Thermal Expansion
Thermal expansion is the change in a material's dimensions with temperature. For small changes, the length of a solid changes as ΔL = αL0ΔT, where α is the linear expansion coefficient, and volume changes as ΔV = βV0ΔT, with β ≈ 3α for isotropic solids. It arises microscopically from the asymmetry (anharmonicity) of the potential between atoms.
Curious
Heat makes atoms vibrate more vigorously, and because pushing atoms together is harder than pulling them apart, their average spacing grows: the material expands. The effect is small for solids, but over long distances it adds up, so engineers leave expansion joints in bridges, pipelines and railways.
Thermometers rely on it (liquid in a glass tube), and so do bimetallic strips in older thermostats, which bend because two bonded metals expand by different amounts. Water is a famous exception: between 0 °C and about 4 °C it contracts as it warms, which is why ice floats and lakes freeze from the top (see Temperature).
Exploring
| Material | α (10−6 K−1, near 20 °C) |
|---|---|
| Invar (Fe–Ni alloy) | ~1.2 |
| Fused silica glass | ~0.55 |
| Steel | ~11–13 |
| Copper | ~17 |
| Aluminium | ~23 |
| Water (volume β) | ~210 (at 20 °C; negative below 4 °C) |
Deep Dive
Microscopic origin. If the interatomic potential were perfectly harmonic (symmetric), increased vibration would not change the average spacing and there would be no thermal expansion (see Quantum Harmonic Oscillator). Anharmonicity, the steeper repulsive wall versus the gentler attractive tail, shifts the mean position outward as amplitude grows. Grüneisen's relation, β = γGCVκT/V, links expansion to heat capacity and compressibility, which explains why α follows the heat capacity's T³ fall at low temperature (see Specific Heat Capacity).
Anomalies. Water's density maximum at 3.98 °C comes from its hydrogen-bonded open structure. Some materials have negative thermal expansion over wide ranges (zirconium tungstate, ZrW2O8, from near 0 K to about 1,050 K) because of low-energy vibrational modes that pull the structure inward. Invar's near-zero expansion, discovered by Charles-Édouard Guillaume, arises from magnetic effects that compensate the normal lattice expansion; Guillaume received the 1920 Nobel Prize in Physics for it (see Ferromagnetism).
Earth system. Warming ocean water expands, and thermal expansion has been a major contributor to observed global mean sea-level rise, alongside meltwater from glaciers and ice sheets; IPCC assessments quantify the relative contributions with stated uncertainty ranges, and the balance between them has shifted over recent decades.
Concept Relationship Map
Requires: temperature, interatomic forces
Enables: thermometry, thermal stress, engineering design
Commonly confused with: holes shrinking on heating
Sources
- Grüneisen, E. (1912). Annalen der Physik, 344, 257–306.
- Mary, T.A., Evans, J.S.O., Vogt, T., Sleight, A.W. (1996). “Negative Thermal Expansion from 0.3 to 1050 Kelvin in ZrW2O8.” Science, 272, 90–92.
- Kittel, C. (2004). Introduction to Solid State Physics (8th ed.). Wiley.