Fig. 2: Structural characterization of optically active α-NaYF₄:Yb:Er core nanocrystals (NCs) after growing homogeneous α-NaYF₄ (top row) and heterogeneous CaF₂ (bottom row) shell domains.

a,b Experimental (black open symbols) and calculated (red solid lines) powder X-ray diffraction (PXRD) patterns together with their difference curve (blue solid lines). The calculated PXRD patterns are the result of full Rietveld (a) and Pawley (b) refinements. The values for the expected R factor (R_exp) and weighted profile R factor (R_wp) are given to assess the quality of the refinements when combined with the visual inspection of the difference curve. Note that the peak at 2θ ≈ 80° (*symbol) does not belong to the cubic crystal structure. Nevertheless, it is properly described by the calculated PXRD pattern because the background was modelled by scaling the signal of the sample holder. The latter is a low background (911)-oriented silicon wafer onto which NCs are drop casted to obtain, after solvent evaporation, a thin film of NCs. The PXRD pattern of the empty sample holder is given in the Supplementary Fig. 2. c, d Representative low magnification high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) images overlaid with their corresponding size distribution histograms. At least ten HAADF-STEM images were acquired at various magnifications and spatial locations on the grid for both the homogeneous (c) and heterogeneous (d) particles. The growth of a homogeneous shell ___domain on core particles (without Ce³⁺ doping) was performed twice with similar results. The growth of a heterogeneous shell ___domain on core particles (without Ce³⁺ doping) was performed four times with similar results. e, f Integrated differential phase contrast (iDPC)-STEM images of a region of individual homogeneous (e) and heterogeneous (f) NCs. Atomic columns that contain rare-earth and fluorine atoms are in yellow and beige, respectively. The exact same α-NaYF₄:Yb:Er core NCs (reported in Fig. 1) and experimental conditions were utilized for the growth of homogeneous and heterogeneous shell domains.