A. Dauger

A high-resolution X-ray diffractometer for the study of imperfect materials

A high-resolution X-ray diffractometer devoted to the study of imperfect materials (mainly oxides and ceramics) is presented. It is based on a rotating anode generator, a four-bounce monochromator, a five-movement sample holder and a curved position-sensitive detector (PSD). This setup allows rapid acquisition of a reciprocal-space map (in less than 10 h) even for very poorly diffracting materials. The two-dimensional instrumental profile is calculated taking into account each optical element in the beam path. The one-dimensional instrumental profiles corresponding to widely used scans (ω scan, θ–2θ scan, rocking curve and powder scan) are also calculated. In the three former cases, the setup exhibits an excellent angular resolution (0.003°), whereas in the latter case the resolution is lowered by one order of magnitude at the benefit of a strong increase in the collected intensity. The possibilities of this diffractometer are illustrated with three examples: an epitaxic layer, a microstructured single crystal and a powder.

Tetragonal zirconia powders from the zirconium n-propoxide-acetylacetone-water-isopropanol system

Abstract As a part of a work concerning densification and toughening of silicate ceramic products, this paper describes the preliminary characterization of a zirconia precursor fabricated through a sol-gel route in the zirconium n-propoxide-acetylacetone-water-isopropanol system. When the molar ratio R = [acac]/[Zr] increases from R = 0 to R = 0.8, the precursor changes from a colloidal precipitate to a polymeric gel with an increasing gelation time. Drying and firing the precipitates leads to the monoclinic stable form of zirconia while the first crystalline phase obtained beyond 500°C from the gel is the metastable tetragonal one. Successive steps of the reactions are investigated by small angle X-ray scattering, differential thermal analysis, thermogravimetry and X-ray diffraction.

Reflection Asymmetric Powder Diffraction with Flat-Plate Sample using a Curved Position-Sensitive Detector (INEL CPS 120)

The reflection flat-sample asymmetric geometry is an attractive set-up for powder diffraction measurements, as compared to either conventional Debye–Scherrer or symmetric Bragg–Brentano geometries. Combined with grazing- or fixed-incidence-angle X-rays, it is suitable for surface-structure or thin-film texture analysis. Furthermore, it allows curved position-sensitive detectors to be used for in situ experiments. In this paper, the major systematic error sources in connection with this geometry are reviewed. It is confirmed that experimental linearization of the curved position-sensitive detector and sample positioning have to be very carefully performed. Simple and automatable procedures are proposed. Then, it is shown that peak-location accuracy leads to satisfactory cell-parameter determination as checked by the use of a silicon international standard reference sample and that structure refinement by the Rietveld method can be performed in very good conditions, as observed with an NaBi2Sb3O11 compound.

XRD and TEM study of heteroepitaxial growth of zirconia on magnesia single crystal

Abstract Zirconia thin films have been deposited on magnesia (001) single-crystal substrates using a sol–gel precursor route. Thermal treatment at 600°C induces the crystallization of polycrystalline thin films containing randomly oriented nanocrystals. Annealing at higher temperature gives rise to the appearance of a progressive heteroepitaxy and breakup of the film into islands. Polycrystalline tetragonal zirconia thin films, several tens nanometer thick, have been studied with an incident X-ray beam angle equal to several tenth degrees. The epitaxial growth has been characterized by XRD under controlled incidence angles and concurrently imaged by TEM on cross-sectional samples. The development of heteroepitaxied single-crystal islands results from abnormal growth of interfacial grains having a lower orientational free energy.

Phenomenological analysis of heterogeneous strain fields in epitaxial thin films using x-ray scattering

A model that allows the quantitative analysis of heterogeneous strain fields in epitaxial thin films using x-ray diffraction (XRD) is presented. Particular emphasis is laid on the modelling of the two-component XRD profiles (i.e. profiles made of the superposition of a narrow coherent Bragg peak and a broad diffuse scattering profile) encountered in the XRD investigation of epitaxial thin films containing localized strain fields. The spatial properties of the strain field are included in a correlation function based on phenomenological parameters such as the defect correlation length ξ and the level of disorder σ∞. No assumption regarding the nature of the defect is hence required. The statistical properties of the strain field are described by means of Levy-stable distributions which allow us to account for profile shapes ranging between the Gaussian and profiles exhibiting pronounced power law-type tails, as well as for asymmetrical profiles. The effects of finite size of the domains (crystallites) over which diffraction is coherent are rigorously taken into account by calculating the auto-correlation function of the crystallite shape including the size distribution effects. The effects of each parameter are presented and discussed in detail and the applicability of the model is illustrated with two examples.

