Abstract
The volumetric growth rate of individual grains has been found empirically to be directly proportional to their individual volume, dV/dt = β(V0 − V). This simple result extends from the relationship \({\mathrm{d}}V/{\mathrm{d}}t=-k{M}_{\mathrm{S}},\) where MS is integral mean curvature of the boundaries of individual grains and k the grain growth rate constant, and the experimentally observed linear relationship between \({M}_{\mathrm{S}}\) and individual grain volume, \({M}_{\mathrm{S}}\) = α(V0 − V). Here, α is a scaling parameter that collapses the relationships for separate times of growth into a single trend. It has been shown that α =\(\gamma {\bar{V}}^{-2/3}\) where γ is an experimentally determined constant ≃ − 2.7 and \({\bar{V}}\) is the mean grain volume. Thus, β = −kα = 2.7k \({\bar{V}}^{-2/3}\), simply proportional to the scale of the overall grain structure. These relationships have been tested successfully in numerous 3D grain growth simulations and experiments. This paper describes the relationships among these kinetic and geometric grain characteristics that provide this surprisingly simple description of 3D grain growth, i.e., a linear relationship between the growth rate of an individual grain and its volume.
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Acknowledgments
The overall program and BRP and RTD gratefully acknowledge financial support from NSF Grants DMR-1035188 and 1307665. They also acknowledge the work of Amy Adams, George Strickland, Brittani Maskley and Dr. Tyler Kaub in the tungsten GPE study, and the simulation work performed by Dr. Catherine Sahi. They gratefully thank Dr. Veena Tikare at Sandia National Laboratories, New Mexico for extensive guidance in the computer modeling portion of these studies. Portions of this work were performed in partial fulfillment of Dr. Sahi’s Ph.D. degree.
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Manuscript submitted March 7, 2021; accepted May 30, 2021.
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Patterson, B.R., DeHoff, R.T. Linear Relationship Between dV/dt and Grain Volume During Grain Growth. Metall Mater Trans A 52, 3849–3859 (2021). https://doi.org/10.1007/s11661-021-06346-x
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DOI: https://doi.org/10.1007/s11661-021-06346-x