This manuscript is concerned with the theory of nucleation and evolution of a polydisperse ensemble of crystals in metastable liquids during the intermediate stage of a phase transformation process. A generalized growth rate of individual crystals is obtained with allowance for the effects of their non-stationary evolution in unsteady temperature (solute concentration) field and the phase transition temperature shift appearing due to the particle curvature (the Gibbs–Thomson effect) and atomic kinetics. A complete system of balance and kinetic equations determining the transient behaviour of the metastability degree and the particle-radius distribution function is analytically solved in a parametric form. The coefficient of mutual Brownian diffusion in the Fokker–Planck equation is considered in a generalized form defined by an Einstein relation. It is shown that the effects under consideration substantially change the desupercooling/desupersaturation dynamics and the transient behaviour of the particle-size distribution function. The asymptotic state of the distribution function (its ‘tail’), which determines the relaxation dynamics of the concluding (Ostwald ripening) stage of a phase transformation process, is derived.

This article is part of the theme issue ‘Transport phenomena in complex systems (part 1)’.

这份手稿涉及相变过程中间阶段亚稳态液体中多分散晶体集合的成核和演化理论。考虑到它们在不稳定温度（溶质浓度）场中的非平稳演化和由于粒子曲率（吉布斯-汤姆森效应）和原子动力学而出现的相变温度偏移的影响，获得了单个晶体的广义生长速率. 确定亚稳态度和粒子半径分布函数的瞬态行为的平衡和动力学方程的完整系统以参数形式解析求解。Fokker-Planck 方程中的相互布朗扩散系数被认为是由爱因斯坦关系定义的广义形式。结果表明，所考虑的影响显着改变了降温/减饱和动力学和粒度分布函数的瞬态行为。分布函数的渐近状态（其“尾部”）决定了相变过程的结束（奥斯特瓦尔德熟化）阶段的弛豫动力学。

本文是主题问题“复杂系统中的传输现象（第 1 部分）”的一部分。