X-Ray diffraction line broadening by stacking faults in SrBi2Nb2O9/SrTiO3 epitaxial thin films

Abstract SrBi 2 Nb 2 O 9 thin films were deposited on (001) SrTiO 3 substrate by sol–gel spin coating. A previous study showed that the film crystallizes with the c -axis normal to the surface. Those epitaxial films are studied by means of X-ray diffraction (XRD) line profile analysis as a function of thermal annealing duration. The line profile analysis of the diffraction patterns collected in ω-2θ scan mode, gives detailed information on the coherently diffracting domain size and microstrains along a given direction. For low annealing duration the width of the (001) diffraction lines reaches values of approximately 1°. In accordance with a recent study, integral breadth and Fourier analysis suggest the presence of stacking faults separated by a mean distance of 5 nm. The profiles exhibit a marked Lorentzian character as expected from a faulted crystal. In addition to faulting, both finite grain size and microstrains contribute to the observed width. When heat treatment time is increased, the breadth and Lorentzian content of the (001) diffraction lines decrease attesting that the stacking fault density is lowered. For a 500-h treatment at 700°C the calculated domain size equals the films thickness. This indicates that stacking faults have almost disappeared: the SBN crystallites of the film have reached an equilibrium state.

Epitaxial zirconia films on sapphire substrates

Abstract The epitaxial development of undoped zirconia films produced via the solution precursor route and deposited by dip-coating on (11 2 0) planes of sapphire is investigated. After drying and firing at 600°C, polycrystalline films are made of nanosized randomly oriented tetragonal ZrO 2 grains. Firing at higher temperatures promotes grain growth and islanding, so producing a layer of heteroepitaxial but isolated grains. Two families of single crystalline islands are identified: {100} tZrO2 //(11 2 0) sapphire and {111} tZrO2 //(11 2 0) sapphire . In-plane growth of flat {100} oriented crystals can be favored by varying the thickness and firing conditions of the films. The heteroepitaxial orientation of the pseudo single crystalline film and the interface structure are examined through X-ray diffraction experiments (low incidence XRD, ω-rocking curves) and cross sectional HRTEM observations.

Highly localized strain fields due to planar defects in epitaxial SrBi2Nb2O9 thin films

Thin films of (00l) oriented SrBi2Nb2O9 epitaxially grown on SrTiO3 by sol-gel spin coating have been studied by means of high-resolution x-ray diffraction reciprocal space mapping. It is shown that these materials contain highly localized heterogeneous strain fields due to imperfect stacking faults (i.e., faults that do not propagate throughout the crystallites building up the film). In the film plane, the strain fields are confined to 11 nm wide regions and characterized by a vertical displacement of 0.18c (where c is the cell parameter) showing that the stacking faults are mainly composed of one additional (or missing) perovskite layer. Prolonged thermal annealing at 700 °C strongly reduces the density of stacking faults and yields a more uniform strain distribution within the film volume without inducing significant grain growth.

A new method for the determination of strain profiles in epitaxic thin films using X-ray diffraction

A new and versatile method is proposed for the determination of strain profiles in epitaxic thin films. It is based on the simulation of the X-ray diffraction (XRD) profiles using cubic B-spline functions to model the vertical lattice displacement profile. The lattice displacement profile, and consequently the strain profile, directly results from a least-square fit of the model to the experimental XRD profiles. No a priori assumption is made regarding the shape of the strain profile. Moreover, as spline functions are used, the recovered lattice displacement profile is smooth and exhibits a minimum curvature, thus avoiding oscillating or saw-toothed unphysical solutions. The potential of this method is illustrated with (100) yttria-stabilized zirconia epitaxic thin films deposited onto (11\bar{2}0) sapphire substrates by sol–gel processing.

Miscut angles measurement and precise sample positioning with a four circle diffractometer

A method is derived for precise sample positioning with a four circle diffractometer. The sample can be oriented either with respect to a crystallographic plane or with respect to the sample surface with an accuracy of about 0.001°. The miscut angles can be easily deduced with an accuracy of a few 1/1000°.