Quantitative phase analysis by powder diffractometry requires accurate measurement of the integrated intensities of the diffracted, lines. When lines are isolated and on simple backgrounds, count integration techniques work very well. However, when one or more lines overlap the line of interest, or a complex background is present, profile fitting techniques are required in order to eliminate interferences.

Profile fitting involves choosing a mathematical model to represent the expected profile shapes. Experience has shown that the profile shapes obtained with a parafocusing powder diffractometer are not easily described and many models have been tried with varying degrees of success. Generally the more free parameters allowed In the model the ‘setter the fits, although, aesthetically one would like to keep the number of free parameters to a minimum.

X-ray powder diffraction (XRD) is widely used for qualitative analysis of the phases in multiphase mixtures. To extend the characterization to the level of quantitative analysis (QA) requires solution of many challenging problems such as elimination of preferred orientation (1,2,3); selection of an appropriate reference standard which closely matches the analyte phase in crystallite size, thermal history, stoichiometry etc. (4); effectively collecting the experimental intensities (5,6); and finally, performing the data reduction and analysis.

The desire to solve the last problem in a general way and to incorporate the “best” procedures developed in several laboratories into one package was one of the stimuli for developing the NBS*QUANT82 system of programs. This system is integrally coupled with the data collection system AUTO (6,7).

X-ray diffraction is ideal for quantitative crystalline phase determination in solid mixtures. Each phase of the mixture will produce its characteristic lines independent of other phases that may or may not be present when diffracting an X-ray beam and will be “proportional” to the amount of the phase present.

The CaNi5 system is unique among the AB5-H systems in that it exhibits three distinct hydrides (β, γ, δ) at pressures below 65 atm. (Sandrock et. al., 1982), The present diffraction study was designed to characterise these phases, only one of which has been previously studied. Nowotny (1942) gave lattice parameters for a number of AB5 (Haucke) phases including CaNi5. Takéuchi et al. (1966) gave parameters for CaNi5. Buschow (1974) reported on the entire Ca-Ni system. Oesterreicher et al. (1980) gave data on CaNi5 and CaNi5H5.5. Ensslen et al. (1981) indexed CaNi5H5.5 (γ-phase) as orthorhombic. Measurements made at NRC on one of the samples studied by Sandrock et. al (1982) and on three samples prepared at NRC are given in Table 1 together with the data from the literature. It is clear that there is a significant sample effect on the observed lattice parameters. It is well known that many AB5 compounds have a range of composition. To avoid variations due to sample effects it was decided to characterise the hydride phases on a single specimen.

A new method for the collection and analysis of high temperature Guinier x-ray data has been devised at The Dow Chemical Co. This technique can be used to monitor various types of structural transformation and thermal expansions up to 900°C. The thermal expansions of α-Al2O3 and two TiO2 structures, anatase and rutile, have been characterized for their use as high temperature internal standards.

The National Enforcement. Investigations Center of the EPA provides support services for the enforcement activities of the Agency. Recently, we have analyzed hazardous wastes as part of efforts to enforce the Resource Conservation and Recovery Act. Inorganic analysis often consists of elemental determinations. However, sometimes it is necessary to identify specific compounds. Some wastes are classified as hazardous by their origin, for instance, the wastes from the manufacture of several chromium pigments. On occasion, it is necessary to trace wastes to their source. In cleaning dumps and treating wastes, knowledge of the compounds present is useful.

Following the discovery of powder diffraction by Debye and Scherrer, a major improvement of the intensity of diffraction patterns was attained by introducing focusing cameras. The focusing principle is exploited in the Seemann-Bohlin camera and with improved general background in the Guinier focusing camera. Guinier used a bent crystal to focus Ka lines from the target radiation. Das Gupta, Schnopper and Metzger reported a modification of the Seemann-Bohlin camera by replacing the slit with a target positioned on the focusing circle. This was further improved by using a microfocus target, 30 x 100 micron, positioned accurately on the focusing circle, Fig. 1 (a). The arrangement was very successful for determining thermal expansion coefficients of elements and a few superconducting alloys at different temperature regions.

