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Thermal properties of materials

Diamond is an electrical insulator, yet its thermal conductivity at room temperature is about 2000 W/(m·K), higher than that of copper (about 400 W/(m·K)). What is the main reason?

  1. ALight carbon atoms with strong covalent bonds give a high sound speed, and the heat-carrying phonons are scattered little
  2. BThe larger the band gap, the more conduction electrons are thermally excited, and these electrons carry the heat just as in metals
  3. CThe crystal contains a great many freely moving holes, which carry most of the heat just as conduction electrons do in metals
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Answer: A. Light carbon atoms with strong covalent bonds give a high sound speed, and the heat-carrying phonons are scattered little

In an insulator, heat is carried mainly by phonons, the waves of lattice vibration. Thermal conductivity is expressed as a product of the heat capacity C, the speed of sound v and the mean free path l, as in κ = (1/3)Cvl. Because diamond has light atoms and strong bonds, its Debye temperature is high, about 1900–2200 K, its speed of sound is large, and at room temperature phonons rarely scatter off each other, so l is long. As a result it reaches about 2000 W/(m·K), exceeding the roughly 400 W/(m·K) of copper. With a band gap as large as about 5.5 eV, diamond has almost no thermally excited electrons or holes at room temperature, so they do not carry heat. In metals such as copper, most of the heat is carried by conduction electrons.

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More Thermal properties of materials questions

  1. Using the Wiedemann–Franz law κ = LσT (Lorenz number L = 2.44×10⁻⁸ W·Ω/K²), which value is closest to the estimated thermal conductivity of copper with an electrical conductivity σ = 5.9×10⁷ S/m at 300 K?
  2. The thermal conductivity of pure copper at room temperature is about 400 W/(m·K), but in brass with about 30% zinc in solid solution it drops to about 120 W/(m·K). What is the main reason?
  3. The lattice thermal conductivity of an insulating single crystal decreases roughly in proportion to 1/T as temperature rises, at temperatures comparable to or above the Debye temperature. What is the main reason?
  4. For silicon (density 2330 kg/m³, specific heat 700 J/(kg·K)), take the room-temperature thermal conductivity as 150 W/(m·K) and the average phonon speed as 6000 m/s. Estimating the phonon mean free path l from κ = (1/3)Cvl, which has the same form as in the kinetic theory of gases (C is the heat capacity per unit volume), which value is closest?
  5. Which value is closest to the thermal diffusivity α = κ/(ρc) of aluminum (thermal conductivity 237 W/(m·K), density 2700 kg/m³, specific heat 900 J/(kg·K))?