The specific heat of simple liquids

The specific heat should be the simplest property of a liquid to calculate because it requires the fewest assumptions. Its prediction provides a necessary test for any theory of condensed matter. We are accustomed, from standard textbooks, to having simple models giving quantitative results for the magnitude and temperature dependence of the specific heat of gases and crystals, but not for liquids. The interstitialcy theory provides such a model, unifying crystalline, liquid and glassy states. According to the theory, simple liquids are crystals containing a few percent of interstitialcies in thermal equilibrium, and glasses are frozen liquids. Relative to the crystalline state, there are two principal contributions to the specific heat of the liquid state, a positive structural term and a negative anharmonic term. For normal stable liquids at temperatures T-m < T < T-c where T-m is the melting and T-c the critical temperature, the anharmonic term dominates at high temperatures. For supercooled liquids in the range T-g < T < T-m, where T-g is the glass temperature, the structural component dominates at low temperatures. At T-g, there is a rapid decrease to zero of deltaC(v). For frozen liquids at T < T-g there are low temperature anomalies due to interstitialcy tunneling, a Debye theta change, and a Boson peak arising from excitations of interstitiatcy resonant modes.