Dependence of Heat Transport in Solids on Length-Scale, Pressure, and Temperature: Implications for Mechanisms and Thermodynamics

Accurate laser-flash measurements of thermal diffusivity (D) of diverse bulk solids at moderate temperature (T), with thickness L of ~0.03 to 10 mm, reveal that D(T) = D&infin
(T)[1 &minus
exp(&minus
bL)]. When L is several mm, D&infin
(T) = FT&minus
G + HT, where F is constant, G is ~1 or 0, and H (for insulators) is ~0.001. The attenuation parameter b = 6.19D&infin
&minus
0.477 at 298 K for electrical insulators, elements, and alloys. Dimensional analysis confirms that D &rarr
0 as L &rarr
0, which is consistent with heat diffusion, requiring a medium. Thermal conductivity (&kappa
) behaves similarly, being proportional to D. Attenuation describing heat conduction signifies that light is the diffusing entity in solids. A radiative transfer model with 1 free parameter that represents a simplified absorption coefficient describes the complex form for &kappa
(T) of solids, including its strong peak at cryogenic temperatures. Three parameters describe &kappa
with a secondary peak and/or a high-T increase. The strong length dependence and experimental difficulties in diamond anvil studies have yielded problematic transport properties. Reliable low-pressure data on diverse thick samples reveal a new thermodynamic formula for specific heat (&part
ln(cP)/&part
P = &minus
linear compressibility), which leads to &part
ln(&kappa
)/&part
P = linear compressibility + &part
ln&alpha
/&part
P, where &alpha
is thermal expansivity. These formulae support that heat conduction in solids equals diffusion of light down the thermal gradient, since changing P alters the space occupied by matter, but not by light.