X-ray diffraction analysis is an excellent analytical tool. But if a certain quality of the results is needed or if solutions of analytical problems are to be obtained in a short time period, the X-ray diffractometer must be automated and the spectra reduced with dedicated algorithms.

In LABORELEC, three programs are principally used to solve the problems encountered in the X-ray diffraction analysis: a modified program given by R. L. Snyder; the search/match G. G. Johnson program (last version); and the POWD5 program.

This paper describes an interactive computer program, INDEX, which was written at Philips Laboratories as part of the software development effort for the APD 3600: Automated Powder Diffractometer. This program reconciles the differences between calculated and observed powder diffractogram “d-spacings” by unit cell parameters refinement and/or correction of observed lines for “significant“ systematic errors. The reconciliation procedures, described below, yield a set of residual differences which may be due to x-ray photon statistics, random gear imperfections, or minor instrumental aberrations. Lattice parameters accuracies of 4-5 parts per 104 can b e obtained routinely on powder diffractometers when systematic effects have been taken into account. The interactive nature of INDEX permits intervention at critical stages where it is most beneficial with a minimal number of keystrokes.

A minicomputer program system for phase Identifications in x-ray powder diffraction is described. The routines written in FORTRAN comprise the users’ special purpose standard-file management (creation of microfiles from the complete JCPDS-data base or own standards, as well as utility routines for corrections, supplements and bookkeeping) and the measured data processing, including raw data acceptance, data reduction by two selectable peak-search routines (trendoriented or 2nd derivative) and an exhaustive search/match procedure through selected microfiles. The data reduction and analysis programs have manifold graphical displays allowing manual interference. In one run up to five phases can be matched. The weight portion of every phase is estimated, using I/I (corundum)- values, Hie whole analysis (in automatic operation) consumes about 1 or 2 minutes of the processor time on a pdp 11/34 minicomputer. This matches well to the data collection times accessible for fast powder diffraction systems /I/.

The advantages of using elemental information to assist in the interpretation of x-ray diffraction (XRD) data are well known and many of the modern search/match algorithms utilize chemical information to make the procedure faster and more reliable (1). Elemental data can also be used to facilitate the quantitation of phases ideittified by x-ray diffraction, in some cases eliminating the need for performing the quantitation based upon the diffraction pattern. There are certain advantages to this approach. The first is that certain difficulties encountered in XRD quantitation such as line overlap, particle statistics, preferred orientation, microabsorption, extinction, and lack of pure Standards are alleviated. The second is that the elemental analysis is, as a rule, easier and more sensitive than the diffraction technique. It therefore should be possible to increase the ease and the accuracy of quantitative phase analysis by utilizing the chemical data available. Since most materials submitted for XRD analysis are in form acceptable for x-ray fluorescence (XRF) analysis, this is the quantitative elemental technique of choice. However, it should be noted that other elemental analysis techniques can be used instead of XRF to furnish the chemical analysis.

A set of experimentally obtained “d” values is subject to a variety of random and systematic errors, some of which are inherent to a given diffractometer configuration and some of which may result from incorrect alignment of the diffractometer or technique in establishing peak positions and subsequent calculation of “d” values. In a previous paper (1) we have discussed the problems involved in the identification and control of errors in the computer controlled diffractometer and in that paper we indicated that it is useful to differentiate between different types of two-theta values. Firstly the Theoretical 20 values are those values which are dependant only on the size and distribution of atoms in the unit cell of the phase. The Practical 20 values on the other hand result when aberrations inherent in a given diffractometer geometry are convoluted with the Theoretical 20 values. In terms of their typical magnitudes the most important of these aberrations in decreasing order are: Specimen Displacement, Axial Divergence, Flat Specimen and Transparency Errors. Other inherent errors include refraction and the effects of focal line and receiving slit widths etc., but these latter effects are generally considered small. At the second level, Experimental 20 values also depend on misalignment errors. The third level errors accrue in the conversion of the experimental 20 value to “d” spacing. These errors may arise simply from round-off errors or from more fundamental reasons arising from the polychromatic nature of the source and uncertainties in the wavelength of the diffracted radiation.

The purpose of this paper is to summarize the theoretical basis and experimental techniques for application of the referenee intensity method to quantitative, multi-component analysis by x-ray diffraction (XRD). Detailed descriptions of the technique and formal error analysis are discussed by Davis (1978, 1980, 1981a, 1981b, 1981c).

In powder diffraction experiments involving mixtures of compounds, identification of each individual phase is complicated by the presence of other phases. The interpretation of such complex patterns is often very difficult, and much effort has gone into computational search-match algorithms which attempt to identify individual phases (Nichols, 1966; Johnson, 1977; Frevel, 1976). The success achieved by these programs and by manual search-match methods accounts for the fact that X-ray diffractionists have, in the past, not actively searched for other techniques that could be used to simplify such complex problems. In a recent work (Nichols & Johnson, 1980), a comparison was made of the search-match methodologies employed by several similar technologies (mass spectroscopy, fingerprint identification, X-ray diffraction etc.). A significant observation was made that only in the X-ray method was there so much emphasis on analysis of phases in their “as received” condition. In the other cases, emphasis was placed on the separation of phases before obtaining the spectra. A classical example is the GC-MS instrument which employs a gas chromatograph to separate phases before the mass spectrographic analysis is carried out on what are, by that time, essentially pure phases.

