Thermodynamic basis for a variational model for crystal growth.

Area of Science:

• Materials Science
• Thermodynamics
• Computational Modeling

Background:

• Standard sharp interface models are used for phase boundary motion during solidification.
• Variational models present an alternative computational approach.

Purpose of the Study:

• To establish a link between variational simulation objective functions and thermodynamic functions.
• To demonstrate the consistency of variational models with nonequilibrium thermodynamics.
• To develop variational models for solidification of pure materials and binary alloys.

Main Methods:

• Formulating conservation laws for internal energy and chemical species.
• Expressing the law of local entropy production in integral form.
• Developing variational principles based on minimizing a time-decreasing free energy.

Main Results:

• A correspondence between variational objective functions and thermodynamic functions was established.
• Variational models were shown to be consistent with nonequilibrium thermodynamics.
• The models successfully reproduced the Gibbs-Thomson boundary condition at the solid-liquid interface for small time intervals.

Conclusions:

• Variational models provide a thermodynamically consistent framework for simulating solidification.
• These models offer a viable alternative to sharp interface models.
• The developed variational principles accurately capture essential physical phenomena during phase transitions.