Materials Research Lecture

Most general answer -- from the degrees of freedom in momenta and positions of nuclei and electrons. More specifically -- most of the entropy comes from vibrations of atoms. The usual interest is in differences of entropy between different states of a material, however, and the configurations of atoms of spins can also make important contributions to differences in entropy.

Entropy plays its biggest role at high temperatures, and high temperatures are arguably more relevant for materials processing and more challenging for materials service. The new feature at high temperatures, however, is the strong coupling between different degrees of freedom. The interactions: phonon-phonon, electron-phonon, magnon-phonon, can all be important for the entropy and free energy of a material. Sorting out these couplings requires analysis of the underlying mechanisms, and I will show some examples that I hope you find interesting.