Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/101802
Title: On the theory of the unsteady-state growth of spherical crystals in metastable liquids
Authors: Alexandrov, D. V.
Alexandrova, I. V.
Issue Date: 2019
Publisher: Royal Society Publishing
Citation: Alexandrov D. V. On the theory of the unsteady-state growth of spherical crystals in metastable liquids / D. V. Alexandrov, I. V. Alexandrova. — DOI 10.1098/rsta.2018.0209 // Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. — 2019. — Vol. 377. — Iss. 2143. — 20180209.
Abstract: Motivated by a large number of applications, we consider the process of non-stationary growth of spherical crystals in a supercooled binary melt. The moving-boundary problem describing the unsteadystate distributions of temperature and impurity concentration around the growing crystal as well as the dynamics of its radius and growth rate is solved by means of the methods of small-parameter expansion and Laplace-Carson integral transform. We show that the growth rate of crystals contains the main contribution (which is proportional to the supercooling degree) and the first correction (which is proportional to 2t, where t is time). The second correction is also found. The non-stationary temperature and concentration fields are determined as power functions of and t. We demonstrate that the first corrections to the dynamics of crystal radius R(t) and its growth rate V(t) play an important role. It is shown that R(t) andV(t) can change more than twice in comparison with the previously known steady-state solution with the course of time. Such a behaviour will significantly modify the dynamics of a polydisperse ensemble of crystals evolving in a metastable liquid. This article is part of the theme issue 'Heterogeneous materials: Metastable and non-ergodic internal structures'. ©2019 The Author(s) Published by the Royal Society.
Keywords: CRYSTAL GROWTH
METASTABLE LIQUID
MOVING-BOUNDARY PROBLEM
PHASE TRANSFORMATION
CRYSTAL GROWTH
CRYSTAL IMPURITIES
DYNAMICS
INTEGRAL EQUATIONS
LIQUIDS
PHASE TRANSITIONS
SUPERCOOLING
CONCENTRATION FIELDS
HETEROGENEOUS MATERIALS
IMPURITY CONCENTRATION
METASTABLE LIQUID
MOVING BOUNDARY PROBLEMS
PARAMETER EXPANSION
STEADY STATE SOLUTION
SUPERCOOLING DEGREES
GROWTH RATE
URI: http://hdl.handle.net/10995/101802
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85062423309
PURE ID: 9063287
d10b60a5-1202-4ae0-84c2-213219e35f61
ISSN: 1364503X
DOI: 10.1098/rsta.2018.0209
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

Files in This Item:
File Description SizeFormat 
2-s2.0-85062423309.pdf619,45 kBAdobe PDFView/Open


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.