Challenges in Measuring the Thermal Conductivity of Conductors

Since 2010, I have been conducting research focusing on a power generation technology using conductors called thermoelectric conversion (sometimes referred to as energy harvesting), for which I build my own samples and measurement equipment. In this article, I will introduce the challenges I faced and the solutions I found during this research.

Measuring Thermoelectromotive Force

It is known that when a temperature difference exists across the ends of a conductor, a voltage proportional to that difference is generated. This is called thermoelectromotive force. The magnitude of the thermoelectromotive force is compared between samples by defining the electromotive force per 1°C temperature difference as the "Seebeck coefficient ( S )." To determine this S , a steady state is required where the sample's temperature and temperature difference have stabilized. Cutting corners here results in unnatural values, so the measurement continues until the temperature reaches a steady state. This is a patient measurement, taking nearly two hours for a single temperature plot.

Measuring Thermal Conductivity

Thermal conductivity is defined as the proportionality constant between heat flux density and the temperature gradient in Fourier's law. It is measured using a method called the "steady-state method," which is similar to the thermoelectromotive force measurement described above. The laser flash method, which differs from the steady-state method, is also commonly used for measuring thermal conductivity. The laser flash method is a technique for obtaining "thermal diffusivity" from the "thermal diffusion time," which is determined by analyzing the heat diffusion from the irradiated surface to the rear surface after heating one side of a flat-plate sample with a laser pulse. Ideally, thermal conductivity is calculated as "thermal diffusivity" × "specific heat capacity" × "density."

The Challenge

Until around February 2020, I was troubled by the constant discrepancy between the "thermal conductivity measured by the steady-state method" and the "thermal conductivity measured by the laser flash method." Despite measuring multiple samples, the thermal conductivity obtained was consistently higher with the "steady-state method" and lower with the "laser flash method." The difference in these values exceeded 20%. The equipment for the "steady-state method" was homemade, and the discrepancy was too large to be explained by the attachment of the electrodes.

"Why are the values so high...? I've already published the results. Maybe I should write a correction."

I was falling into self-doubt. However, when I consulted a fellow researcher at a meeting in February, he offered some welcome words: "It's a natural result. The laser flash method measures different values from the steady-state method." While the discrepancy in measurement results was not a problem to be solved by relying on others, his words were exactly what I needed to resolve my worries. This challenge and its resolution served as an opportunity to relearn something "fundamental": that experimental values obtained by understanding and verifying the principles and details of the equipment are trustworthy, even if they differ from others' reports.

Nature is honest, so let's conduct our experiments and measurements with confidence, always paying close attention to the underlying principles!