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This paper describes the extension of the classic Avrami equation to nonisothermal systems with arbitrary temperature-time history and arbitrary initial distributions of transformed phase. We start by showing that through examination of phase change in Fourier space, we can decouple the nucleation rate, growth rate, and transformed fraction, leading to the derivation of a nonlinear differential equation relating these three properties. We then consider a population balance partial differential equation (PDE) on the phase size distribution and solve it analytically. Then, by relating this PDE solution to the transformed fraction of phase, we are able to derive initial conditions to the differential equation relating nucleation rate, growth rate, and transformed fraction.
Bibliographical noteFunding Information:
This work was supported by the National Science Foundation, Grant No. 1941543, NSF Engineering Research Center for Advanced Technologies for Preservation of Biological Systems (ATP-Bio).
© 2021 Author(s).
PubMed: MeSH publication types
- Journal Article
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ATP-Bio: NSF Engineering Research Center for Advanced Technologies for the Preservation of Biological Systems (ATP-Bio)
9/1/20 → 8/31/25
Project: Research project