Thermal Mode Spectroscopy for Thermal Diffusivity of Millimeter-Size Solids

Heat conduction possesses (thermal) modes in analogy with acoustics even without oscillation. Here, we establish thermal mode spectroscopy to measure the thermal diffusivity of small specimens. Local heating with a light pulse excites such modes that show antinodes at the heating point, and photothermal detection at another antinode spot allows measuring relaxation behavior of the desired mode selectively: The relaxation time yields thermal diffusivity. The Ritz method is proposed for arbitrary geometry specimens. This method is applicable even to a diamond crystal with $\sim 1\mathrm{mm}$ dimensions.

Figure 1

Thermal modes of the aluminum triangular pyramid. The Ritz method was used to calculate the relaxation time and corresponding temperature distribution of the tetrahedron with the dimensions in Table 1. (a) Schematic of the specimen shape. Dimensions $a$, $b$, and $c$ are shown in Table 1. (b)–(i) Distributions of the absolute value of the temperature change on the inclined plane from modes 1 to 8.

Figure 2

Numerical simulation of a surface-temperature change caused by a heat pulse. The heat pulse is applied (a) on the center of the edge side along the $x_2$ axis and (b) on the surface center, and temperature evolutions at characteristic points (shown in the upper illustrations with red circles) are shown. The green broken lines indicate the solution of the bulk diffusion. The relaxation-time values determined by fitting the exponential function to the simulated data are shown. The mode figures are also shown. $\mathrm{\Delta }T(t)=T(t)-T(0)$ denotes the temperature change.

Figure 3

Mode-selective measurements. (a) Relaxation curves for mode 3 and mode 6 of the aluminum tetrahedron in Table 1. Broken lines are relaxation curves calculated by the Ritz method. (b) Comparison between measured (solid lines) and theoretical (broken lines) relaxation curves of the ${\tau }_{100}$ and ${\tau }_{200}$ modes for the monocrystal diamond in Table 1. The mode figures for the temperature change and excitation and detection points are illustrated. The oscillations in the relaxation curves are background signals caused by the laser-power fluctuation in the probe light, which appeared irregularly.