A Fortran 77 computer program has been developed for the quantitative analysis of minerals by multiphase profile analysis of the complete powder diffraction pattern. Featured are full-matrix least-squares refinement of 14 Rietveld “instrumental parameters” (phase scales, asymmetry, preferred orientations (March model), linewidths, instrument zero, lineshapes and unit cell dimensions), Brindley particle absorption contrast factors and amorphicity corrections. The program uses a crystal structure Databank, which contains information on absorption coefficients, unit cell data and crystal structures for some 90 common minerals. New minerals can be easily added. Structure parameters are also refinable by a profile decomposition method using a program called STRUCT. The sum of the calculated patterns, derived from the crystal structure data, is fitted to the observed pattern by a program called TRACSCAL which runs in singlepass multiphase mode and, after the above corrections have been applied, the weight percentages of the component phases are calculated from the Rietveld scaling factors.

The program runs on an IBM-compatible AT computer with 640K of RAM, on an extended memory AT, or a mainframe system. Examples of its use are given with standard mixtures and naturally occurring specimens. On an AT computer with 20MHz clock speed a scaling run, including data input, reading of the pattern, processing of (hkl) files, calculation of the profile and one cycle of least squares fitting takes about 30 seconds for binary standard mixtures and about 2.5 minutes for a 7-phase natural bauxite pattern containing 320 independent (hkl) reflections.

A comparison between the results of ab initio structure determination from X-ray powder diffraction data of a new cadmium hydroxide nitrate, Cd5(OH)8 (NO3)2·2H2O (SG C2/m), and those obtained from single crystal data is presented. The powder diffraction pattern has been analysed by an indexing method and fitting techniques. A total of 119 unambiguously indexed reflections has been extracted and used in subsequent treatment. The power of powder techniques to index the pattern and to find the structure model by normal Patterson and Fourier methods is clearly shown. The refinement of approximate coordinates has been carried out by the Rietveld method (444 reflections). The comparison of results with those obtained from single crystal data (2218 reflections) shows that the precision of positional parameter values is lower by a factor of 10, on average, in the powder study. These results are discussed in terms of crystallographic parameters (number of reflections used, number of parameters to refine, contrast between atoms) and, also, in terms of sample dependent properties (preferred orientation effect, impurity). Finally, the crystal structure has been derived from powder data with a precision probably sufficient for most purposes.

Diffraction peak broadening analyses were carried out on diffraction profiles of several reflections from hot-pressed α-Al2O3 containing 29, 18 and 10 volume % β-SiC whiskers. The data were analyzed and compared using four different integral breadth methods for microstrain and crystalline size. All four methods gave comparable results, within an order of magnitude, for the microstrains in each phase: (2-15 × 10−4 for the matrix and (6-19 × 10−4 for the whiskers). Microstrains in both matrix and whiskers decreased with decreasing volume % of whiskers for all four methods. Trends in the crystallite size were less consistent but for the matgrix, an incrfease from ∼665 to 1565Å was found with decreasing whisker content using DeKeijser's method.

A new preparation procedure to obtain tetragonal pure zirconia powders is reported together with a detailed analysis of the profile of X-ray Diffraction (XRD) peaks. The crystallization kinetic up to 800°C is described through r.m.s. microstrain and crystallite size distributions. The results of two methods of profile analysis are compared. After thermal treatments up to 100°C the samples of amorphous gel prepared crystallize in the tetragonal structure. The monoclinic phase occurs only above this temperature. Moreover the tetragonal to monoclinic transformation has a strong effect in changing the shape of the distributions. Studying the crystallite size distributions we can infer a critical size of about 300 Å for the tetragonal crystallites to transform. The shape of the mean crystallite of a fully tetragonal sample is also described.

Described is a method of sample preparation for multiple Guinier Cameras (DeWolff, 1948). This technique practically eliminates cross-contamination of adjacent samples and is easy to employ.

Samples for Guinier cameras are usually applied to a thin adhesive coated foil. For multiple Guinier cameras, however, samples pose some technical problems. Manufacturers usually supply a slotted die for sample preparation. Figure 1 shows schematically such a die for a Seifert/Huber camera. For this type of camera, the manufacturer recommends application of the powdered sample by means of a small brush, or by dusting while the adjacent slots are covered by adhesive tape (Seifert, undated). These methods are simple, but easily result in sample being spilled into an adjacent slot. The following method, though involving more steps, eliminates this problem.

