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Based on thermodynamic principles, we derive expressions quantifying thenon-harmonic vibrational behavior of materials, which are rigorous yet easilyevaluated from experimentally available data for the thermal expansioncoefficient and the phonon density of states. These experimentally- derivedquantities are valuable to benchmark first-principles theoretical predictionsof harmonic and non-harmonic thermal behaviors using perturbation theory, abinitio molecular-dynamics, or Monte-Carlo simulations. We illustrate thisanalysis by computing the harmonic, dilational, and anharmonic contributions tothe entropy, internal energy, and free energy of elemental aluminum and theordered compound FeSi over a wide range of temperature. Results agree well withprevious data in the literature and provide an efficient approach to estimateanharmonic effects in materials.

Modeling non-harmonic behavior of materials from experimental inelastic neutron scattering and thermal expansion measurements