Phase identification by X-ray diffraction techniques in a complex mixture would be greatly simplified if the component phases could be physically separated. As opposed to current computer search-match algorithms for phase identification, which presuppose a single diffraction scan on a carefully prepared sample, we propose multi-scan data-taking on a not-so-carefully prepared sample so as to exploit certain aberrations in the diffracted intensities. The result can effectively be a physical separation by diffraction. Examples include exploitation of samples having a preferentially oriented component as well as samples with components having differing crystallite sizes. The techniques can involve diffractometer as well as film techniques.

In the preceding volume in this series, we described a stepping motor automation package for XRD data acquisition, based on the Apple microcomputer with an interface card that produces the stepping motor pulses and counts X-ray pulses from the normal X-ray detector and amplifier. We are presently using the system to automate a General Electric XRD-5 diffractometer mechanism, by replacing the original synchronous motor with the stepping motor, and installing 10:1 reduction gear instead of the chain drive to drive the double worm gears. This gives 2500 steps of the motor per degree two theta. Motor pulses are counted by a small machine language routine which also handles accelerating the mechanism when slewing over long angular ranges.

In the past, we were limited to manual methods for the identification process. Identification was done manually with a data base of reference spectra (in card and search manual format) supplied by the Joint Committee on Powder Diffraction Standards (JCPDS). Most single substances can be identified with relative ease using this approach. But when the number of components gets much beyond two, the measured pattern is a complex composite of sub-patterns which makes the identification a tedious and uncertain process taking 60 to 90 minutes per pattern in most simple cases.

The authors previously reported stress measurement in stainless steel by the use of monochromatic Cr-Kβ X-rays and a position sensitive proportional counter. Results indicated that a stress value can be obtained with high precision on account of the subtraction of background and the elimination of αFe(211) peak by Cr-Kα X-rays. The major disadvantage of this method, however, is that the intensity of Kβ X-rays monochromatized is essentially weak and it is complicated to eliminate Kα X-rays for practical use.

Among the limitations of the classical methods for measuring stresses by X-ray diffraction, the existence of stress gradients constitutes a particularly delicate problem. On the theoretical plane, this problem has been tackled by Dölle, Hauk and Cohen. These authors showed that whilst the gradients of the shear stresses σ13 and σ23+ are relatively easy to bring to the fore, as their presence is reflected in an opening out of the curves for 2θ ϕ ψ =f (sin2ψ), those of the direct stresses σ11, σ22 an σ33 are very difficult to detect. In the latter case it is demonstrated that even when the gradients attain very high values, the curves of 2θ ϕ ψ =f (sin2ψ) remain practically linear. This may invite one to apply the classical sin2ψ law, with the result that the stress values so determined do not correspond with the real mechanical state of the surface of the specimen.

X-ray stress analysis is a nondestructive method enabling one to measure residual and loading stresses in polycrystalline materials. Known as a difficult method for several decades, the introduction of microprocessors allowed the automation of the measuring procedure and the subsequent storage and computation of diffraction data. Also the availability of position sensitive counters increased the efficiency of the method. Nowadays a residual stress or loading stress determination can be a problem of a few minutes if the time required for installation and alignment of the equipment is neglected. As the penetration of the X-ray beam into the investigated surface of polycrystalline materials is low and only a few micrometers the obtained information is that of a surface stress state. A further specialty of the method is the selective nature of X-ray stress analysis: lattice strains are measured in certain crystallographic directions. Therefore the elastic anisotropy of the single crystal has to be taken into account. If second phases are present in the investigated sample, also the effect of heterogeneity contributes to the stress analysis. Therefore, the “X-ray elastic constants” had to be introduced.

