Questions: Thermal Properties of Materials

Question 1

An engineer selects a material for a heat sink that must rapidly conduct heat away from a processor. She considers copper, alumina (Al₂O₃ ceramic), and polyethylene. Which should she choose, and why?

• A. Alumina — ceramics are denser and absorb heat more effectively than metals
• B. Polyethylene — polymers have high specific heat so they store the most energy per kilogram
• C. Copper — metals have free electrons that serve as efficient heat carriers, giving thermal conductivity orders of magnitude higher than ceramics or polymers
• D. Alumina — it has a higher melting point than copper, so it survives high processor temperatures better

Answer: (C)

Thermal conductivity depends on the dominant heat carrier. In metals, free electrons carry thermal energy (the same electrons that carry electrical current), giving copper ~400 W/m·K. Ceramics like alumina rely on phonon transport — quantized lattice vibrations that scatter more readily than electrons — giving ~30 W/m·K. Polyethylene relies on even weaker phonon coupling through van der Waals chains, giving ~0.5 W/m·K. For a heat sink the goal is high conductivity to move heat fast, not high heat capacity to store it.

Question 2

A steel shaft is fitted with a ceramic sleeve in a precision instrument. After repeated thermal cycling, cracks appear at the steel-ceramic interface. What is the most direct cause?

• A. The ceramic fatigues more quickly than steel because it is less ductile
• B. Steel has a higher thermal conductivity, so it heats and cools faster than the ceramic, creating a temperature gradient
• C. Steel and ceramics have different thermal expansion coefficients — when heated, each tries to expand by a different amount but is constrained by the other, generating shear stress at the interface
• D. Ceramics have higher heat capacity than steel, so they store more thermal energy and retain stress after cycling

Answer: (C)

Thermal stress at a bonded interface arises from expansion coefficient mismatch: σ ≈ E · Δα · ΔT. Steel has a thermal expansion coefficient of ~12 × 10⁻⁶ /°C; many structural ceramics are ~6-8 × 10⁻⁶ /°C. When the assembly heats up, steel wants to expand about twice as much but is constrained by the bonded ceramic. The resulting interfacial shear stress accumulates with each thermal cycle until it exceeds the bond or material strength. This is why matching thermal expansion coefficients is a critical design constraint in solder joints, turbine coatings, and glass-to-metal seals.

Question 3

Diamond has higher thermal conductivity than copper despite being an electrical insulator, because its extremely stiff covalent bonds allow phonons to propagate very rapidly with minimal scattering.

• T. True
• F. False

Answer: True

This is the most important exception to the 'metals are the best thermal conductors' rule. Diamond's thermal conductivity (~2000 W/m·K) is roughly five times higher than copper's (~400 W/m·K). Because diamond has no free electrons, its only heat carrier is phonons. However, the C-C covalent bond is among the stiffest in nature, and the low atomic mass of carbon produces phonons with very high velocity and long mean free path (little scattering). These two effects combine to give diamond exceptional phonon-mediated thermal conductivity — demonstrating that the mechanism (electron vs. phonon) does not predetermine the result; the quality of the phonon transport is what matters.

Question 4

Materials with high thermal conductivity typically also have high electrical conductivity, because both properties rely on the same microscopic carriers.

• T. True
• F. False

Answer: False

The Wiedemann-Franz law states that thermal and electrical conductivity track together in metals — because in metals, the same free electrons carry both. But this relationship breaks down for non-metals. Diamond is the definitive counterexample: it has the highest thermal conductivity of any known material but is an excellent electrical insulator with essentially zero free electrons. Its thermal conductivity comes from phonons, not electrons. The general rule (metals conduct both well; insulators conduct neither well) has real exceptions because the two properties have different microscopic mechanisms.

Question 5

Why do ceramics and polymers generally have much lower thermal conductivity than metals, and what physical mechanism is responsible for the difference?

Model answer: In metals, free electrons are the dominant heat carriers. Electrons move rapidly through the lattice and can transport thermal energy efficiently across macroscopic distances, giving metals thermal conductivities typically in the range of 10–400 W/m·K. Ceramics and polymers are electrical insulators with no free electrons, so they must rely on phonons — quantized lattice vibrations — as their only heat carriers. Phonons scatter at grain boundaries, defects, and lattice irregularities more readily than electrons, and their group velocities are generally lower. This makes phonon transport much less efficient, giving ceramics typically 1–30 W/m·K and polymers below 1 W/m·K. Diamond is the exception: its exceptionally stiff bonds and low atomic mass create unusually fast, long-range phonons despite having no free electrons.

Understanding the carrier type (electrons vs. phonons) is the key to predicting and designing thermal behavior across material classes. It explains why a metal heat sink outperforms a ceramic one of identical geometry, and why strategies to improve ceramic thermal conductivity focus on reducing phonon scattering (e.g., single-crystal growth, reducing defect density).