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This work presents a fast and direct controlled routine for the fabrication of fully dense alumina based on the reactive spark plasma sintering (reactive-SPS) of boehmite ( γ -AlOOH) nano-powders obtained by the sol-gel technique. The evolution of the transition aluminas during sintering has been studied. Some boehmite powders were seeded with α -Al 2 O 3 particles prior to the gelation. Boehmite seeded powders exhibited a direct transition to α -Al 2 O 3 at 1070 ° C, enhancing the transformation kinetics and lowering the required temperature by more than 100 ° C. For comparison, other samples were prepared by previously annealing the seeded and unseeded boehmite powders. Thus, α -Al 2 O 3 powders were obtained and were sintered by standard-SPS. A detailed structural and mechanical characterization is presented, comparing the hardness and indentation fracture resistance for different grain sizes and porosities. Both the reactive-SPSed samples and the standard-SPSed samples showed a high hardness (18-20 GPa), whereas the reactive-SPSed samples exhibited a lower indentation fracture resistance due to a large grain size ( ∼ 10 μ m). Improvements of this procedure for obtaining smaller grain size are discussed. In summary, the presented technique brings a revolutionary fast method for the fabrication of fully dense alumina, as this process reduces the time and temperature required for alumina densification.

An analysis of the sunspot observations made by Hevelius during 1642-1645 is presented. These records are the only systematic sunspot observations just before the Maunder Minimum. We have studied different phenomena meticulously recorded by Hevelius after translating the original Latin texts. We re-evaluate the observations of sunspot groups by Hevelius during this period and obtain an average value 7% greater than that calculated from his observations given in the current group database. Furthermore, the average of the active day fraction obtained in this work from Hevelius' records previous to the Maunder Minimum is significantly greater than the solar activity level obtained from Hevelius' sunspot observations made during the Maunder Minimum (70% vs. 30%). We also present the butterfly diagram obtained from the sunspot positions recorded by Hevelius for the period 1642-1645. It can be seen that no hemispheric asymmetry exists during this interval, in contrast with the Maunder Minimum. Hevelius noted a ~3-month period that appeared to lack sunspots in early 1645 that gave the first hint of the impending Maunder Minimum. Recent studies claim that the Maunder Minimum was not a grand minimum period speculating that astronomers of that time, due to the Aristotelian ideas, did not record all sunspots that they observed, producing thus an underestimation of the solar activity level. However, we show the good quality of the sunspot records made by Hevelius indicates that his reports of sunspots were true to the observations.

A new software (Soonspot) for the determination of the heliographic coordinates and areas of sunspots from solar images is presented. This program is very user-friendly and the accuracy of its results has been checked by using solar images provided by the Debrecen Photoheliographic Data (DPD). Due to its applicability in the studies of historical solar observations, the program has been used to analyze the solar drawings carried out by Hevelius in the 17th century.

Analytical expressions are formulated that enable the lognormal distribution of nanocrystallite sizes and the mean-squared crystal lattice microstrain in both doped and undoped nanocrystalline ceramics to be routinely determined by X-ray diffractometry. Importantly, these expressions, which are also applicable to most well-annealed nanocrystalline metals/alloys, are developed under the consideration that both the experimental and instrumental X-ray diffraction peaks are modeled by split Voigt functions to account for the (hitherto widely ignored) intrinsic peak asymmetry. The general analytical expressions of this new single-peak line-broadening method are then particularized to the case of small nanocrystallites with uniform composition for which a reasonable simplification (i.e., symmetrization of the experimental peak) can be made without compromising the accuracy of the results. Next, as an example of application the method developed is applied to the characterization of a nanocrystalline ceramic powder, and the nanocrystallite sizes so-determined are validated by transmission electron microscopy. The more complete and reliable microstructural information offered by this single-peak line-broadening method could contribute towards the accurate characterization of both doped and undoped nanocrystalline ceramics, and of most well-annealed nanocrystalline metals/alloys as well, a topic of particular research interest today.

