In a number of laboratories data from the X-ray pole-figure goniometer are now processed numerically to obtain a suite of complete and normalized pole- figures. From these pole-figures the preferred orientat ion of the grains in a monomineralic aggregate is determined using spherical harmonic analysis and represented as a frequency distribution of the Euler angles Ψ, θ, ø, termed the “orientation distribution function” (ODF),When the frequency density of grain orientations is plotted in a Cartesian coordinate system with Ψ, θ, ø, as axes,it must have a translation periodicity Of 2π or less along each of the axes, because the Euler Angles are angles of rotation.

Several interesting phenomena involving ultra-soft X-rays and synthetic multilayer crystals were studied as a result of the on-going process of improving the Rigaku Mode] 3630 Wafer Analyzer for the measurement of BPSG (1000-2500 Å) and other thin films.1-3 These phenomena can be divided into four categories; “ghost” peaks, diffraction from the substrate, fluorescence from the multilayer and higher order lines from the multilayer. Each of these is a potential snurce nf error in the measurement of ultra-soft X-rays, Fortunately, as will be shown, each can be readily dealt with.

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.

Machine parts made of ceramics are usually finished by grinding. Residual stresses as well as defects introduced by grinding will influence the fracture strength and the function of ceramics parts. Although several investigations used the X-ray diffraction method to measure the grinding residual stresses, their grinding conditions were rather limited.

In the present study, sintered alumina ceramics of 99% purity were ground with a resinoid diamond wheel (#140 grain size number) under various grinding conditions. The effects of depth of cut and stock removal on the residual stress was measured with the X-ray method.

Quantitative analysis by x-ray powder diffraction methods has become increasingly important in recent years with the availability of computer-controlled automatic powder diffractometers. All data gathering techniques require suitable reference standards to scale the measured data properly. One means of achieving this scaling is through the reference Intensity ratio which is defined as the intensity ratio of the strongest diffraction maximum of a substance to the strongest maximum of a reference material in a 1:1 mixture “by weight. These ratios may he measured or they may he calculated if the crystal structures of the materials are accurately known.

Interest in advanced thermoplastic composites for use in high performance structures stems from their order of magnitude improvement in fracture toughness and delamination resistance over epoxy based composites, their strong solvent resistance, and the possibility of dramatically lower fabrication costs through processing flexibility. The chemical and mechanical properties of semicrystalline thermoplastics depend on the morphology of the material, such as the crystallinity content and spherulite size. We describe here the use of x-ray diffraction to characterize the degree of crystallinity of the polyetheretherketone-graphite composite system, a leading thermoplastic candidate for use in aerospace vehicles. In reflection, diffraction from the microcrystalline graphite fibers dominates the scattered signal and must be adequately accounted for. The technique is useful on large samples and for quality control. In transmission, the graphite signal is weak, thus simplifying data analysis; however, sample thickness must be limited.

The diffraction, reflection, absorption, fluorescence, and the electronic emission that results from the interaction with ultrasoft X-rays (λ > 10 A) are presented as practical bases for microanalysis. Recent developments on sources and detectors for the ultrasoft X-radiations are described. A preliminary report on a current investigation on low-energy photo-Auger electron analysis and on a new type of low-energy electron spectrometer is also presented.

The state of stress in a material, as represented by the stress tensor, can be measured using x-ray or neutron diffraction techniques. A stress tensor measured using diffraction represents an experimental estimate of the true state of stress in the material. The measured stress tensor will include both instrumental and counting statistical errors. With careful measurement techniques, instrumental errors can be minimized, and accurate results can be obtained. The errors in the measured stress tensor that are due to counting statistics can be estimated using well established error propagation techniques. Unfortunately, these errors cannot be analytically propagated through the solution to the eigenvalue problem which yields the principal stresses and directions. Without estimates of the errors associated with the principal stresses and directions, the values determined for these quantities are of limited value.

