Anisotropy of segregation at grain boundaries and surfaces

The purpose of this article is to review analytical models of the anisotropy of segregation to grain boundaries (GBs) and surfaces, and to evaluate their predictions. A summary of Gibbsian interfacial thermodynamics is provided as an introduction to the topic. This is followed by a historical overview of previous analytical models. A recently developed model of the dependence of GB segregation on the five macroscopic parameters of GB orientation is outlined, and illustration of how this formulation reduces to the particular cases of segregation to simpler types of interfaces is provided. In addition, some specific aspects of interfacial segregation, which have either been problematic or have lacked satisfactory explanation, are addressed. These include (a) the relationship between the compositions on the two sides of a given GB; (b) the difficulty of meaningful definitions of segregation-free energy (and related thermodynamic quantities such as enthalpy and entropy); (c) the so-called compensation temperature, at which the anisotropy of interfacial segregation seems to vanish; (d) the relationship between surface and GB segregation; and finally (e) an attempt to determine whether segregation increases or decreases interfacial energy anisotropy, and the consequences thereof on the equilibrium crystal shape of alloys. Where possible, comparisons are made with the results of experiments or computer simulations.