T. H. de Keijser

Use of the Voigt function in a single‐line method for the analysis of X‐ray diffraction line broadening

The use of the Voigt function for the analysis of the integral breadths of broadened X-ray diffraction line profiles forms the basis of a rapid and powerful single-line method of crystallite-size and strain determination which is easy to apply. To avoid graphical methods or interpolation from tables, empirical formulae of high accuracy are used and an estimation of errors is presented, including the influence of line-profile asymmetry. The method is applied to four practical cases of size-strain broadening: (i) cold-worked nickel, (ii) a nitrided steel, (iii) an electrodeposited nickel layer and (iv) a liquid-quenched AlSi alloy.

Applicabilities of the Warren-Averbach Analysis and an Alternative Analysis for Separation of Size and Strain Broadening

The validities of the Warren–Averbach analysis and of an alternative analysis for separation of size and strain contributions to diffraction line broadening are investigated. The analyses are applied to simulated and experimental line profiles. The Fourier coefficients of the simulated line profiles are derived from expressions for the distortion field around specific lattice defects: misfitting inclusions and small-angle grain boundaries. Applicability tests are also performed on experimental powder diffraction line profiles taken from plastically deformed specimens: thin aluminium layers and ball-milled molybdenum powders. It is concluded that for both methods finite but different classes of specimen exist for which they give meaningful results. In practice, each time an analysis is performed the results must be tested against common (physical) sense and all information available on the specimens.

Diffraction-Line Broadening due to Strain Fields in Materials; Fundamental Aspects and Methods of Analysis~"

Broadening of (X-ray) diffraction lines is often due to the distortion fields associated with lattice defects as dislocations. A generally applicable flexible model for distributions of lattice defects and their distortion fields is presented. The model allows a straightforward calculation of diffraction-line profiles. Parameters of the model are the average distance between the defects, the extent of the distortion fields and the mean-squared strain. The order dependence of the shape and width of line profiles is studied as a function of these model parameters. The adequacy for practical application of two methods frequently used to analyse X-ray diffraction-line broadening (the Warren–Averbach analysis and the Williamson–Hall analysis) is investigated by applying them to calculating line profiles. The `size and `strain parameters deduced by the methods mentioned are discussed with reference to the strain-field model parameters. It is concluded that only in limiting cases can the results be related directly to the microstructure. Experimental line profiles taken from a ball-milled tungsten powder are used to show that the line profiles calculated on the basis of the strain-field model pertain to realistic situations. It is shown that, in principle, an interpretation of measured line broadening is possible directly in terms of strain-field parameters.

New methods for diffraction stress measurement: a critical evaluation of new and existing methods

New methods of diffraction stress analysis of polycrystalline materials, consisting of cubic elastically anisotropic crystallites, are proposed and compared with existing methods. Whereas for the existing methods knowledge of the diffraction elastic constants is presupposed, three new methods are presented that require only knowledge of the (macroscopic) mechanical elastic constants. The stress values obtained with these new methods on the basis of the mechanical elastic constants are more reliable than those obtained with the methods on the basis of the diffraction elastic constants. New and existing methods are illustrated by means of measurements of X-ray diffraction from a magnetron-sputtered TiN layer.

Chemical constitution and microstructure of TiCx coatings chemically vapour deposited on Fe-C substrates; effects of iron and chromium

TiCx coatings were chemically vapour deposited in an industrial reactor on Fe-C substrates with carbon contents between 0.06 and 1.20 wt % C. Electron probe microanalyses showed that significant amounts of chromium and iron were present in the coatings and that chromium was also present in the substrate region adjacent to the coatings. By comparing calculated and measured lattice parameters (corrected for the internal stresses present) it became evident that the chromium was in solid solution in TiCx, whereas the iron was not. This was confirmed by micro Auger electron spectroscopy and X-ray diffraction phase analyses. The carbon to metal ratio,x, of the TiCx coatings decreased with increasing distance to the coating/substrate interface. The effect of iron on the X-ray diffraction line broadening and hardness of the coatings was large (in contrast with the effect of chromium) and increased with increasing distance to the coating/substrate interface because of a decreasing iron particle size. The TiCx crystallite size was small and constant throughout the thickness of the coatings. The chromium present in the substrate region adjacent to the TiCx coatings influenced the microstructure of the substrate by formation of iron, chromium-carbides and reduced the growth rate of the coatings.

The X-ray diffraction line broadening due to the diffractometer condition as a function of 2θ

The line profile due to diffractometer instrumental conditions was obtained from the measured line profile of a standard specimen by eliminating the spectral broadening, applying a model for the wavelength distribution. Under common experimental conditions, it was found that for 2 theta >50 degrees the spectral broadening is dominant in the line profile, and that for the larger 2 theta values for small values of the harmonic number the Fourier coefficients corresponding to the broadening caused by the instrumental conditions may be assumed to be independent of 2 theta .

Development of modern analysis techniques for characterization and testing of coatings

Abstract This paper presents some developments in methods and techniques for the analysis of deposited materials. These concern X-ray diffraction, electron probe microanalysis, X-ray photo-electron spectroscopy and soft X-ray emission spectroscopy.

A tool for X-ray diffraction analysis of thin layers on substrates: Substrate peak removal method

A method is proposed that removes the substrate peaks from a diffraction pattern recorded from a substrate covered with a thin layer, using a separate measurement of the uncovered substrate. The obtained diffractogram without substrate peaks can then be used for the characterization of the microstructure of the thin layer. As an example, the method is shown to yield good results for a TiN layer deposited on a tool-steel substrate.

Occurrence of incoherent α"-Fe16N2 at room temperature in iron-nitrogen martensite observed by neutron and X-ray diffraction

Aging behaviour of iron-nitrogen martensite (about 5 at.% N) at room temperature is investigated by neutron and X-ray diffraction experiments. An attempt is made to reveal the configuration of the nitrogen atoms during the aging processes especially by means of neutron diffraction, since the scattering lengths of iron and nitrogen atoms are almost the same. Two successive processes are distinguished: a redistribution of nitrogen atoms in the iron matrix and the formation of incoherent Fe16N2. During about the first 40 h of aging a decrease in the integrated intensity (10-20%) of the neutron and X-ray (002) martensite reflection is observed. This reduction is ascribed to the change in mean square displacement of iron atoms close to occupied interstices within nitrogen-enriched regions. After only about 1 d of aging, incoherent Fe16N2 has already formed. The changes in the integrated intensities of the precipitate and martensite reflections indicate that, during the precipitation process, Fe16N2 and ferrite are formed locally while the nitrogen content of the remaining martensite is unchanged.