Phonon-confinement entropy and the formation of CeH2.84 nanoplates by fracture

Particles formed during the reaction of cerium with hydrogen fractured into stacked plates with fully separated plate thicknesses averaging 100 nm and a finer partially separated thickness of 30 nm. The phonon density of states of these particles, measured using inelastic neutron scattering, showed a low-energy feature that could not be accounted for in the phonon-dispersion curves of bulk crystals but was similar to a feature predicted for the confinement of phonons in nanoplates. The shift of modes to lower energies indicates that excess vibrational entropy is created by the fracture. We argue that this excess entropy contributes to the observed fracture pattern by introducing a characteristically weak size for fracture.