Three related quantities
Heat behavior in a solid is described by several properties that are easy to confuse.
- Thermal conductivity says how readily heat flows through the material under a temperature difference.
- Specific heat capacity says how much energy is needed to raise the temperature of a given mass by one degree.
- Thermal diffusivity says how fast a temperature change spreads through the material. It combines the other two.
The relationship is straightforward: conductivity equals diffusivity multiplied by density multiplied by specific heat capacity. This matters in practice because diffusivity is often the easiest quantity to measure directly, and conductivity is then calculated from it using separate measurements of density and heat capacity.
The laser flash method
The most widely used technique for diffusivity is the laser flash method. A thin, flat disc of the material is held at a chosen temperature. One face is struck by a very short pulse of energy, from a laser or a flash lamp, and a detector watches the temperature of the opposite face. The back face warms with a delay that depends on how fast heat crosses the sample.
The thicker the sample or the slower the material, the longer the delay. A simple analysis relates the time for the back face to reach half of its maximum temperature rise to the diffusivity and the thickness. Real analyses apply corrections for heat lost from the sample and for the finite length of the pulse.
Because the experiment is quick, it can be repeated across a range of temperatures, which gives the trend of heat transport from room temperature to high temperatures. This is valuable for materials used in furnaces and engines.
Other approaches
Several other methods suit particular situations.
- Steady-state methods impose a known heat flow through a sample and measure the temperature difference. They are conceptually direct and work well for materials with moderate conductivity, but they need good control of heat losses and take longer.
- Transient hot-wire and hot-disc methods use a heater-sensor placed in or on the sample. They are common for bulk materials and powders.
- Differential scanning calorimetry is used to measure specific heat capacity by comparing the heat needed to warm the sample and a reference.
- Thermal expansion is measured separately with a dilatometer, which tracks length changes as the sample is heated. This is the key input for matching thermal expansion in assemblies.
- Thin-film techniques use optical pulses to probe films a few micrometers thick or less, where the laser flash method does not work.
Why samples of the same material differ
Anyone comparing published thermal values quickly notices that the numbers vary. Several genuine reasons explain this.
Purity and structure. In a very good conductor such as diamond, heat is carried by lattice vibrations, and these are scattered by defects, impurities and grain boundaries. Nitrogen impurities, isotopic makeup and boundaries between crystals can all lower the measured value. Single crystals, polycrystalline films and composites therefore differ, even though all are labeled diamond. The underlying reasons are discussed under thermal conductivity.
Porosity and density. Pores interrupt heat flow. Ceramic parts with different amounts of leftover porosity from sintering will not conduct equally.
Direction. Fiber composites and layered films are anisotropic. Heat may travel readily along the fibers or along a film and poorly through its thickness.
Temperature. Most solids change their conductivity with temperature, so a single number is meaningful only with its test temperature.
Surface and interfaces. In a coating on a substrate, the interface between them adds thermal resistance. The measured result for a layered sample reflects both layers and the boundary.
Sources of error in the measurement itself
Even a well-chosen method has pitfalls. Sample thickness must be accurately known and uniform. Very reflective or transparent samples may need a thin absorbing coating (often graphite) so that they absorb the pulse and emit a measurable signal, and that coating contributes its own small effect. Heat losses, pulse shape and detector response all need correction. For high-conductivity samples, the temperature rise at the back can be so rapid that thin discs push the limits of the timing electronics.
Using thermal data wisely
For designers of heat spreaders, thermal interface materials and furnace linings, a thermal number is a starting point. Whether it applies to a real part depends on how closely the tested sample matched the part in composition, structure and temperature. Where performance is critical, measurements on representative samples or on the finished component are worth asking for.