A SELF-CONSISTENT ACOUSTICS MODEL OF INTERFACE THERMAL RESISTANCE

This paper develops an analytically tractable acoustics model of thermal resistance of interfaces between dissimilar materials. It shows that a consistent development of the concept that heat in dielectrics is carried by lattice vibrations inevitably leads to the conclusion that heat-carrying acoustic waves must obey the introduced principle of heat radiation instead of the Sommerfeld radiation condition used in acoustics. The principle of heat radiation is adequate to the nature of thermal vibrations, and it provides more channels for coupling between waves propagating in contacting media than is allowed by the conventional acoustics model. Another distinctive feature of the approach to heat transport presented here is the systematic use of the introduced parametrization of thermal vibrations in terms of four random parameters with certain statistical characteristics. Using this parametrization we get an explicit description of ensembles of thermal vibrations with nonvanishing heat flux, which appear to be different from equilibrium ensembles described by the Bose-Einstein statistics. The important, but still auxiliary, results outlined above are used to derive an equation of compatibility that connects the heat flux and the temperatures on both sides of the interface. This equation makes it clear that a nonvanishing heat flux cannot be maintained at equal temperatures, and it provides a way of calculating the temperature differential corresponding to a given heat flux. The obtained numerical and qualitative results are in line with expectations.