MSE Seminar - I.C. Noyan

“Sampling in Powder Diffraction and Its Ramifications”

Abstract: The information volume of a measurement is the specific volume within a sample from which the actual data used in subsequent analyses are obtained. If the information volume is smaller than the sample volume, attributing its parameters to the entire sample volume assumes that such parameters are homogeneously distributed. For most reported values this assumption is implicit, and frequently it is not tested. In powder diffraction, where Bragg selectivity limits data acquisition to grains satisfying the von Laue conditions, the information volume is a subset of the grains illuminated by the incoming beam; such volumes usually con-tain a small number of grains and are discontinuous in direct space1,2. Using “strain” values from such volume subsets in continuum mechanics formulations assumes, implicitly, that these subsets are representa-tive volume elements that are equal to continuous direct-space volumes3. In the first part of this presenta-tion, we discuss a simple analytical formalism based on the Lorentz-Scherrer equation and Bernoulli statis-tics for estimating the fraction of crystallites (and associated uncertainty parameters) contributing to all finite Bragg peaks of a typical powder pattern obtained from a static polycrystalline sample. We test and validate this formalism using numerical simulations, and show that they can be applied to experiments using monochromatic or polychromatic (pink-beam) radiation. In the second part we extend this treatment to grain-sampling conditions which must be satisfied before diffraction-based strains can be used in non-de-structive applied or residual stress analysis, and discuss errors caused by incomplete sampling

References.

[1]M. Alican Noyan, I. Cevdet Noyan, Powder Diffraction, 40, 44 (2025)

[2]M. Hazar Şeren, Darren C. Pagan, and I. Cevdet Noyan, Journal of Applied Crystallography, 56, 1144 (2023)

[3]I. Cevdet Noyan, Darren C. Pagan, ASM Handbook on Residual Stresses, 25A, 1, (2025)

Speaker Bio:

Dr. Noyan was one of the first researchers to combine the theory of micromechanics with that of x-ray and neutron diffraction. He and his group develop x-ray and neutron characterization techniques for non-destructive analysis of structures, with applications spanning suspension bridge cables, integrated circuits, and nanostructures. Noyan and his co-workers also work on the theory of scattering, with particular emphasis on defining the information volumes from which diffraction data are measured, and quantification of the uncertainties associated with such data.

Prof. Noyan was a member of the organizing committee of the Denver X-ray Conference and co-editor of the Advances in X-Ray Analysis from 1993 through 2019. He is a fellow of the American Physical Society. He has received the Blackall Machine Tool and Gage Award from the American Society of Mechanical Engineers in 2006, and the Jenkins Lifetime Achievement (2015) and Hanawalt (2019) awards from the International Centre for Diffraction Data.