Kinetics of nonisothermal phase change with arbitrary temperature–time history and initial transformed phase distributions

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 r...

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Bibliographic Details
Published in:The Journal of chemical physics 2021-12, Vol.155 (21), p.211101-211101
Main Authors: Kangas, Joseph, Bischof, John C., Hogan, Christopher J.
Format: Article
Language:English
Subjects:
Avrami equation
Initial conditions
Nonlinear differential equations
Nucleation
Partial differential equations
Phase change
Physics
Size distribution
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Summary: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.
ISSN:0021-9606
1089-7690
DOI:10.1063/5.0072299