Each of the RIR based methods for carrying out quantitative X-ray powder diffraction analysis are described and a consistent set of notation is developed. The so called “standardless” analysis procedures are shown to be a special case of the internal-standard method of analysis where the normalizing assumption is used. All analytical methods, other than the Rietveld whole pattern matching procedure, require the use of explicitly measured standards, typically in the form of RIR values. However, if only semi-quantitative results can be tolerated, the standards may be obtained by using published RIR and relative intensity values. The exciting new techniques of whole pattern fitting and Rietveld constrained quantitative analysis are also described in RIR notation and shown also to be forms of the internal-standard method with the normalization assumption. The quantitative results obtained from Rietveld quantitative analysis are derived from computed standards in the form of computed, normalized, RIRN values. The normalization assumption in Rietveld analysis allows the exclusive use of computed standards and comes as close to a “standardless” analysis as one can achieve: relying on the absence of amorphous material and on the validity of the structural models. Relationships are given for obtaining quantitative analysis from these RIRN values obtainable from the least-squares scale factors.

This paper describes a new method for the simultaneous determination of mineral composition, mass thickness and mass absorption coefficient of a thin layer of a crystalline substance deposited on a crystalline substrate.

The samples were deposited on membrane disc filters, consisting of mixtures of cellulose acetate and cellulose nitrate. Quantitative results are achieved by measuring the diffraction intensity of the analyte and the attenuation of a reflection of the crystalline material supporting the deposited sample. The mean accuracy of the analysis was found to be: ≈ 3% for mass thickness, ≈ 1% for mass absorption coefficient and ≈ 4% for quantitative mineralogical determination.

In most of the practical problems of the quantitative X-ray analysis, obtaining working equations including only intensity ratios without the sample mass-absorption coefficient is impossible, unless an internal standard is added to the sample. It is shown that the internal standard may be unnecessary if some chemical data are added to the XRD information used. Experimental results justify this claim.

The Debye Scherrer method (1917) of determining a crystal system by observation of X-ray interferences on randomly oriented crystal particles amounts in the mathematical problem to deriving quadratic equations for three variables from unknown integer multiples of these variables. In my opinion it is not only physically, but also mathematically reasonable to treat this problem from a geometrical point of view. Let L,M, and N be three non-parallel vectors. Vectors P can be derived by multiplication with the integers n1, n2 and n3, so that

P = n1L + n2 M + n3 N.

The crystal structure of Tl4V2O7 is solved ab-initio from powder diffraction data collected in Debye-Scherrer geometry using an Inel X-ray Position Sensitive Detector. The structure has been determined from Rietveld analysis in space group ml, Z = 1, with a = 5.9388(2)Å and c = 7.7322(3)Å. The structure of Tl4V2O7 is built up from isolated V2O7 groups aligned along the trigonal c axis. Thallium atoms alternate along a 3-fold axis. The presence of stereochemically active lone pairs is demonstrated and their positions are calculated using a self-consistent electrostatic model. The influence of sample absorption is briefly discussed and the results are compared with those obtained in Bragg-Brentano geometry using flat-plate specimen.

We have examined the barium ferrite powder X-ray diffraction patterns in the PDF using experimental and calculated diffractograms. An improved calculated diffractogram is proposed. The result indicates that the primary peak of barium ferrite is not (107) but is (114).

Powder diffraction patterns have been calculated for nine isostructural rhombohedral M2(SO4)3 (M = Sc, Ti, V, Cr, Fe, Ga, Y, Rh, In) phases, and for four isostructural monoclinic M2(SO4)3 (M = V, Fe, In, Tl) phases. The pattern for monoclinic Fe2(SO4)3 is the first reported for this phase. Because structure data are available only for the two Fe2(SO4)3 polymorphs, the powder patterns of the other trivalent metal sulfates were approximated using the structure data of the isostructural Fe phases with the scattering factors and previously determined cell parameters of the various metal sulfates. These calculated patterns are termed an approximation by isostruduralism.

