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The Theory of the Stability of the Solid‐Liquid Interface under Constitutional Supercooling (I)
Author(s) -
Delves R. T.
Publication year - 1966
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.19660160229
Subject(s) - supercooling , interface (matter) , thermal diffusivity , diffusion , stability (learning theory) , thermodynamics , transient (computer programming) , steady state (chemistry) , amplitude , stability criterion , physics , mathematical analysis , mathematics , chemistry , statistical physics , optics , discrete time and continuous time , computer science , pulmonary surfactant , gibbs isotherm , machine learning , operating system , statistics
This paper discusses the stability of the solid‐liquid interface when a crystal is grown from a melt which contains a segregating component. The transient motion of the interface in response to a thermodynamic fluctuation in concentration is calculated using the time dependent diffusion equations. An expansion is made in powers of the amplitude of the fluctuation, the first order terms are found exactly, and some important higher order terms are included. The interface is either stable and returns to its original flat shape or else distorts exponentially with time into the cellular shape. The stability condition is exactly the original constitutional supercooling criterion of Tiller et al. Physical and mathematical arguments show that the interface is either stable or unstable and that no steady state slightly perturbed interface can exist. This paper is restricted to the special case of infinite thermal diffusivity, and does not include effects on an atomic scale.