Use of Rietveld refinement to fit a hexagonal crystal structure in the presence of elastic and plastic anisotropy

Abstract

When multiple elastic diffraction peaks are obtained from an x-ray or neutron source, data analysis is commonly performed using a Rietveld refinement applied to the entire pattern, rather than simply performing single peak fits. In the simplest case the crystal structure is assumed to be ideal despite the presence of stresses which, coupled with the elastic and plastic anisotropy of individual grains, can result in a nonisotropic response of the polycrystal. A first step to account for this anisotropy in the refinement is to include an anisotropic strain parameter. In an earlier work [J. Appl. Phys. 82, 1554 (1997)] we included elastic anisotropy into a Rietveld refinement and discussed its validity in the elastic and plastic regimes for a cubic crystal structure. Here we extend the discussion to include anisotropy in hexagonal crystal structures. The agreement between single peak fits and the Rietveld refinement modeled single peak positions is considered for hexagonal close packed beryllium in the presence of an applied compressive load, in both the elastic and plastic regime (to $\text{∼1\%}$ plastic strain). Agreement is found to be good in the elastic and early plastic regime, where only basal slip is assumed to be active. At higher loads, where prism slip and/or basal fracture are also assumed to be active, agreement is poorer for some diffraction planes. The implications for residual stress measurements are considered.