates. Specific attention is drawn to deviations in critical load ( P R ) data from ideal quadratic dependence on coating thickness ( d ), i.e. P R ∝ d 2 , especially at low d values. It is postulated that these deviations are attributable to the existence of distributions in flaw size and location, in relation to the bell-shaped tensile stress fields responsible for initiation of the radial cracks at the coating lower surface. A statistics-based expression is derived for the mean values of P R in terms of flaw density and size distribution. Data from model bilayers consisting of glass plates of different thicknesses d bonded to polycarbonate substrates are used as an illustrative case study. Controlled pre-abrasion flaws are introduced into the lower glass surfaces before joining into the bilayer configuration, to enable a priori characterization of distribution parameters by image analysis. Finite element modelling is used to determine the tensile stress distribution at the coating lower surface. The predicted statistics-based P R ( d ) function is shown to fit the data within uncertainty bounds. Implications concerning the continued usefulness of the ideal, P R ∝ d 2 relation for designing ceramic coatings for failure resistance are considered.

Analytical formulation of the variance method of line-broadening analysis for Voigtian X-ray diffraction peaks

An alternative formulation of the variance method for the line-broadening analysis of polycrystalline materials is presented. It maintains the theoretical basis of the earlier formulations of the variance method, but differs in the manner of calculating the variance coefficients of the line profiles. In the proposed formulation, these are evaluated analytically in terms of the shape parameters of Voigt functions fitted to the X-ray diffraction data. Explicit expressions are thus derived for calculating the (surface-weighted) crystal sizes and (root-mean-square) lattice microstrains from the integral breadths of the Gauss and Lorentz components of the Voigt functions that model the experimental and instrumental line profiles.

Measurement of fiber orientation in short-fiber composites

Abstract The degree of fiber orientation in short-fiber composites plays an important role in determining many properties of these materials. In order to predict the toughening of a composite by using fiber reinforcements, we must consider the orientation of fibers as described probabilistically by the distribution function f(ψ), where ψ is the angle which each fiber makes with the normal to the crack face. Here, a method for the characterization of the fiber orientation is built up in successive steps. In a first step the measurements of a planar array of fibers is afforded by extracting the important statistical information contained in a calculated Fraunhofer diffraction pattern of the fiber distribution. Subsequently, a method is proposed allowing us to derive the relevant f(ψ) distribution from the two-dimensional characterization of two orthogonal plane sections of the composite.

X-ray powder diffraction analysis of a silicon carbide-based ceramic

Abstract Accurate X-ray powder diffraction (XRD) analysis of SiC-based ceramics is a difficult task due to the significant overlap of the Bragg reflections from the different SiC polytypes. For this reason, results obtained by traditional XRD methods are, in general, unsatisfactory. Here, we have applied the Rietveld and two line-broadening (variance and integral breadth) methods to analyze a liquid phase-sintered SiC sample. The Rietveld method was used to carry out the quantitative phase-composition analysis and to resolve (as a first step) the overlapped SiC Bragg reflections. Starting from the Rietveld results, the different SiC peaks were then unambiguously obtained by a Levenberg–Marquardt non-linear least-squares fit. Subsequently, the variance and integral breadth methods were used to perform the microstructural analysis. It is shown not only that the procedure is especially useful, but also that both line-broadening methods lead to similar crystallite sizes. The co-existence of β (3C) and α (4H and 6H) SiC polytypes and the nanometric diffraction domain sizes for the SiC polytypes were also found. Finally, these results are discussed in the light of the β to α partial transformation that took place during the sintering.

Structure determination of di-μ-hydroxo-bis[(2-(2-pyridyl)phenyl-κ2N,C1)palladium(II)] by X-ray powder diffractometry

The title compound was synthesized in the form of a powder, and was studied by elemental analysis, IR spectroscopy, thermogravimetry and mass spectroscopy. Its crystal structure was then determined by X-ray powder diffractometry, using X-ray diffraction data collected in the reflection Bragg-Brentano geometry. The methodology followed in the present study to resolve the crystal structure consisted of peak indexing, then the use of the Monte-Carlo/parallel tempering search algorithm, and finally Rietveld refinement coupled with difference-Fourier synthesis. We found that the crystals are composed of monoclinic unit cells, with 1.5 molecules in the asymmetric unit and therefore six molecules per unit cell. In addition, we concluded that the complexes adopt a planar conformation, forming trimers created by groups of parallel molecules.

Fundamental parameters approach in the Rietveld method: a study of the stability of results versus the accuracy of the instrumental profile

The Rietveld refinement method is a valuable tool for structural and microstructural analysis of a variety of crystalline materials. In spite of many important developments in the last decade, most current Rietveld programs suAer from a number of drawbacks. In order to overcome these disadvantages, the ‘‘fundamental parameter approach’’ (FPA) has been used recently. The FPA uses a convolution-based method to build up X-ray line profiles. Instrumental and sample aberrations are calculated from first principles, and convoluted with the emission profile to form the final line profile. Although this methodology eliminates the need for a standard, in practice some instrumental parameters must be refined, resulting in certain empiricism in this procedure. Therefore, the comparison with a strain-free and ‘infinite crystallite size’ standard becomes necessary. In this work we have performed a study of the stability of quantitative analysis and microstructural results versus simulated inaccurate instrumental profiles. All the FPA calculations were performed on X-ray diAraction data from a technologically attractive and scientifically challenging system: liquidphase-sintered SiC (LPS SiC). # 2000 Elsevier Science Ltd. All rights reserved.

Microstructural characterization of Y-PSZ (4 mol%) polycrystals by means of X-ray diffraction experiments

Abstract A quantitative determination of the phase abundance on Y-PSZ (4 mol%) polycrystals is performed by X-ray diffraction (XRD). Our procedure takes account of the strong peak overlapping, the presence of t′ phase and preferred orientation artifacts. The individual reflections of each phase are fitted to Pearson VII functions. The influence of the preferred orientation is handled by a procedure in which an expansion in spherical harmonics allows us to relate the measured integrated intensities to the “randomoriented” ones. The method is used to study the microstructural evolution of two sintered samples (1550°C and 1650°C) heat treated in air at 1600°C and subsequently air cooled.