Thermodynamics of the Invar Transition: Phonons vs. Magnetism

Phonons, electrons, spins and their interactions determine the thermodynamic behavior of materials. These interactions are at the core of the invar effect, where the volume of a material is unchanged with increasing temperatures or pressures. The invar transition is characterized by a magneto-volume transition with competing thermodynamic effects: a change in magnetism from a ferromagnetic high spin state to a low spin state with temperature or pressure is accompanied by a decrease in volume, counteracting the usual thermal expansion. We revisit the classic Fe-Ni invar system (Fe64Ni36) to explore the underlying interactions between phonons and magnetism. By measuring the phonon spectrum through nuclear inelastic X-ray scattering and the magnetic evolution though synchrotron Moessbauer experiments at several pressures and temperatures, we quantified the changes in vibrational and magnetic entropies through the invar transition. These two pieces of entropy have opposing effects on the free energy, explaining the underlying thermodynamic drive of the invar effect and the resulting unchanging volume that gives invar its name.