The use of Fourier analysis in the interpretation of X-ray line broadening from cold-worked iron and molybdenum

Measurements of the line shapes in the :Debye--Scherrer spectra of iron and molybdenum, cold worked by filing, have been made using a Geiger-counter spectrometer. Fourier coefficients of the broadening functions have been calculated, using the coefficients for the annealed specimen as a measure of the instrumental broadening. The values of the r.m.s, strain deduced from the 110 and 220 reflexions do not coincide, but differ by 30--50%. An investigation into the coefficients of theoretical line shapes has been made, and a similar effect has been found for the ease of broadening due to a 'Cauchy' strain distribution. Equations which have previously been thought to make no a priori assumptions as to line shape are shown to hold onkv for very restricted eases not likely to occur in practice. The unavoidable numerical errors in calculating the coefficients from any profile resembling a 'Cauchy', even with better-than-average experimental accuracy, appear to make rigorous analysis impossible. A semi-empirical approach is suggested, which, at least for the iron and molybdenum results, allows an accuracy bracket to be placed on the interpretation. The reliability of some important previous results is discussed.