The comminution of a typical submicrometre B4C powder with a high-energy mill (i.e., a shaker mill) operated in air in either a dry or a wet environment was investigated. It was found that dry shaker milling (i.e., high-energy ball-milling) is able to progressively refine the B4C particles to the nanoscale. While this is accompanied by oxidation and aggregation, these are not serious drawbacks. Wet shaker milling in methanol (i.e., conventional ball-milling) resulted only in a moderate B4C particle refinement with greater contamination by the milling tools, which limits its usefulness. It was also found that both dry and wet milling modify the B4C crystal structure, attributable to carbon enrichment. Consequently, dry shaker milling was found to be more recommendable than wet shaker milling to provide B4C starting powders with superior sinterability. A comparative densification study by spark-plasma sintering confirmed this recommendation, and also showed the usefulness of dry shaker milling to obtain refined B4C microstructures for structural applications.

In this paper we analyze a small collection of sunspot drawings made at the Astronomical Observatory of the Spanish Navy in the period from April 1, 1884 to August 18, 1884. We calculate the area and the heliographic coordinates of the observed sunspots. From these coordinates, we obtain the solar rotation rate in this period. Finally, we compare our results with the data recorded by the Royal Greenwich Observatory.

Two tin dioxide samples undergone to different thermal treatments have been studied by X-ray diffraction profile analysis, using the modified Williamson-Hall and Warren-Averbach methods. Assuming {101} slip system and screw dislocations, the area and volume-weighted average particle sizes have been evaluated for both samples. The assumed log-normal particle size distribution has been calculated from these values. This distribution is in good agreement with the derived from SEM micrographs for the sample with lower particle size. Values of the dislocation densities were estimated around 10 14 m −2 for the sample with lower grain size and around 10 12 m −2 for the sample with greater grain size. The difference in the results for the analyzed samples could be explained from the difference between the treatments after synthesis.

A wide set of 3 mol% Y2O3-stabilized ZrO2 (3YSZ) powders have been synthesized by the sol–gel method without modifiers from solutions of zirconium n-propoxide and yttrium acetate prepared with different water/Zr molar ratio and zirconium concentration, and the effect of these two synthesis variables on the pressureless sinterability of the 3YSZ powders has been investigated. It was found that the sinterability increases with increasing zirconium concentration and water/Zr molar ratio, which is attributed to the smaller cluster size developed during the sol–gel synthesis. Implications for the preparation of more sinterable 3YSZ powders are discussed Fil: Mamana, Nadia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Instituto de Física de Rosario. Universidad Nacional de Rosario. Instituto de Física de Rosario; Argentina Fil: Ortiz, Angel L.. Universidad de Extremadura. Badajoz; España Fil: Sánchez Bajo, Florentino. Universidad de Extremadura. Badajoz; España Fil: Caruso, Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Instituto de Física de Rosario. Universidad Nacional de Rosario. Instituto de Física de Rosario; Argentina

Solar rotation rates can be measured from changes in sunspot positions. In this paper, we propose using digital camera images taken with small telescopes to determine the solar rotation rate at different heliographic latitudes. This low-cost practical experiment can be performed easily by undergraduate students, introducing them to topics related to solar physics. The data obtained in this work from the analysis of sunspots observed in 2010, 2011 and 2012 were compared with current models of solar rotation, showing good agreement.

The accuracy of the Rietveld method in determining the lattice parameters of polytypes in multiphase SiC ceramics was investigated as a function of the polytype composition and of the polytype crystallite size, using as benchmarks two sets of standard X-ray diffraction (XRD) patterns obtained by computer simulation. It was found that the Rietveld method is remarkably accurate, but also that the measurement of lattice parameters is sensitive to the polytype composition and to the polytype crystallite size. In particular, the accuracy of Rietveld-calculated lattice parameters for a given polytype not only decreases with increasing number of polytypes in the SiC ceramics, but also depends on which other polytypes are present. These two findings are interpreted based on the severity of the corresponding peak overlap phenomenon in the XRD patterns. In addition, the accuracy of the Rietveld analyses also decreases with decreasing crystallite size of the polytypes, which is due to the progressive loss of definition in the location of the peak maxima and to the greater severity of the peak overlap, both resulting from the corresponding peak broadening. This identification of the confidence limits of the Rietveld-calculated lattice parameters for a wide range of microstructural features may have important implications for the future characterization of SiC ceramics by XRD.

