Nucleation and particle growth with fluctuating rates at the intermediate stage of phase transitions in metastable systems

D V Alexandrov,I G Nizovtseva

doi:10.1098/rspa.2013.0647

D V Alexandrov, I G Nizovtseva

Open Access

https://doi.org/10.1098/rspa.2013.0647

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Abstract

An exact analytical solution of an integro-differential model describing the transient nucleation of solid particles (nuclei) and their growth with fluctuating rates at the intermediate stage of bulk phase transitions in metastable systems is constructed. Two important cases of the Weber–Volmer–Frenkel–Zel'dovich and Mier nucleation kinetics are detailed for supercooled melts and supersaturated solutions.

Highlights

Supersaturation or supercooling of a metastable system is a main driving force for the two dominant phenomena of bulk phase transitions: nucleation and crystal growth
The initial and final stages of the process respectively connected with characteristic times τ1 and τ3 have been studied theoretically in detail, but the intermediate behaviour is much less understood. This is connected with unsurmountable mathematical difficulties of solving the nonlinear integro-differential equations for the intermediate stage of bulk phase transitions
The main task of this study is to develop a new theoretical approach for the construction of exact analytical solutions of the integro-differential model, describing the nucleation kinetics and particle coarsening with fluctuating rates at the intermediate stage of phase transitions for a broad range of process conditions

Summary

Introduction

Supersaturation or supercooling of a metastable system is a main driving force for the two dominant phenomena of bulk phase transitions: nucleation and crystal growth. The initial and final stages of the process respectively connected with characteristic times τ1 and τ3 have been studied theoretically in detail (see, among others, [6,7,8,9]), but the intermediate behaviour (characteristic process time τ2) is much less understood This is connected with unsurmountable mathematical difficulties of solving the nonlinear integro-differential equations for the intermediate stage of bulk phase transitions. The main task of this study is to develop a new theoretical approach for the construction of exact analytical solutions of the integro-differential model, describing the nucleation kinetics and particle coarsening with fluctuating rates at the intermediate stage of phase transitions for a broad range of process conditions

The model

Exact analytical solutions

Concluding remarks