The use of empirical analysis techniques for the simultaneous determination of the thickness and composition of thin film samples usually requires a suite of well characterized similar type standards. While this may be adequate for a quality control application, this requirement severely limits the utility of X-ray fluorescence in the analysis of thin films in a service lab or research environment.

The use of fundamental parameters in the analysis of thin films allows the simultaneous determination of the thickness and composition of single and multiple layer thin film unknown samples without the use of similar type standards.

Residual stress measurements were made on a ground rail steel (0.75 %C) using the newly developed ϕ-integral method and the conventional ψ-differential method. The strains <εϕψ> were measured as a function of the azimuth angle ϕ, the angle of rotation about an axis perpendicular to the specimen surface, from 0° to 360° in steps of 15°, at fixed tilt angles ψ, the angle between the normals to the specimen surface and the reflecting planes (hkl), set between 0° and 45° in steps of 9°.

It was found that <εϕψ> plotted as a function of ϕ is not periodic with the period of 180° and consequently exhibits the so-called ψ-splitting when plotted as a function of sin2ψ at constant ϕ. The Fourier coefficients of the function <εϕψ> plotted versus ϕ were used to evaluate the strain tensor <εij> in the integral method. Assuming that isotropic elasticity theory is applicable, the stress tensor <σij> was calculated, and excellent agreement was found between the values determined with the ϕ integral and ψ-differential methods.

Recent studies indicate that, if the stress/strain field within the irradiated volume in an x-ray stress determination experiment is inhomogeneous, oscillations occur in the interplanar spacing vs. sin2ψ plots. There is, however, little work on the degree of inhomogeneity required to cause a given oscillation, the uniqueness of the stress fields that can cause a given set of oscillations, or the error caused by applying the traditional methods currently in use to oscillatory data.

In this paper, numerical modeling and eiasto-plastic finite element analysis was used to determine the strain fields in the diffracting volume of a polycrystalline sample under load. The elastic strain fields obtained from the analysis were then averaged over the regions that would diffract in an x-ray experiment/and then correlated to x-ray strain data to obtain an idea of the problems described ahove.

An unexplained anomalous sin2ψ split in x-ray stress measurements has consistently resulted from the use of Cr Kα radiation with nickel and austenitic stainless steels. Both, materials have diffraction peaks at low back-reflection angles for this radiation (nickel: 20 ⋍ 134°, austenitic stainless steel: 20 ⋍ 128°). The anomalous split is not evident when the measurements are made using Cr Kβ radiation, In an attempt to explain the errors produced by the Cr Kα radiation, focusing circle effects were analyzed and compared to experimental measurements made with both Cr Kα and Cr Kβ radiation on nickel-based samples,

In the field of X-ray stress analysis, a diffraction plane at a high Bragg angle region has to be selected in order to determine the precise value of stress. But stress analysis using a most desired (hkl)- plane is not always possible. The use of synchrotron radiation (SR) enables the stress analysis using many (hkl)-planes with high accuracy by providing a perfectly monochromaticed X-ray beam having an optional wave length. Such features of SR ate most suitable for the stress analysis on materials having preferred orientation.

The results of an experimental study on residual stresses within the encapsulation layers of electronic components are described. For this study, silicon wafers were coated with a flexibilized cycloaliphatic formulation filled with 30 and 40 (vol.) % of Cu particles. The residual stresses were determined by measuring the radii of curvature of the encapsulated wafers. The stress in the Cu particles at the surface was also measured by X-Ray diffraction. It was seen that the stresses within the structure are primarily macro-stresses, with little stress present within the Cu particles. Comparison of the experimental values to those calculated from linear elasticity theory also indicate relaxation within the composite during curing.

Residual strains and stresses were determined in both phases of a hot pressed α-Al2O3 composite containing 25 wt % β (cubic) SiC whiskers using conventional x-ray diffraction and profile analysis. Both phases in this composite were randomly oriented as confirmed by back reflection pinhole photographs. The reflections found most useful with Cu Kα radiation were: 511 + 333 for β-SiC at -134° 2θ and 146 for α-Al2O3 at -136° 2θ. The peak shift and broadening observed in these reflections, relative to the starting powders, were largely due to the two phases mutually constraining each other elastically. This was confirmed by the reversal of the peak shift and most of the broadening in the SiC reflections when the Al2O3 matrix was etched away. Using the method of Cohen and Noyan, it was found possible to separate the macrostresses from the microstress components in each phase. The microstresses were largely hydrostatic; of the order of 895 MPa (130 ksi) compressive in the whiskers and 370 MPa (54 ksi) tensile in the matrix. The macrostresses were ~79 MPa (11.5 ksi) tensile.

