Results are given of an assessment of a Rietveld-type X-ray powder diffraction pattern fitting structure refinement technique for assaying powdered mixtures as an alternative to conventional discrete peak empirical methods of the type described by Klug and Alexander (1974) and Chung (1974). The values obtained for a mixture of corundum and α-quartz, following calibration of the instrument with a profile of the former, indicate that this technique has excellent potential as an analytical tool.

A computer program for analysing two-component interstratified structures by two different Fourier transform methods is described. The first method consists of the calculation of the X-ray diffraction intensity function, and in the second one (direct method) the distribution function of interlayer distances is calculated. The programs have been written in compiled GWBASIC for an Olivetti M-24 microcomputer (MS-DOS operating system), and they may also be run on any IBM compatible personal computer. As an example, this program is applied for the analysis of a chlorite-smectite interstratified mineral.

The Powder Diffraction File of crystallographic data has been converted from printed data cards to a computer database. Extensive testing, review, and editing of the database were completed, the history and first stages of which are presented. Computer programs used to create and analyze the database are described.

The effect of solid emulsifiers, added at the level of 10%, on the lattice parameters of tristearin and trilaurin, has been studied by powder X-ray diffraction method. The presence of sorbitan monostearate and glycerol-l-stearate affects slightly the lattice constant a in tristearin; on the other hand, although sorbitan monostearate causes an increase in a of trilaurin, glycerol-l-stearate does not. The presence of sorbitan monolaurate and glycerol-l-laurate affect a of trilaurin similarly to the long chain emulsifiers.

A correlation between the effect on a and the increase in melting point has been found.

The presence of the emulsifier does not alter drastically the lattice dimensions of the fat. The slight dissimilarity in crystal structure between tristearin and trilaurin is confirmed by the diverse effects of the emulsifiers on the internal structure of the fat.

Lattice thermal expansion of a number of compositions in the tetragonal (P4mm) single cell region of the lead zirconate titanate Pb(ZrxTi1−x)O3 system have been measured by high temperature X-ray diffraction. Polynomial coefficients which describe the temperature dependence of the lattice constants of each composition below and above the ferroelectric-paraelectric transition temperature are given.

The performances of Seeman-Bohlin (S-B) and Bragg-Brentano (B-B) diffractometers with flat thin film samples were compared on the basis of equal instrumental aberrations. It was found that the S-B arrangement has only a marginal advantage as regards diffracted intensity, and that both types of diffractometer may be successfully employed for characterization of thin films. Diffraction data obtained with very thin metallic films (down to 30 Å) are included for illustration. In order to eliminate reflections from the singlecrystal substrate in the B-B diffractometer, sample tilting was employed. Provided the tilting angle remains within 0.5°, sample tilting causes only moderate additional broadening of the thin film peaks.

The construction and use of a captive inert atmosphere cell for the preservation of atmospherically sensitive samples during X-ray diffraction is described.

Fourier transform methods of smoothing and interpolation are applied to X-ray diffraction data. It is shown that, frequently, too small a step size is used. Major gains are to be expected by selection of the optimum step size and use of these methods.

A comparison of Fourier transforms of diffractograms of quartz measured between 67 and 69° 2θ, collected at varying step intervals (0.1 to 0.01° 2θ) was used to illustrate these applications. By examining the Fourier transform of the diffractogram and noting where it decays to die baseline, a reasonable estimate of the optimal step interval can be obtained. In addition, Fourier interpolation can be used to enhance the appearance of the diffractogram, approximating a continuous plot.

My students and I have developed a LOTUS 1-2-3 spreadsheet to aid in data reduction tasks associated with preparing powder diffraction data for publication in the Powder Diffraction File (PDF) (1987) and this journal. Portions of a sample spreadsheet and the formulae in each of the computational cells are given in the Table 1. The concept of this spreadsheet should apply to any of the available computer spreadsheet programs, although the specific codes for the mathematical functions may differ.

The user enters data only into columns C, D and F-H. All other entries will be calculated from the input data. Observed 2θ angles are entered into column D. The corresponding d-spacing is calculated in column A. The Miller indices of these peaks are entered into column C. Prior to use of the spreadsheet, the observed 2θ angles and hkl's had been used to refine unit cell parameters using the Appleman and Evans (1973) least squares unit cell parameter refinement computer program implemented for the IBM PC by Garvey (1986).

The trihydrated rubidium trioxalato-chromate(III), Rb3(Cr(C2O4)3)·3H2O cristallizes in the monoclinic system with:

The space group is P21/c. CuKα wavelength 1.541778.

The Debye-Scherrer technique and filtered Cu Kα, radiation were used to obtain powder data for reflections to an angle of 2θ = 155°; a vertical scanning diffractometer was used to obtain intensity data to an angle of 2θ = 99°. The space group is with Z = 4. The lattice parameters of the tetragonal unit cell were measured to be a = 6.189 (1) Å and c = 12.391 (1) Å with c/a = 2.002 The unit cell volume was calculated as U = 474.6 (2) Å3 and the X-ray density as Dx = 6.07 ± 0.003 gm cm−3. By comparing measured and theoretical intensity values, the sublattice distortion parameter x was estimated to be x = 0.227 (12).

Fifteen reference patterns of oxides, nitrides, borides, carbides, silicides, and sulfides are included in this report. The general methods of producing these X-ray powder diffraction reference patterns are described in this Journal, Vol. 1, No. 1, pg. 40(1986).

Samples were mixed with one or two internal standards: silicon (SRM640a), silver, tungsten, or fluorophlogopite (SRM675). Expected 2θ values for these internal standards are specified in the methods described (ibid.). Data were measured with a computer controlled diffractometer. The POWDER-PATTERN system of computer programs was used to locate peak positions, to calibrate the patterns, and to perform indexing and least-squares cell refinement. A check on the overall internal consistency of the data was also provided by a computer program.

Intensities were measured as peak heights above background and were read manually from strip charts. To minimize preferred orientation effects, the powders were passed through a 400 mesh sieve and were mixed with an amorphous diluent material, glass powder. Samples were prepared by side-drifting the mixture into the holder or by dusting a thin layer on a glass slide coated with a thin smear of silicone grease.

The support and interest of the ICDD in this project is gratefully acknowledged. The expert guidance of R. Roth of the Ceramics Division on material synthesis and the careful review of the manuscript by S. Block of the Ceramics Division and A. D. Mighell of the Reactor Division are fully appreciated. Acknowledgement is also extended to D. Minor for performing sample analysis by using SEM. In the production of these standard powder patterns, the ability to search NBS CRYSTAL DATA has proven invaluable.