Hume-Rothery rules

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The Hume-Rothery rules are a set of basic rules describing the conditions under which an element could dissolve in a metal, forming a solid solution. There are two sets of rules, one which refers to substitutional solid solutions, and another which refers to interstitial solid solutions.

[edit] Substitutional Solid Solution Rules

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

1. The atomic radii of the solute and solvent atoms must differ by no more than 15%:

$% \mbox{ difference} = \left ( \frac{(r_{solute} - r_{solvent})}{r_{solvent}} \right ) * 100 \le 15%$

2. The crystal structures of solute and solvent must match.

3. Maximum solubility occurs when the solvent and solute have the same valency. Metals with lower valency will tend to dissolve metals with higher valency.

4. The solute and solvent should have similar electronegativity. If the electronegativity difference is too great, the metals will tend to form intermetallic compounds instead of solid solutions.