F. Sánchez-Bajo

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.

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.

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.

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.

The prolific polytypism of silicon carbide

A worked example of polytypism is presented, aimed at assisting undergraduates in the learning and instructors in the teaching of this topic. In particular, this crystallography concept, not necessarily obvious for beginners, is illustrated pedagogically using to that end the model case of the prolific polytypism of silicon carbide (SiC). On the basis of concepts that are easily assimilated by students (i.e. simple topological constraints) this article first presents a unified description of the polytypism phenomenon in SiC that allows one to understand without difficulty the existence of its numerous polytypic variants and how they develop. Then the various notations used to designate these different polytypes are described, and finally the crystal structures of the most common are discussed. This worked example is thus expected to contribute to motivating undergraduates in the study of a crystallography topic that often is not treated in sufficient depth in class.

On the Reliability of the de la rue Sunspot Area Measurements

In the 19th century De la Rue, Stewart, and Loewy carried out a compilation of drawings and photographs of the solar sunspots in the period 1832–1868. From these drawings and photographs, they determined fortnightly values of the sunspot areas. In this work, monthly values of the sunspot areas for the period 1832–1868 are calculated and the reliability of these data in terms of the solar activity indices is discussed.

A Measure of the Solar Rotation During the Maunder Minimum

In this paper we present a measure of the synodic solar rotation rate derived from an analysis of a Flamsteed drawing, corroborating the decrease of the solar rotation in the deep Maunder minimum (1666–1700).