Hume-Rothery rules, named after William Hume-Rothery, are a set of basic rules that describe the conditions under which an element could dissolve in a metal, forming a solid solution.
However, this approach limits assessing advanced alloys which are commonly multicomponent systems.
Where they are being considered as critical contact criterion describable with Voronoi diagrams.
[8] This could ease the theoretical phase diagram generation of multicomponent systems.
For alloys containing transition metal elements there is a difficulty in interpretation of the Hume-Rothery electron concentration rule, as the values of e/a values (number of itinerant electrons per atom) for transition metals have been quite controversial for a long time, and no satisfactory solutions have yet emerged.