A modern analytical laboratory of a large corporation manufacturing paper, construction materials and chemicals must be sufficiently diversified in methodology to provide accurate results in the shortest possible time. Among other techniques the implementation of an automated “menu” driven wavelength dispersive spectrometer allowed for the setting-up of a variety of quantitative X-ray fluorescence methods.

This paper describes a technique of measuring the volume percent retained austenite in steel using ordinary filtered X-radiation and an X-ray diffractometer. As compared with conventional rate-meter recordings or microphotometer traces of diffraction peaks, the subject technique extends the range of austenite determinations from the usual 7 % down to 1 %. It markedly improves over the entire range of measurement.

Essentially, the technique consists of step scanning the profile of each selected martensite and austenite diffraction line and recording the corresponding intensity within a known probable error. The step-scanning, fixed-count, and counting-rate, recording operations are performed automatically by a counting-rate computer. The integrated intensity of each diffraction line is obtained by summation of intensity increments above background in accordance with the “trapezoidal rule.” For hardened steel, the best peak-to-background ratio is secured using filtered Cr Ka radiation with the vanadium filter located in the diffracted beam. The volume percent retained austenite is determined by direct comparison of the integrated intensity of an austenite line with the integrated intensity of a marten site line and from the relationships between intensity and concentration for the martensitic and austenitic phases.

An application of the subject technique was its use in determining the retained austenite behavior of carburized 9310 steel. The volume percent austenite retained on the surfaces of as-quenched specimens was determined as a function of carburizing potential. The amount of retained austenite subsequently transformed by various combinations of tempering, refrigerating, and retempering treatments was successively ascertained. The amount of retained austenite determined using the subject technique compared closely with the amount of retained austenite measured by metallographic examination. However, the reproducibility of results was better for the X-ray method as compared to metallographie examination. The nondestructive nature of the X-ray method permitted successive measurements on the same surface following repeated thermal treatments.

Solid solutions are pervasive in minerals and in industrial inorganic materials. The analyst is often called upon to provide qualitative and quantitative X-ray phase analysis for specimens containing solid solutions when all that is available are Powder Diffraction File (PDF) data or commercial standards for the end members. In an earlier paper (1) we presented several examples of substantial errors in accuracy of quantitative analysis that can arise when the crystallinity and composition of the analyte standard do not match those of the analyte in the sample of interest. We recommended that to obtain more accurate quantitative analyses, one should determine the analyte composition (e.g., from XRF on grains seen in a SEM or from comparison of cell parameters with those of the end members) and synthesize an analyte standard with this composition and with a crystallinity approximating that of the analyte (e.g., as determined from peak breadth or α1/ α2 splitting).

The development of intense synchrotron radiation sources during the last twenty years has enabled several types of x-ray spectroscopy and scattering techniques to come into practical use. One of the most significant methods for the characterization of extremely dilute samples is high resolution x-ray absorption-edge spectroscopy. The technique is usually divided into two separate methods according to whether the x-ray absorption near edge structure (XANES) or the extended x-ray absorption fine structure (EXAFS) is analyzed. XANES features are due mainly to bound-state electronic transitions just below, and on the low energy side of the edge, and to multiple scattering resonances on the top of the edge and at somewhat higher energies. EXAFS features are oscillations due to ejected photoelectron back scattering interference processes in the close vicinity of the absorber atom. XANES analysis is used to determine atom valence, atom site distortion from regular geometries, and other details of the atom site. EXAFS features can be analyzed to recover interatomic distances between the absorber atom and its first few shells of neighbors, as well as the number and types of these neighbors. Together these techniques can provide an atomspecific probe of die short-range structure within almost any type of condensed matter.

The utilization and optimization of the properties of materials follows most effectively from a detailed knowledge and understanding of the positions and energetics of their constituent atoms, generally obtained from scattering/diffraction experiments involving electrons, neutrons or electromagnetic radiation. For the most part, these experiments are undertaken on individual crystals of the material, thereby preserving the resolution (and information content) of the three-dimensional reciprocal lattice. However, many of the substances of greatest academic and technical importance either do not crystallize with dimensions large enough for single-crystal studies, or display the properties of maximal interest only when present in finely-divided (powdered) form. In a diffraction experiment, the reciprocal lattice is then collapsed on to the single dimension of the 2θ scale.

