Heat pulse propagation by second sound in dielectric crystals

Abstract

A non-linear thermodynamic model describing heat pulse propagation in dielectric crystals at low temperature is proposed. This work is a generalization of those of Cattaneo and of Guyer and Krumhansl, and is complementary to an earlier paper (Lebon G, Torrisi M and Valenti A 1995 J. Phys.: Condens. Matter 7 1461), which was mainly devoted to a linear approach. The model is based on extended irreversible thermodynamics, and uses as field variables the temperature, the heat flux, and the flux of the heat flux. Unlike the simple phonon gas model, the present formalism is compatible with the experimental observation that second sound is temperature dependent. In this paper, explicit expressions for the internal energy and velocity of propagation of weak discontinuities are determined. By making use of experimental data for NaF and Bi, the values of the relevant parameters have been evaluated.