Complexions in a modified Langmuir-McLean model of grain boundary segregation

TL;DR

This paper revises the Langmuir-McLean model of grain boundary segregation, revealing that the most probable segregation differs from the standard relation and can exhibit multiple stable interface compositions.

Contribution

It introduces a modified model accounting for vacancy content ratios, showing the existence of multiple stable segregation states for given bulk compositions.

Findings

Two stable interface compositions can exist for the same bulk composition.

Vacancy content ratio significantly influences the shape of the segregation isotherm.

The standard Langmuir-McLean relation is an approximation, not an exact description.

Abstract

The Langmuir-McLean isotherm is often interpreted as providing an approximation to the most probable grain boundary segregation as a function of the bulk mole solute fraction $x_B$, even though $x_B$ is not an independant parameter in the free energy minimization on which it is based. In this paper it is shown that the most probable segregation for a specified $x_B$ differs from the standard Langmuir-McLean relation. Numerical solution of the derived equation suggests that two potentially stable interface compositions are associated with most bulk compositions. One solution represents a state with an excess of solute along the boundary relative to the bulk, while the other represents a deficit. The vacancy content ratio between the interface and the bulk plays a large role in determining the shape of the derived isotherm.