The use of quantitative x-ray diffraction (XRD) as an analytical technique has recently become increasingly popular. There ate primarily two reasons for this increasing interest in a relatively old discipline. The first is simply the need for quantitative phase analysis. This need arises from several sources such as government regulations on respiratory quartz, industrial quality control, and material research. X-ray diffraction provides a readily available technique for bulk phase analysis on chemically similiar phases. For phases which are elementally distinct, our sister science, x-ray fluorescence, can more easily provide the quantitation needed. The second reason for the increasing interest in quantitative XRD is the ready availability of automated powder diffractometers. These instruments remove much of the tedium involved in the collection and reduction of the data.

A strictly focussing Guinier diffractometer using a linear position-sensitive proportional counter (PSPC) to detect the diffracted x-rays is described. The data collection time for a complete pattern can so be reduced to minutes Instead of hours as it used to be in conventional film- or counter-Guinier systems. The PSPC collects all diffracted x-rays over several degrees of 2 Theta in parallel and composes the full pattern by a continuous scan over the whole 2 Theta range. This principle was described in Adv. In X-Ray Anal. Vol. 22, 255 ff and 24, 123 ff. for Bragg-Brentano diffractometers.

I report the experimental setup to obtain an x-ray beam from germanium monocrystal of unusually small angle of vertical divergence of the order of 2 sec. of arc without using any collimator. The production and the properties of the highly collimated beam of x-ray will be described. A rectangular piece of germanium 1” × 1” and of thickness 0.5 mm has been cut with specific orientation of crystallographic planes (111) and (110). The 1” × 1” surface is parallel to (111) planes and the surface of one edge is parallel to (110) planes suitable for Borrmann channelling via (220) planes.

An application of energy dispersive diffractometry to the measurement of residual strains (stresses) in the interior of industrial materials is described with particular emphasis on the use of high energy (up to 250 keV) x-ray photons. The use of high energy photons permits better penetration into materials. Hence diffraction data for evaluating bulk residual strains can be obtained in the transmission geometry in contrast with the conventional angular dispersive diffractometry, which uses Bragg reflections from the surface of materials. The reliability and sensitivity (detectability of small strains) of the energy dispersive method are demonstrated through its application to mapping of residual stress distributions across weld zones in Alaskan pipe line segments (API5LX65). The detectability of strain variations within materials depends on x-ray optical resolution and statistics.

This note describes a diffractometer technique that is successful on specimens that yield sharp diffraction peaks but that have grain sizes somewhat too large to give reliable results with the usual powder diffraction methods, owing to the peak profiles being distorted or displaced by having too few grains reflecting, Such specimens are not uncommon in stress analysis and the errors encountered are sometimes reduced by oscillating the specimen through an angle range, Δβ, of a degree or so about the diffractometer axis, thereby increasing the number of recorded reflections. The technique discussed here is basically a single crystal technique rather than a powder technique, and with a diffractometer capable of measuring reflections at high angles on both sides of the initial beam this technique would amount to W. L. Bond's precision method. For the usual diffractometer, however, high diffraction angles must be measured on one side only, even though some instruments permit the lower angle reflections to be measured on both sides for accurately locating the zero of the 2θ scale. We are discussing a technique as applied to these usual types of diffractometers.

Compressive residual stress is one of the essential elements which contributes to the exceptional fracture resistance of case-hardened components. The sign and magnitude of residual stress are determined by transformation characteristics, thermal and mechanical histories of the steel. Accurate determination of residual stresses is essential in research on case-hardened steels.

Practitioners of wavelength-dispersive x-ray spectroscopy are always seeking better dispersing devices. The wavelength-dispersive instrument is called a “crystal spectrometer” because natural or synthetically-grown crystals are most often used. Occasionally, other “manufactured” dispersers are suggested for specific applications: highly oriented polycrystalline graphite provides much higher intensities than the crystals usually used for the K-lines of P, S and Cl; Langmuir-Blodgett films (heavy metal salts of fatty acids) provide 2d-spacings over the range of 70 to 130 A, making soft x-ray spectroscopy practical in a wavelength range for which natural crystals are not available.

This paper presents a new method to measure the thickness of very thin films on a substrate material using energy dispersive x-ray diffractometry. The method can be used for many film-substrate combinations. The specific application to be presented is the measurement of phosphosilicate glass films on single crystal silicon wafers.

The purpose of this study was to develop a quick and valid X-ray method to determine the alteration models for acidic and intermediate type of altered rocks. Four alteration minerals--alunite, kaolinite, montmorillonite, and sericite--and total quartz in certain altered porphyritic rocks were determined and evaluated by using the APD (Automatic Powder Diffractometer) system with external standard methods.

The findings indicate that the APD system can successfully be used in the quantitative analysis of these five mineral phases. The best results are obtained from samples with low iron minerals and of a grain size not coarser than 325 mesh.

An X-ray diffraction (XRD) technique is employed to determine the presence or absence of crystalline phases in glass batch and to determine its homogeneity qualitatively and quantitatively.

Sample preparation problems are discussed, and promising techniques for sample preparation are presented. Qualitative batch homogeneity determination is accomplished by comparing the integrated intensity of a particular reflection of the reference sample to that of the unknown sample. Quantitative batch determination is accomplished by using the internal standard method. Three replicated data sets indicate that the standard deviation of kaolinite and colemanite are higher than those of quartz and calcite. However, the overall data from the quantitative analyses lie within an acceptable range of precision and accuracy.

The majority of pharmaceutical dosage forms are marketed as tablets which are formulated to satisfy various basic requirements. The analysis of the resultant multicomponent pharmaceutical and product is usually a lengthy task.

This paper describes the complementary use of X-ray diffraction (XRD) and X-ray fluorescence spectroscopy (XRS) to characterize and quantify excipients in pharmaceutical tablets.