Hume-Rothery rules

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The 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[edit]

For substitutional solid solutions, the Hume-Rothery rules are:

1. The atomic radius of the solute and solvent atoms must differ by no more than 15%:
 \% \mbox{ difference} = \left ( \frac{r_{solute} - r_{solvent}}{r_{solvent}} \right ) \times 100\% \le 15\%.
2. The crystal structures of solute and solvent must match.
3. Complete solubility occurs when the solvent and solute have the same valency.[1] A metal dissolves in a metal of higher valency to a greater extent than in one of lower valency.
4. 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[edit]

For interstitial solid solutions, the Hume-Rothery rules are:

1. Solute atoms must be smaller than the interstitial sites in the solvent lattice.
2. The solute and solvent should have similar electronegativity.[2]


  1. ^ Foundations of Materials Science and Engineering, 4th ed., W. Smith and J. Hashemi, pp.139-140 (2006).
  2. ^ "Hume-Rothery Rules
    3. They should show a wide range of composition". Van Nostrand's Scientific Encyclopedia. John Wiley & Sons, Inc. 2002. 


Further reading[edit]

  • Mizutani, Uichiro (2010). Hume-Rothery Rules for Structurally Complex Alloy Phases. Taylor & Francis. ISBN 978-1-4200-9058-1.