Doped fluoride nanocrystals may be used in the future as a promising probe in bio$-$imaging technologies.

The luminescence of Thulium $(T{m}^{3+})$ ions in such nanomaterials needs to be studied. Since the

luminescent properties of $T{m}^{3+}$ have a strong dependence on the local crystal field, it is important to study

the atomic structure of $T{m}^{3+}$ doped nanocrystals.

The following figure shows the diffraction patterns of polycrystalline $Pb{F}_2$ as a function of the

temperature dependent $T{m}^{3+}$ dopant concentration $x.Pb{F}_{2}T{m}_{x}P{b}_{1-x}{F}_2$

Eq$.1$: interplanar distance for a cubic crystal system:

$(\frac{1}{d^2}{)}_C=\frac{h^2+k^2+l^2}{a^2}$

Eq$.2$: interplanar distance for a tetragonal crystal system:

$(\frac{1}{d^2}{)}_T=\frac{h^2+k^2}{a^2}+\frac{l^2}{c^2}$

A$)$

Based on the figure above, would you recommend measuring this compound at a synchrotron

diffractometer? Why?

B$)$

What happens to the Bragg reflections as $T{m}^{3+}$ progressively substitutes for $P{b}^{2+}?$

What does this change in Bragg reflections indicate?