Fig. 1: Structural analysis for the NPs.

a Transmission electron microscopy (TEM) image and size distribution of α-NaYF4 NPs doped with 1 mol% Er3+ (NP1). b Schematic representation of NP1 containing one Er3+ ion. c Cubic lattice unit cell of NaYF4 indicating the positions of Na+, Y3+, and F− host ions as well as Er3+ dopants. The cubic lattice was adapted from ref. 14 for α-NaYF4. d Er3+-Er3+ distance distribution for NP2 calculated with Monte Carlo model (inset: Monte Carlo model of the number of Er3+ ions and the mean Er3+-Er3+ distance for NP2). e Mean Er3+-Er3+ distance for the NPs as a function of the Er3+ content. Gray labels indicate the number of Er3+ ions within the NP as determined by ICP analysis. TEM images and Er3+-Er3+ distance distributions for all other compositions are given at the ESI.