# X-ray diffraction line profile analysis for defect study in Zr-2.5% Nb material

TL;DR: In this paper, the authors presented the X-ray diffraction peaks shape analysis and their broadening with different thermal treatments in Zr -2·5% Nb pressure tube material and the peak shape was analyzed using Fourier transformation and information about coherent domain size, micro-strain and dislocation density could be obtained from the Fourier coefficients of the peak.

Abstract: The microstructure characterization by X-ray line profile analysis is possible for determination of dislocation density, micro-strain within grains due to dislocation and average cohe rent domain size (sub- grain) within the grain. This study presents the X -ray diffraction peaks shape analysis and their broadening with different thermal treatments in Zr -2·5% Nb pressure tube material. The peak shape is analysed using Fourier transformation and information about coherent domain size, micro-strain and dislocation density could be obtained from the Fourier coefficients of the peak. Analysis of broadening of the peaks by integral breadth method also gives the coherent domain size, dislocation density and micro -strain present in the mate- rial. The results from the X-ray techniques are comparable to those obtained from direct observation of transmission electron microscopy. The measured yield strength increases with dislocation density. An empir i- cal relationship is obtained for the yield strength from the dislocation density of the material. The measured strength is in agreement with the one calculated from dislocation density.

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### "X-ray diffraction line profile anal..." refers methods in this paper

...…techniques of X-ray line profile analysis: (i) Fourier space technique under which Fourier analysis (Warren 1968) also forms a part, and (ii) real space techniques like (a) integral breadth (Wagner and Aqua 1964), (b) variance analysis (Wilson 1962) and (c) peakfitting methods (Keijser et al 1982)....

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...Alternatively, βC and βG of a peak are determined from the value of integral breadth and full width half maxima of the peak using well established relationships (Keijser et al 1982)....

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932 citations

### "X-ray diffraction line profile anal..." refers background in this paper

...The instrumental broadening (b) is a function of Bragg’s diffraction angle, θ, (Caglioti et al 1958)....

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625 citations

### "X-ray diffraction line profile anal..." refers methods in this paper

...Kα2 separation Using software with α1/α2 ratio as 0⋅5 Sample rotation No (Stationary) 3.1 Fourier analysis In the Fourier analysis the line breadth is corrected for instrumental broadening using Stoke’s (1948) correction....

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146 citations

### "X-ray diffraction line profile anal..." refers methods in this paper

...…techniques of X-ray line profile analysis: (i) Fourier space technique under which Fourier analysis (Warren 1968) also forms a part, and (ii) real space techniques like (a) integral breadth (Wagner and Aqua 1964), (b) variance analysis (Wilson 1962) and (c) peakfitting methods (Keijser et al 1982)....

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