Modelling Dislocation-Induced Anisotropic Line Broadening in Rietveld Refinements Using a Voigt Function. II. Application to Neutron Powder Diffraction Data

Abstract

In paper I [Wu et al. (1998). J. Appl. Cryst. 31,[356][357][358][359][360][361][362] an approach was developed to the problem of modelling dislocation-induced X-ray or neutron-diffraction-line broadening. This paper applies those findings to the Rietveld refinement of the neutron powder diffraction profiles of deuterium-cycled LaNi5 and/%PdD0.66. These interstitially modified materials exhibit, respectively, strong and weak anisotropic strain broadening. The broadening in LaNi5 is consistent with a dislocation slip system a/3 (2110) {0]-10}, in agreement with transmission electron microscopy studies. In PdD0.66 the model predicts a regular distribution of screw dislocations, which remains to be confirmed by other techniques.

Anisotropic diffraction peak broadening and dislocation substructure in hydrogen-cycled LaNi5and substitutional derivatives

“…They are one order of magnitude higher than those usually observed in plastically deformed metals, such as zirconium, for which a value of 4 Â 10 10 cm À2 was determined from X-ray powder diffraction data (Klimanek & Kuz Ïel, 1989). Surprisingly, the value of 4.8 Â 10 12 cm À2 as determined for LaNi 5 by Wu et al (1998) from neutron powder diffraction data is still higher by an order of magnitude. Dislocation densities of this magnitude have not been observed in any of our samples and are in strong contrast with those observed in plastically deformed metals.…”

“…It can be shown that P 9 3M. We have determined the values of P independently for each pro®le from the ratio between the Lorentz ( L ) and Gauss ( G ) integral breadths of the diffraction pro®les according to the approximation proposed by Wu et al (1998):…”

“…Transmission electron microscopy (TEM) work by Kim et al (1995) on fully activated LaNi 5 has revealed the presence of a very dense dislocation structure, which was created during the ®rst hydrogenation. A breakthrough in the modelling of peak breadths was achieved by Wu et al (1998), who successfully applied the theory of Krivoglaz (1969) as speci®ed by Klimanek & Kuz Ïel (1988) for hexagonal systems. They succeeded in modelling the peak broadening in neutron powder diffraction patterns of cycled LaNi 5 by dislocations of the slip system 1/3h2 Å 110i{01 Å 10} and reported a dislocation density of 4.8 Â 10 12 cm À2 .…”

Nanocrystalline materials studied by powder diffraction line profile analysis

“…Anisotropic crystallite shape are a delicate phenomenon [26] which has been treated by special elegance in the case of ZnO nanoparticles [23]. Finally, anisotropic strain broadening is a general feature of powder patterns [43][44][45][46][47][48][49][50][51][52][53][54][55][56], which is generally related to dislocations and the elastic properties of crystals. In the present work a few typical examples are reviewed where the microstructure of nanocrystalline materials has been characterized by the method of XLPA.…”

Solving crystal structures of metal and chemical hydrides

“…The broadening can be qualitatively modeled by empirical models, such as the general model proposed by [Stephens (1999)]. Quantitative modeling allowing also the determination of dislocation type and density [Wu et al (1998[Wu et al ( ), Č erný et al (2000] was possible by applying the theory of Krivoglaz [Krivoglaz (1969)] modified for hexagonal symmetry in [Klimanek andKužel (1988, 1989)]. …”