Cd3(BO3)2 was prepared by a solid state reaction between B(OH)3 and Cd(OH)2 at low temperatures ranging between 523° and 623° and at a pressure of 10−4 – 10−5 Hg mm. The crystal structure has been refined by Rietveld analysis of X-ray powder diffraction data. The compound crystallizes in the orthorhombic system, space group Pnnm, Z = 2, with cell parameters of a = 5.967(5) Å, b = 4.78 (0) Å and c = 9.009(5) Å.

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.

X-ray powder diffraction patterns of orthorhombic- and rhombohedral-distorted perovskite PrNiO3 obtained at room temperature, 200°, 400°, 500°, and 600°C were analyzed and evaluated. An examination of the diffraction profiles shows essentially no line broadening indicating that the PrNiO3 powders synthesized by solid state reaction are well-crystallized and probably strain-free. The reliability and accuracy of the patterns were evaluated, and the figures-of-merit were in triple digits for the 500° and 600°C patterns of the rhombohedral phase and double digits for the more complex orthorhombic diffraction patterns recorded at room-temperature, 200°, and 400°C. Values of lattice parameters refined from the observed diffraction peak positions agree with those obtained from the Rietveld whole-pattern fitting analysis to within 1–2 × 10−4.

Three members of the family [Cu(C14H15N3)X2]·nH2O [X = N3(n = 1); NCS and Br(n = 0)], C14H15N3, = N-(2′-(6-methyl) pyridyl) methylene-2-(2′-pyridyl)ethylamine)] (pymep), have been prepared by reaction in solution. Crystal data determined with the aid of single crystal methods, powder diffraction data, and densities determined by flotation methods are presented.

A series of five synthetic tetrahedrite-group minerals has been prepared and examined using powder X-ray diffraction in order to update current powder data and provide a validation test of cell dimension prediction equations. The tetrahedrites (nominally (Cu10X2)Sb4S13 with X = Zn, Cd, Mn, Hg and Fe) have the following properties: zincian tetrahedrite, a = 10.3833 (1) Å, Dx = 4.974 (1) g/cm3, F30 = 264 (0.004, 31), M20 = 279; cadmian tetrahedrite, a = 10.5066 (1) Å, Dx = 5.073 (1) g/cm3, F30 = 208 (0.004, 37), M20 = 249; manganoan tetrahedrite, a = 10.4384 (1) Å, Dx = 4.822 (1) g/cm3, F30 = 274 (0.003, 33), M20 = 302; mercurian tetrahedrite, a = 10.5071 (1) Å, Dx = 5.570 (1) g/cm3, F30 = 150 (0.006, 35), M20 = 156; ferroan tetrahedrite, a = 10.3630 (1) Å, Dx = 5.002 (1) g/cm3, F30 = 253 (0.004, 33), M20 = 281. The experimental unit cell dimensions obtained in this study are in excellent agreement with calculated values produced using regression equations developed previously.

The compound AlNbO4 has been studied by single crystal X-ray precession photographs and X-ray powder diffraction. Unit cell dimensions were calculated using a least squares analysis that refined to a Δ2θ° of no more than 0.03°. A monoclinic cell was found with space group C2/m, a = 12.1558(5)Å, b = 3.7345(2)Å, c = 6.4886(3)Å, and β = 107.613(4)°.

An indexed powder diffraction pattern and related crystallographic data are reported for a new phase, BaCu(C2O4)2·6H2O, which was a major product in the coprecipitation of barium and copper oxalates.

Recent developments in the Rietveld method for the analysis of powder diffraction data have seen the method evolve from its original purpose of crystal structure refinement to nclude the determination of phase abundance in polycrysalline mixtures and the estimation of crystal size and strain parameters. However, the Rietveld method is not easy to use and may deter many powder diffractionists, who are not inerested in structure refinement per se, from using the method in its non-structural applications.

In order to overcome the difficulties in using the Rietveld method, a program, QPDA (for Quantitative Powder Diffraction Analysis), has been written that sets the conditions necessary for a single or multi-phase refinement, runs the Rietveld program and extracts phase abundance and size/strain information from the refined parameters. The program comprises a user-friendly, default-driven system of subroutines, written initially in VAX Fortran, and operates from a database of inorganic materials frequently encountered in a wide range of minerals and materials science industries.

Equations (3) and (5) should be corrected to read as follows: