A method for using syncrotoron-radiation parallel-beam X-ray diffractometry for precise lattice parameters and strains of γ-γ′ type Nickel base superalloys at elevated temperature is described. The superalloys have γ′ precipitates which are an ordered L12 structure based on Ni3Al, in y-matrices having a disordered FCC structure. Lattice misfit between γ and γ′ phases was very small and peaks reflected from γ and γ′ phases made unresolved clusters of peaks.

Profile fitting with a pseudo-Voigt function is used to resolve overlapping peaks. Instrumental broadening of the peak profile was removed using a deconvolution method. The standard errors of the calculated peak angle were less than 0.002°. The elastic strain of the γ′ precipitates in the alloys were smaller than those of γ-matrices.

Advances over the last ten years in computer automation and control, compact and portable x-ray sources, and reliable and efficient detector systems have allowed X-Ray Determination of Residual Stress (XRDRS) measurements to become a viable method of evaluating the state of stress in metals, alloys, and ceramics. However, problems associated with incorrect XRDRS equipment operation and poor experimental technique are prevelant in industry, necessitating better operator training and education. Therefore, an interactive computer workstation, called RS/hyper, was developed to lead the operator towards correct operating procedures and reliable experimental technique.

Proper machine setup, machine maintenance, radiation safety, experimental technique, theoretical understanding, and limited data evaluation are presented in RS/hyper. Graphical aids are used extensively to avoid confusion and misinterpretation of theoretical concepts and equipment instructions. RS/hyper is interactive, allowing the user to learn about topics at a comfortable level of explanation. Compared to written texts and references, RS/hyper has been shown to reduce training and problem solving time by a factor of 16.

RS/hyper will train novice users of XRDRS equipment so that the data acquired from such machines will be reliable in an industrial environment. Also, since the software educates the user, data will be more accurately represented before interpretation. The experienced user should find RS/hyper useful as a reference to XRDRS and related information.

The authors have developed two independent software packages that store x-ray peak locations, integrated intensities and full-width half-maximum intensity data as a function of diffractometer tilt and orientation angle; this information is used to compute residual stress tensor values. Each program retrieves the fitted x-ray peak locations from a dBASE-compatible data set that is independent of both x-ray diffractometer and acquisition software. Machine-specific routines have been coded to transfer peak data and general diffraction setup information from several different x-ray acquisition platforms into this common format. The two database management programs provide stand-alone storage, retrieval, analysis and graphic output of data, and thus have become practical laboratory vehicles toward establishing a standard database format for storing x-ray strain measurements and the residual stress values calculated therefrom.

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. X-ray residual stress has been confirmed to be a particularly useful parameter when studying the fracture surfaces of high strength steels. The method has been applied to the fracture surface of fracture toughness and fatigue specimens.

To evaluate the plastic zones of dynamic fracture, instrumented Charpy impact tests of high carbon bearing steels are conducted. The amount of plastic zone size left on the fracture surface is evaluated from the X-ray diffraction profiles. An analysis is presented of the relationship between the X-ray diffraction profiles and fracture mechanics parameters. The results are discussed in correlations between dynamic stress intensity factor and absorbed energy values. A good correlation exists between the plastic zone size and the dynamic stress intensity factor.

The fraction of retained austenite is determined from X-ray diffraction profiles at surfaces of fractures and also beneath the surfaces of fractures.

It shows the work hardening is introduced by the strain energy in the plastic zones. The values of the proportionality constant, α, determined for various kinds of dynamic fracture are related to half-value breadth by the function

where B0 and BF are average of half-value breadth which are given by core of material and plastic zone of dynamic fracture.

X-ray fractography was applied to the fatigue fracture surface of ZAS (Zinc Alloy for Stamping) alloy, which has composite microstructures: Zn-phase, Al-phase and Zn-Cu phase. The fatigue test was conducted by using compact tension specimens. Residual stresses were measured on and beneath fatigue fracture surfaces. The plastic zone size was determined from residual stress distributions beneath the fatigue fracture surfaces. The results are discussed in connection with fracture mechanics and fracture processes.

Mechanical and X-ray elastic constants of four types of ZrO2 were measured for (133) planes with Cr-Kα radiation. The main differences among the specimens were the chemical components, the sintering method and the heat-treatment. It was found that the elastic constants were affected by the heat-treatment, but little by the other factors. The influence of the method of the peak determination on the result was also examined. The residual stresses at the knife edge were determined.

We have developed a technique for determining the atomic elastic constants from measurements of the Debye-Waller factors. The Debye-Waller factors are obtained by Rietveld refinement of time-of-flight neutron diffraction data and interpreted in terms of an atomic Debye-Waller temperature. The method is applicable to powders and to materials that must be encapsulated for safety or environmental reasons. We will illustrate our technique with applications to actinide metals, to metallic hydrides and to high-temperature superconductors.

One of the most difficult tasks in applied and residual stress measurement of polycrystalline materials using x-ray diffraction is dealing with preferred orientation and large grain size.

A common solution to large grain size problems has been to choose a larger aperture, but in certain cases this is undesirable and/or impossible. When preferred orientation has been identified as the problem, the common approach has been to choose another diffraction plane or oscillate the x-ray diffraction head during data collection. Remedies such as these can distort the peak breadth and are often not sufficient to totally negate the grain size and preferred orientation effects.

A technique described as the “step scan with virtual window” has been developed jointly at MTL (formerly Canmet) and Proto Mfg. Ltd. to deal specifically with the aforementioned effects of grain size and preferred orientation.

This paper highlights some of the problems that arise in stress analysis of materials exhibiting preferred orientation and large grain size. Subsequently a comparison of the results obtained using standard diffraction technique, oscillation and the “step scan with virtual window” is made.

X-ray diffraction line-profile analysis on tetragonal forms of SnO2 (cassiterite), MnO2 (pyrolusite), and previously studied TiO2 (rutile), which were subjected to high pressure shock loading, show that residual lattice strain and coherent “crystal” size are a function of shock parameters. An interesting observation on a sample of MnO2 concerns the recovery of cubic Mn2O3 (bixbyite) in the material subjected to 22 GPa, indicating a shock-induced chemical synthesis.

In the case of asymmetric X-Ray powder diffraction, usually used for stress analysis, the peak broadening is a function of the following instrumental parameters: divergence angle of incident and diffracted X-Ray beams (equatorial divergence), divergence angle of Soller slits (axial divergence), tilt angle ψ, and the intrinsic parameters of the sample (Bragg angle, size and mosaicity of the microcrystals, crystallographic imperfections due to atom impurities). This effect of peak broadening is discussed quantitatively, independent of the form of the peak, by using an approximation of a constant distribution of the intensities of diffracted X-Ray beams. The broadening effect due only to the ψ tilt of the sample surface is studied in this work. The results are compared with experimental data obtained on ceramic composite material: α-Al2O3/SiC(whisker).

In this paper, the advantages and disadvantages of using the asymmetric 2θ scanning technique with a fixed incident angle α are described. Vertical-scan powder diffractometers with long horizontal parallel slits with an aperture of 0.05° and parallel-beam synchrotron radiation with λ = 1.54 Å and α = 10°, 2°, and 1° were used to collect α-Al2O3, silver behenate CH3(CH2)20COOAg, and Si powder diffraction patterns. The synchrotron radiation data were analyzed by profile fitting, and the results were compared with those obtained by the conventional θ-2θ scanning technique. As expected, significantly higher intensities were obtained from the asymmetric diffraction data with α = 10°. At smaller α = 2° and 1°, however, the intensities were reduced because of a smaller effective beam height. The peak positions remained practically unchanged for the data obtained with α = 10°, but displaced toward higher 2θ angles for α = 2° or lower, and, consequently a refractive-index correction was needed. Profile shape was slightly broadened and became more Lorentzian in asymmetric diffraction with highly oblique incidence of the beam. The change in shape was, however, negligibly small. The results showed that intensive and reliable powder diffraction data can be obtained from asymmetric diffraction by fixing the incident beam at a sufficiently large angle to fully illuminate the available sample surface.

Position sensitive detectors provide efficient X-ray detection over large solid angles; this capability has revolutionized X-ray diffractometry by reducing data collection time. This paper describes testing of a new single-axis position sensitive detector designed to locate 0.6-2 Angstrom X-rays. Dead time, quantum efficiency, energy resolution, and spatial resolution were measured. Standard powder diffraction patterns were observed with the detector, and data sets are presented. The impact of detector performance parameters on diffraction experiments is discussed.

Line-profile analysis is important for material evaluation as well as x-ray stress analysis. In the general case, the half-value breadth of the Kα doublet is used as the line-profile parameter, but it is preferable to use the half-value breadth of the Kα1 diffraction profile because of high resolution.

The Ladell x-ray diffractometer (LD) is designed to study “practical” polycrystalline materials. These are materials which exhibit some combination of texture, strain, and large grain size, or are inhomogeneous or anisotropic in other ways. LD features which make this possible are: the ability to study crystal planes inclined to the sample surface; a versatile reflection geometry; high 2θ resolution via a focusing geometry; a large irradiated sample area (up to 1.5 cm2) for improved intensity and sampling statistics; the ability to examine different sample areas to test for homogeneity; and the use of one sample with no instrument reconfiguration. Scans and/or applications are described that measure texture, strain, twinning, improve quantitative phase analysis, and eliminate substrate scattering.

The LD makes use of five independent computer controlled motions. These enable one to study a large fraction of that part of reciprocal space which is accessible by reflection. Instrument geometry and scans are described in terms of α, θ and reciprocal space diagrams. The effect of specimen displacement on peak position is described as are the effects of a number of geometrical factors on integrated intensity.

Conventional pole figure instruments consist of a scintillation detector mounted on a 4-circle goniometer operating under computer control. A few instruments make use of a linear PSD detector, which allows collecting data for multiple pole figures sinmltaneously. A PSD does not reduce the required data collection time for the primary pole figure; however, it does save time by eliminating the need to recollect multiple pole figure data. By using a 2D “area” detector, one can simultaneously collect multiple pole figures and reduce the data collection time for the primary pole figure, such an area detector pole figure processing package, GADDS v2, was developed at Siemens and will be discussed.

Lately available X-ray optics and 4-axis sample cradles increased the versatility of the Siemens D5000 diffractometer to high resolution applications. The possibilities of the D5000 HR hardware setup are illustrated by presenting diffraction measurements on systems relevant to semiconductor and thin film technology. Well known theoretical approaches are used for the software supported interpretation of the data.

We have developed a new type of powder diffractometer. The diffractometer has the potential of both high count rates and very high resolution when used at a synchrotron source. The laboratory based instrument can achieve an order of magnitude improvement in count rate over existing methods with proper optics. The method uses a focusing diffracted beam monochromator in combination with a multichannel detector. The incident x-rays fall on a flat plate or capillary sample and are intercepted by a bent focusing monochromator which has the focus of the bend at the sample surface. The powder diffraction lines emerging from the bent crystal monochromator are detected by a linear or 2-dimensional detector. This allows us to eliminate the background from fluorescence or other scattering and to take data over a range of 3° to 4° instead of one angle at a time thereby providing a large improvement over conventional diffractometers.

A single function for the elimination of errors in precision lattice parameter determination has not been developed for the Bragg-Brentano x-ray diffractometer method, because of the different angular dependencies of the systematic errors. A review of the error functions shows that all but one can be calculated from the instrumental settings and known properties of a sample under investigation. The residual sample displacement error can be then be eliminated by using extrapolation plots or computer methods to correct the data to cosθcotθ plots. The slopes of cosθcotθ plots can also be used to align high temperature furnaces and low temperature cryostats mounted on x-ray diffractometers.

Using a high purity germanium solid state detector with sufficiently high energy resolution to discriminate between copper Kα and Kβ radiation, the superlattice reflections of the ordered Cu-Zn β′ brass structure have be detected by the anomalous dispersion effect. By coupling the high purity germanium solid state detector to a multichannel analyser, the superlattice reflections of the β′ brass structure were also detected by energy dispersive x-ray diffraction. Other applications for this combination of high resolution detector, electronic energy discriminator and multichannel analyser are indicated.