Conventional X-ray stress analysis is based on the so called "linear sin2ψ" law and yields average two axial stresses in the irradiated surface layer of polycrystalline specimens. Three examples are given in this paper where either strong deviations from the linear law are observed due to stress gradients or where the linear law yields wrong results because of three axial stresses. Special experimental techniques are described and formalisms are given for the evaluation of the corresponding stress fields which are in the described cases more complicated than usual.

A Debye-Scherrer camera (radius 572 mm) was designed for the use at the Photon Factory BL-6A2. It uses 4 pieces of the Imaging Plate to cover 0° ∼ 160° in 2θ. The profiles measured by the camera had 0.083° full width at half maximum (FWHM) and were rather symmetric compared with conventional X-ray source. The observed profiles were well represented by either the split Pearson VII or pseudo-Voigt function. In order to examine the performance of the new camera, the whole powder data of LiF was analyzed by the Maximum Entropy Method(MEM). The MEM analysis of LiF was successfully accomplished using 20 measured structure factors and gave R(Bragg) 0.25%. The density distribution obtained represented a characteristic feature of ionic crystals and was consistent with the theoretical result of the self-consistent LCAO method.

Fine focus X-ray tubes developed for projection X-ray microscopy can also be used for X-ray micro-analysis. Areas about 10 microns in diameter of thin sections have been analyzed by measuring differences in X-ray transmission, with particular reference to the determination of calcium in biological materials and in minerals. The high intensity of this X-ray point source has permitted micro-fluorescence analysis of similar small areas with high sensitivity and reasonable time. The same electron optical system has been used for micro-emission analysis of rock slices and mineral grains. By scanning the electron beam over the specimen surface and recording either the scattered electrons or the emitted X-rays, a two-dimensional picture can be displayed of the physical features or of the distribution of a particular element respectively. The analysis of a selected, volume of 1 cubic micron in the surface has been obtained by plotting the characteristic line emission spectrum with a crystal spectrometer and proportional counter. The sensitivity is 0. 1% or 10−1 gram. Micro-beam X-ray diffraction has also been used with a stationary X-ray source both for transmission and back reflection with a 10 minute exposure from a 10 micron diameter area.

The stress tensors were measured with x-ray diffraction in both the ferrite and cementite phases of a 1080 steel specimen deformed in uniaxial tension. The macro- and micro-stresses were separated for all the components of the stress tensors. All the components except the hydrostatic components of the micro-stresses could be determined without an accurate value of the unstressed lattice parameter. Tensile stresses were found in the cementite and compressive stresses in the ferrite along the deformation direction. The tensile stresses in the cementite were quite large.

A prototype X-ray fluorescence system for chemical and phase microanalysis of materials has been developed and tested. Preliminary work with this system has indicated X-ray fluorescence detection limits on the order of 40 picograms for heavier elements such as gold when using a 100 micron collimator, 400 second counting time and a silver anode operating at 12 Kw. Phase identification by X- ray diffraction can be obtained from the same spot. A proposed design for an improved system providing greater elemental sensitivities and capable of semi-automated operation has been completed.

The recovery and recrystallization of cold rolled copper during reverse bending fatigue at room temperature has been studied with x-ray diffraction, optical microscopy and transmission electron microscopy techniques. Recovery of x-ray line breadth was recorded as a function of number of cycles at all strain amplitudes investigated. Recrystallization was observed to take place only at small strain amplitudes (life of 106 to 107 cycles). The rate of nucleation of the recrystallized grains increases with increasing strain amplitude and is a linear function of the number of cycles. The formation and growth of the grains was confined to regions near the surface of the specimen. Since comparable thermal recovery occurs at approximately 435°F it is concluded that the dynamic generation and migration of numerous point defects during fatigue is responsible for the room temperature recrystallization.

With fluorescent X-ray analysis as routine work, the correction term for the coexistent element can be expressed as linear terms of the weight fraction of the element because the compositions of samples are limited to a small range. Usually those correction factors which require a great deal of work are obtained experimentally. The authors have obtained theoretical equations of fluorescent X-ray intensity which are in good agreement with experimental values. The linear correction factors are obtained from derivatives of those equations, and their values can be easily calculated with a computer. The experimental X-ray intensity versus the weight fractions is usually expressed as a line. However, the linear approximation is not correct over a wide range of the composition. The second derivative of the theoretical equation explains the deviation from the linear approximation and gives the range where the linear approximation is allowed. The calculations are applied to the analysis of stainless steels, several low-alloy steels, and iron ores, and experimental results are corrected by the calculated results. Correction factors for Ni Kα, Fe Kα, Cr Kα, Mn Kα, and Cu Kα in stainless steels and Cr Kα and Mn Kα in low-alloy steels are calculated for coexistent elements such as carbon, silicon, titanium, chromium, manganese, copper, niobium, and molybdenum. For example, standard deviations of chromium and manganese analyzed results in lowalloy steels decrease from 0.169 and 0.044% to0.030 and0.023%, respectively, with theoretical corrections. In the analysis of iron ore, the fluorescent X-ray intensity of iron is affected by combined oxygen, which is different for the various compounds of iron oxides, and other impurities such as alumina, silica, and lime. The correction factors of these are obtained by calculation, and the standard deviation decreases from 1.70 to 0.44% for 55.1 to 68.5% iron. It is found by experiment that the theoretical values have about 1 or 2% of relative errors, and their derivatives also have relative errors of the same order of magnitude. But the ranges of coexistent elements are usually small, a few percent at most in routine work, and the theoretical values can be used in practical analyses.

