Instabilities of the liquid solid interface

Bodensohn et al.¹ observed that a sudden temperature change of the liquid above 1.1 K caused the interface between solid and liquid⁴He to become corrugated; they proposed that the instability of the interface was caused by the introduction of a heat current induced by the temperature gradient. Subsequently Grinfeld² showed that a non hydrostatic stress of the crystal could cause an instability; this idea was put forward by Balibar, Edwards and Saam³ to explain the observation of Bodensohn et al. A more detailed analysis has been given recently by Bowley and Nozières⁴. The two causes of instability are analyzed in the present paper for both normal³He and superfluid⁴He. The phase diagram and critical heat current for normal³He are presented. The corrugations will appear most rapidly near the minimum of the melting curve at 0.32 K and need a temperature gradient of order a few µK/cm. For superfluid⁴He the inability of the liquid to support thermal conduction (heat is transported by second sound) changes the nature of the instability, with the result that dissipation at the interface becomes important. As a consequence only the Grinfeld instability is observable in practice so that corrugations appear with wavelength between 6 and 8 mm.