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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.
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.
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