Diffraction and the Cahn-Hilliard Equation

Microstructural characteristics of spinodal decomposition are periodicity and alignment. Periodicity arises from wavelengths associated with the fastest-growing initial mode. At later times, the characteristic periodic length increases due to microstructural coarsening. Periodicity can be detected by diffraction experiments. 

Periodic microstructures can be corroborated by observations of wavevectors /3 in transmission electron microscope (TEM) images, particularly if the sample is oriented with the modulation waves directed perpendicular to the electron-beam direction (e.g., with the beam along [001] for a crystal with (100) modulations). 

If there is alignment, contrast in TEM images is strong, because of the periodic strain field in the crystal. Selected-area diffraction shows evidence of such alignment by the location of satellite intensities around the Bragg peaks arising from the modulation of atomic scattering factors, lattice constant, or both [19]. In Fig. 18.10, the electron diffraction effects, expected from an f.c.c. crystal with (100) composition waves, are depicted with a [001] beam direction. 

Hilliard. Spinodal Decomposition, pages 497-560. American Society for Metals, Metals Park, OH, 1970. 

Cahn and W.C. Carter. Crystal shapes and phase equilibria A common mathematical basis. Metall. Trans., 27A(6) 1431-1440, 1996. 

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