Intermediate‐Temperature Specific Heat of Solids and the Rationale Behind the Maier–Kelley Empirical Formula

The heat capacity of solids at intermediate‐to‐high temperatures is of fundamental importance to several fields ranging from geology to material science. It depends on a variety of factors, with anharmonicity and, ultimately, melting playing a pivotal role. In this work, we develop a basic‐principles model from an analytically tractable semiharmonic oscillator Hamiltonian. The resulting specific heat expression depends not only on the Einstein temperature of the material but also on other physical parameters. We compare our predictions with experimental data for copper, aluminum, lead, silicon, and germanium with rather satisfactory results, especially considering that there are no fitting parameters in our theory. We finish this work by showing that our results formally justify the otherwise purely empirical formula by Maier and Kelley, also providing its coefficients in terms of elementary physical quantities.