Figure 1

Coordination polyhedra $Q_m^n$ of Te atom found in tellurite crystals, with $m=\text{number}$ of bonded O atoms and $n=\text{number}$ of bridging O atoms. Adapted from Ref. 13.Reuse & Permissions

Figure 2

Mean-square displacement of atoms in liquid tellurite at $T=2400\text{K}$.Reuse & Permissions

Figure 3

Pair distribution functions (partial and total) of the liquid tellurite model averaged over 1 ps of molecular-dynamics simulation at $T=2400\text{K}$ (extending the time average over 2 ps the results do not change appreciably on the scale of the figure). The density corresponds to the experimental density of the glass (see text).Reuse & Permissions

Figure 4

O–Te–O and Te–O–Te angle distributions of liquid tellurite averaged over 1 ps of molecular-dynamics simulation at $T=2400\text{K}$ (extending the time average over 2 ps the results do not change appreciably on the scale of the figure). Inset: time-averaged distribution of coordination numbers.Reuse & Permissions

Figure 5

(Color online) Evolution of the population of $Q_m^n$ structural units as a function of time in liquid ${\text{TeO}}_2$ at $T=2400\text{K}$. Only species in concentration larger than 1% are shown.Reuse & Permissions

Figure 6

(Color online) Time evolution of the type of $Q_m^n$ polyhedra defining the environment of three selected Te atoms in liquid ${\text{TeO}}_2$ at 2400 K. The $Q_m^n$ character is indicated by the couple of integers $m,n$. All other Te ions, not considered here, display a similar behavior.Reuse & Permissions

Figure 7

Mean-square displacement of atoms in liquid tellurite at $T=1000\text{K}$.Reuse & Permissions

Figure 8

Pair distribution functions (partial and total) of the liquid tellurite model averaged over 10 ps of molecular-dynamics simulation at $T=1000\text{K}$. The density corresponds to the experimental density of the glass (see text).Reuse & Permissions

Figure 9

O–Te–O and Te–O–Te angle distributions of liquid tellurite averaged over 10 ps of molecular-dynamics simulation at $T=1000\text{K}$. Inset: time-averaged distribution of coordination numbers.Reuse & Permissions

Figure 10

(Color online) Evolution of the population of $Q_m^n$ structural units as a function of time in liquid ${\text{TeO}}_2$ at $T=1000\text{K}$. Only species in concentration larger than 1% are shown.Reuse & Permissions

Figure 11

Temperature of the ${\text{TeO}}_2$ model as a function of time. (a) Quenching from the melt within Born-Oppenheimer molecular dynamics. (b) Quenching from the melt within the ab initio molecular-dynamics scheme of Kühne et al. (Ref. 31) (see text).Reuse & Permissions

Figure 12

(a) Partial pair-correlation functions $g_{\alpha \beta }\left(r\right)$ of the tellurite glass model at 300 K averaged over 2 ps. (b) Total pair-correlation function $g\left(r\right)$ compared with experimental neutron-diffraction data adapted from Ref. 6 (see text).Reuse & Permissions

Figure 13

O–Te–O and Te–O–Te angle distribution functions in the model of $g{\text{-TeO}}_2$ at room temperature.Reuse & Permissions

Figure 14

(Color online) Theoretical partial structure factors of ${\text{TeO}}_2$ glass.Reuse & Permissions

Figure 15

(Color online) Theoretical total structure factor of ${\text{TeO}}_2$ glass compared with experimental neutron-scattering data (circles) from Ref. 6.Reuse & Permissions

Figure 16

Bond angle distribution of $g{\text{-TeO}}_2$ resolved for different polyhedra: (a) $Q_3^n$ and (b) $Q_4^n$ and $Q_5^5$ polyhedra.Reuse & Permissions

Figure 17

(Color online) Variation of the $Q_m^n$ population in $g{\text{-TeO}}_2$ as a function of the cutoff distance $R_{\text{max}}$ used to define Te–O bonds for a snapshot geometry from the MD run at 300 K (populations can deviate from the average values in Table ). The vertical dashed line indicates the value $R_{\text{max}}=2.36\text{Å}$ adopted here and in Ref. 13. Only species in concentration larger than 1% are shown.Reuse & Permissions

Figure 18

Root-mean-square variation of Te–O distance as a function of the average Te–O distance for Te–O bonds in $g{\text{-TeO}}_2$ at 300 K. The vertical dashed line indicates the cutoff distance $R_{\text{max}}=2.36\text{Å}$ used in the definition of $Q_m^n$ units (see text). The points in the shaded area correspond to Te–O bonds whose length fluctuates enough to cross back and forth the $R_{\text{max}}$ threshold, leading to the fluctuations in the $Q_m^n$ populations shown in Fig. 19.Reuse & Permissions

Figure 19

(Color online) Evolution of the population of $Q_m^n$ structural units as a function of time in $g{\text{-TeO}}_2$ at $T=300\text{K}$. Only species in concentration larger than 1% are shown.Reuse & Permissions

Figure 20

(Color online) Structure of the 96-atom model of $g{\text{-TeO}}_2$. (a) Ball-stick and (b) stick views are reported. In panel (a), large dark (blue) and light (cyan) spheres represent Te in $Q_4^n$ and $Q_3^n$ polyhedra, respectively. Small dark (red) spheres are bridging O atoms. Small light (orange) spheres are nonbridging O atoms.Reuse & Permissions

