Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Crystallite Size and Residual Strain/Stress Modeling in Rietveld Refinement

Published

Author(s)

Davor Balzar, N Popa

Abstract

We consider thft problem of microstructure modeling in Rietveld refinement, in particular of crystallite size and residual strain/stress andpropose the improvements to existing models. For the crystallite-size modeling, we consider the size-broadened profile given by thelognormal and gamma size distributions of spherical crystallites. An analytical approximation for the size-broadened profile is derived thatcan be analytically convolved with the strain-broadened and instrumental-broadened profiles. The method is tested on two CeO2 powders;one shows super-Lorentzian profiles that we successfully model under the assumption of a broad lognormal size distribution. We showthat the Voigt function, as a common model for a size-broadened profile, fails for both very narrow and broad size distributions. We arguethat the size-broadened line profile is not very sensitive to variations in size distribution and that an apparent domain size or even column-length distribution function can correspond to significantly different size distributions. In regard to the residual strain/stress modeling, wepropose a novel approach to model diffraction line shifts caused by elastic residual or applied stresses in textured polycrystals. The modelyields the complete strain and stress tensors as a function of crystallite orientations, as well as the average values of macroscopic strain andstress tensors. It is particularly suitable for introduction in Rietveld-refinement programs. The requirements on refillable parameters for allcrystal Lane classes are given. The effects of sample symmetry are also included and conditions for strain invariance to both symmetriesare discussed.
Proceedings Title
Analysis of Microstructure and residual Stress by Diffraction Methods, International Conference | 3rd | Diffraction Analysis of the Microstructure of Materials | Springer
Volume
68
Conference Dates
December 1, 2001
Conference Location
Trento, IT
Conference Title
Springer Series in Materials Science

Keywords

crystallite size, residual strain, Rietveld refinement

Citation

Balzar, D. and Popa, N. (2004), Crystallite Size and Residual Strain/Stress Modeling in Rietveld Refinement, Analysis of Microstructure and residual Stress by Diffraction Methods, International Conference | 3rd | Diffraction Analysis of the Microstructure of Materials | Springer, Trento, IT (Accessed May 22, 2024)

Issues

If you have any questions about this publication or are having problems accessing it, please contact reflib@nist.gov.

Created July 1, 2004, Updated February 17, 2017