Analysis of strain error sources in micro-beam Laue diffraction

Micro-beam Laue diffraction is an experimental method that allows the measurement of local lattice orientation and elastic strain within individual grains of engineering alloys, ceramics, and other polycrystalline materials. Unlike other analytical techniques, e.g. based on electron microscopy, it is not limited to surface characterisation or thin sections, but rather allows non-destructive measurements in the material bulk. This is of particular importance for in situ loading experiments where the mechanical response of a material volume (rather than just surface) is studied and it is vital that no perturbation/disturbance is introduced by the measurement technique. Whilst the technique allows lattice orientation to be determined to a high level of precision, accurate measurement of elastic strains and estimating the errors involved is a significant challenge. We propose a simulation-based approach to assess the elastic strain errors that arise from geometrical perturbations of the experimental setup. Using an empirical combination rule, the contributions of different geometrical uncertainties to the overall experimental strain error are estimated. This approach was applied to the micro-beam Laue diffraction setup at beamline BM32 at the European Synchrotron Radiation Facility (ESRF). Using a highly perfect germanium single crystal, the mechanical stability of the instrument was determined and hence the expected strain errors predicted. Comparison with the actual strain errors found in a silicon four-point beam bending test showed good agreement. The simulation-based error analysis approach makes it possible to understand the origins of the experimental strain errors and thus allows a directed improvement of the experimental geometry to maximise the benefit in terms of strain accuracy.