As early as 1974 cracking was observed in the austenitic stainless steel piping systems of several Boiling Water Reactors [1,2]. Failure analysis indicated that the cracks developed through intergranular stress-corrosion cracking and an active interest in residual stress measurement methodologies developed. This paper describes the procedures and demonstration testing employed to provide absolute residual stress measurement, nondestructively, on the inside surface of pipe specimens. A Ruud-Barrett position sensitive detector (PSSD)* was used to build an EPRI pipe stress analyzer which was developed for these residual stress measurements [3,4].

Certain machining processes (e.g. turning, grinding, …) lead to a splitting up and an opening out of the curve of 2θ ϕ ψ = f (sin2ψ). In order to determine the complete stress tensor, it is necessary in this case to use the Dölle-Cohen method but this requires the knowledge of the diffraction angle 2θo for the unstressed material. Such a material, however, is extremely difficult to obtain in practice and the method usually employed uses annealed powder for this measurement. In our study, we show that it is nevertheless possible to determine the angle 2θo on a specimen for which the curve of 2θ ϕ ψ = f (sin2ψ) does not open out. Applying the Dölle-Cohen method to turning of a medium carbon steel, we have been able to bring to the fore: (i) the presence of an opening out of the curve 2θ ϕ ψ = f (sin2ψ), for measurements made in the direction of lay, which is attributed to a shear stress σ23, and (ii) shear stress σ12 which causes a rotation of the stress distribution diagram σϕ = f(ϕ) in the plane of the specimen.

X-ray topography is one of several methods used by the semiconductor industry to measure stress of thin films deposited on single crystal substrates. A procedure to determine stress values directly from the X-ray topographic image by measuring the separation of the Kα1-Kα2 X-ray peaks is reviewed. Although less sensitive than the single-crystal technique, it has been found applicable to monitor stress levels in films such as CVD silicon nitride on silicon wafers. This technique may also be used to quantify the plastic deformation of wafers that is induced by semiconductor processes.

The powder diffraction x-ray technique commonly used to measure strain in polycrystalline materials requires a knowledge of the elastic constants in order to convert the strain into a stress value. For many materials, these constants are not always known. Another technique to measure strain is the x-ray lattice curvature (substrate bending) method which requires no knowledge of the film elastic constants. The strain is measured in the substrate and requires only the elastic constants of the substrate to convert the measured strain into stress. Using a combination of the powder diffraction technique and a double crystal lattice curvature technique, the elastic constants of TaSi2 and WSi2 have been determined for various crystallographic directions.

A curved, one-dimensional position-sensitive detector has been designed and constructed for the measurement of the scattering patterns from non-crystalline materials. The chamber is a one-dimensional, pressurized, gas-filled detector with delay line readout for position encoding. It covers an angular range of 45° in 2θ, and its quantum efficiency is 80% and 50% for 17.5 and 60 KeV x-rays, respectively, when using a Xe-20%CO2 gas mixture at 7 atm.

A ϕ-ψ diffractometer has been designed and constructed to evaluate residual stresses in polycrystalline samples by x-ray diffraction. It permits rotations of the x-ray diffraction apparatus, consisting of an x-ray tube and a position-sensitive proportional counter, about two axes ϕ and ψ. The ϕ-rotation from 0° to 360° is carried out about the normal to the surface of the stationary sample, whereas the ψ-motion consists of a rotation from -45° to +45° about an axis lying in the sample surface and the diffraction plane, but perpendicular to the diffraction vector. This ϕ-ψ diffractometer permits the application of the ϕ- and ψ-differential and integral methods for the evaluation of the strain tensor and its gradient averaged over the depth of x-ray penetration into the sample. Assuming that isotropic elasticity theory is applicable, the stress tensor can then be evaluated from the measured strain tensor.

The technique analysing the cause and mechanism of fracture from the information obtained by X-ray irradiation on the fractured surface is called “X-ray fractography.” As a basic study of X-ray fractography the residual stress on the fatigue fractured surface and some parameters of the fracture mechanics were investigated.