Conal E. Murray, T. Graves-Abe, et al.
Applied Physics Letters
The determination of stress in polycrystalline aggregates by diffraction-based methods relies on the proper choice of grain interaction model that links the observed strain to the elastic stress state in the ensemble. It is shown that for single-phase, polycrystalline samples composed of crystals with cubic symmetry, x-ray elastic constants (XEC) calculated under the Kröner model are equal to those from a weighted combination of Reuss and Voigt XEC, where the weighting factor is only a function of the single crystal elastic tensor coefficients. This weighting factor, xKr, generally scales with elastic anisotropy factor, A, with a value close to the Neerfeld limit for elastically isotropic materials (A 1). Materials that possess large values of A, and correspondingly small xKr, exhibit a greater deviation between the Neerfeld and Kröner limit XEC. A dimensionless parameter, Q, based on a different combination of elastic coefficients than A, demonstrates a monotonic trend with respect to xKr and may serve as a better metric for describing the elastic response of a polycrystalline ensemble as interrogated by x-ray diffraction. For crystals possessing lower symmetry, a similar analysis reveals that Kröner XEC are not a unique combination of Voigt and Reuss limits. In the case of hexagonal crystal symmetry, x Kr for a particular material varies as a function of the orientation parameter of the crystal, indicating that the degree of elastic anisotropy of the constituent crystals may impact the determination of stress depending on the choice of x-ray reflection. © 2013 AIP Publishing LLC.
Conal E. Murray, T. Graves-Abe, et al.
Applied Physics Letters
Sean M. Polvino, Conal E. Murray, et al.
Applied Physics Letters
Conal E. Murray
Journal of Applied Physics
Conal E. Murray, S. Polvino, et al.
Thin Solid Films