The Hume-Rothery Rules, Conditions for Unlimited Solid Solubility
In order for an alloy system, such as copper-nickel to have unlimited solid solubility, certain conditions must be satisfied. These conditons, the Hume-Rothery rules, are as follows:
• size factor: the atoms must be of similar size, with no more than 15% difference in atomic radius, in order to minimize the lattice strain.
• crystal structure: the materials must have the same crystal structure; otherwise, there is some point at which a transition occurs from one phase to a second phase with a different structure.
• valence: the atoms must have the same valence; otherwise, the valence electron difference encourages the formation of compounds rather than solutions.
• electronegativity: the atoms must have approximately the same electronegativity. If the electronegativities differ significantly, compounds again form — as when sodium and chlorine combine to form sodium chloride.
Hume-Rothery's conditions must be met, but they are not necessarily sufficient, for two metals to have unlimited solid solubility.
Similar behavior is observed between certain compounds, including ceramic materials. The solubility of interstitial atoms is always lmited. Interstitial atoms are much smaller than the atoms of the host element, thereby violating the first of Hume-Rothery's conditions.