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 AffiliationGeorge Mason University
Author Email
Author Postal MailDepartment of Mathematical Sciences George Mason University, MS 3F2 Fairfax, VA 22030
Notes
Based on joint work with Stanislaus Maier-Paape and Evelyn Sander.
KeywordsSpinodal decomposition, Cahn-Hilliard equation

Documents to download

  • 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.

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