The effect of heat flow and nonhydrostatic strain on the surface of helium crystals

Abstract

Experiments to measure the kinetic coefficients of the helium crystal surface, which have been criticized by Grabinski and Liu,1 are analyzed to determine the effect of heat flow through the surface and the effect of nonhydrostatic crystal strain. The experiments studied are the low-temperature measurements of the damping of melting-freezing waves in4He, the high-temperature relaxation of the4He crystal surface after an electrostatic disturbance, the relaxation in shape of a3He crystal, and the measurement of the Onsager cross-coefficient using a heat current in4He. After a review of the theory, in which the dependence of the growth coefficient on the thermal conditions of the experiment is discussed, the corrections to published results due to heat flow are shown to be small and within the experimental errors. The effect of nonhydrostatic strain is shown to be second order and consequently negligible in most existing measurements of kinetic or static properties. However, if sufficiently large, nonhydrostatic strain produces an instability of the surface that was predicted by Grinfeld.7 This effect may explain a corrugation of the surface observed by Bodensohn et al.9 during rapid cooling. The threshold for the Grinfeld instability and the frequency and damping of melting-freezing waves below the threshold is discussed. We propose a new experiment to study the instability and to measure the elastic and plastic properties of the crystal.