# Spinodal decomposition

### Patterns and Simulations

By Thomas Wanner
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If all the components of a metal alloy are heated to a high enough temperature, they will quickly form an almost perfect homogeneous mixture. If this mixture is then rapidly quenched below a certain temperature, the solution solidifies. Depending on the concentrations of the involved metals, different processes of phase separation may set in. During a process called spinodal decomposition, the components immediately start to separate again, thereby forming a highly inhomogeneous fine-grained structure exhibiting a characteristic length scale. Depending on the relative concentrations of the involved metals, one can observe connected snake-like patterns, or disconnected patterns. The included pictures and movies show the decomposition process and observed patterns for a binary alloy, i.e., an alloy consisting of two metals. The underlying mathematical model is the Cahn-Hilliard partial differential equation.

Pattern in 2D, equal mass: A sample pattern observed on a square domain. The two involved components have equal mass.

Pattern in 2D, different mass: A sample pattern observed on a square domain. The two involved components have different mass.

Evolution in 1D, equal mass: A sample decomposition movie observed for a 1D domain. The two involved components have equal mass.

Evolution in 2D, equal mass: A sample decomposition movie observed on a square domain. The two involved components have equal mass.

Evolution in 2D, different mass: A sample decomposition movie observed on a square domain. The two involved components have different mass.

 Author Institutional Affiliation George Mason University Author Email [email protected] Author Postal Mail Department of Mathematical Sciences George Mason University, MS 3F2 Fairfax, VA 22030 Notes Based on joint work with Stanislaus Maier-Paape and Evelyn Sander. Keywords Spinodal decomposition, Cahn-Hilliard equation

• Pattern in 2D, equal mass:(.jpg, 24.45 KB) - 4859 download(s) A sample pattern observed on a square domain. The two involved components have equal mass.
• Pattern in 2D, different mass:(.jpg, 22.9 KB) - 5258 download(s) A sample pattern observed on a square domain. The two involved components have different mass.
• Evolution in 1D, equal mass:(.gif, 181.28 KB) - 5260 download(s) A sample decomposition movie observed for a 1D domain. The two involved components have equal mass.
• Evolution in 2D, equal mass:(.gif, 2.21 MB) - 4873 download(s) A sample decomposition movie observed on a square domain. The two involved components have equal mass.
• Evolution in 2D, different mass:(.gif, 1.81 MB) - 5088 download(s) A sample decomposition movie observed on a square domain. The two involved components have different mass.