A procedure to estimate the aerosol extinction parameters of Angstrom's formula using data acquired with photometric broadband standard filters, the Johnson–Cousins filters, is presented. The method is based on the transformation of the heterochromatic magnitudes to the equivalent mean wavelength monochromatic magnitudes by an iterative approach, correcting subsequently the effects of water-vapour extinction in the longer-wavelength filters. As an example, the procedure has been used in the determination of the extinction parameters at the location of our observatory using the filters B, V, Rc and Ic on the night of 2008 August 28.

Valuable information about the evolution of solar activity is recorded in early sunspot drawings, especially during 17th–19th centuries. In this context, we have developed a computer program to analyze historical drawings showing the trajectories of sunspots across the solar disk. As an example, we have analysed the drawings published in the book De heliometri structura et usu by Zucconi (1760) . These drawings span the period from April 1754 to June 1760. We present the Butterfly diagram for those years. The ending of solar cycle 0 and the beginning of solar cycle 1 are clearly noted in this diagram.

We experimentally studied the restoring force of a length of stretched elastic cord. A simple analytical expression for the restoring force was found to fit all the experimental results for different elastic materials. Remarkably, this analytical expression depends upon an elastic-cord characteristic parameter which exhibits two limiting values corresponding to two nonlinear springs with different Hooke's elastic constants. Additionally, the simplest model of elastic cord dynamics is capable of exhibiting a great diversity of nonlinear phenomena, including bifurcations and chaos, thus providing a suitable alternative model system for discussing the basic essentials of nonlinear dynamics in the context of intermediate physics courses at university level.

Solar rotation rate has been measured using the sunspot positions recorded by W.C. Bond during the period 1847 – 1849 at the Harvard College Observatory. From the drawings carried out by Bond we have selected the sunspots and groups of sunspots with more reliable positions presented in three or more drawings on successive days. We have calculated from the positions of the selected sunspots (41 in total) a synodic rotation rate of ω=[(12.92±0.08)−(1.5±1.0)sin 2φ] degrees/day, where φ is the heliographic latitude. This rate, although slightly lower, is similar to the actual solar rotation rate, confirming no important changes in the solar rotation during the last 160 years.

A custom processor based on reconfigurable hardware technology is proposed in order to compute the figure of merit used to measure the quality of the fit of X-ray diffraction peaks. As the experimental X-ray profiles can present many peaks severely overlapped, it is necessary to select the best model among a large set of reasonably good solutions. Determining the best solution is computationally intensive, because this is a hard combinatorial optimization problem. The proposed processors, working in parallel, increase the performance relative to a software implementation.

A new normalized sunspot-area series has been reconstructed from the series obtained by the Royal Greenwich Observatory and other contemporary institutions for the period 1874 - 2008 and the area series compiled by De la Rue, Stewart, and Loewy from 1832 to 1868. Since the two sets of series do not overlap in time, we used as a link between them the new version of sunspot index number (Version 2) published by SILSO (Sunspot Index and Long-term Solar Observations). We also present a spectral analysis of the normalized area series in search of periodicities beyond the well-known solar cycle of 11 years and a study of the Waldmeier effect in the new version of sunspot-number and the sunspot-area series presented in this study. We conclude that while this effect is significant in the new series of sunspot number, it has a weak relationship with the sunspot-area series., Comment: 16 pages, 5 figures, to be published in Solar Physics

New ephemeris and the absolute parameters—masses, radii and luminosities—of the contact systems VW LMi and BX Dra have been obtained, by means of the analysis of the minima data available in the literature (for the determination of the ephemeris) and combining the previously published spectroscopic information and the results of the Wilson-Devinney method using photometric data (for the determination of the absolute parameters). The VW LMi O−C analysis confirms the multiplicity of the system detected previously from the spectroscopic data. Masses of the VW LMi contact system primary and secondary components are 1.67 ± 0.02M ⊙ and 0.70 ± 0.02M ⊙, respectively. The corresponding radii are 1.709 ± 0.007R ⊙ and 1.208 ± 0.006R ⊙, respectively. For the BX Dra contact system the masses are 2.19 ± 0.13M ⊙ and 0.63 ± 0.06M ⊙, and the radii, 2.13 ± 0.04R ⊙ and 1.26 ± 0.03R ⊙, for the primary and secondary, respectively. In both cases, the estimated luminosities seem to be slightly greater that the values derived from the Hipparcos distances.

