The Effect of Cold-Work Distortion on X-Ray Patterns

TLDR

Modern experimental techniques enable accurate measurement of peak shapes, allowing interpretation based on precise reflection profiles. The study aims to derive a strain distribution function from Fourier transforms of An coefficients by measuring multiple diffraction orders. The method uses a cosine Fourier series to model peak shapes, plots An coefficients versus order to separate distortion from size broadening, and computes rms strain values over length scales na³ from these coefficients. RMS strain values decrease with increasing length na³, indicating non‑uniform strains in cold‑worked metal.

Abstract

With modern experimental technique, it is possible to measure a peak shape with sufficient accuracy to justify an interpretation based on the precise shape of the reflection. The corrected shape is represented by a cosine Fourier series and a set of An coefficients determined. A plot of the An coefficients vs. n will distinguish between distortion and particle size broadening. From the An coefficients, root mean square values of strain averaged over lengths na3 are obtained. The decrease in these values for increasing length na3 is a direct indication of the non-uniform nature of the strains in cold-worked metal. By measuring several orders of a given plane, it is theoretically possible to obtain a distribution function of the strains directly from a Fourier transform of the An coefficients.