Figure 1

The ${\mathrm{TeO}}_4$ bipyramidal unit, building block of the three ${\mathrm{TeO}}_2$ polymorphs. The two small circles indicate the Te lone pair. Dark (light) spheres indicate Te (O) atoms.Reuse & Permissions

Figure 2

Structure of $\alpha \text{−}{\mathrm{TeO}}_2$. (a) Perspective view, two unit cells are shown; $\mathrm{O}2$ and $\mathrm{O}3$ ($\mathrm{O}1$ and $\mathrm{O}4$) label the equatorial (axial) oxygen atoms. (b) Four unit cells are drawn along $c$ axis.Reuse & Permissions

Figure 3

(a) Lattice parameters $(a,c)$, (b) bond lengths, and (c) bond angles of $\alpha \text{−}{\mathrm{TeO}}_2$ as a function of unit cell volume. The arrow indicates the theoretical equilibrium value. The series in (a) correspond (from bottom to top) to $a$ and $c$ axes. $\mathrm{Te}\text{−}\mathrm{O}3$ and $\mathrm{Te}\text{−}\mathrm{O}1$ are the bond lengths of the axial and equatorial bonds, respectively.Reuse & Permissions

Figure 4

Layered structure of $\beta \text{−}{\mathrm{TeO}}_2$. (a) A projection along the $ab$ plane. (b) Sketch of a single layer. $\mathrm{O}1$ and $\mathrm{O}2$ ($\mathrm{O}{1}^{\prime }$ and $\mathrm{O}{2}^{\prime }$) label equatorial (axial) atoms.Reuse & Permissions

Figure 5

(a) Lattice parameters $(a,b,c)$, (b) bond lengths, and (c) bond angles of $\beta \text{−}{\mathrm{TeO}}_2$ as a function of unit cell volume. The arrow indicates the theoretical equilibrium value. The three series in (a) correspond (from bottom to top) to $b$, $c$, and $a$ axes. The atom labels refer to Fig. 4. $\mathrm{Te}\text{−}\mathrm{O}1$ and $\mathrm{Te}\text{−}\mathrm{O}2$ are equatorial bonds, while $\mathrm{Te}\text{−}\mathrm{O}{1}^{\prime }$ and $\mathrm{Te}\text{−}\mathrm{O}{2}^{\prime }$ are axial bonds.Reuse & Permissions

Figure 6

Structure of $\gamma \text{−}{\mathrm{TeO}}_2$. Two unit cells are drawn. (a) Three-dimensional structure. (b) Chainlike structure obtained by breaking the longest $\mathrm{Te}\text{−}\mathrm{O}$ bond of the ${\mathrm{TeO}}_4$ units of (a). $\mathrm{O}1$ and $\mathrm{O}2$ ($\mathrm{O}{1}^{\prime }$ and $\mathrm{O}{2}^{\prime }$) label equatorial (axial) atoms.Reuse & Permissions

Figure 7

(a) Lattice parameters $(a,b,c)$, (b) bond lengths, and (c) bond angles of $\gamma \text{−}{\mathrm{TeO}}_2$ as a function of unit cell volume. The arrow indicates the theoretical equilibrium value. The three series in (a) correspond (from bottom to top) to $c$, $a$, and $b$ axes. The atom labels refer to Fig. 6.Reuse & Permissions

Figure 8

Electronic band structure of (a) $\beta \text{−}{\mathrm{TeO}}_2$ and (b) $\gamma \text{−}{\mathrm{TeO}}_2$. The orthorhombic irreducible Brillouin zone is reported in the inset, equal in shape (but not in size) for both crystals.Reuse & Permissions

Figure 9

Angular dispersion of $E$ and $A_2$ IR-active modes in $\alpha \text{−}{\mathrm{TeO}}_2$. Dashed lines represent unshifted (i.e., TO) $E$ modes.Reuse & Permissions

Figure 10

IR absorption [$\alpha \left(\omega \right)$, cf. Eq. (4)] spectra for polycrystalline samples of $\alpha$-, $\beta$-, and $\gamma \text{−}{\mathrm{TeO}}_2$; linewidths in $\alpha \text{−}{\mathrm{TeO}}_2$ are taken from experimental data on single crystals (Ref. 29). In the absence of experimental data, the linewidths of $\beta$- and $\gamma \text{−}{\mathrm{TeO}}_2$ are chosen analogously to those of the $\alpha$ phase, i.e., $5{\mathrm{cm}}^{-1}$ for modes with frequency lower than $150{\mathrm{cm}}^{-1}$, and $15{\mathrm{cm}}^{-1}$ for higher-frequency modes.Reuse & Permissions

Figure 11

Raman spectra of $\alpha \text{−}{\mathrm{TeO}}_2$ single crystal for different scattering geometries. Theoretical spectra (th.) are computed with the BLYP functional at experimental lattice parameters. The experimental spectra at $85\mathrm{K}$ are adapted from Ref. 33. The character of the modes active in each scattering geometry is also reported. The linewidths of the theoretical peaks are fitted on the experimental spectra whenever the correspondence is unambiguous. The Raman intensities are reported on a logarithmic scale for sake of comparison with the experimental data of Ref. 33. The experimental peak is normalized to the strongest peak of the corresponding theoretical spectrum.Reuse & Permissions

Figure 12

Phonon dispersion relations and density of states of $\alpha \text{−}{\mathrm{TeO}}_2$, calculated with BLYP functional at the experimental lattice parameters.Reuse & Permissions

Figure 13

Unpolarized Raman spectra of polycrystalline $\alpha$-, $\beta$-, and $\gamma \text{−}{\mathrm{TeO}}_2$ for backscattering geometry. Theoretical spectra are calculated with the BLYP functional at the experimental lattice parameters. Experimental spectra are also shown for comparison (Ref. 7). For each phase the experimental spectrum is normalized over the strongest high-frequency peak of the theoretical spectrum.Reuse & Permissions

Figure 14

Angular dispersion of IR-active modes in $\beta \text{−}{\mathrm{TeO}}_2$.Reuse & Permissions

Figure 15

Angular dispersion of IR-active modes of $\gamma \text{−}{\mathrm{TeO}}_2$.Reuse & Permissions

Figure 16

(Color online) Displacement pattern of the phonons responsible for the main Raman peaks of polycrystalline $\alpha \text{−}{\mathrm{TeO}}_2$ (cf. Fig. 13). The ${\mathrm{TeO}}_2$ molecules formed by the two shorter equatorial bonds are shadowed.Reuse & Permissions

Figure 17

(Color online) Displacement pattern of the phonons responsible for the main Raman peaks of polycrystalline $\beta \text{−}{\mathrm{TeO}}_2$ (cf. Fig. 13). The ${\mathrm{TeO}}_2$ molecules formed by the two shorter equatorial bonds are shadowed.Reuse & Permissions

Figure 18

(Color online) Displacement pattern of the phonons responsible for the main Raman peaks of polycrystalline $\gamma \text{−}{\mathrm{TeO}}_2$ (cf. Fig. 13). The ${\mathrm{TeO}}_2$ molecules formed by the two shorter equatorial bonds are shadowed.Reuse & Permissions