Intragranular strain estimation in far-field scanning X-ray diffraction using a Gaussian process.

Axel Henningsson,Johannes Hendriks

doi:10.1107/s1600576721005112

Axel Henningsson, Johannes Hendriks

Open Access

https://doi.org/10.1107/s1600576721005112

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Abstract

A new method for estimation of intragranular strain fields in polycrystalline materials based on scanning three-dimensional X-ray diffraction (scanning 3DXRD) data is presented and evaluated. Given an a priori known anisotropic compliance, the regression method enforces the balance of linear and angular momentum in the linear elastic strain field reconstruction. By using a Gaussian process (GP), the presented method can yield a spatial estimate of the uncertainty of the reconstructed strain field. Furthermore, constraints on spatial smoothness can be optimized with respect to measurements through hyperparameter estimation. These three features address weaknesses discussed for previously existing scanning 3DXRD reconstruction methods and, thus, offer a more robust strain field estimation. The method is twofold validated: firstly by reconstruction from synthetic diffraction data, and secondly by reconstruction of a previously studied tin (Sn) grain embedded in a polycrystalline specimen. Comparison against reconstructions achieved by a recently proposed algebraic inversion technique is also presented. It is found that the GP regression consistently produces reconstructions with lower root-mean-square errors, mean absolute errors and maximum absolute errors across all six components of strain.

Highlights

Three-dimensional X-ray diffraction (3DXRD), as pioneered by Poulsen (2004) and co-workers, is a nondestructive materials probe for the study of bulk polycrystalline materials
In this paper we are concerned with reconstruction of intragranular strain, and we focus on the final step of analysis and proceed with the assumption that all preceding quantities have been computed
By selecting a continuous differentiable Fourier basis for the Beltrami stress functions, a static equilibrium prior can be incorporated into the reconstruction, guaranteeing that the predicted strain field will satisfy the balance of both angular and linear momentum

Summary

Introduction

Three-dimensional X-ray diffraction (3DXRD), as pioneered by Poulsen (2004) and co-workers, is a nondestructive materials probe for the study of bulk polycrystalline materials. The experimental technique is typically implemented at synchrotron facilities where access to hard X-rays (!10 keV) facilitates the study of dense materials with sample dimensions in the millimetre range. In contrast to powder diffraction, 3DXRD enables studies on a per-grain basis, which requires that the Debye–Scherrer rings consist of a set of well defined, separable single-crystal peaks. By various computer-aided algorithms (cf Lauridsen et al, 2001), the single-crystal diffraction peaks can be segmented and categorized on a per-grain basis, enabling the study of individual crystals within a sample. Typical quantities retrieved from such analyses are the grain average strain and average orientation (Poulsen et al, 2001; Oddershede et al, 2010). From further analysis it possible to retrieve an approximate grain topology map (Poulsen & Schmidt, 2003; Poulsen & Fu, 2003; Markussen et al, 2004; Alpers et al, 2006)

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