  A systematics of grain boundary (GB) segregation transitions and critical
phenomena has been derived to expand the classical GB segregation theory. This
study uncovers when GB layering vs. prewetting transitions should occur and how
they are related to one another. Moreover, a novel descriptor, normalized
segregation strength, is introduced. It can represent several factors that
control GB segregation, including strain and bond energies for both general and
small-angle GBs, as well as misorientation for small-angle GBs, which had to be
treated separately in prior models. In a strong segregation system with a large
normalized segregation strength, first-order layering transitions occur at low
temperatures and become continuous above GB roughing temperatures. With
reducing normalized segregation strength, the layering transitions gradually
merge and finally lump into prewetting transitions without quantized layer
numbers, akin to Cahn's critical-point wetting model. Furthermore, GB
complexion diagrams with universal characters are constructed as the GB
counterpart to the classical exemplar of Pelton-Thompson regular-solution
binary bulk phase diagrams.
