Spinodal Decomposition:
A pictorial view of the formation of binary alloys

If a homogeneous high-temperature mixture of two metallic components is rapidly cooled to a lower temperature, then a sudden phase separation can set in. That is, the mixture becomes inhomogeneous and forms a fine-grained structure, more or less alternating between the two metal components. This numerical numerical simulation shows the phase separation occuring, as modeled by the Cahn-Hilliard equation. The color represents the concentration of the two metals. Green corresponds to an even mixture of metal A and metal B. Red corresponds to all metal A, blue to all metal B. Notice that the mixture starts out as an even mixture, and after some time, becomes an inhomogeneous mixture. Although the patterns formed are not completely symmetric, they are also not random. Understanding these patterns has been the subject of much research, going back to the original works of Cahn and Hilliard. Numerical simulations and subsequent analytical results have been carried out jointly with Thomas Wanner to understand these patterns. Our work has lead to a new approach to understanding the underlying mechanism for this pattern formation.

Starring: The Cahn-Hilliard equation
Director: Evelyn Sander
Filmed on location in two dimensions
Based on two original articles of Evelyn Sander and Thomas Wanner

For more information, see our upcoming article Monte Carlo simulations for spinodal decomposition, to appear in the Journal of Statistical Physics, as well as a preprint of our theoretical results, Unexpectedly linear behavior for the Cahn-Hilliard equation.

The Equation
d/dt(u)=-laplacian(epsilon^2 laplacian u + f(u))
with Neumann boundary conditions and where -f is the derivative of a double-well potential.
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