Methods have been developed for autopsy tissue analysis using a proton-induced X-ray emission (PIXE) system optimized for thin sample analysis. The system uses 2 MeV protons, thus limiting sample thickness to several milligrams per square centimeter. Calibration was accomplished with standard solutions spotted onto Nuclepore filters, which were subsequently irradiated in a uniform proton flux. X-ray yields measured with a Si (Li) detector were corrected for proton energy loss in the filter matrix as well as X-ray attenuation. Corrections for proton energy loss were determined from empirical parameters relating proton energy to X-ray cross sections. Typical filter thickness and penetration of the sample solution into the filter matrix were measured allowing calculation of proton energy attenuation and X-ray absorption corrections. The method was used in routine analyses for sixteen elements in seven types of human tissue. Accuracy was evaluated with standard reference materials and atomic absorption analyses.

Obsidian from eight localities in the San Francisco volcanic field of Northern Arizona was analyzed for 21 minor and trace elements (Ti, Mn, Fe, Co, Zn, Rb, Sr, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, W, Au, Hg, Th) usincf x-ray fluorescence analysis. All samples exhibited irregular analyzing surfaces. This was a more in-depth study of a previous study (1) in which a very small number of standards were used.

The data, in the form of intensity ratios relative to iron, were statistically analyzed and the trace and minor element patterns established. The obsidian clustered into four well-defined groups each consisting of two localities: Government Mountain/Obsidian Tank, Slate Mountain/Kendrick Peak, Robinson Crater/O'Leary Peak, and RS Hill/Spring Valley. The four distinct groups were treated individually to refine the separation between the similar sites. Classification function coefficients were calculated for each locality, then used to identify the source of thirteen obsidian artifacts recovered from a Northern Arizona archaeological site.

In this paper an attempt is made to review in rather broad perspective the origins and history of quantitative methods in diffraction analysis, at the same time leaving an in-depth examination of the present state of the art to other better qualified contributors to this conference. Space limitations preclude mention of many significant contributions, for which I am very sorry. It will be possible to review only a number of pivotal historical events, while also taking note of certain other researches that seem representative of historical and present-day trends.

The birth of quantitatively meaningful analysis in the mid-1930s depended upon a realisation of, and allowance for, the alteration of the diffracted intensities resulting from absorption of x-rays by the specimen. Furthermore, advances in the art achieved during the past forty years have been closely related to improvements in the treatment of the absorption factor.

An investigation was undertaken by the Bureau of Mines at College Park, Md., to determine the effect of various combinations of collimators, analyzing crystals and detectors on line intensities, line-to-backgrouhd ratios, and spectral resolution. The research showed that line broadening due to mosaic crystal surfaces was greatly reduced and line splitting from faults was eliminatedby the use of two fine collimators (0.005 inch, spacing, 4 inch length). Line intensities were reduced, but lineto- background ratios arid line profiles were substantially improved with double collimators. Pulse height discrimination resulted in marked improvement in the line-to-background ratio in the long-wave length region, 2 to 10 A, but was much less effective for shorter wave lengths.

The counter tube diffractometer method for determining d spacings is often rejected for precision work because of lack of information concerning the nature and significance of the inherent errors. Errors concerned with the geometry of the method, the nature of the X-ray source, and the technique of collecting data have all been analyzed previously in some detail. The findings of these analyses, which are scattered throughout the literature, are reviewed briefly. Errors arising from imperfections in the instrument and misalignment of the X-ray source with respect to the diffractometev have been studied experimentally. The results are presented and discussed in terms of the resultant error in the determination of the lattice parameter of a cubic crystal. Errors determined both analytically and empirically are discussed in relation to the extrapolation procedures commonly used for diffractometers. It is shown that, depending on the construction of the instrument, the effect of imperfections in the gears may almost double the error in the final extrapolated value of a lattice parameter.

A novel x-ray spectrograph for the analysis of light elements has been developed based on previous computations and confirming experiments by one of as (H. K. Herglotz). The major components of the instrument are an efficient fluorescent source, a totally reflecting mirror, and an open window photomultiplier. Identification of wavelengths in the range 15 < λ < 80 Å is achieved by the wavelength dependence of the critical angle of reflection of an x-ray beam incident on a suitably chosen low absorption reflector. As the incident angle is increased through the critical angle for a particular wavelength, the reflected beam intensity is sharply reduced; hence, a periodic vibration of the incident beam through a small angular range about the critical angle furnishes a strong a.c. reflected signal characteristic of one narrow wavelength band only.

Initial results promise a simple, easy-to-operate instrument for the routine analysis of elements boron to fluorine.

