Leading scientists working in the field of thermal properties of materials have recently emphasized that we have only one true thermal transport coefficient, namely thermal conductivity. Their rationale is that only thermal conductivity gives a measure of the extent to which a certain material can transport thermal energy. This in turn has implications for how to properly approach thermal diffusivity, which would by the same token not be referred to as a thermal transport property. Indeed, an interesting consequence of the axiom is that neither thermal diffusivity nor the recently much-discussed thermal effusivity would be considered thermal transport properties. The reason being that it is necessary to know the volumetric specific heat in order to calculate the thermal conductivity from measurements of thermal diffusivity and thermal effusivity.
The optical method called Laser Flash was first described by Parker et al in J. Appl. Phys. 32, 1679 in 1961. Most measurements of thermal diffusivity of solid materials over large temperature ranges have since then been produced by this method. However the obvious short-coming of this method is that a separate measurement must be made of the volumetric heat capacity if information on the thermal conductivity is required.
One should however note that it is possible to obtain both the thermal conductivity and the thermal diffusivity from a single transient recording through the Transient Plane Source (Hot Disk) method – as described in the international standard ISO 22007-2 of 2008. As the volumetric specific heat is simply the ratio between thermal conductivity and thermal diffusivity, the Hot Disk method has since become perhaps the most trusted experimental method for measuring the volumetric heat capacity of comparatively large volumes of homogeneous solids. This was demonstrated by Taylor et al. at the Cavendish laboratory in their technical report from 2019, in which they measure the heat capacity over a temperature range from 25 K to 300 K.
The issue of an experimental method for determining thermal effusivity has been vigorously debated of late. The 2022 International Thermal Conductivity Conference in Lowell, Massachusetts, organized a special workshop to deal with this issue. Voices were raised that the scientific community should abandon measurements of thermal effusivity outright. However, whatever views one may hold on the matter, one should not abandon the possibilities of obtaining information on thermal transport, including thermal effusivity, provided the quantity can be measured in a reliable manner. Matters have been moving fast since 2022 and now, we have an international standard on the measurement of thermal effusivity – ISO 22007-7 – employing the TPS (Hot Disk) arrangement.
A few words here on the measurement of thermal effusivity. When solving the thermal conduction equation, assuming an infinitely long and thermally insulated rod, divided into two parts by a plane heating and sensing probe between the two mating surfaces, the solution for the one-dimensional heat flow will show a simple time dependence. From the slope of temperature recordings versus the square root of time, a constant is obtained, which is the square root of the product of the thermal conductivity and the volumetric heat capacity. This constant was denoted “b” in the classic study Conduction of Heat in Solids (1959) by H.S. Carslaw and J.C. Jaeger. If the volumetric heat capacity is known, we can consequently calculate the thermal conductivity of the rod material via the thermal effusivity.
A different way to use the TPS (Hot Disk) method is to place a Hot Disk probe between two plane surfaces of a substrate, with a diameter somewhat larger than the diameter of the probe. One then performs an experiment, which is aborted so that the probing depth is kept below a small fraction of the probe radius. In this way one can avoid the need to thermally insulate the rod-shaped substrate. It can also be mentioned here that probes, which deviate in design from the Hot Disk probe, have of late been introduced and denoted MTPS (Modified Transient Plane) probes. The limitations of the so-called MTPS probe method (which is, strictly speaking, not a TPS method, nor in alignment with ISO 22007-2 or 7) in determining the thermal effusivity have been critically investigated by S. Yeon and D.G. Cahill in Rev. Sci. Instrum. 95(3) 10.1063/ 5.0191859.
A unique facility, related to the measurement of thermal effusivity with a TPS method, is the possibility to obtain both the thermal diffusivity and the thermal conductivity in the through-plane direction, related to the plane of the probe. In all other probe measurements – using isotropic, anisotropic or slab configurations – the thermal diffusivity is determined in the in-plane direction.
Silas Gustafsson, Ph.D.
Inventor of the TPS technique,
Hot Disk AB Co-founder and Senior Advisor.