The calculated patterns were used to evaluate reference powder data for these phases in the Powder Diffraction File (PDF). All but two of the PDF patterns were found to differ substantially from the calculated patterns in the stronger peaks used for identification, and to be missing weak peaks that may be confused for impurities during phase identification.

A new X-ray diffraction pattern for the compound cerium oxygen apatite, Ce4.67[SiO4]3O is suggested. The compound was prepared by the solid state reaction of the oxides, CeO2 and SiO2 and has a hexagonal crystal structure with the lattice constants a = 9.6578 Å and c = 7.1187 Å. The sample of the most recent PDF pattern 31-0336* (Visser, 1978) for this compound is believed to be contaminated with significant quantities of N owing to the fact that it was prepared by mixing Ce2O3 and Si3N4 and its very close resemblance to the pattern displayed in the PDF 33-0333 given for the cerium “nitrogen” apatite, Ce5[SiO4]3N.

The cubic Al18Ti2Mg3 phase (184 atoms/unit cell, Z = 8, space group Fdm) has been fabricated by reaction hot isostatic pressing. Quantitative energy dispersive X-ray analysis showed the phase to have nearly ideal stoichiometry. Interplanar spacings and diffraction peak intensities have been determined by X-ray diffraction. The experimental data show good agreement with the pattern calculated using atomic site positional parameters for A118Cr2Mg3, confirming that A118Cr2Mg3 is the prototype for A118Ti2Mg3.

The crystal structure of the high-temperature phase of Sr2ZnWO6 prepared by air quenching from 1200° C has been determined by means of X-ray powder diffraction. β-Sr2ZnWO6 belongs to the cubic system, with space group Fm3m and a lattice parameter a = 7.9266 Å at room temperature. Its measured density is Dm = 6.93g/cm3, and each unit cell contains four formula weights.

The crystalline structure of the M2CuWO6 phases with M = Ba or Sr was obtained from X-ray powder diffraction at room temperature with CuKα radiation. The phases are isostructural with tetragonal unit cells, space group I4/m and Z = 2. The parameters for the Sr2CuWO6 phase are: Mr = 518.6, a = 5.42693(5) Å, c = 8.4087(1) Å, V = 247.65(1) Å3, Dx = 6.954 Mg/m3, μ = 77.75 mm−1, F(000) = 454, R = 0.0375 for 24 reflections; the parameters for the Ba2CuWO6 phase are: Mr = 618.1, a = 5.56392(8) Å, c = 8.6274(1) Å, V = 267.08(1) Å3, Dx = 7.683 Mg/m3, μ = 157.0 mm−1, F(000) = 526, R = 0.0506 for 27 reflections. Cell parameters were obtained from Rietveld refinement. The crystalline structure is based on the perovskite structure. It is laminar with ordered alternating WO6 deformed octahedra and CuO2 planar squares along the [110] direction, joined by corners and rotated perpendicular to the [001] direction. The samples are electrica insulators.

Metal cimetidine isothiocyanates, M(C10H16SN6)2(NCS)2, where M = Co(II), Ni(II) and Cu(II), have been investigated by means of X-ray powder diffraction. Unit cell dimensions were determined from powder diffractometer data. Refined cell parameters (monoclinic with a primitive cell), powder data, calculated densities and Z value are presented.

X-ray powder diffraction and optical data are presented for a vanadium-rich dravite from Silver Knob, Mariposa County, California, U.S.A. The limited compositional variability observed for vanadium-rich dravite is due to the presence of a Tschermaks substitution whereby the substitution of Al for Si in the tetrahedral ring is charge balanced by trivalent for divalent cation substitution in the octahedral sites in the structure. Vanadium-rich dravite is uniaxial negative with ε = 1.646(2) and ω = 1.676(2). Refined unit cell dimensions are a = 15.9599(10) and c = 7.1889(2); F30 = 111(0.009; 30); M20 = 80; and Dx = 3.07. An indexed X-ray powder diffraction pattern is also presented.