Nucleation and Growth of an Ensemble of Crystals during the Intermediate Stage of a Phase Transition in Metastable Liquids

被引：8

作者：

Toropova, Liubov, V ^{[1
,2
]}

Makoveeva, Eugenya, V ^{[3
]}

Osipov, Sergei, I ^{[4
]}

Malygin, Alexey P. ^{[4
]}

Yang, Yang ^{[5
,6
]}

Alexandrov, Dmitri, V ^{[3
]}

机构：

[1] Ural Fed Univ, Dept Theoret & Math Phys, Lab Math Modeling Phys & Chem Proc Multiphase Med, Lenin Ave 51, Ekaterinburg 620000, Russia

[2] Friedrich Schiller Univ Jena, Otto Schott Inst Mat Forsch, D-07743 Jena, Germany

[3] Ural Fed Univ, Dept Theoret & Math Phys, Lab Multiscale Math Modeling, Lenin Ave 51, Ekaterinburg 620000, Russia

[4] Ural Fed Univ, Inst Nat Sci & Math, Lenin Ave 51, Ekaterinburg 620000, Russia

[5] East China Normal Univ, Key Lab Polar Mat & Devices, Shanghai 200241, Peoples R China

[6] East China Normal Univ, Phys Dept, Shanghai 200241, Peoples R China

来源：

CRYSTALS | 2022年 / 12卷 / 07期

基金：

俄罗斯科学基金会;

关键词：

nucleation; crystal growth; phase transformation; supercooled liquid; crystal-size distribution; POPULATION BALANCE MODEL; NONLINEAR EVOLUTION; KINETICS; CRYSTALLIZATION; SOLIDIFICATION; SIZE;

D O I：

10.3390/cryst12070895

中图分类号：

O7 [晶体学];

学科分类号：

0702 ; 070205 ; 0703 ; 080501 ;

摘要：

In this paper, an analytical method of solving the integro-differential system of kinetic and balance equations describing the evolution of an ensemble of crystals during the intermediate phase of the bulk crystallization process is described. The theory is developed for kinetic equations of the first- and second order corresponding to the absence and presence of fluctuations in particle growth rates. The crystal-size distribution function as well as the dynamics of metastability reduction in a supercooled melt (supersaturated solution) are analytically found using the saddle-point and the Laplace transform methods. The theory enables us to obtain the crystal-size distribution function that establishes in a supercooled (supersaturated) liquid at the beginning of the final stage of a phase transformation process when Ostwald ripening, coagulation and fragmentation of crystals are able to occur.

引用

页数：19