Variable stars offer interesting possibilities from the point of view of educational applications, from the experimental collection of data to analysis to obtain physical information. In this paper, brightness measurements of two periodic variable stars easily accessible with small telescopes are presented and analysed. This practical experiment is highly appropriate for educational use in undergraduate physics and astrophysics laboratories and allows students to approximate scientific research.

We have developed a novel, analytical model for the determination of grain size distributions in nanocrystalline (nc) materials with low internal stresses by X-ray diffractometry (XRD). The model assumes explicitly that the XRD peaks are pseudo-Voigtian and that the grain size distributions are lognormal, both of which are assumptions amply supported by the experimental evidence. It was found analytically that the grain size dispersion depends on the shape of the XRD peaks only, whereas the grain size median depends on both the shape and width of the XRD peaks. In addition, the theoretical predictions resulting from the model were validated using standard XRD peaks obtained by computer simulation from first principles. Particular emphasis is given to the discussion of the validity limits of the model, and to the analysis of the influence of the characteristics of the grain size distributions on the nature of the XRD peaks. We then show how to calculate the average and apparent grain sizes from the grain size distribution determined with the model, and how this compares with the Scherrer method. Implications for the characterization of (undistorted and distorted) nc-materials are indicated, and a case study of an nc-powder of cubic ZrO 2 is presented. The application of the model itself is simple, involving only the fit of a pseudo-Voigt function to a single XRD peak followed by the use of two equations. This suggests that the model may have an important role to play in the characterization of nc-materials.

ZrO 2 –3 mol% Y 2 O 3 -coated AISI 310 stainless steel was nitrided using a plasma produced by dc pulsed discharge in a mixture of N 2 and H 2 at an equilibrium temperature of 450 °C. The phase structure and surface morphology were investigated by X-ray diffractometry and atomic force microscopy, respectively. Glow discharge optical emission spectrometry was used to measure the depth composition of samples. The mechanical properties were studied by means ultramicrohardness indentation tests. Nitrogen atoms enter in the zirconia substituting to the oxygen atoms in the network. However, the nitrogen content measured in zirconia coating is greater than the allowed maximum content of nitrogen in doped-zirconia solid solution. The ion-nitriding process alters the surface topography of the zirconia coatings. The nitruration improves the mechanical responses of the ZrO 2 –3 mol% Y 2 O 3 -coated AISI 310 stainless steel.

A new polymorphic method to determine phase compositions of SiC-based ceramics from their X-ray diffraction profiles has been proposed. Basically, this polymorphic method differs from others already proposed in the literature as follows: (1) a set of parameters is introduced to take into account the possible overlap between different groups of peaks and, (2) a square system is used instead of an overdetermined system to determine the phase composition. The accuracy of the method has subsequently been evaluated using a set of standard X-ray diffraction patterns as a benchmark and the corresponding absolute mean and maximum errors were found to be as low as 2.7 and 6.4%, respectively. In addition, it was also found that the method is much more effective than its polymorphic counterparts, as no physically meaningless negative compositions were found in this study. Moreover, the practical application of the method is quite simple and the phase composition can be determined quickly even using a conventional scientific pocket calculator. We have then demonstrated that the use of the proposed method to determine phase compositions of SiC-based ceramics has several important advantages over other polymorphic methods in terms of enhanced simplicity, accuracy and effectiveness. Parallel analyses of a commercially available α-SiC powder and of a liquid-phase-sintered SiC ceramic further reinforced these arguments.

The thermal behavior of the hyperfine interaction at Zr sites on two sol-gel derived 6 mole% CaO-ZrO2 powders, obtained from the particulate and non-particulate regimes, has been studied by Perturbed Angular Correlations and complementary techniques. The aim was to get experimental support on the thermal stability of the obtained material in order to see the advantages of the different preparation regimes. The results could be interpreted in terms of the different microstructures and nanoscopic configurations exhibited by the resulting powders. After crystallization both powders showed the hyperfine nanoconfigurations of metastable tetragonal zirconia. In the sample obtained following the hydrolysis and the condensation processes via a particulate regime, the undesirable phase transformation towards the monoclinic form of zirconia is inhibited up to higher temperatures.

