---
title: "Solid solutions and solid-solution strengthening"
subject: "Material Science"
chapter: 5
key: "semester_3/material_science:solid-solution-strengthening"
source: https://www.bctengineer.com/q/semester_3/material_science/solid-solution-strengthening
site: BCT Engineering
---

# Solid solutions and solid-solution strengthening

Material Science · Chapter 5: Solidification, Phase Relations and Strengthening Mechanism

- Asked in: year not given, 5 marks
- Video: [Solid solution hardening](https://www.youtube.com/watch?v=14WeQp_UfNo) — Introduction to Materials Science and Engineering
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/material_science/solid-solution-strengthening
- Whole chapter: https://www.bctengineer.com/md/semester_3/material_science/chapter-5

## Question

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

## 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.

## Answer

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.

| Basis | Substitutional | Interstitial |
|---|---|---|
| Position of solute | Replaces solvent atom at lattice site | Sits in voids between solvent atoms |
| Size of solute | Similar to solvent (within 15%) | Much smaller (radius ratio below 0.59) |
| Examples | Cu-Ni, Cu-Zn (brass) | C, N, H, O in iron |
| Solubility | Can be complete | Limited |

#### 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.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Which solute forms interstitial solutions in iron?
   A. Cu
   B. Ni
   C. C, N, H, O
   D. Cr
   Answer: C. Small atoms occupy voids. (Key point: Interstitial)

2. Which is a Hume-Rothery rule?
   A. Atomic sizes differ by less than ~15%
   B. Different crystal structures
   C. Very different electronegativity
   D. Size mismatch over 50%
   Answer: A. Size within 15%, same structure, similar electronegativity and valency. (Key point: Hume-Rothery)

3. Why does solid-solution strengthening occur?
   A. Solute removes dislocations
   B. Solute distorts lattice; stress fields hinder dislocations
   C. Grains grow
   D. Conductivity rises
   Answer: B. Dislocations interact with stress fields. (Key point: Strengthening)

4. Solid solution strengthening effect on ductility/conductivity:
   A. Both increase
   B. Ductility up
   C. Both decrease
   D. No change
   Answer: C. Strength rises, ductility and conductivity fall. (Key point: Effect)

## Related in other subjects

- [Geotechnical problems and their solutions](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Ageotechnical-problems-solutions) — Soil Mechanics, chapter 1, asked 2×
- [Climate change causes, impacts and solutions for LDC](https://www.bctengineer.com/question.md?key=semester_7%2Ftechnology_environment_and_society%3Acc-solution-ldc) — Technology, Environment and Society, chapter 6
- [Case study: feasibility, drawbacks, convincing](https://www.bctengineer.com/question.md?key=semester_5%2Finstrumentation_ii%3Acs-2072kartik-feasibility) — Instrumentation II, chapter 10