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Considerable progress has been made in the theoretical understanding of the vibrational properties of silicate glasses. Most of the work done so far, however, is on the vibrational density of states (VDOS) of amorphous SiO₂ (a-SiO₂). Despite the fact that Raman and infra-red (IR) spectra are very sensitive probes of the local structure of amorphous materials, there have been only a few calculations of the Raman and IR spectra of a-SiO₂. This is mainly due to the fact that the coupling coefficients linking these optical spectra with the VDOS are strong functions of the vibrational frequency.

Raman and IR spectra of binary and multi-component silicate glasses are considerably less well understood theoretically even with the enormous amount of experimental vibrational spectra published and the importance of these glasses to the material and earth sciences. Various empirical rules, established mainly by comparing Raman spectra of alkali silicate glasses and crystals, are currently used to relate, for example, the position and the intensity of the high-frequency bands in the range from 800 to 1200 cm^-1 to the distribution of non-bridging oxygens (NBO). So far, there are only a few calculations on normal modes and the vibrational spectra of small isolated silicate units typical for depolymerized silicate glasses.

We have made the first realistic VDOS and Raman intensity calculations of Na₂Si₄O₉ glass (denoted hereafter NS4) using a Kirkwood-type potential allowing us to compare the character of the vibrational modes in depolymerized alkali silicate glasses with amorphous SiO₂. We have chosen the NS4 composition because it can serve as a simple model for more complicated multi-component high-silica glasses and its structure as well as vibrational spectra have been intensively studied by neutron diffraction, reverse Monte Carlo simulations, Raman and nuclear magnetic resonance (NMR) spectroscopy.

Computer models with periodic boundary conditions were first generated by molecular dynamics (model NS4_I) and reverse Monte Carlo simulations (model NS4_II). Division of the VDOS of a-SiO₂ and NS4 glasses into bands with different stretching character, participation ratio, bridging-oxygen motion as well as phase quotient is illustrated in Fig. 3.6-1. The band edges are shown to correspond to strongly localized modes. With increasing degree of depolymerization the general character of the vibrational modes qualitatively remains the same, which implies that the vibrational properties of silicate glasses are a completely local phenomena reflecting the rigidity of the SiO₄ tetrahedra.
 

Fig. 3.6-1: Vibrational density of states with labels indicating the main peaks in VDOS.

The calculated Raman spectra for the NS4 glass are, generally, in good agreement with experiment (Fig. 3.6-2). The VV polarized Raman spectra arise mainly from bond-stretching scattering mechanisms that depend on the derivative of the parallel bond polarizability. On the contrary, the depolarized VH spectra arise from mixed bond-stretching and bond-bending scattering mechanisms. The calculations show that the perpendicular polarizability of the silicon - bridging oxygen bonds is an order of magnitude smaller than the derivative of the parallel bond polarizability and that their ratio is not affected by the presence of short-range disorder or depolymerization.

Partial Raman spectra of short-range units composed of different numbers of non-bridging oxygens (Q-species) in the Na₂Si₄O₉ glass were calculated and compared with empirically established rules for determination of Q-speciation from polarized Raman measurements. We do observe that the Q³ species give rise to a strong polarized band with a maximum at about 1095 cm^-1 and a shoulder at about 1010-1050 cm^-1 as commonly interpreted. Similarly, the Q²
 

Fig. 3.6-2: Experimental (-�) and calculated (- - - ) polarized Raman spectra for the NS4_II model.

species exhibit a well resolved peak at about 950 cm^-1. However, the shapes of the Q³ and Q² peaks are in fact rather complex and conventional decomposition into symmetric Gaussian contributions seems to be an oversimplification. A detailed discussion of the implications of the present simulations for the interpretation of the Raman spectra of alkali silicate glasses and melts requires additional calculations of VDOS and the Raman spectra on glass models with a larger range of compositions. Such calculations are in progress.