Equivalence of the Boson Peak in Glasses to the Transverse Acoustic van Hove Singularity in Crystals

We compare the atomic dynamics of the glass to that of the relevant crystal. In the spectra of inelastic scattering, the boson peak of the glass appears higher than the transverse acoustic (TA) singularity of the crystal. However, the density of states shows that they have the same number of states. Increasing pressure causes the transformation of the boson peak of the glass towards the TA singularity of the crystal. Once corrected for the difference in the elastic medium, the boson peak matches the TA singularity in energy and height. This suggests the identical nature of the two features.

Figure 1

DOS (a)–(c) and reduced DOS (d)–(f) of the sodium silicate glass at various pressures and of the crystalline counterpart of the glass, the aegirine crystal. The arrows show the transverse acoustic (TA) van Hove singularity of the crystal and the boson peak (BP) of the glass. The symbols at $E=0$ in (d) show the Debye levels calculated from the measured density and sound velocity. The dashed lines in (d) emphasize the consistency of the reduced DOS with the Debye levels. The dashed-dotted line in (d) indicates the transformation of the boson peak towards the TA singularity. The filled areas of the DOS of the ambient glass (b) and the aegirine crystal (c) correspond to the filled areas of the reduced DOS within the FWHM of the boson peak (e) and of the TA singularity peak (f), respectively. The dashed lines in (b),(c),(e),(f) show the Debye levels. The hatched part of the filled area in (b),(c) marks the excess of states over the Debye level.

Figure 2

(a) The calculated dispersion relations for the aegirine crystal. The size and intensity of symbols is proportional to the fraction of vibrational energy related to iron atoms. (b) The calculated iron-partial and total DOSs. In order to emphasize the match of the two DOS at low energy, the iron-partial DOS is divided by the mass-ratio coefficient $m_{\mathrm{Fe}}/⟨m⟩$ 15. The arrows show the positions of the transverse acoustic (TA) van Hove singularity.

Figure 3

The pressure dependence of (a) density, (b) longitudinal and (c) transverse sound velocity of the sodium silicate glass. The solid and open circles show the results of two independent measurements. The lines are to guide the eye.

Figure 4

Reduced density of states of the sodium silicate glass at various pressures and of the aegirine crystal in Debye units. The dashed lines emphasize the consistency of the reduced DOS with the Debye level $3E_D^{-3}$. The blue arrow in (b) shows the boson peak at ambient pressure. The red arrow in (b) emphasizes the shoulder of the reduced DOS at 11 GPa.

Figure 5

(a) The effective size $q_0$ of the pseudo- (for the sodium silicate glass) and of the average (for the aegirine crystal) Brillouin zone. The line shows the linear fit to the glass data only. (b) The model used to calculate $q_0$. (c) The current correlation functions $J_T(q,E)$ from Ref. 32. (d) The dynamic structure factors $S_T(q,E)$ recalculated from $J_T(q,E)$ shown in (c). The dashed lines emphasize the dispersive (c) and nondispersive (d) behavior of the $J_T(q,E)$ and $S_T(q,E)$ peaks, respectively. (e) The energy positions of the peaks in $J_T(q,E)$ from Refs. 9, 32 and in the recalculated $S_T(q,E)$. The vertical dashed line shows the boundary of the pseudo-Brillouin-zone (half of the first sharp diffraction peak position [32]).