MODELLING DISLOCATION-INDUCED LINE BROADENING IN RIETVELD REFINEMENTS USING A VOIGT FUNCTION. E.H. Kisi2, E. Wu1, and E.MacA. Gray1. 1 School of Science, Griffith University, QLD 4111, Australia; 2 Dept. Mechanical Eng., University of Newcastle, NSW 2308, Australia
The theory of dislocation-induced X-ray or neutron diffraction peak broadening developed by Krivoglaz et al. [1] and Wilkens [2] has been adapted for Rietveld refinement of powder profiles. Information on both the slip system and the dislocation density in the crystallites is evaluated from a the shape of the profile via a Voigt function fit.
The integral breadth of the dislocation-broadened peaks is related to the dislocation structure of the crystal by ß = [[rho]][[chi]][[florin]](M)tan2[[theta]] [2], where [[rho]] is the dislocation density, [[chi]] is the orientation factor [3], [[florin]](M) is a dimensionless function of M, M = r [[rho]]1/2 is a dislocation interaction parameter [2], where r denotes the outer cutoff radius of the dislocation strain field.
We incorporated this theory into Rietveld refinement by using a Voigt function, with integral breadth ßV = ßG/[[Omega]](iy), to fit the theoretical profile of a dislocation-broadened peak, with various values of M [2]. Here [[Omega]] is the complex error function, y = ßL/[[pi]]1/2ßG is the peak shape parameter, and ßL and ßG are the integral breadths of the Lorentzian and Gaussian components. This yielded a numerical relationship between the parameters y and M, which were then incorporated into the Lorentzian and Gaussian half-widths. Hence, for a given form of [[chi]], both M and [[rho]] can be determined by a refinement. We will discuss the application of this treatment to structure refinements and dislocation analyses of neutron diffraction patterns of LaNi5 and Pd deuterides.
[1] M.A. Krivoglaz, O.V. Martynenko & K.P. Ryaboshapka, Fiz. Metal. Metallov., 55 1983 5-17.
[2] M. Wilkens, phys. stat. sol. (a), 2 1970 359-370.
[3] P. Klimanek & R.Jr Kuzel, J. Appl. Cryst., 21 1988 59-66.