Quantifying the uncertainty of synchrotron-based lattice strain measurements

Abstract

Crystallographic lattice strains – measured using diffraction techniques – are the same magnitude as typical macroscopic elastic strains. From a research perspective, the main interest is in measuring changes in lattice strains induced during in-situ loading: either from one macroscopic stress level to another or from one cycle to the next. The hope is to link these measurements to deformation-induced changes in the internal structure of crystals, possibly related to inelastic deformation and damage. These measurements are relatively new – little experimental intuition exists and it is difficult to discern whether observed differences are due to actual micromechanical evolution or to random experimental fluctuations. If the measurements are linked to material evolution on the size scale of the individual crystal, they have the potential to change the ideas about grain scale deformation partitioning processes and can be used to validate crystal-based simulation frameworks. Therefore, understanding the uncertainty associated with the lattice strain experiments is a crucial step in their continued development. If the measured lattice strains are of the same order as the random fluctuations that are part of the measurement process, documenting the strains can create more confusion than understanding. Often lattice strain error is quoted as ±1 × 10−4. This simple value fails to account for the range of factors that contribute to the experimental uncertainty – which, if not properly accounted for, may lead to a false confidence in the measurements. The focus of this paper is the development of a lattice strain uncertainty expression that delineates the contributing factors into terms that vary independently: (i) the contribution from the instrument and (ii) the contribution from the material under investigation. These aspects of uncertainty are described, and it is then possible to employ a calibrant powder method (diffraction from an unstrained material with high-precision lattice constants) to quantify the instrument portion of the lattice strain uncertainty. In these experiments, the instrument contribution to the uncertainty has been found to be a function of the Bragg angle and the intensity of the diffracted peaks. To develop a model for the instrument portion of the lattice strain uncertainty two datasets obtained using a MAR345 online image plate at the Cornell High Energy Synchrotron Source and a GE 41RT amorphous silicon detector at the Advanced Photon Source have been examined.