Thermal conductivity

Definition

Thermal conductivity is an intrinsic material property that quantifies how effectively heat is conducted through a substance due to a temperature gradient. It is commonly denoted by k (also λ or κ) and has SI units of W/(m·K). In continuum heat transfer, Fourier’s law describes the relation between heat flux and temperature gradient:

  • Vector form: q = −k ∇T, where q is heat flux (W/m²).
  • One-dimensional form for a slab: Q = −k A (dT/dx), where Q is heat rate (W), A is cross-sectional area, and dT/dx is the temperature gradient.

For a component of thickness L, the thermal conductance G and thermal resistance R_th are:

  • G = k A / L
  • R_th = L / (k A)

Key technical characteristics

  • Heat carriers and mechanisms:
    • Metals: heat is conducted mainly by electrons.
    • Ceramics and polymers: heat is carried predominantly by lattice vibrations (phonons).
    • Semiconductors: both electrons and phonons contribute, with relative importance depending on doping and temperature.
    • At very high temperatures or in porous/transparent media, thermal radiation can contribute to an effective conductivity.
  • Temperature dependence:
    • Metals typically show decreasing k with increasing temperature (increased electron scattering).
    • Many crystalline dielectrics show a peak in k at low temperature and decreasing k at higher temperatures (phonon–phonon Umklapp scattering).
    • Amorphous polymers often have low k with modest variation over common temperature ranges.
  • Anisotropy and tensor nature:
    • In oriented or layered materials (e.g., fiber composites, graphite, some polymers), k depends on direction; in such cases, conductivity is a second-rank tensor. In-plane k can be orders of magnitude higher than through-thickness k.
  • Composites and porous media:
    • Effective k depends on constituent properties, volume fractions, morphology, filler orientation, percolation, porosity, moisture, and especially interfacial thermal resistance (also called Kapitza resistance) between phases or across contacts.
  • Interfaces and contacts:
    • Real interfaces introduce significant contact resistance that can dominate the overall thermal path. It is mitigated by thermal interface materials (TIMs), surface flatness, contact pressure, and high-quality bonded or sintered joints.

Related properties and terms

  • Thermal resistivity: the reciprocal of k (useful for insulators).
  • Thermal conductance G and thermal resistance R_th: geometry-dependent measures for a specific part or stack, contrasted with the intrinsic property k.
  • Thermal diffusivity α = k / (ρ c_p): governs transient heat propagation (ρ is density, c_p is specific heat capacity).
  • Thermal effusivity e = sqrt(k ρ c_p): governs how a surface exchanges heat with its surroundings (relevant to touch temperature and surface thermal response).
  • Heat transfer coefficient h (W/(m²·K)): a surface/geometry parameter for convection and conduction at boundaries; distinct from bulk k but coupled in system models.
  • k-value or λ-value: common engineering shorthand for thermal conductivity.

Measurement and standards

  • Steady-state methods:
    • Guarded hot plate (e.g., ASTM C177) and heat flow meter (ASTM C518) for bulk materials and insulation.
    • Specific setups for through-plane resistance of TIM stacks (e.g., ASTM D5470).
  • Transient methods:
    • Laser flash analysis (ASTM E1461) measures thermal diffusivity; k is obtained via k = α ρ c_p.
    • Transient plane/line source methods (e.g., ISO 22007 series for polymers).
    • Specialized techniques (e.g., 3-omega) for thin films and microscale layers.

Results depend on temperature, humidity, sample preparation, density/porosity, and measurement direction; report conditions alongside k.

Typical room-temperature ranges (approximate)

  • Polymer foams: 0.02–0.05 W/(m·K)
  • Unfilled polymers: 0.1–0.4 W/(m·K)
  • Thermally conductive polymer composites: ~1–20 W/(m·K) (higher in-plane values possible with strong filler alignment)
  • Glass and low-k ceramics (e.g., silica glass): ~1–2 W/(m·K)
  • Alumina ceramics: ~20–30 W/(m·K)
  • Silicon carbide, aluminum nitride: ~120–180 W/(m·K)
  • Metals:
    • Steels: ~15–60 W/(m·K)
    • Aluminum: ~150–230 W/(m·K)
    • Copper: ~390–400 W/(m·K)
  • Carbon-based:
    • Graphite in-plane: ~300–1700 W/(m·K); through-thickness ~5–20 W/(m·K)
    • Carbon fibers (pitch-based, along fiber): up to hundreds of W/(m·K)
    • Diamond: ~2000–2500 W/(m·K)
  • TIMs and gap fillers (greases, gels, pads, cured elastomers): typically ~1–10+ W/(m·K); phase-change materials ~1–5 W/(m·K)

Factors that influence k

  • Composition, phase, and crystal structure; grain size and texture
  • Defects, impurities, and isotopic composition (notably in high-purity crystals)
  • Density, porosity, and moisture content
  • Filler type, size, loading, surface functionalization, and orientation (in composites)
  • Operating temperature and environment (including vacuum or gas fill in porous materials)
  • Sample thickness and characteristic dimensions (size effects can reduce k at micro/nanoscales due to boundary scattering)

Applications and design relevance

  • High-k materials are used to spread and remove heat (e.g., heat sinks, spreaders, cold plates, substrates, die attach, busbars).
  • Low-k materials provide insulation and thermal barriers (e.g., foams, aerogels, mica/ceramic papers, multilayer shields).
  • Accurate k data underpin thermal simulations and reliability assessments across electronics, energy systems, aerospace, building envelopes, and transportation.
  • Example: In electric vehicles, high-k components (heat spreaders, cooling plates, TIMs) aid battery, power electronics, and motor cooling, while low-k barriers and insulations help protect nearby components and manage thermal runaway risks.

Manufacturing and microstructure control

  • Metals: casting, rolling, and heat treatment manipulate purity, grain size, and texture to tailor k.
  • Ceramics: powder processing, sintering, densification, and grain-boundary control reduce thermal resistance.
  • Polymers and composites: extrusion, injection/compression molding, calendering, and additive manufacturing can align platelets or fibers to induce directional k; surface treatments improve filler–matrix coupling to lower interfacial resistance.
  • Lamination, impregnation, potting, and sintered/bonded interfaces create engineered heat paths and reduce contact resistance.

Notes for use

  • Specify k together with temperature, direction (if anisotropic), density/porosity, and measurement method.
  • Distinguish intrinsic k from system-level metrics (R_th, G, and h), and account for interface resistances when designing thermal paths.

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