It is shown that the integrated intensities of diffraction lines from calcite and aragonite powders prepared by precipitation vary markedly, due to variations in sample packing efficiency arising from different degrees of polydispersity in the particle size distributions. Since prolonged grinding to equalize initially divergent distributions changes the polymorph composition, the packing effect imposes the principal limitation on the precision of the x-ray method for certain types of calcium carbonate preparations.

A very accurate 8X8 matrix approach to dynamical theory of X-ray diffraction in which fewer approximations are made than in the classic vonLaue approach, is described here. The method is related to the very general matrix method of Kokushima and Yamakito, and is particularly suited to numerical solution with a computer. It can be used to solve problems in ideal, undistorted crystals with high precision even at near grazing incidence without special consideration of refraction or external reflection. It is also easy to apply to problems where periodicity of oblique Bragg planes varies in the direction normal to the surface. Such strain may be induced, for example, by variation of composition with depth. Certain problems wherein simultaneous diffraction by two sets of Bragg planes occurs can also be treated by this approach.

The relation of the X-ray small-angle scattering parameters to the results of transmission electron microscopy for spherical Guinier-Preston zones was investigated. Experimentally, the Guinier radius is found to equal (<R7>/<R5>1/2) and the Porod radius to equal <R3>/<R2>. These results were theoretically predicted by Baur and Gerold, A log normal distribution was found to be in close agreement with the experimental data. The use of this distribution allowed the size-distribution curve of spherical Guinier-Preston zones to be constructed from the X-ray parameters and from a knowledge of the metastable miscibility gap. This approach is used to follow the evolution of size distribution in both Al-Ag and Al-Zn alloys. The application of this approach to nncleation and growth as well as redistribution processes is discussed. Growth paths are established from the size distribution evolution curves through an Nv> construction. A brief discussion of the technique is included.

We describe an adaptation of photon excited x-ray fluorescence analysis which is optimized for the analysis of small samples. A fine focus x-ray tube is used in conjunction with small diameter detector collimators in order to focus on a small sample volume with as high sensitivity as possible. Sample areas of less than 1 mm diameter can be analyzed with ppm detectability. In applications involving the analysis of human hair samples, a minimum detectable limit of 10 ppm Hg can be realized in a 1 mm long segment of a single hair in a counting time of 200 seconds. Simultaneous measurements of the sample mass can be obtained from the intensity of the incoherent scattering. An automated x-ray fluorescence analysis system using the technique for the scanning of elemental profiles in such hair samples will be described.

A series of FORTRAN IV programs have been written to aid in qualitative x-ray fluorescence (XRF) analysis. These programs have been implemented on a DEC PDP 11/34 computer with an RSX-11M operating system and access the NIH elemental data base (1). The programs and their application to XRF analysis in our laboratory will be described.

In the microprobe analyzer, a portion of the high energy electrons impinging on the surface are backscattered from the sample and re-emitted at high energy levels. Low energy (less than 50 eV) or secondary electrons also ate emitted. Both the electron backscatter yield and the secondary electron yield are related to the mean atomic number of the target material and, hence, may be used to provide information about the target composition. Unfortunately, however, the secondary electron yield is very sensitive to the surface condition of the specimen and various instrument parameters. This complicates the otherwise simple linear relationship between sample composition and electron backscatter yield.

It is shown that the effects due to secondary electrons can be minimized by biasing the sample, and that good results can be obtained in the analysis of binary systems. The limitations and utility of the method are discussed, and backscatter yields are determined.

There are several methods for the measurement of retained austenite in steels, which influences mechanical behavior and corrosion resistance of steels. Among them, X-ray diffraction methods using a wide angle goniometer or X-ray stress analyzer are commonly used because the methods are non-destructive, giving useful information about residual stress or lattice strain as well.