Layered Synthetic Microstructures (LSMs) were first reported as commercially available diffracting structures for routine x-ray spectrochemical analysis in 1984 (Nicolosi et al.). Innitially, these devices (PX-1 and PX-2) were intended for use as alternatives for Thallium Acid Phthlate (TAP) and Lead Octadeconate (LOD) for improved stability and diffracted intensity. Improvements in the analytical performance of X-Ray Spectrometers for the elements carbon to magnesium has met, and in some cases exceeded, innitial expectations. Having captured the interest of many new possible applications, developments for LSMs with larger 2d-spacing and greater reflectivity have continued.

Previous instruments employing LSMs have had difficulty in measuring X-Ray energies below the carbon K-series characteristic. Below the carbon K-edge energy, several significant phenomenon combine to reduce sensitivity. Among these are: 1) Reduced reflectivity of conventional LSMs, 2) Increased absorption at the polypropylene window of the detector, and 3) Greater electronic noise.

The X-ray diffraction patterns from fibrous polymers are generally characterized by a small number of relatively broad overlapping peaks often overlaid with a diffuse halo. Single fibres give the same pattern as a parallel bundle of fibres, so that the pattern is equivalent to the rotation pattern of a single crystal. Despite the inherent difficulty of insufficient well-defined reflections, all commercially useful fibres have been indexed, starting with cellulose, through nylon 66 and polyester, to the more recent fibres, such as Nomex and Kevlar. Only the structural complexities of the natural fibres of keratin (wool and hair) remain to be fully determined.

Many sophisticated computations have been carried out to refine unit-cell constants; unfortunately, much of this work is of doubtful value to those interested in fibre characterisation. Fibres are semicrystalline materials and their molecules are insufficiently well ordered for precision calculations of atomic positions. Indeed, there can be significant error involved in evaluating unit-cell constants from overlapping peaks, unless precise profile resolution is carried out.

When the accuracy of a lattice parameter determination is carried beyond about 0.01 % it becomes of special importance to consider the equivalence of λ and θ in solving the Bragg equation for d. A reference angle on the observed diffractometer profile must be identified with the corresponding wavelength, of the incident X-ray spectral distribution. Exact identity is not possible because the diffractometer profiles are broadened, distorted asymmetrically, and displaced from their correct positions by amounts dependent on the shape of the incident spectral lines, the angular separation of the Kα1,2 doublet lines, and the specimen, instrumental, and geometrical aberrations innerent in the experimental method. The aberration functions vary with the experimental conditions and are Bragg-angle-dependent, thereby introducing systematic errors which are not eliminated by extrapolation procedures.

Most of the published diffractometer measurements of lattice parameters have used as the reflection angle, 28, of the diffractometer profile the peak P(2θ) or the midpoint of chords at various heights above background M1/2(2θ), M2/3(2θ), etc., of the Kα1 line. The relationship between these various angular measures of the line profile is not constant; P(2θ) may be equai to, greater than, or less than M1/2(2θ), depending on the asymmetry of the line profile. The X-ray wavelengths currently used in diffractometry refer to the peak P(λ) of the spectral distribution. The use of P(λ) with different angular measures of the diffractometer profiles results in a range of d's from which different values of the lattice parameters are calculated. The selection of arbitrary methods of defining 2θ does not take into account the significant aspects of the diffraction process, nor does it facilitate the correction of the data for systematic errors inherent in the experimental measurements.

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.

For many years Layered Synthetic Microstructures (LSM's) have been used successfully as dispersive devices. The commercial variety introduced in 1984 offered significantly greater stability and diffracted intensity characteristics over Thallium Acid Phthalate (TAP) crystals. These devices offer superior sensitivity for fluorine, sodium and magnesium in all but a few applications where resolution is very critical. Subsequently, a variety of these devices have been optimised for analysis of the lower atomic number elements.

Recently, several industrial applications have required the development of LSM's with 2d spacings optimised to enable quantitative analysis of oxygen, nitrogen, carbon and even boron. In these applications, the large incremental difference in characteristic wavelength per atomic number step limits the dynamic range of elements over which the LSM can be optimised. These considerations are discussed as they relate to routine analyses of very low atomic number elements by sequential Wavelength Dispersive Spectrometry (WDS).

Newly developed fabrication techniques are used to produce curved LSM's for use with the focusing optics of simultaneous WDS. Application of these curved devices for the analysis of Mg in steel, Na in slags and F in glass will be discussed.

Finally, an application which requires the analysis of thin films on semiconductor devices will be described. In this method, characteristic K-spectra and L-spectra of low and high atomic number elements, respectively, are selected for optimum sensitivity to the surface composition.

Two-dimensional geometry information contained in SAED spot patterns augmented with EDS elemental data is employed in a computerized phase identification of microcrystalline particles. The initial chemistry screening of a laboratory managed database using the 'bitmap' concept is followed by a geometry search/match treating of the spot patterns as planar sections through the reciprocal lattice of a candidate phase. The identification is selective, fast, and yields to a complete automatization,

This paper reviews x-ray fluorescence (XRF) matrix correction methods which use scattered radiation and discusses their typical analytical applications. It also discusses some of the underlying assumptions of these methods and thus provides a basis for estimating their merits and limitations in quantitative analytical applications.