Average and Local Crystal Structure of β-Er:Yb:NaYF₄ Upconverting Nanocrystals Probed by X-ray Total Scattering

The average and local structures of ∼22 nm β-Er:Yb:NaYF 4 upconverting nanocrystals were probed using a dual-space approach combining Rietveld and pair distribution function analysis of X-ray total scattering. Comparison of the fits provided by the structural models derived from P 6̅2 m, P 6̅, and P 6 3 / m space groups demonstrates that the latter yields a crystallochemically meaningful description of the nanocrystals’ average and local structures. This result is in line with those previously reported for bulk β-Na 3 x RE 2– x F 6 ( x ∼ 0.45; RE = Y, Er, Tm, Yb) using powder X-ray diffraction,1 and for β-NaREF 4 (RE = Y, Lu) nanocrystals using solid-state NMR;2 however, it differs from those reported in studies of β-NaREF 4 (RE = La, Gd, Er) single crystals, which favored the structural model derived from the P 6̅ space group.3 The proposed structural model features sodium cations distributed in four translation-equivalent chains, each shifted relative to the others along the c axis. Interestingly, the structural model derived for the mineral gagarinite (NaCaREF 6, P 6 3 / m ), in which sodium cations are distributed in eight chains, also provides an adequate fit to the X-ray scattering data. The potential implications of this finding are discussed from the perspective of the size dependence of the crystal structure of β-NaREF 4 .