Figure 21

Electronic density of states of the $g{\text{-TeO}}_2$ model from Kohn-Sham orbitals at the supercell $\Gamma$ point. The zero of energy corresponds to top of the valence band. The projection of the DOS on $s$ and $p$ atomic wave functions of O and Te atoms is also shown. The Kohn-Sham energies have a Gaussian broadening of 0.1 eV.Reuse & Permissions

Figure 22

(Color online) (a) Wannier centers (gray spheres) in the $g{\text{-TeO}}_2$ model. Large (blue) and small (red) dark spheres represent O and Te atoms, respectively. Near the front $Q_3^2$ and $Q_4^4$ units are clearly visible. (b) Selected Wannier isosurfaces enclosing 50% of the electronic charge.Reuse & Permissions

Figure 23

(a) Theoretical vibrational density of states of $\alpha {\text{-TeO}}_2$ (Ref. 7). (b) Vibrational density of states (shaded black line) of the $g{\text{-TeO}}_2$ model from phonons at the supercell $\Gamma$ point. Phonon frequencies have a Gaussian broadening of $10{\text{cm}}^{-1}$. Superimposed it is shown the inverse participation ratio [spikes, Eq. (8)] of vibrational modes. The effect of the macroscopic electric field (LO–TO splitting) is not included.Reuse & Permissions

Figure 24

Vibrational DOS of the $g{\text{-TeO}}_2$ model from phonons at the supercell $\Gamma$ point, including LO-TO splittings for $\mathbf{q}$ along (0,0,1), (0,1,0), and (1,0,0). The vibrational spectrum without the contribution of the macroscopic electric field is drawn as the shaded curve for comparison. Phonon frequencies have a Gaussian broadening of $10{\text{cm}}^{-1}$.Reuse & Permissions

Figure 25

The projections of the vibrational DOS of $g{\text{-TeO}}_2$ on all O atoms (black line), bridging O atoms (BO, dashed line), and nonbridging O atoms (NBO, dotted line) are reported together with the total DOS (shaded dashed curve). The effect of the macroscopic electric-field (LO-TO splitting) is not included. Phonon frequencies have a Gaussian broadening of $10{\text{cm}}^{-1}$.Reuse & Permissions

Figure 26

Projection of the vibrational density of states on the normal modes of the $\text{Te}{\left({\text{O}}_{\text{eq}}\right)}_2$ molecules (see text): translations, librations, bendings, and stretchings. Phonon frequencies have a Gaussian broadening of $10{\text{cm}}^{-1}$.Reuse & Permissions

Figure 27

(a) The vibrational DOS of $g{\text{-TeO}}_2$ projected on BO. For each O atom the eigenmodes are projected along the three directions sketched in the inset: along Te–Te $\left(x\right)$ of the Te–O–Te bridge, normal to the latter in the Te–O–Te plane $\left(y\right)$, and normal to the Te–O–Te plane $\left(z\right)$. (b) Projection on stretchings of short (equatorial-like, $<2\text{Å}$) and long (axial-like, $>2\text{Å}$) Te–O bonds. (c)–(g). The relative contribution to the projection on Te–O stretchings from the five types of $Q_m^n$ units present in the glass model. Phonon frequencies have a Gaussian broadening of $10{\text{cm}}^{-1}$.Reuse & Permissions

Figure 28

(a) Dielectric function $ϵ\left(\omega \right)$ (real and imaginary parts). (b) Theoretical IR absorption spectrum $\alpha \left(\omega \right)$ in atomic units compared with the experimental data (Ref. 18). The experimental intensities are rescaled to the maximum of the theoretical spectrum.Reuse & Permissions

Figure 29

(a) Theoretical Raman spectrum of tellurite glass in the unpolarized backscattering setup with a frequency independent linewidth of $20{\text{cm}}^{-1}$ (dotted line) or a variable linewidth (continuous line) fitted to experimental Raman spectra of crystalline ${\text{TeO}}_2$ (see text and Fig. 30). (b) Theoretical Raman spectra of $g{\text{-TeO}}_2$ for incoming and outgoing photons with parallel (VV) and perpendicular (HV) polarizations. A frequency-dependent linewidth is used as in panel (a). The absolute Raman differential scattering cross section (without the Bose occupation factor) is reported for the theoretical spectra. (c) Experimental Raman spectra of tellurite glass (solid line) and of liquid ${\text{TeO}}_2$ (dashed line) (Ref. 18) at $770°\text{C}$ are compared with the theoretical Raman spectrum with frequencies scaled by a factor 1.1 (see text) and the frequency-dependent linewidth as in panels (a) and (b). All the theoretical and experimental spectra are obtained for a laser frequency of 514.5 nm (Ar laser). For $g{\text{-TeO}}_2$ $T=300\text{K}$. (d) Theoretical Raman spectra with and without the contribution of the macroscopic electric field (see text).Reuse & Permissions

Figure 30

Linewidth of the most intense experimental Raman peaks of $\alpha$-, $\beta$-, and $\gamma {\text{-TeO}}_2$ polycrystals (Ref. 10). The frequencies correspond to the theoretical data of Ref. 7. The interpolated dashed line has been used to assign the linewidths of the Raman peaks in $g{\text{-TeO}}_2$ (cf. Fig. 29).Reuse & Permissions