Researchers Develop Mathematical Relation to Measure Grain Properties


Researchers from London Institute for Mathematical Sciences suggested that 2D image and electron diffraction data can offer size and shape distributions of a material’s grains

According to Robert Farr Lava who studies myriad edible and inedible materials at the London Institute for Mathematical Sciences, lava and ice cream have a lot in common as molten ice cream and lava both flow as slurries, which are fluids full of solid particles. However, the solid forms of both materials consist of randomly oriented crystalline grains. Moreover, it is complex to determine 3D structures of both materials as it requires costly and tedious imaging techniques. Now, Farr in collaboration with Jacobs Douwe Egberts, a beverage company in the U.K. has derived a mathematical relation that allows quick measurement of the size and shape of a grains of a material by using a 2D image and electron diffraction data. The findings published in the journal Physical Review Materials on July 31, 2018, could be applicable to any isotropic polycrystalline material.

The methods commonly used to determine the size and shape distributions of a material’s grains include, x-ray tomography and iterative imaging process. In x-ray tomography, the structure is deduced by merging multiple 2D x-ray images taken at different angles, whereas in iterative imaging process, a thin layer at the surface of a sample is repeatedly sliced off to acquire an image after each cut. The novel method, however, allows the grain properties to be captured in a single shot. The novel approach includes a 2D electron microscope image and a simultaneously collected crystal orientation data from back-scattered electrons. A mathematical relation is fed with these data to calculate the grain distributions. The researchers verified the approach on simulated materials consisting of randomly oriented ellipsoids or rectangular block. Moreover, the approach was tested on a piece of basaltic rock, which is solidified lava.



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