Role of fluttering dislocations in the thermal interface resistance between a silicon crystal and plastic solid He4

Abstract

A quantum solid (solid 4 He) in contact with a classical solid defines a new class of interfaces. In addition to its quantum nature, solid 4 He is indeed a very plastic medium. We examine the thermal interface resistance upon solidification of superfluid 4 He in contact with a silicon crystal surface (111) and show that dislocations play a crucial role in the thermal interface transport. The growth of solid 4 He and the measurements are conducted at the minimum of the melting curve of helium (0.778 K and ∼25 bar). The results display a first-order transition in the Kapitza resistance from a value of R K,L = (80 ± 8) cm 2 K/W at a pressure of 24.5 bar to a value of R K,S = (41.7 ± 8) cm 2 K/W after the formation of solid helium at ∼25.2 bar. The drop in R K,S is only of a factor of ∼2, although transverse phonon modes in solid 4 He now participate in heat transmission at the interface. We provide an explanation for the measured R K,S by considering the interaction of thermal phonons with vibrating dislocations in solid 4 He. We demonstrate that this mechanism, also called fluttering, induces a thermal resistance R F l ∝ N d T −6 , where T is the temperature and N d is the density of dislocations. We estimate that for dislocation densities on the order of ∼10 7 cm −2 , R F l predominates over the boundary resistance R K,S. These fundamental findings shed light on the role of dislocations and provide a quantitative explanation for previous experiments which showed no measurable change in the Kapitza resistance between Cu and superfluid 4 He upon solidification of the latter. This demonstrates the possibility of using dislocations as an additional means to tailor thermal resistances at interfaces, formed especially with a plastic material.