At modest temperatures, and especially above 1000 K, most of the entropy of solids comes from atomic vibrations. In 1907, Einstein proposed a quantized harmonic oscillator as a starting point. Today, normal modes of crystal vibrations are quantized, and the quanta are called "phonons." Phonons in crystals were first measured by inelastic neutron scattering in the 1950s. Using inelastic neutron scattering and electronic structure calculations, we have compared the entropy from phonons to the entropy obtained by calorimetry. In short, excellent agreement is found when all known sources of entropy are included, such as from electrons, spins, and interactions between phonons, electrons, and spins. Interactions that cause only small departures from harmonic behavior are treated with many-body perturbation theory. Neutron scattering revealed new anharmonic features in the phonon spectra of NaBr and Cu2O. These anharmonic features, such as phonon frequency doubling and intermodulation sidebands, can be understood with molecular dynamics or methods based on the Heisenberg-Langevin equation or the Schrödinger-Langevin equation. For Cu2O and ZnO, we found diffuse inelastic intensity (DII) at high energies, well above the phonon bands. This DII originates from brief anharmonic interactions between atoms as they vibrate, and is a new probe of anharmonic interatomic potentials.
