Phase-Field Modeling for Eutectic Solidification

Published

April 1, 2004

Author(s)

Jonathan E. Guyer, William J. Boettinger, James A. Warren, Geoffrey B. McFadden

Abstract

A diffuse interface (phase field) model for a simple electrochemical system is developed. We describe the minimal set of components needed to model an electrochemical interface and present a Lagrangian derivation of te governing equations. With a simple set of assumptions: mass and volume contstraints, Poisson's equation, ideal solution thermodynamics in the bulk, and a simple description of the competing energies in the interface, the model captures the charge separation associated with the equilibrium double layer at the electrochemical interface and the decay of the electrostatic potential in the electrolyte agrees with the classical Gouy-Chapman and Debye-Huckel theories. We calculate the surface energy, surface charge, and differential capacitance as functions of potential and find qualitative agreement with existing theories and experiments. In particular, the differential capacitance curves exhibit complex shapes with multiple extrema, as exhibited in many electrochemical experiments.

Citation

Jom

Volume

56

Issue

No. 4

Pub Type

Journals

Keywords

double layer, electrochemistry, phase field

Citation

Guyer, J. , Boettinger, W. , Warren, J. and McFadden, G. (2004), Phase-Field Modeling for Eutectic Solidification, Jom (Accessed December 21, 2024)