**Fourier Components**

Cahn and Hilliard formulated a theory for the amplification (or attenuation) of an arbitrary composition fluctuation by considering, with Debye, the Fourier components of the composition rather than the composition itself. Thus, for a concentration fluctuation:

one obtains for the change in free energy on forming fluctuations:

The *solution is then unstable* (*ΔF* < 0) for all fluctuations of wave number *β* smaller than a critical wave number *β _{c}* given by:

or *for all fluctuations of wavelength λ = 2π/β which are longer than a critical wavelength* given by:

From these equations, it is seen that the incipient surface energy, reflected in the gradient energy term, prevents the solution from decomposing on too small a scale. This concept was first introduced by Hillert, and shows that as the spinodal is approached, the critical wavelength approaches infinity.

Read more about this topic: Spinodal Decomposition

### Famous quotes containing the word components:

“Hence, a generative grammar must be a system of rules that can iterate to generate an indefinitely large number of structures. This system of rules can be analyzed into the three major *components* of a generative grammar: the syntactic, phonological, and semantic *components*.”

—Noam Chomsky (b. 1928)