An improved method for the determination of microstructural parameters by diffraction-profile Fourier analysis

Abstract

The analysis of the influence of the background and truncation errors on the Fourier transform of the diffraction profile is extended with respect to the work that has already been done by others and a critical evaluation of the established Fourier methods for the determination of the microstructural parametersaverage dimensions of crystallites and paracrystalline microdomains, lattice-distortion parameters and cumulants of the strain distribution -is presented. It is shown that, contrary to the case of the cosine transform and of its logarithm whose functional behaviour is drastically changed by the truncation error, the first derivative of that transform is modified by this error only by an oscillatory factor which multiplies the first term of its series expansion. The suggestion follows of using this derivative function in the least-squares or curve-fitting determination of the microstructural parameters. It seemed proper to check these theoretical results by comparing them with experimental data, determining by a simple curve-fitting procedure based on this derivative function the microstructural parameters of a high-density polyethylene fibre in directions perpendicular to the fibre axis. The parameters so obtained are in good agreement with the structural data found in the literature for the same material. It is concluded that the use of this derivative function makes possible the reliable determination of important features of the microstructure of materials by a single-line Fourier technique even in the presence of a large truncation error.

X-ray diffraction line broadening: modeling and applications to high-Tc superconductors

“…4.2). Zocchi [ 73 ] suggested that fitting the straight line through the first derivatives of the Fourier coefficients, instead of through the coefficients themselves, would solve the “hook”-effect problem.…”

The determination of crystal size and disorder from X-ray diffraction photographs of polymer fibres. 1. The accuracy of determination of Fourier coefficients of the intensity profile of a reflection

“…They almost certainly apply also to methods used when only a single order is visible. The separation of size and disorder from a single reflection (Mignot & Rondot, 1975;Zocchi, 1980;Nandi, Kuo, Schlosberg, Wissler, Cohen & Crist, 1984) depends entirely on the use of normalized coefficients of the orders which we have shown to be in serious error. Rational function extrapolation might still be valid, but the methods of testing this which we have described cannot be used when only one order of a reflection is available.…”

X-ray analysis of different starch granules

“…This method does not take into account the possible lattice distortions like paracrystalline disorder present in these starches. The inadequacies that exist in Scherrer's method have been pointed out by earlier investigators (Warren 1955(Warren , 1959Mignot and Rondot 1975;Zocchi 1980;Nandi et al 1984).…”