text: Grain boundaries are the preferential site for segregation of impurities, which may form a thin layer with a different composition from the bulk and a variety of atomic structures that are distinct from the abutting crystalline phases. For example, a thin layer of silica, which also contains impurity cations, is often present in silicon nitride.
  Grain boundary complexions were introduced by Ming Tang, Rowland Cannon, and W. Craig Carter in 2006.
  These grain boundary phases are thermodynamically stable and can be considered as quasi-two-dimensional phase, which may undergo to transition, similar to those of bulk phases. In this case structure and chemistry abrupt changes are possible at a critical value of a thermodynamic parameter like temperature or pressure. This may strongly affect the macroscopic properties of the material, for example the electrical resistance or creep rates. Grain boundaries can be analyzed using equilibrium thermodynamics but cannot be considered as phases, because they do not satisfy Gibbs'definition: they are inhomogeneous, may have a gradient of structure, composition or properties. For this reasons they are defined as complexion: an interfacial material or stata that is in thermodynamic equilibrium with its abutting phases, with a finite and stable thickness (that is typically 2–20 Å). A complexion need the abutting phase to exist and its composition and structure need to be different from the abutting phase. Contrary to bulk phases, complexions also depend on the abutting phase. For example, silica rich amorphous layer present in SiN, is about 10 Å thick, but for special boundaries this equilibrium thickness is zero. Complexion can be grouped in 6 categories, according to their thickness: monolayer, bilayer, trilayer, nanolayer (with equilibrium thickness between 1 and 2 nm) and wetting. In the first cases the thickness of the layer will be constant; if extra material is present it will segregate at multiple grain junction, while in the last case there is no equilibrium thickness and this is determined by the amount of secondary phase present in the material. One example of grain boundary complexion transition is the passage from dry boundary to biltilayer in Au-doped Si, which is produced by the increase of Au.