Definitions
from Wiktionary, Creative Commons Attribution/Share-Alike License.
- adjective chemistry Describing the
transformation of a system of two or morecomponents in ametastable phase into twostable phases
Etymologies
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Examples
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In this post, I will discuss CH equation in the context of spinodal decomposition.
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Replacing, and eliminating the necessity of assuming negative diffusion coefficients in the study of spinodal decomposition is but only one aspect of the CH equation.
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It is also well known that the work of Cahn and Hilliard is but a continuum version of that of Hillert (whose Ph D thesis, discussing spinodal decomposition was apparently given to Cahn by Hilliard [8]).
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Cahn, in his 1961 Acta Metallurgica paper [4] traces some of the ideas of spinodal decomposition in solids to Gibbs, and in his Institute of Metals lecture in 1968 [6] traces the name and the concept of spinodal to van der Waals,
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[8] J W Cahn, Reflections on diffuse interfaces and spinodal decompositons, in
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Acta Metallurgica in 1961 [4], Cahn discusses the study of spinodal decomposition in solids (including the elastic stress effects due to the lattice parameter differences between the two phases).
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For those of you who might be interested in solving the CH equation numerically, a C code that uses spectral methods (and FFTW) to solve CH spinodal decomposition is available for download (under GPL license) from
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This strong resemblance between Fick's second law (Eq. 2) and CH equation (Eq. 1) is not accidental; CH can indeed be considered as a generalisation of Fick's second law; in fact, CH is the result of a study of spinodal decomposition - a phenomenon which also brought out the limitations of Fick's second law.
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[4] J W Cahn, On spinodal decomposition, Acta Metallurgica,
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