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Write Hume-Rothery rules for the formation of alloys.

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Hint: The Hume-Rothery rules are named after William Hume-Rothery. They are a set of rules that govern whether an element will dissolve in a metal in order to form a solid solution.

Complete step by step answer:
The Hume-Rothery rules are named after William Hume-Rothery. They are a set of rules that govern whether an element will dissolve in a metal in order to form a solid solution. Since there can be substitutional solid solutions as well as interstitial solid solutions, therefore the rules will be different for each type of solid solution:
For substitutional solid solutions:
In substitutional solid solutions, the atoms of the host element are replaced by the atoms of another element. The Hume-Rothery rules for such alloys are:
- The difference between the atomic radius of the solute and the solvent atoms should not be greater than 15%.
- The crystal structure of the solute and the solvent elements should be similar.
- The solute atoms will be completely soluble in the solvent matrix if the solute and the solvent atoms have the same valency.
- For the formation of the solid solution (alloy) the electronegativities of the solute and the solvent atoms should be similar.
For Interstitial solid solutions:
In interstitial solid solutions, the atoms of an element occupy the interstitial site present in the host element crystal structure. The Hume-Rothery rules for such alloys are:
- The difference between the solute and the solvent atoms should be more than 15% such that the solute atoms are smaller than the solvent atoms.
- The electronegativities of the solute and the solvent atoms should be similar.
- The valency of the two elements should be similar or equal.
Hence the Hume-Rothery rules are explained.
Note: For the substitutional solid solutions, the probability for the solubility of a metal of higher valency with a metal of lower valency is greater. Also two different elements tend to form intermetallic compounds rather than substitutional solid solutions if the electronegativity difference between their atoms is large.