Structural determination using X-ray powder diffraction is usually restricted to relatively simple structures, although powder diffraction data are frequently used to refine, via the Rietveld method, approximately known structures. In this work, the relatively complex crystalline structure of a compound of high pharmaceutical interest (C11H12N4S2) has been firstly ab initio determined from its X-ray powder diffraction pattern and subsequently refined by the Rietveld method. This refined structure is in excellent agreement with that obtained previously from single-crystal data. As a consequence of the severe overlapping between adjacent reflections, direct methods failed, whereas we obtained good outcomes with ‘real space’ methods. This work shows that within the current state-of-art (hardware, software, numerical methods, etc.), relatively complex structures can be afforded by means of powder diffraction.

In the 19th century De la Rue, Stewart, and Loewy carried out a compilation of drawings and photographs of the solar sunspots corresponding to the interval 1832–1868. Using these drawings and photographs, they determined fortnightly values of the percentage of the solar photosphere covered by the sunspots. In this work, we have performed a spectral analysis of these data in order to determine possible periodic signals. In addition to the 11-year solar cycle, short cycles of about 330 days and 30–50 days have been recovered, lacking the 150–160 days period discovered by other authors using several solar activity indicators.

Results of the photometric analysis by means of the Wilson-Devinney method, combined with an empirical massradius relation for LC IV stars support the hypothesis that GX Gem is a well detached evolved system of subgiant stars. The solution is consistent with the known spectroscopic parameters obtained by Popper (1996) and the photometric data of Lacy (2002a). (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

We present the results of the differential V light curve analysis of NN Del. We show that NN Del is an EA eclipsing binary system with a period of 99.27 days and a highly eccentric orbit. Photometric solutions obtained using the Russell and the Wilson-Devinney models seem to indicate that both components are very similar in radii and luminosities (assuming a F5 spectral type). Constraints imposed on the V luminosity of the system by the HIPPARCOS data suggest that the components of the system could be subgiants instead of main sequence stars.

The Maunder Minimum (1645-1715 approximately) was a period of very low solar activity and a strong hemispheric asymmetry, with most of sunspots in the southern hemisphere. In this paper, two data sets of sunspot latitudes during the Maunder minimum have been recovered for the international scientific community. The first data set is constituted by latitudes of sunspots appearing in the catalogue published by Gustav Sp\"orer nearly 130 years ago. The second data set is based on the sunspot latitudes displayed in the butterfly diagram for the Maunder Minimum which was published by Ribes and Nesme-Ribes almost 20 years ago. We have calculated the asymmetry index using these data sets confirming a strong hemispherical asymmetry in this period. A machine-readable version of this catalogue with both data sets is available in the Historical Archive of Sunspot Observations (http://haso.unex.es) and in the appendix of this article., Comment: 14 pages, 1 figure, accepted for publication in "Advances in Space Research"

Two pieces of as-sintered 3mol% yttria tetragonal zirconia polycrystals were joined and the electrical response of this composite was compared with the one of its counterparts. The joined sample showed higher electrical conductivity than the assintered sample. This effect was attributed to the joining process.La respuesta eléctrica de la unión superplástica de dos muestras de 3mol% Y-TZP ha sido comparada con la de una muestra sin unir. La muestra unida presenta una conductividad eléctrica mayor que la muestra sin unir. Este aumento de conductividad se atribuye al proceso de unión.

This Letter studies the robustness of the inhibition of bidirectional chaotic escape of a harmonically driven oscillator from a quartic potential well by the application of weak parametric excitations. We show that Melnikov-method-based theoretical predictions for harmonic escape-inducing excitations also work in the presence of external noise, and for chaotic-escape-inducing excitations having a sharp Fourier component with a sufficiently high power.

In solar images the brightness of the Sun decreases from the centre of the disc toward the limb. This effect is called solar limb-darkening. In this work, measurements performed with very simple experimental equipment are presented and discussed, comparing the obtained values of the linear limb-darkening coefficient with results from theoretical solar atmosphere models included in the literature. This low-cost practical experience is highly appropriate for educational use in undergraduate laboratories.

