Clay mineral quantification by XRD is difficult when mixed-layer clay minerals and discrete clay types are both present. New procedures for peak decomposition and pattern simulation offer increased opportunities to obtain mineral abundance estimates. This proposed methodological sequence, for quantitative representation (QR) of complex clay samples, involves: (1) determination of layer type, mixed-layer proportion and order (R); (2) simulation of XRD patterns using MULCALC, an adaptation of NEWMOD; and (3) interpretation of the clay assemblage by fitting the whole pattern with CLAY++, a statistical program. The product is a QR of individual phases or a summation of layer types. The absence of quantitative reference standards means results cannot be checked for accuracy, but the statistical fit is highly reproducible and less prone to operator error. The QRs may be obtained with simulated or actual reference mineral patterns in the database. Results for freshwater marsh samples illustrate the approach.

Veatchite polytypes were properly identified from several localities relying solely on micro powder diffraction data. Diagnostic differences in their respective calculated patterns gave reliable identification results when compared with measured data. This permitted the confirmation of co-existing veatchite-1A and -2M on the same specimen from the Billie Mine, Inyo County, California as flat elongated crystals (-1A) and flat rhombic plates (-2M), respectively. On the specimen from the Sterling Borax Mine (Lang), type-locality for veatchite-2M, the polytype veatchite-1A was confirmed from radiating rhombic plates. From the type specimen for veatchite-1A (rhombic plates), collected from the borate deposit in Emet, Turkey, an additional unknown polytype of this mineral was discovered, but lacks suitable material for a complete characterization. At the Penobsquis deposit near Sussex in New Brunswick, Canada, only veatchite-2M was encountered. The area between 20 and 25°2θ holds the following diffraction signatures: -1A (two sets of double peaks at approximately 21.5 and 24.5°2θ), -1M (single peaks at 20 and 23°2θ) and -2M (double peaks at 20 and 23°2θ). The unknown polytype from Emet, Turkey differs from polytype-1A in that same range by having single peaks at the 21.5 and 24.5° instead of double peaks.

A method is described to determine the standard deviation of a peak position due to counting statistics. In this method, the statistical noise for a peak is first simulated based on the model of Poisson distribution and then imposed on the peak. The peak position is then determined by a profile fitting routine. By repeated application of these processes on a given peak, one obtains a number of slightly different peak positions and hence their corresponding standard deviation. This method can be applied to a peak described by any analytical function or a set of any number of digitized points. Investigation of the precision of peak positions was carried out by applying this method on various analytical peaks located at low, medium, and high 2θ angles. The results showed that the standard deviation of a peak position decreases with increasing P/B and P/σ, where P is the net peak count above the background B and σ=(P + B)½ is the estimated standard deviation for noise. It increases with increasing peak width and Δ2θ, the step size used to digitize the peak profiles. It decreases as the 2θ range of simulation and fitting increases up to 2θ=3 FWHMs (full width at half maximum) and remains at a constant value thereafter. The standard deviation of the position of a real peak obtained by ten repeated measurements is 0.0034°; the corresponding result obtained by the current method is 0.0035°. This peak is best fitted by a Pearson-VII function and the standard deviation obtained by this method is 0.013° when only the head portion with intensity ≥85% maximum net intensity is simulated and fitted. The corresponding result obtained by the traditional method of parabola fitting is 0.0055°. Therefore, the precision of a peak position also depends on the peak shape.

A simple procedure was devised for the preparation of a standard KCl powder to be used for the experimental determination of the instrumental profile in the Bragg–Brentano geometry. The standard was tested on several diffractometers, and narrow Bragg reflections in the range 28°–132° were recorded adopting various experimental conditions. Profiles were modeled with analytical functions, to describe the trend of width and shape of the instrumental profile as a function of the diffraction angle. Some indications were given to perform reliable profile fitting and line broadening analysis; a high resolution setup, obtained by employing narrow slits, large goniometer radius, and a monochromator in the diffracted beam, gives narrow reflections, even though the intensity of the diffracted beam is considerably reduced. The choice of these experimental conditions, which can be achieved using the majority of the commercial instruments, leads to symmetrical profiles, even at relatively low angle (2Θ=28°), which are highly recommended for reliable profile fitting and line broadening analysis.

A general expression is proposed for the peak profile produced by a system of simple-shape crystalline domains (sphere, cube, tetrahedron, octahedron) whose size is dispersed according to a gamma distribution. The analytical expression obtained is particularly suited to “on the fly” pattern simulation or profile fitting for nanocrystalline materials. An advantage of using the proposed profile expression is that it always corresponds to a physically meaningful, though a priori fixed, size distribution, whereas the traditionally employed Voigtian profiles can produce unphysical negative size distributions for certain combinations of profile parameters. The peak profile depends on the distribution mean and variance instead of the more common empirical parameters of peak width and shape.