Specific heats of liquids and phonon theory

Abstract

Abstract The measured ratio of the specific heats γ for liquid metals near the melting point and for the liquid insulator argon just above its melting point differ considerably. For metals, γ ∼ 1.2 or 1.3 while for argon γ ∼ 2.2. Furthermore, the measured specific heat at constant volume, per atom, is near to 3k B and always slightly greater, for metals, in contrast to argon for which C v ∼ 2.3 k B near the melting point. These observations suggest that a phonon model should be good in liquid metals, but that a very ‘anharmonic’ situation exists in liquid argon. That the softer core and longer range potentials characteristic of metals will lead to γ values near to unity is confirmed by using an inequality due to Schofield to obtain an upper bound for γ. In a model of liquid Na, using the long-range oscillatory potential of Paskin and Rahman which fits the neutron structure factor, we obtain γ ∼ 1.2. The same inequality for argon yields γ ∼ 3.5. The main contribution for argon comes from the region inside ...