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. There are two sets of rules; one refers to substitutional solid solutions, and the other refers to
interstitial solid solutions.
Substitutional solid solution rules
For substitutional solid solutions, the Hume-Rothery rules are as follows:
Complete
solubility occurs when the solvent and solute have the same
valency.[2] A metal is more likely to dissolve a metal of higher valency, than vice versa. [3][4][5]
The solute and solvent should have similar
electronegativity. If the electronegativity difference is too great, the metals tend to form
intermetallic compounds instead of solid solutions.
Interstitial solid solution rules
For
interstitial solid solutions, the Hume-Rothery Rules are:
Solute atoms should have a smaller radius than 59% of the radius of solvent atoms. [6][7]
Valency factor: two elements should have the same valence. The greater the difference in valence between solute and solvent atoms, the lower the solubility.
Solid solution rules for multicomponent systems
Fundamentally, the Hume-Rothery rules are restricted to binary systems that form either substitutional or interstitial solid solutions. However, this approach limits assessing advanced alloys which are commonly multicomponent systems. Free energy diagrams (or
phase diagrams) offer in-depth knowledge of equilibrium restraints in complex systems. In essence the Hume-Rothery rules (and
Pauling's rules) are based on geometrical restraints. Likewise are the advancements being done to the Hume-Rothery rules. Where they are being considered as critical contact criterion describable with
Voronoi diagrams.[9] This could ease the theoretical phase diagram generation of multicomponent systems.
For
alloys containing TM elements there is a difficulty in interpretation of the Hume-Rothery electron concentration rule as the e/a values for
transition metals have been quite controversial for a long time and no satisfied solutions have yet emerged.[10][11]
^Callister, William D.; Rethwisch, David G. (January 2018). Materials Science and Engineering: An Introduction (10th ed.). Wiley. p. 992.
ISBN978-1-119-40549-8.
^Foundations of Materials Science and Engineering, 4th ed., W. Smith and J. Hashemi, pp.139-140 (2006).
^Callister, William D.; Rethwisch, David G. (January 2018). Materials Science and Engineering: An Introduction (10th ed.). Wiley. p. 992.
ISBN978-1-119-40549-8.
^VALENCY EFFECTS AND RELATIVE SOLUBILITIES IN TRANSITION METAL ALLOYS D. A. Goodman* and L. H. Bennett National Bureau of Standards, Washington DC, 20234 R. E. Watson Brookhaven National Laboratory.