The role of the lattice in the $gamma to alpha$ phase transition of Ce: a high pressure neutron and x-ray diffraction study

The temperature and pressure dependence of the thermal displacements and lattice parameters were obtained across the $gamma to alpha$ phase transition of Ce using high-pressure, high-resolution neutron and synchrotron x-ray powder diffraction. The estimated vibrational entropy change per atom in the $gamma to alpha$ phase transition, $Delta S^{gamma - alpha}_{rm vib} approx (0.75 pm 0.15)$k$_{rm B}$, is about half of the total entropy change. The bulk modulus follows a power-law pressure dependence which is well described using the framework of electron-phonon coupling. These results clearly demonstrate the importance of lattice vibrations, in addition to the spin and charge degrees of freedom, for a complete description of the $gamma to alpha$ phase transition in elemental Ce.