# NaYF4 Microstructure, beyond Their Well-Shaped Morphology
## 3 Results and Discussion
### Phase Identification and Doping Dependence  
The mixture of the \(\alpha\)-NaYF\({}_{4}\) and \(\beta\)-NaYF\({}_{4}\) structures (visibles in Figure 4a) can easily be studied independently since they exhibit clearly different diffraction patterns. In Figure 4b, we present  
Figure 3: Two TEM images of NaYF\({}_{4}\) NPs from the two batches presenting two NPs populations (**(a)** NR11 and **(b)** NR13). one typical diffraction pattern obtained for a mixture of theses two types of phases. Not all of our syntheses result in a mixture of \(\alpha\)-NaYF\({}_{4}\) and \(\beta\)-NaYF\({}_{4}\) nanoparticles--we focused our work on \(\beta\)-NaYF\({}_{4}\) nanorods as this phase provides the interesting optical properties. As previously mentioned, the \(\beta\)-NaYF\({}_{4}\) NPs can adopt three different crystalline structures, with space groups depending on the synthesis parameters known to be P6\({}_{3}\)/m, P\(\overline{6}\) and P\(\overline{6}\)2m (see Figure 4) [26]. The main difference between the powder diffraction patterns lies in an extra peak from the (001) planes for the P\(\overline{6}\) and P\(\overline{6}\)2m compared with the P6\({}_{3}\)/m patterns at 2\(\theta\) = 11.70\({}^{\circ}\) in our experimental conditions. The intensity of this peak is very low, estimated around 2% of the maximum diffraction peak intensity and below 0.1% respectively for P\(\overline{6}\) and P\(\overline{6}\)2m. This small difference is usually not visible in XRPD done with a usual laboratory diffractometer and was at the origin of long discussions in the literature [13; 14]. The P\(\overline{6}\) and P-62m can only be distinguished by a quantitative analysis of the peak intensities. A synchrotron facility is required to properly determine the symmetry of NaYF\({}_{4}\) NPs. For the \(\beta\)-NaYF\({}_{4}\) NRs, among the thirteen studied samples, only one of them presents a detectable specific peak of the P\(\overline{6}\) or P\(\overline{6}\)2m structure. Furthermore, the intensity of this peak is very low (0.1% of the maximum intensity) indicating that only a negligible portion or region of the particles was obtained with this structure. For these reasons, only the P6\({}_{3}\)/m structure was considered in the following for our NPs. After the phase identification, the Fullprof software [29; 30] was used in profile matching mode with a constant scale factor in order to perform a microstructural analysis. The XRPD patterns were fitted with a Thompson-Cox-Hastings function [31] (a modified pseudo-Voigt function) to extract, for each phase (\(\alpha\) and/or \(\beta\)-NaYF\({}_{4}\)), the cell parameters and the width and breadth (full width at half  
Figure 4: NaYF\({}_{4}\) nanoparticles (**a**) Transmission Electron Microscopy (TEM) image with small cubes (\(\alpha\)-NaYF\({}_{4}\)) big nanorods (\(\beta\)-NaYF\({}_{4}\)) NR01 (**b**) typical X-ray pattern of these particles (**c**) TEM NPs sizes S (L = lenght, D = diameter) and (**d**) cell parameter dependences vs Gd nominal doping with blue triangles and red squares for the main set of cell parameters of each batch and green squares and green circles for the second set of cell parameters. maximum FWHM and integral breadth IB) of the Bragg peaks. Our study focuses on profile fitting and diffraction line broadening analysis. As said previously, the particles are doped with a constant nominal concentration of ytterbium (18 mol%) and erbium (2%) and we only changed the gadolinium concentration (from 0% to 60%). On the contrary to EDX focusing on single or few NPs, XRPD gives a global and averaged analysis of the sample. Figure 4d presents the evolution of the cell parameters with the nominal gadolinium content of the \(\beta\)-NaYF\({}_{4}\) phase. In some samples (NR03, NR 04 and NR06), two \(\beta\)-NaYF\({}_{4}\) phases are identified, a main peak is observed at the expected position and a second one slightly shifted (shoulder or separated peak, associated to other set of cell parameters shown in Figure 3d with a green star or circle).