Nasr M. Ghoniem and Daniel D. Walgraef

in Instabilities and Self-Organization in Materials

Published in print February 2008 | ISBN: 9780199298686
Published online May 2008 | e-ISBN: 9780191720222 | DOI:

Series: Monographs on the Physics and Chemistry of Materials


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This chapter examines the morphological instabilities of interfaces between the liquid and solid phases as the phase transformation process is completed. It first presents the problem of melting and solidification, in which the classical ‘Stefan problem’ is introduced as a fundamental model upon which melting and solidification studies are based. It then discusses some general aspects of phase change in pure, single-species systems. The attractiveness of the Stefan problem stems from the fact that the model is amenable to analytical solutions, and as such, it furnishes the physical understanding of more complex analysis of coupled heat and mass transport in a binary system. It also leads to the analysis of morphological surface instabilities and dendrite formation. The emergence of interfacial morphological instabilities in electro-chemical deposition is studied, exposing the rich variety of interfacial structures that arise in this case.

Keywords: heat transfer; melting; solidification; Stefan problem; binary alloys; dendrite growth; electro-deposition

Chapter.  17290 words.  Illustrated.

Subjects: Condensed Matter Physics

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