Scientific Achievement

Researchers from the Superconducting Magnet Program in the Accelerator Technology & Applied Physics Division at Lawrence Berkeley National Laboratory (Berkeley Lab) have demonstrated an up-dimensioning procedure for approximating the 3D grain size distribution of a microstructure from 2D cross-sections for equiaxed grains (grains whose sizes are approximately equal in each direction). While grain size analysis has an established history and is widely used by the ASTM International (formerly the American Society for Testing and Materials) standards, this work sheds new light on understanding different 2D methodologies through synthetic grain structures by allowing a more detailed and easily scalable study of grain microstructure.

Significance and Impact

Introducing defects such as grain boundaries into a material’s lattice is undertaken to achieve specific properties; for example, small grains lead to higher yield stress. It is commonly applied in structural material analysis. Traditionally, grain size analysis is presented using 1D parameters and measured by 2D grain cross-sections obtained from polished surfaces or fractographs, which are image projections of the 3D structure. Such an approach loses information about the actual 3D grain size due to image acquisition or segmentation limitations and artifacts like incomplete grain exposure. Synthetic data is essential in providing unparalleled statistics with options to integrate and study data acquisition artifacts and laying the foundation for analyzing other grain distributions, such as columnar and composite grains, in similar depth.

Additionally, this method permits the direct comparison of techniques that would otherwise be impossible to use on the same sample volume. The analysis performed on the synthetic equiaxed structure allowed the researchers to propose an up-dimensioning procedure for approximating 3D grain sizes using the distribution obtained from 2D images. This procedure is more robust to differing imaging conditions because it eliminates the reliance on smaller grain projections.

Realistic fractograph rendering of a synthetically generated structure. (Credit: Berkeley Lab)

The work directly impacts the assessment comparison of fine grain size materials such as niobium-tin (Nb₃Sn), which is the workhorse superconductor for high-field particle accelerator magnets. For example, in Nb₃Sn superconductors, very small grain sizes increase the maximum supercurrent carrying capability by a phenomenon called “flux-pinning.” However, differing determination methods and uncertain artifacts during image analysis would complicate the quantitative analysis of grain sizes.

This research suggests an alternative procedure for determining the true 3D grain size parameter, which is possible without changing how images are acquired or segmented. However, it requires a more substantial analysis than ASTM International standards. Nevertheless, realistic synthetic grain structure data can train artificial intelligence/machine learning (AI/ML) models to automatically perform instance segmentation (grain labeling). The work opens the door for improving the accuracy and speed for analyzing the effects of novel design parameters on the Nb₃Sn wire performance.

Research Details

Generating synthetic grain structures

The computer graphics software application Blender was used to generate a rectangular prism. In this prism, a random distribution of points is used to subdivide the volume into “cells” or “grains” via a Voronoi tessellation. This process yields a simulated equiaxed grain structure.

Synthetic cross-sections

a) Approximated and actual 3D grain size distributions alongside the 2D fractograph
distribution. The bins of the fractograph grains represent the sample 𝐷!”. The approximated 3D grain
size distribution of a synthetic data sample was derived from its 2D fractograph distribution of
equivalent diameters using 15,464 grains and kernel density estimation. b) Three approximations of the
grain volume distribution, varying the order of approximation (A), conversion to 3D volume (C), and
mirroring of the grain distribution across the mode (M). (Credit: Berkeley Lab)

Fracture surface cross-sections were generated by iteratively removing grains that fall outside a specified surface that can be planar or a function, simulating brittle intergranular fracture.  Polished surface cross-sections were generated by bisection cuts across the grain structure along a plane, simulating metallographic grinding, polishing, and etching processes that expose an artifact-free microstructure. Appropriate lighting and texture rendering generate realistic micrographs similar to those obtained from a scanning electron microscope.

One-to-one grain matching

As the structure is generated, every grain’s characteristics can be obtained and matched to individual correspondence in the 2D and 3D forms for statistical comparisons. This permits a massive data collection with more complete 3D information than is practically attainable. As a result, the commonly used linear intercept and planimetric methods could be evaluated, shedding light on their discrepancy with the actual 3D distribution parameters.

Up-dimensioning approximation of 3D grain size

An “up-dimensional” approximation of 3D grain size from a 2D cross-section is possible because equiaxed grains are mostly convex and roughly symmetric, each sampled grain cross-section has an upper limit set by its 3D grain size, and there exists a mode value in the underlying distribution. These reasons are agnostic to the Voronoi tessellation method or grain model used. Together, these underpinnings suggest a stable approximation of the average 3D grain size.

Contacts: Ian Pong and Kevin Gillespie

Researchers: Ian Pong and Jean-Francois Croteau (Berkeley Lab); Kevin Gillespie (University of California, Berkeley); and Algirdas Baskys (Berkeley Lab and European Organization for Nuclear Research)

Funding: The U.S. Department of Energy’s Office of Science, Office of High-Energy Physics under the U.S. Magnet Development Program

Publication: Gillespie, K., Baskys, A., Pong, I., and Croteau, J.-F. “Updimensioning strategy derived from synthetic equiaxed grain structures for approximating 3D grain size distributions from 2D visualizations with 1D parameters,” Sci. Rep. 14, 23007 (2024). https://doi.org/10.1038/s41598-024-73090-8

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