Phonon density of states in lanthanide-based nanocrystals

TL;DR

This study investigates how nanocrystal size affects phonon density of states in lanthanide-based materials, revealing enhanced surface phonon modes in ultra-small nanocrystals and implications for their optical properties.

Contribution

It provides the first detailed analysis of size-dependent phonon density of states in lanthanide nanocrystals using combined neutron and X-ray scattering.

Findings

Enhanced low-energy phonon states in 5 nm nanocrystals

Surface phonon modes contribute to size effects

Size effects on quantum yield are minimal in larger nanocrystals

Abstract

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, $E \leq 15\,\rm{meV}$, in ultra-small (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 ultra-small 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 report constitutes the first step toward the rationalization of size effects on the modification of the absolute upconversion quantum yield of upconverting nanocrystals.