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

Abstract

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.

A study of stress relaxation in AZ31 using high-energy X-ray diffraction

“…The measured reciprocal vector associated with reflection i, g ðiÞ , is related to the reciprocal vector in the (undeformed) reference, g ðiÞ 0 , through the tensorF ÀT as [4,5], g ðiÞ ¼F ÀTgðiÞ 0 : ðA:1Þ…”

“…One pathway to gain deeper understanding of mechanical response at the mesoscale is through use of high-energy X-ray radiation from synchrotron sources. Procedures are well established for evaluation of the lattice strain tensor and grain orientation using hard X-rays [1][2][3][4][5][6]. Different kinds and arrangements of detectors provide for a wide variety of experimental approaches.…”

Grain Centre Mapping — 3DXRD Measurements of Average Grain Characteristic

“…Two complementary open-source software packages exist; the HEXRD data analysis tools developed by Bernier and co-workers Edmiston et al, 2011), and the FABLE suite of programs developed in collaboration between Risø DTU and the ESRF (http://fable.wiki.sourceforge.net/). The file formats used in both are similar, so in principle one can start the data analysis with modules from one package and carry on using software from the other.…”

A Note on Residual Stress, Lattice Orientation and Dislocation Density in Crystalline Solids

“…Thus the dislocation density is not measured directly but rather inferred from the measured lattice orientation and strain fields. Measurement of the orientation and elastic strain fields together means that the full distortion field K(x) is available [13], and hence that the residual stress field is determined in principle via constitutive equations such as (22) 2,3 . Thus experiments that yield the dislocation density also yield the residual stress to the same degree, at least in principle, granted the availability of the elastic moduli.…”