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Thermal properties of materials

What is the main cause of solids expanding when heated (thermal expansion)?

  1. AThe interatomic potential is asymmetric (anharmonic), so as the vibration amplitude grows, the average distance between atoms increases
  2. BThe interatomic potential is parabolic (harmonic), and both the vibration amplitude and the average interatomic distance grow with temperature
  3. CAs temperature rises, the atoms themselves become larger
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Answer: A. The interatomic potential is asymmetric (anharmonic), so as the vibration amplitude grows, the average distance between atoms increases

The interatomic potential has an asymmetric shape: repulsion rises steeply as atoms approach, while on the separating side the attraction weakens gradually. As temperature rises and the vibration amplitude grows, atoms swing farther toward the separating side, so the average interatomic distance, the center of the vibration, increases, and this is thermal expansion. If the potential were parabolic (a harmonic oscillator), the vibration would remain symmetric about the equilibrium position however large the amplitude, so the average distance would not change and no thermal expansion would occur. The size of the atoms themselves (the extent of their electron clouds) hardly changes with temperature. Anharmonicity is also the cause of phonon-phonon scattering, which is connected to thermal conductivity having a finite value.

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