# NaYF4 Microstructure, beyond Their Well-Shaped Morphology
## 3 Results and Discussion
### Microstructural Analysis
In first approximation, it appears that the size obtained  
Figure 5: (**a**) Shape factor for each peak of four typical samples (NR04, NR07, NR09, NR10) and the most different sample (NR13) (**b**) Mean shape factor versus the expected gadolinium concentration. Figure 6: Halder-Wagner plot for a typical sample. by XRD is close to the diameter of the NPs observed by TEM. This lead us to study more carefully the crystallinity of our NPs to understand the meaning of this characteristic size. The previous observation was assuming an isotropic NPs shape, supposed to be spherical. Now a Scherrer-type analysis was used, where only the Lorentzian contribution is considered for each individual reflection in order to take into account eventual anisotropic broadening, to obtain the size of the crystallite, a needle-like model was applied--with a main axis along the c axis or [001] direction. Remember that by this method it is at best a mean value of the size of the coherent domains of a supposedly unimodal distribution of crystallites which is obtained for each (hkl) Bragg peak. From this analysis, the three dimensions of the crystallites in our NPs can be extracted. All of them present a longer length along the [OOI] direction and a smaller size in the corresponding orthogonal [hk0] directions. Moreover, in most cases, the length along this direction [hk0] is slightly smaller than the apparent size observed by TEM. We summarized the crystallite sizes in the Table 5 with again the apparent size for an easier comparison. \begin{table}
\begin{tabular}{l l l l l l l l l} \hline  & \multicolumn{2}{c}{**TEM Size (nm)**} & \multicolumn{1}{c}{**AR**} & \multicolumn{1}{c}{**Gd**} & \multicolumn{1}{c}{\(y=ax+b\)**} & \multicolumn{1}{c}{**Shape**} & \multicolumn{1}{c}{**Crystallite**} & \multicolumn{1}{c}{**Microstrain**} \\  & \multicolumn{1}{c}{**L**} & \multicolumn{1}{c}{**D**} & \multicolumn{1}{c}{**(mole \%)**} & \multicolumn{1}{c}{\(a\)**} & \multicolumn{1}{c}{\(b\)**} & \multicolumn{1}{c}{**Factor**} & \multicolumn{1}{c}{**Size (nm)**} & \\ \hline NR01 & 835 & 113 & 7.4 & 0 & 1.16 & 1.69 & 0.89 & 85 & 2.5\(\times\) 10\({}^{-4}\) \\ NR02 & 1390 & 234 & 5.9 & 0 & 0.92 & 0.42 & 0.82 & 108 & 1.3\(\times\) 10\({}^{-4}\) \\ NR03 & 718 & 108 & 6.6 & 5 & 1.35 & 0.29 & 0.77 & 74 & 1\(\times\) 10\({}^{-4}\) \\ NR04 & 935 & 160 & 5.8 & 5 & 0.98 & 0.46 & 0.83 & 102 & 1.35\(\times\) 10\({}^{-4}\) \\ NR05 & 375 & 70 & 5.4 & 15 & 1.69 & 0.79 & 0.81 & 59 & 1.7\(\times\) 10\({}^{-4}\) \\ NR06 & 465 & 70 & 6.6 & 15 & 1.44 & 2.9 & 0.76 & 69 & 3.4\(\times\) 10\({}^{-4}\) \\ NR07 & 640 & 100 & 6.4 & 15 & 1.3 & 0.8 & 0.81 & 77 & 1.8\(\times\) 10\({}^{-4}\) \\ NR08 & 400 & 55 & 7.2 & 30 & 2.01 & 0.36 & 0.8 & 50 & 1.2\(\times\) 10\({}^{-4}\) \\ NR09 & 156 & 62 & 2.5 & 30 & 2.01 & \(-\)0.21 & 0.73 & 50 & n.s. \\ NR10 & 130 & 70 & 1.9 & 30 & 2.04 & 0.53 & 0.77 & 49 & 1.5\(\times\) 10\({}^{-4}\) \\ NR11 & 260 & 55 & 4.7 & 30 & 2.21 & 1.08 & 0.80 & 45 & 2\(\times\) 10\({}^{-4}\) \\ NR12 & 137 & 45 & 3 & 45 & 2.83 & 0.72 & 0.77 & 35 & 1.7\(\times\) 10\({}^{-4}\) \\ NR13 & 60 & 45 & 1.3 & 60 & 3.9 & \(-\)6 & 0.78 & 26 & n.s. \\ \hline \end{tabular}
\end{table} 
Table 4: Main parameters of the studied NPs (with L for Length, D for Diameter, AR for Aspect Ratio) and the parameters from the Halder-Wagner graph with the apparent size and microstrain obtained for each of them. Here only the expected gadolinium concentration is given. (n.s. negative microstrain even if the value is very close to zero).