Thermodynamic explanation of the Invar effect by computation and experiments

Phonons, electrons, spins and their interactions give the entropy and free energy of magnetic materials. A Maxwell relation implies that the pressure dependence of these entropy contributions must somehow sum to zero, to give Invar materials their known zero thermal expansion. With experiments and computations, we evaluated these thermodynamic contributions from lattice vibrations and spin disorder versus pressure for Fe-36%Ni Invar. From nuclear resonant inelastic X-ray scattering and Mössbauer spectroscopy at varying temperatures and pressures, we measured the phonon density of states and the magnetization, and determined their individual contributions to the entropy of Invar. Calculations of the phonon modes performed with an ab initio effective potential method that includes the magnetic disorder are able to capture the anomalies in the thermal expansion, and are in good agreement with experiments. The low thermal expansion of Invar is explained by the cancellation of entropy effects from lattice vibrations and spin disordering.