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Polycrystals illuminated by high-energy X-rays or neutrons produce diffraction patterns in which the measured diffraction peaks encode the individual single crystal strain states. While state of the art X-ray and neutron diffraction approaches can be used to routinely recover per grain mean strain tensors, less work has been produced on the recovery of higher order statistics of the strain distributions across the individual grains. In the setting of small deformations, we consider the problem of estimating the crystal elastic strain tensor probability distribution from diffraction data. For the special case of multivariate Gaussian strain tensor probability distributions, we show that while the mean of the distribution is well defined from measurements, the covariance of strain has a null-space. We show that there exist exactly 6 orthogonal perturbations to this covariance matrix under which the measured strain signal is invariant. In particular, we provide analytical parametrisations of these perturbations together with the set of possible maximum-likelihood estimates for a multivariate Gaussian fit to data. The parametric description of the null-space provides insights into the strain PDF modes that cannot be accurately estimated from the diffraction data. Understanding these modes prevents erroneous conclusions from being drawn based on the data. Beyond Gaussian strain tensor probability densities, we derive an iterative radial basis regression scheme in which the strain tensor probability density is estimated by a sparse finite basis expansion. This is made possible by showing that the operator mapping the strain tensor probability density onto the measured histograms of directional strain is linear, without approximation. The utility of the proposed algorithm is demonstrated by numerical simulations in the setting of single crystal monochromatic X-ray scattering. The proposed regression methods were found to robustly reject outliers and accurately predict the strain tensor probability distributions in the presence of Gaussian measurement noise. [Display omitted] • Per-grain strain probability densities are extracted from X-ray diffraction data. • The presented method estimates the strain PDF from histograms of directional strain. • Gaussian strain PDFs have a closed form solutions and a known null-space. [ABSTRACT FROM AUTHOR]

A variety of features broadly classed as deformation microstructure elements are created during the plastic deformation of polycrystalline metals. While virtually all elements of deformation microstructure are composed of dislocations, describing the creation and evolution of larger-scale elements in terms of interactions between individual dislocations is a goal that has not yet been achieved. A hierarchical approach is thus favored in which structure creation and evolution are described at a range of length scales, from the nanometer to millimeter scale. [Copyright &y& Elsevier]

First results are presented on the simultaneous observation of the elastic strain tensor as a function of load of 10 individual grains, deeply embedded in the bulk of a polycrystalline Al tensile sample. The experimental technique is based on the use of focused high energy synchrotron radiation in transmission geometry. After each load step diffraction patterns are collected with a large-area X-ray detector system for a series of different angular and lateral sample positions. An automated indexing routine was used to assign sets of diffraction spots to individual grains. The strain tensor components as well as the individual grain position within the sample were then fitted from the diffraction spot positions. A maximum tensile load of 48 MPa was applied. Deviations in strain of up to 600 × 10-6 are observed between respective strain components of individual grains. [Copyright &y& Elsevier]