Medium-Range Structural Properties of Vitreous Germania Obtained through First-Principles Analysis of Vibrational Spectra

We analyze the principal vibrational spectra of vitreous ${\mathrm{GeO}}_2$ and derive therefrom structural properties referring to length scales beyond the basic tetrahedral unit. We generate a model structure that yields a neutron structure factor in accord with experiment. The inelastic-neutron, the infrared, and the Raman spectra, calculated within a density-functional approach, also agree with respective experimental spectra. The accord for the Raman spectrum supports a Ge-O-Ge angle distribution centered at 135°. The Raman feature $X_2$ is found to result from vibrations in three-membered rings, and therefore constitutes a distinctive characteristic of the medium-range structure.

Figure 1

Calculated (solid line) and measured (circles) [3] neutron static structure factor of $v\mathrm{\text{−}}{\mathrm{GeO}}_2$ at room temperature. We used neutron scattering lengths for Ge and O of 8.193 and 5.805 fm, respectively [33].

Figure 2

Calculated (solid line) neutron vibrational density of states ($v$-DOS) of $v\mathrm{\text{−}}{\mathrm{GeO}}_2$ at room temperature, compared to corresponding experimental data from Refs. 13 (solid circles) and 14 (dashed line). The experimental data were scaled with respect to the calculated curve, the former to match the height of the highest peak, and the latter to show the same integrated area. In the calculation of the spectrum [19], we used transferred momenta in the range $0.5–4.5{\AA }^{-1}$ [13].

Figure 3

Comparison between calculated (solid line) and measured [14] (dashed line) infrared spectra of $v\mathrm{\text{−}}{\mathrm{GeO}}_2$, for (a) the imaginary part of the dielectric function and (b) the energy loss function. A Gaussian broadening of $19{\mathrm{cm}}^{-1}$ was used.

Figure 4

Calculated (solid line) and measured (dashed line [14]) HH and HV Raman spectra of $v\mathrm{\text{−}}{\mathrm{GeO}}_2$. The calculated spectra are scaled to match the integrated intensity of the experimental HH spectrum. For clarity, the intensities in the high-frequency range were scaled by a factor of 5. Vibrations associated with $X_1$ are illustrated graphically. Inset: Ge-O-Ge angle distribution in the model structure of $v\mathrm{\text{−}}{\mathrm{GeO}}_2$. Contributions to the HH spectrum and to the angular distribution originating from three-membered rings are shaded. Gaussian broadenings of $19{\mathrm{cm}}^{-1}$ and 2.5° are used.