Transient nucleation kinetics of crystal growth at the intermediate stage of bulk phase transitions

被引：82

作者：

Alexandrov, D. V. ^{[1
]}

Malygin, A. P. ^{[1
]}

机构：

[1] Ural Fed Univ, Dept Math Phys, Ekaterinburg 620000, Russia

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2013年 / 46卷 / 45期

基金：

俄罗斯基础研究基金会;

关键词：

POPULATION BALANCE MODEL; BATCH CRYSTALLIZATION; NONLINEAR EVOLUTION; SOLIDIFICATION; GRANULATION; MELTS; ZONE; SIZE;

D O I：

10.1088/1751-8113/46/45/455101

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

A complete analytical solution of an integro-differential model describing the transient nucleation of solid particles and their subsequent growth at the intermediate stage of phase transitions in metastable systems is constructed. A Fokker-Plank type equation for the density distribution function is solved exactly for arbitrary nucleation kinetics. A non-linear integral equation with memory kernel connecting the density distribution function and the system supercooling/supersaturation is analytically solved on the basis of the saddle-point method for the Laplace integral. The analytical solution obtained shows that the process at the intermediate stage is divided into three phases: initially the high rate nucleation stage occurs, then this process is accompanied by the particle growth reducing the level of metastability, and finally the mechanism of particle coarsening becomes predominant.

引用

页数：16

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