The temperature and pressure dependence of the thermal displacements and lattice parameters were obtained across the gamma-->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-->alpha phase transition, DeltaS(gamma-alpha)(vib) approximately (0.75+/-0.15)k(B), is about half of the total entropy change. The bulk modulus follows a power-law pressure dependence that 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-->alpha phase transition in elemental Ce.