The diffraction elastic constants have been measured for the 211 and 310 peaks of a high-strength, low-alloy ferritic steel using X-rays and neutrons. The X-ray measurements were performed using both a uniaxial tension and a bending device. The neutron measurements were performed using a uniaxial tensile device. Ten X-ray and four neutron measurements were made for each case. Statistical errors were calculated and compared with the standard deviations of the average values. In addition, neutron measurements were made for the 310 peak utilizing an interior probe volume.

The results indicate that the calculated statistical errors and the observed standard deviations were almost the same for each radiation. The X-ray and neutron tensile device measurements yielded similar results within experimental error. Furthermore, the X-ray tensile and bending results were similar as were the neutron internal volume measurements. These results suggest that near-surface X-ray measurements adequately sample the bulk material in the case of steel, and that different measurement techniques can be used to obtain reliable diffraction elastic constants.

Residual stresses in dental castings are widely held to be the cause of distortion and change of fit in ceramic bonded to metal dental restorations. Residual stresses are thought to result from the casting process and from ceramic/metal mismatch of thermal expansion coefficients. Such stresses have not been confirmed experimentally. The purpose of this study was to measure residual stress with x-ray diffraction at the various porcelain application steps for two noble dental alloys with two dental opaque porcelains.

X–ray fractography is a new method utilizing the X–ray diffraction technique to observe the fracture surface for the analysis of the micromechanisms and mechanics of fracture.

In the present study, X–ray fractography was applied to brittle fracture of alumina ceramics. The first part deals with our new method of pre–cracking of ceramics. Pre–cracking was introduced to a singleedge notched specimen by longitudinal compression. Then the fracture toughness tests were conducted with pre–cracked specimens as well as notched ones. The effect of the notch radius on the fracture–toughness value was determined. The second part describes the result of X–ray fractography.

The residual stress left on the fracture surface is one of the important parameters in X-ray fractography and has been used to analyze fracture mechanisms in fracture toughness and fatigue tests especially of high strength steels.

In the present paper, the distribution of residual stress beneath the fracture surface made by stress corrosion cracking was measured by the X-ray diffraction method. Stress corrosion cracking tests were conducted by using compact tension specimens of 200°C tempered AISI steel in 3.5% NaCl solution environment under various electrode potentials. The effect of electrode potential on the growth kinetics of stress corrosion cracking is discussed on the basis of residual stress distribution.

A new method is proposed for evaluating rapidly the diffraction peak broadening by using the standard deviation of a Gaussian function approximating the diffraction peak. This value, called the Gaussian curve parameter (GCF), is given by

The use of the GCP permits rapid and nondestructive measurement of plastic strain and hardness of quenched and tempered steels with an automated X-ray stress analyzer using a personal computer. The GCP increases with increasing hardness of quenched and tempered steels. It also increases with increasing plastic strain by stretching. Furthermore, the GCP can be used for rapidly evaluating hardening of quenched steels.

Hematite (α-Fe2O3) powder compacts have been subjected to controlled, quantitative high pressure shock loading at peak pressures from 8-27 GPa and preserved for post shook analysis. The broadened x-ray diffraction peak profiles have been analyzed to determine the residual lattice strain and the coherent crystallite sizes. Maximum modification effects are observed near 17 GPa with strain values near 3 x 10-3 and size values near 200 Å suggesting annealing at higher shock pressure, resulting from the higher shock temperature.

In spite of the wide availability of automated diffractometers and advanced data reduction software, numerous traditional problems still exist that make highly precise and accurate quantitative analyses of complex mixtures difficult. The problems include particle statistics, primary extinction, microabsorption, preferred orientation, overlapping and broad reflections, variation in standard data with composition, availability of pure standards, and detection of amorphous and trace phases. Our analyses of rocks use the matrix flushing method on < 5μm particle-size material mixed with a 1.0-μm corundum internal standard to minimize the first four effects. Integrated intensities are used, and we employ several peaks from each phase whenever possible. We overcame overlap problems through iterative calculations using integral, multiple peaks or with profile refinement. Use of observed and calculated diffraction patterns for every phase enables us to predict the effects of composition and preferred orientation on RIRs. This allows us to correct for these effects if reference intensity ratios (RIRs) are known as a function of composition and orientation. Detection of amorphous phases is a significant problem, and standard mixtures reveal that amounts of amorphous components below 30% are difficult to detect. The poor detection limit and the nature of the diffraction band from amorphous phases make internal standard or spiking methods the best approach for analyzing samples containing amorphous materials. The Rietveld method of quantitative analysis has the potential to minimize all of the above problems. This method requires a knowledge of the crystal structures of all component crystalline phases, but no calibration data are necessary, structural and cell parameters can be varied during the refinement process, so that compositional effects can be accommodated and precise cell parameters can be obtained for every phase. Since this method fits the entire diffraction pattern and explicitly uses all reflections from every phase, complex, overlapped patterns can be easily analysed. In addition, this method presents the opportunity to correct for preferred orientation and microabsorption during data analysis.

