Precision of lattice strain and orientation measurements using high-energy monochromatic X-ray diffraction

A systematic framework for estimating the uncertainty associated with measurements of finite stretch and orientation of a crystalline lattice using monochromatic X-ray diffraction is presented. A hierarchical method is implemented, in which uncertainties in the locations of diffraction peaks are communicated to the lattice stretch and rotation parameters by using the classical method of weighted least squares. This enables the uncertainty of the lattice stretch and rotation parameters to be estimated from a single full rotation scan. This method is applied to diffraction data obtained from a ruby single crystal as an idealized case for validation, and an example application is demonstrated by analyzing a strained and plastically deformed polycrystalline titanium alloy, β21S. For the ruby single crystal, it was possible to attain average uncertainties for lattice orientation and strain that were found to be comparable to standard statistical analysis of repeated measurements. For the titanium alloy, a single grain was analyzed, and a precision of 0.03° for lattice orientation and 100–250 × 10⁻⁶ for lattice strain components was obtained. The basic framework of the uncertainty analysis is generally applicable, although specific results are unique to monochromatic X-ray diffraction experiments.