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 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. Published under an exclusive license by AIP Publishing.

Automated summary

This paper extends the classic Avrami equation to nonisothermal systems with arbitrary temperature-time history and initial distributions of transformed phase. By examining phase change in Fourier space, a nonlinear differential equation relating nucleation rate, growth rate, and transformed fraction is derived. Analytical solutions for the population balance partial differential equation on the phase size distribution are obtained, and initial conditions for the differential equation linking nucleation rate, growth rate, and transformed fraction are derived.