A phase field model for the gallium permeation of aluminum grain boundaries

Abstract

Interfaces, such as grain boundaries, solid-liquid interfaces and solid-solid heterophase interfaces, are important features found in materials. Material properties such as fracture toughness, corrosion susceptibility and high temperature creep are influenced by grain boundary physics. The structure of grain boundaries affects their properties. In this thesis, we have developed a predictive model for a particular grain boundary structure-property relationship: the permeation of liquid gallium through aluminum grain boundaries. Liquid gallium is known to permeate through aluminum grain boundaries. The reduction in interface energy by the replacement of one Al-Al grain boundary interface with two Al-Ga interfaces drives the permeation. The speed of permeation depends on factors which affect the Al-Al grain boundary energy, such as grain boundary crystallography, applied stress, and temperature. Literature suggests two major hypotheses for the permeation mechanism: front propagation, and diffusion and coalescence. We have used phase field methods to develop a predictive model for the permeation of gallium through individual aluminum grain boundaries. The model uses location dependent grain boundary energy (LDGBE) distributions for aluminum grain boundaries to predict permeation velocities. Importantly, by changing the model's parameters, its behavior can be adjusted smoothly from front propagation, to diffusion and coalescence. We have used experimental data collected by Hugo and Hoagland, along with LDGBE maps computed by our collaborators, to infer the parameters of the phase field model. The inference has been done in a Bayesian framework, which gives us estimates of the model parameters with quantifiable uncertainty. The inferred model parameters strongly support the front propagation hypothesis. We discuss the implications of this inference and potential limitations of our methodology.