For many years the International Centre for Diffraction Data has sponsored round robins covering various aspects of X-ray powder Diffraction with the objective of illuminating and understanding current practices and problems associated with, the analysis of diffraction data. As computer analysis of diffraction data becomes ever more sophisticated, analytic capabilities are extended and the performance, not only of the instrumentation must be checked, but also that of the software which converts the measured data into useful results. In recent years, therefore, we have personally participated in a cell parameter round-robin, a d-spacing round-robin, a peak hunting round-robin, and, most recently, the present intensity round-robin and a line profile round-robin. Still others are in progress or being planned.

In earlier papers, the reference intensity method (RIM) of quantitative x-ray diffraction was described in terms of the theoretical basis (Davis, 1980), error propagation (Davis, 1981), filter sample preparation technology for eliminating preferred orientation (Davis and Johnson, 1982; Davis, 1986), and special applications to amorphous-bearing samples using mass absorption measurements (Davis and Johnson, 1987). This paper describes application of counting statistics to the determination of the lower limit of detection (LLD) of components quantitatively measured by the RIM procedure. With this discussion, virtually all phases of the RIM methodology will have been described.

The method for quantitative X-ray diffraction analysis of multiphase mixtures presented here is based on transmission measurements of thin samples. The integral of all reflections of interest are measured with a position sensitive detector at one time while the transmission factor of the sample is measured simultaneously with a scintillation counter. The method has the advantages that only a few (1-5) mg of substance are required, absorption effects due to sample matrix are measured directly and the method is automated. The measurements are made with the STOE/ Nicolet Automatic Focusing X-ray Diffraction system in conjunction with the STOE/Nicolet Curved Position Sensitive Detector.

Methods for, and results from, x-ray diffraction analysis of large numbers of fly ash samples obtained from U.S. power plants are described. Qualitative XRD indicates that low-calcium/Class F fly ash (usually derived from bituminous coal) consists typically of the crystalline phases quartz, mullite, hematite and magnetite in a matrix of aluminosilicate glass. Highcalcium fly ash (derived from low-rank coal) has a much more complex assemblage of crystalline phases that typically includes these four phases plus lime, periclase, anhydrite, alkali sulfates, tricalcium aluminate, dicalcium silicate, melilite, merwinlte and a sodalite-structure phase. Glass compositions among the particles are more heterogeneous and range from calcium aluminate to sodium calcium aluminosilicate, Every ash studied Is mixed with an internal Intensity standard (rutile) so that Intensity ratios can be used to make comparisons of the relative amounts of crystalline phases. An error analysis was performed to define the level of uncertainty in making these comparisons. These intensity ratios will be used for quantitative XRD phase analyses when reference intensity ratios for each fly ash phase become available.

The use of coal, as either a primary energy source or as a source of feedstock chemicals, has been complicated by the noxious and toxic chemical species formed in its gaseous effluents and also by the huge quantities of ash vhich result from its processing. Both the noxious gases and the ash have been the subjects of Federal legislations.

X-ray powder patterns (XRPP), composed of atom-pair and self x~ray scattering and the diffraction produced by crystalline phases, have long been used to investigate coals and particularly their combustion ashes (1-3). Over twenty different crystalline phases have recently been reported to exist in certain lignite fly ash (3). Analysis of the crystalline phases has typically been emphasized in previous papers involving coals and ashes, but the amorphous scattering has been given little treatment.

The recent discovery of superconducting oxide ceramics with critical temperatures (Tc) near 100°K has stimulated research at an unprecedented pace. Single phase YBa2 Cu30x (x = 6.9), the subject of most of the interest, is an oxygen deficient 1:1:3 stacked perovskite derivative, (The structure of this materials has been described by a number of authors, many of whom are referenced by Jorgensen et al.) At room temperture it has an orthorhombic structure with lattice parameters near: a = 3.82Å, b = 3.88Å, and c - 11.68 Å. At lower oxygen values (x≤6.5) the structure is tetragonal with lattice parameters near: a = 3.86 and c = 11.80. It has been suggested that tetragonal YBa2 Cu30x is not superconducting. YBa2 Cu30x, regardless of oxygen content, is referred to here as 123.