Phase Initiation Mechanism and Evolution Using Surface Evolver

Author

Juan Baek

Date of Award

2024

First Advisor

Anne O'Dwyer

Second Advisor

Michael Bergman

Abstract

Phase initiation and evolution play a crucial role in research and manufacturing, particularly in areas such as polycrystalline thin films and displays. However, investigating the fundamental theory behind these processes has been challenging due to the complexity of mathematical calculations and the difficulty of observing phase transformations in condensed phases experimentally. Professor Ken Brakke of Susquehanna University has developed a program called Surface Evolver, originally designed to study capillarity physics of microdroplets. We can utilize this program for simulating evolution of a new phase beyond the simple classical Nucleation Theory. By minimizing the energy of the “inter-phase” interface as it undergoes a transformation subject to constraints, Surface Evolver uses various mathematical tools, including Green's Theorem and vector calculus to simulate the evolution of a new phase. A priori, we must explicitly identify the shape and constraints of the solid/liquid interface. By understanding the relationship between contact angles on surfaces and interfacial energies, we can accurately simulate the evolution of a solid. We also develop a thermodynamic analysis by recognizing that curvature is a property of solid/liquid interfaces in mechanical equilibrium, resulting in the derivation of a critical curvature where the Gibbs-Thomson condition holds. We further demonstrate the effectiveness and efficiency of this method by showing that free-energy evolution plots that are normally sought after by researchers, are readily available from our curvature-volume evolution diagrams with fewer restrictions.

Recommended Citation

Baek, Juan, "Phase Initiation Mechanism and Evolution Using Surface Evolver" (2024). Senior Theses. 1684.
https://digitalcommons.bard.edu/sr-theses/1684