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A SPACE–TIME FINITE ELEMENT MODEL TO STUDY THE INFLUENCE OF INTERFACIAL KINETICS AND DIFFUSION ON CRYSTALLIZATION KINETICS
Author(s) -
KIT K. M.,
SCHULTZ J. M.
Publication year - 1997
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19970730)40:14<2679::aid-nme187>3.0.co;2-y
Subject(s) - diffusion , isothermal process , crystallization , crystal growth , kinetics , finite element method , thermodynamics , space (punctuation) , materials science , crystal (programming language) , growth rate , function (biology) , mathematical analysis , mechanics , mathematics , geometry , physics , classical mechanics , computer science , evolutionary biology , biology , programming language , operating system
We present a space–time finite element formulation to study the cooperative growth of adjacent needle‐like crystals in a two‐dimensional, binary melt. It is assumed that the system is isothermal and that the compositions of the melt and the crystals are different. The growth rate of the crystals is taken to be a function of the melt composition in front of the growing crystals, and the composition of the melt as a function of space and time is determined by the diffusion equation. The positions of the growth fronts of each crystal are tracked. Good agreement is found between the numerical solution of an approximated one‐dimensional problem and an analytical solution. Numerical results of the simulation of the growth of isolated and adjacent crystals are presented. © 1997 John Wiley & Sons, Ltd.