LXX. The thermal conductivity of solid helium at high densities

Thermodynamic properties and melting of solid helium

The melting properties and thermodynamic functions of solid helium have been determined at temperatures from 4 to 26° K and at pressures up to 3000 atm. The upper temperature corresponds to about five times the critical temperature of helium; it was therefore possible to measure properties of the solid state in a range which has not yet been attained for any other substance. The melting curve shows no signs of an approach to a solid-fluid critical point; in fact, the difference between the phases becomes more pronounced at higher melting temperatures. The internal energy at 0° K was calculated from the experimental data and was found to be in good agreement with the theoretical values based on the Slater-Kirkwood potential, using 9/8 Rθ as an estimate of the zero-point energy ( θ being the Debye characteristic temperature). A first-order transition in the solid was revealed; its equilibrium line cuts the melting curve at 14.9° K and moves to higher temperatures at higher densities. The heat of transition is very small, about 0.08 cal/mole. The transition is assumed to correspond to a change of crystal structure from hexagonal to cubic close-packed. At the highest pressure solid helium is compressed to less than half its volume under equilibrium conditions at absolute zero, and the Debye θ is increased five times. It was hence possible to test the Lindemann melting formula for a single substance over a very wide range. The formula was found to fit the experimental data satisfactorily, although the value of the constant in it differed somewhat from the classical value.