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.

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).

Silicon carbide (SiC), owing to its unique combination of chemical and physical properties, is the material of choice for advanced engineering applications both at room and high temperatures. Due to the difficulty of SiC to be solid-state sintered, nowadays there has been growing interest in liquid-phase sintering (LPS) of SiC. Here, there is a critical need for developing methodologies for the accurate X-ray diffraction characterization of the microstructures of these ceramics as their microstructural evolution is not yet totally understood. Thus, the aim of the present work is to apply a procedure for the accurate line-broadening study of any given phase in LPS SiC ceramics. To that end, we have pressureless liquid-phase sintered (at 1950 °C for 0.5 h in flowing Ar atmosphere) a specimen starting from a commercially available β-SiC powder and using the simultaneous addition of Al 2 O 3 and Y 2 O 3 . The resulting material was subsequently characterized using X-ray powder diffraction; more specifically, the Rietveld method was applied for the quantitative phase-composition analysis and the Warren–Averbach method for determining the mean crystallite size, the crystallite size distribution and the root-mean-square strain along the crystallographic direction of the β-SiC polytype. The nanometric nature of the crystallite size distribution is finally related with the stacking faults in the SiC starting powder.

Y2O3-stabilized ZrO2 (YSZ) powders have been prepared by the sol–gel method using different synthesis parameters. Specifically, zirconium n-propoxide was dissolved in propanol at pH 0.5 or 5 (provided by HNO3), with or without acetic acid in the hydrolysis medium. Subsequently, the YSZ powders obtained by gelation and drying of these solutions was characterized using scanning and transmission electron microscopies, X-ray diffractometry, and N2-adsorption. Compacts made from these YSZ powders which were then sintered were also analyzed. It was found that the pH of the hydrolysis medium has a notable influence on the microstructure, morphology, color, crystallinity, and sintering behavior process of these YSZ sol–gel powders. It was also found that the use of acetic acid also affects the YSZ powder features, and results in compacts with higher residual porosity after sintering. Finally, the compacts prepared from the YSZ powders obtained at pH 5 and without acetic acid exhibit the greatest sinterability Fil: Mamana, Nadia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Instituto de Física de Rosario. Universidad Nacional de Rosario. Instituto de Física de Rosario; Argentina Fil: Díaz Parralejo, Antonio. Universidad de Extremadura. Badajoz; España Fil: Ortiz, Angel L. Universidad de Extremadura. Badajoz; España Fil: Sánchez Bajo, Florentino. Universidad de Extremadura. Badajoz; España Fil: Caruso, Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Instituto de Física de Rosario. Universidad Nacional de Rosario. Instituto de Física de Rosario; Argentina

X-ray powder diffraction (XRD), in conjunction with an analysis routine, is the method of choice for performing quantitative phase-composition measurements in multi-phase mixtures. However, accurate determination of phase compositions in SiC-based ceramics, which can contain a multitude of SiC polytypes with overlapping Bragg reflections, is a difficult task. In order to determine the best analysis method for the quantitative phase-composition measurement in SiC-based ceramics, a critical comparison between two commonly used analysis methods — polymorphic method (Ruska) and whole pattern method (Rietveld) — was performed. Owing to the difficulty in obtaining high-purity standard mixtures of SiC polytypes experimentally, we have simulated a set of XRD patterns corresponding to different SiC polytype mixtures of wide ranging compositions as standards. Within the polymorpic method, the following three different approaches were used: (i) raw XRD peak heights were obtained and corrected for mean background level; (ii) a non-linear Levenberg-Marquardt least-squares fit was used to obtain peak heights; and (iii) using the same fitting procedure as in (ii) integrated intensities were obtained. We demonstrate that the Rietveld method yields the most accurate phase-composition measurements, with mean and maximum errors of 0.5 wt.% and 0.9 wt.%, respectively. In the polymorphic method, we show that a fitting procedure is essential for the improvement in the accuracy of the analysis. Furthermore, we find that the use of integrated intensities, obtained from the fit, for quantitative XRD analyses gives results that are less accurate compared with when corrected raw peak heights are used.

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.

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.

