Phonon density of states in lanthanide-based nanocrystals

We report a combined inelastic neutron- and x-ray-scattering study of the phonon density of states of the nano- and microcrystalline lanthanide-based materials $NaY_{0.8}Yb_{0.18}Er_{0.02}F_{4}$ and $NaGd_{0.8}Yb_{0.18}Er_{0.02}F_{4}$. While
large (20 nm) nanocrystals display the same vibrational spectra as their microcrystalline counterparts, we find an enhanced phonon density of states at low energies, $E\leq 15 meV$, in ultrasmall (5 nm) $NaGd_{0.8}Yb_{0.18}Er_{0.02}F_{4}$
nanocrystals which we assign to an increased relative spectral weight of surface phonon modes. Based on our observations for ultrasmall nanocrystals, we rationalize that an increase of the phonon density of states in large
nanocrystals due to surface phonons is too small to be observed in the current measurements. The experimental approach described in this paper constitutes a step toward the rationalization of size effects on the modification of the absolute upconversion quantum yield of upconverting nanocrystals.