Low-Temperature Specific Heat of ⁴He Films in Restricted Geometries

Abstract

Confinement of superfluid helium to a system of random small (~ 100Å) pores markedly affects its properties, as was demonstrated by Pobell et al.¹; they observed the oscillations of superfluid helium in a U tube filled with tightly packed lampblack or porous Vycor glass and noted a large increase in the normal fluid density over that of the bulk. At low temperatures they saw a linear dependence of ρ _n on T in contrast to the bulk T ⁴ dependence derived from other experiments. Padmore² proposed a model for long-wavelength phonons in a “zero-dimensional geometry” that gave a linear temperature dependence and a constant heat capacity at low temperatures given by

$$C = (V/{d^3}){k_B}$$

where V is the total volume of the He II in the porous system, d is the average pore diameter, and k _B is Boltzmann’s constant. Heat capacity measurements on helium in disordered, restricted geometries have been made by other workers, but they have only been made at temperatures greater than 0.5°K, which is too high to test Padmore’s prediction. These measurements have also been done on partially filled pores and have pointed out interesting properties of helium films under these conditions.

Work supported in part by the National Science Foundation through Grant No. GP-27736 and also under Grant No. GH-33637 through the Cornell Materials Science Center, Report No. 1861. This work also received support from the U.S. Atomic Energy Commission under contract AT (11-1)-3151, Technical Report No. COO-3151-10.