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Solid solutions and solid-solution strengthening

Short answer

A solid solution is a single-phase alloy with solutes dissolved in the solvent lattice. Substitutional solutes replace atoms (similar size); interstitial solutes fit in voids (much smaller). Hume-Rothery rules: <15% size difference, same crystal structure, similar electronegativity and valency. Lattice distortion by solute atoms impedes dislocation motion, strengthening the alloy.

What is a solid solution? Distinguish substitutional and interstitial solid solutions, state the Hume-Rothery rules and explain why solid-solution strengthening occurs.

A solid solution is a single-phase crystalline alloy in which solute atoms are dissolved in the lattice of the solvent (like sugar in water), with the solvent crystal structure retained.

BasisSubstitutionalInterstitial
Position of soluteReplaces solvent atom at lattice siteSits in voids between solvent atoms
Size of soluteSimilar to solvent (within 15%)Much smaller (radius ratio below 0.59)
ExamplesCu-Ni, Cu-Zn (brass)C, N, H, O in iron
SolubilityCan be completeLimited

Hume-Rothery rules (substitutional, extensive solubility)

  1. Atomic sizes differ by less than about 15%.
  2. Same crystal structure.
  3. Similar electronegativity (so no compound forms).
  4. Similar valency (a metal dissolves a higher-valency metal more readily than the reverse).

Strengthening

Solute atoms of different size distort the lattice and create stress fields around them. Dislocations interact with these fields, so more stress is needed to move them. Thus yield strength, tensile strength and hardness increase, while ductility and conductivity decrease. Strengthening rises with solute content and with the size mismatch. Example: 70/30 brass is stronger than pure copper; carbon in iron gives strong steel.

✓ Answer checked by Claude Opus 5.5 (high effort)

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