Elastic-strain tensor by Rietveld refinement of diffraction measurements

Abstract

A procedure to obtain all components of the elastic-strain tensor by simultaneous Rietveld refinement of diffraction patterns collected at different specimen orientations is described. The refined lattice parameters yield the hydrostatic strain component. If the lattice constants of the unstrained reference specimen are not known, the deviatoric strain tensor can still be determined. An anisotropic strain component may be refined for cubic and hexagonal crystal structures along with the isotropic. The method is applied to Al/SiC ͑short whisker͒ composites and systematic errors are assessed.

The determination of a stress-free lattice parameter within a stressed material using elastic anisotropy

“…Analysis of data using this approach within a Rietveld re®nement has shown it to be an accurate and extremely useful description (Balzar et al, 1998;Daymond et al, 1997), allowing a qualitative description of elastic and plastic deformation when used to allow the separation of strains into components, such that…”

Elastic strain and stress determination by Rietveld refinement: generalized treatment for textured polycrystals for all Laue classes

“…An alternative approach to a traditional sin 2 É method of strain determination has been described by Ferrari & Lutterotti (1994) and Balzar et al (1998). It includes the re®nement of strain-and stress-related parameters in a Rietveld (1969) re®nement program.…”

Strain and stress tensors of rolled uranium plate by Rietveld refinement of TOF neutron-diffraction data

“…A common procedure for the determination of residual strains is based on the directional measurements of the interplanar d spacings, the so-called sin 2 method [1]. An alternative approach was proposed [3,4] that includes the refinement of parameters related to strain and stress in Rietveld refinement [5]. In this way, the complete strain and stress tensors can be obtained along with all other structural and microstructural information.…”

“…This approach is particularly helpful in cases of multiple phases and/or low crystalline symmetry samples with overlapping reflections, as strain and stress determination does not rely only on very few Bragg reflections but the approach takes advantage of all available reflections. This procedure was successfully applied to the Al/SiC (short whisker) composites [4] using GSAS [6], which contains a model for anisotropic strain correction for cubic and hexagonal symmetry. A few published approaches allow for accurate modeling of diffraction-line shifts in Rietveld refinement for all Laue symmetries without making a Voigt or Reuss approximation [7][8][9].…”