The Shape of Diffraction Peaks — X-ray Line Broadening
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During processing, the shape of a diffraction peak can change (as well as shift) and this is called “X-ray Line Broadening”. This broadening can be an important signature. For example, as shown in Fig. 8.1 (from ), for peened soft steels this can be even more important in controlling fatigue life than the induced stress. For a well-annealed sample, the peak shape depends on the size of the source, finite divergences of the slits at the x-ray tube and the receiving slits, the range of wavelengths in the beam, and the fact that in a diffractometer a flat specimen is only tangent to the focusing circle at one point.1 As a soft sample is deformed, there are local strains due to the strain fields from dislocations and dislocation arrays. The material is broken into regions with slight tilts with respect to one another due to these arrays, subgrain boundaries, etc. Constructive interference occurs only within each such region, and the peak (from such a region) is larger in angular extent the smaller is such a region. This is so because when the region is small there are not as many planes to cause destructive interference away from the exact Bragg angle. To see this more clearly we adopt a treatment by Cullity .
KeywordsResidual Stress Fourier Coefficient Reciprocal Space True Function Sine Term
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