Thermal Excitations and Helium 3 Crystallization

Abstract

The main reason for studying the crystallization of helium is that, at low temperature, its two isotopes can be made very pure and diffusion problems in bulk phases can be neglected. Then, the dissipation which limits the growth rate takes place at the moving liquid-solid interface, and some information on the crystallization processes can be obtained. The one fact that thermal excitations are different in helium 4 and in helium 3 makes the crystallization of these two quantum systems rather different from one another. Helium 4 was studied some years ago. In helium 3, recent experiments and theoretical articles show that the growth rate is maximum at T_m = 0.32 K where the latent heat vanishes and the growth is isothermal. Below T_m, a temperature difference usually develops between the liquid and the crystal, and the growth rate is much smaller, as a consequence of the necessary flow of a large latent heat through the Kapitza resistance of the liquid-solid interface. This Kapitza resistance is smaller than previously thought, because of the good coupling between transverse modes in the (Fermi) liquid and transverse phonons in the solid. The latent heat is released on the liquid side of the interface, and the intrinsic (or isothermal) growth rate is found to be limited by the momentum exchanges during the reflection of (Fermi) quasiparticles by the crystal lattice.