  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.