La determinacion de las fracciones en peso de las fases mediante difraccion de rayos X es enormemente complicada en ceramicos a base de SiC debido al intenso solapamiento entre las reflexiones Bragg de los diferentes politipos. No obstante, el metodo de Rietveld constituye una herramienta poderosa para resolver este problema. En este trabajo se utiliza el metodo de Rietveld al objeto de determinar las fracciones en peso de las diferentes fases para una muestra de SiC sinterizado en fase liquida (LPS SiC). Nuestros resultados ponen tambien de manifiesto la necesidad de incorporar correcciones debidas a orientacion preferencial para efectuar un analisis cuantitativo preciso.

The deconvolution of X-ray diffraction profiles is a basic step in order to obtain reliable results on the microstructure of crystalline powder (crystallite size, lattice microstrain,etc.). A procedure for unfolding the linear integral equationh=g finvolved in the kinematical theory of X-ray diffraction is proposed. This technique is based on the series expansion of the `pure' profile,f. The method has been tested with a simulated instrument-broadened profile overlaid with random noise by using Hermite polynomials and Fourier series, and applied to the deconvolution of the (111) peak of a sample of 9-YSZ. In both cases, the effects of the `ill-posed' nature of this deconvolution problem were minimized, especially when using the zero-order regularization combined with the series expansion.

The evolution of microstructure and electrical behaviour of nanocrystalline ZrO 2 - 3mol% Y 2 O 3 samples with respect to thermal cycles have been investigated. The sample, that initially consisted of 77.8%wt of tetragonal and 22.3%wt monoclinic phases, eliminates the tetragonal phase by means of a low temperature t → m phase transformation in which the content of monoclinic phase reaches 96%wt. This transformation affects significantly the electrical properties of the sample, increasing the grain boundary resistivity in successive thermal cycles, whereas the bulk contribution remains unchanged. The growth of the grain boundary resistivity is believed to be due to the presence of microcracks that accommodate the larger size of monoclinic grains.

In recent years, several profile-shape functions have been successfully used in X-ray powder diffraction studies. Here, a new profile function for approximating the X-ray diffraction peaks is proposed. This model, based on a Gaussian function multiplied by a correction factor in the form of a series expansion in Hermite polynomials, can be employed in the cases where there are peak asymmetries. The function has been tested by using samples of α-Al2O3and 9-YSZ (yttria-stabilized zirconia), yielding generally satisfactory results.

The relative abundances of the polymorphs present in samples of 9 mol% magnesia-partially stabilized zirconia (Mg-PSZ) have been determined by Rietveld analysis of X-ray powder diffraction data. The composition of the samples is mainly dominated by the tetragonal content. Preferred orientation and anisotropic line broadening effects on this majority phase were observed. It is shown that the consideration of these microstructural effects during the Rietveld refinement is not only important with the aim of improving the refinement but also indispensable to obtain the accurate proportion of the phases.

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.

A modified application of the variance method, using the pseudo-Voigt function as a good approximation to the X-ray diffraction profiles, is proposed in order to obtain microstructural quantities such as the mean crystallite size and root-mean-square (r.m.s.) strain. Whereas the variance method in its original form is applicable only to well separated reflections, this technique can be employed in the cases where there is line-profile overlap. Determination of the mean crystallite size and r.m.s. strain for several crystallographic directions in a nanocrystalline cubic sample of 9-YSZ (yttria-stabilized zirconia) has been performed by means of this procedure.

The precise microstructural characterization of the yttria-partially stabilized zirconia (Y-PSZ) system by means of X-ray diffractometry (XRD) experiments faces a serious challenge: the discrimination between the cubic, c, and pseudocubic, t{prime}, phases. The authors show how the confusion between the two phases goes beyond a simple qualitative problem, because the relative abundances for all the present polymorphs can be substantially modified. This is particularly true for the amount of transformable tetragonal phase, which is of paramount importance for the design of zirconia-based tough ceramics. Similarly, they show that a conclusive discrimination between c and t{prime} phases is possible on the basis of XRD experiments by a careful application of the Rietveld method and by emphasizing some subtle details around the angular domain close to the {l_brace}200{r_brace} planes. The procedure is applied to samples of Y-PSZ (4.7 mol%).