A direct method is described for determining depth profiles (z-profiles) of diffraction data from experimentally determined τ-profiles, where z is the depth beneath the sample surface and τ is the 1/e penetration depth of the X-ray beam. With certain assumptions, the relation between these two profile functions can be expressed in the form of a Laplace transform. The criteria for fitting experimental τ-data to functions which can be utilized by the method are described. The method was applied to two τ-data sets taken from the literature: (1) of residual strain in an A1 thin film and (2) of residual stress in a surface ground A12O3/5vol% TiC composite. For each data set, it was found that the z-profiles obtained were of two types: oscillatory and nonoscillatory. The nonoscillatory profiles appeared to be qualitatively consistent for a given data set. The oscillatory profiles were considered to be not physically realistic. For the data sets considered, the nonoscillatory z-profiles were found to lie consistently above the corresponding τ-profiles, and to approach the τ-profiles at large z, as expected from the relation between the two.

Mass attenuation coefficient corrections, for Rietveld phase analysis with an external compositional calibration standard, may be made using Compton scattering intensities measured by X-ray fluorescence spectrometry. The method is mainly useful for Rietveld phase analysis when mixing an internal standard is impossible or undesirable. The validity of the method has been demonstrated using a suite of alumina-zirconia powders of known composition. Also presented are results for a typical application—determination of phase composition depth profiles defining the graded compositional character of an aluminium titanate/zirconia-alumina ceramic composite.

X-ray diffraction and neutron spectra present a peak assembly whose maxima are centered at angles corresponding to Bragg's law.

Analysis of diffracted intensity profiles in each peak can be used to estimate such morphologic characteristics of the samples as preferred orientation (Brindley and Kurtosy, 1961; Martin, 1966); crystallite sizes (Scherrer, 1919; Warren and Averbach, 1950; Wilson, 1962; and Guérin et al., 1986); and crystal shapes (Wilson, 1949). Such analysis can also be used to estimate the determination of residual stress and lattice defects (Warren and Averbach, 1950; Wilson, 1963). In such studies, a detailed analysis of the diffraction distribution is required and consequently adjustment of intensity values must be carried out, as they are affected by systematic errors in the measuring apparatus (for detailed description, see Klug and Alexander, 1974 and Wilson 1967).

X-ray powder diffraction and single-crystal data are reported for a series of isomorphous compounds with the general chemical composition (Fe,Al)3(K,NH4,H3O)H14 (PO4)8·4H2O. The compounds are monoclinic with space group C2/c. Unit-cell parameters were determined on the mixed salt (Fe0.84,Al0.16)3KH14(PO4)8·4H2O, as obtained from sludge precipitated in commercial shipping-grade wet-process phosphoric acid. Single-crystal studies and refined powder diffraction data provided unit-cell parameters of a= 16.908(9) Å, b = 9.588(2) Å, c = 17.539(5) Å, and β = 91.06(4)°.

Aluminum borate (9Al2O3·2B2O3) whiskers were chemically synthesized in potassium sulphate flux by using the starting chemicals of aluminum sulphate and boric acid. The synthesis temperature of 1075 °C was found to be the optimum with respect to whisker morphology. A tentative X-ray diffraction (XRD) pattern was suggested for the whiskers produced after heating at 1150 °C. The product purity, phase composition, and whisker morphology were investigated by XRD, energy dispersive X-ray spectroscopy, and scanning electron microscopy, respectively.

In recent years, grazing incidence angle attachments have been shown to be very useful in the phase identification of thin polycrystalline films. These devices are sold commercially as attachments to standard powder diffractometers. The attachment normally consists of a long soller slit assembly and a flat crystal monochromator. The soller slit with or without the monochromator is mounted on the diffracted beam side. In this paper we discuss the effects of different configurations from collimator to monochromator on diffraction data. An understanding of these effects is essential in order to obtain more reliable information on phase transformations, crystallite size, microstrain, and residual stress studies.

A more accurate X-ray diffraction pattern for the high speed steel carbide Fe3W3C is presented. This pattern includes the low angle reflections omitted from previous studies. A wider homogeneity range for the M6C carbide phase at 1200° C is suggested.

Indexed X-ray powder diffraction data are reported for two energetic materials, oxalylhydroxamic acid and 2-diazo-4, 6-dinitrophenol (DDNP). For these two compounds, powder diffraction data calculated from single-crystal structure determinations are also presented and compared to the experimentally observed powder diffraction data. To evaluate the reliability of the experimentally obtained intensities, an intensity figure of merit, IX(N), based on an average percent difference between observed and calculated intensities for a limited number of strong and moderately-strong lines is proposed as a more useful measure of agreement than R1. For N lines with Icalc > X% relative intensity, IX(N) is defined as

This is compared to

which involves a summation over all lines.

A chemical and mineralogical investigation of a Moroccan pyrophyllite is presented. X-ray powder diffraction has been largely used for phase identification and crystal symmetry determination. It is shown that this mineral has a triclinic symmetry with cell parameters: a=5.160 Å, b=8.993 Å, c=9.360 Å, α=90.77°, β=100.57°, and γ=89.71°.