Theory of the kinetic coefficients of the atomically rough surface of 4He crystals

The growth coefficient K (the velocity of growth per unit chemical potential difference) and the Onsager cross-coefficients b1 and b2, coupling growth and heat flow, are calculated for atomically rough surfaces of hcp 4He crystals. The calculation is based on the premise, suggested by Andreev and Parshin, that growth is limited by the collision of phonons and rotons with the interface. The calculated K is compared with that obtained by Keshiskev et al. from the damping of melting-freezing waves. The theory assumes that the excitations are in the ballistic regime where their mean free path is large compared to the wavelength of the melting-freezing waves. In the experiment only the phonons satisfy this condition, yet the theory agrees with the data even when roton scattering is important Irreversible thermodynamics requires that the cross coefficients b1 and b 2 be equal. This is shown by direct calculation. The value of b1 and b2 depends on the ratio of two integrals over the phonon transmission coefficient and it is evaluated for two models of the transmission. The theory agrees fairly well with a recent measurement of b1. A calculation of the dissipation in the hydrodynamic regime, where the free path is short, shows that the damping of melting-freezing waves should have a different dependence on frequency compared to the ballistic regime.

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