Vibrational dynamics of YPO${}_4$ and ScPO${}_4$ single crystals: An integrated study by polarized Raman spectroscopy and first-principles calculations

A thorough study of the vibrational dynamics of xenotime YPO${}_4$ and its isomorphs, pretulite ScPO${}_4$ single crystals, with tetragonal zircon structure, was carried out by means of an integrated approach consisting of both polarized micro-Raman scattering spectroscopy and first-principles calculations. Polarized Raman scattering experiments were performed at room temperature either in the 180${}^{°}$ or in the 90${}^{°}$ geometry on both samples under different crystal orientations set by a micromanipulator. All the 12 independent components of the polarizability tensor, expected on the basis of the group theory for both YPO${}_4$ and ScPO${}_4$, were selected in turn and assigned in symmetry. In particular, it was possible to unambiguously identify a ${\mathrm{B}}_{1g}$ mode peaked at 316 cm${}^{-1}$ in YPO${}_4$ and two ${\mathrm{B}}_{1g}$ modes peaked at 350 and 677 cm${}^{-1}$ in ScPO${}_4$, respectively, all of them never reported before. These observations were corroborated by the results of first-principles calculations, based on density functional theory in the generalized gradient approximation, performed to determine Raman and infrared vibrational modes. In fact, an excellent agreement between computational and experimental results has been found.

Figure 1

Crystallographic tetragonal zircon structure of RPO${}_4$ ($R=$ Y, Sc). The $c$ axis is vertical, $a$ and $b$ axes define the basal plane, while grid, small, and large open circles denote O, P, and R atoms, respectively. The atoms are numbered in the same way adopted for the eigenvector’s calculation (see Table ).

Figure 2

Room-temperature polarized Raman spectra of YPO${}_4$ obtained in 90${}^{°}$ scattering geometry [panels (a), (b), and (c)] and in backscattering geometry [panel (d)] with $Z^{\prime }=\mathrm{Z̄}$) for different polarization and orientation settings (see text). The asterisks label the spillover modes. The crystal orientation represented in the inset of panel (a) is common also to panels (b) and (c). Finally, the ${\mathrm{B}}_{1g}(2)$ mode peaked at 316 cm${}^{-1}$ can be observed only after proper magnification, as evidenced in the inset of panel (d).

Figure 3

Room-temperature polarized Raman spectra of ScPO${}_4$ obtained in 90${}^{°}$ scattering geometry [panels (a), (b), and (c)] and in backscattering geometry [panel (d)] with $Z^{\prime }=\mathrm{Z̄}$) for different polarization and orientation settings (see text). The asterisks label the spillover modes. The crystal orientation represented in the inset of panel (a) is common also to panels (b) and (c). Finally, the ${\mathrm{B}}_{1g}(2)$ and ${\mathrm{B}}_{1g}(3)$ modes, peaked at about 350 and 677 cm${}^{-1}$, respectively, can be observed only after proper magnification, as evidenced in the insets of panel (d).