Elastic anomalies at terahertz frequencies and excess density of vibrational states in silica glass

Abstract

We study the temperature dependence of acousticlike excitations measured by means of inelastic x-ray scattering at terahertz frequencies in silica glass. The apparent sound velocity shows, between 300 and 1600 K, the same temperature variation measured, at lower frequencies, by Brillouin light scattering. On the contrary the vibrations at the boson peak (BP) present a much stronger temperature dependence, as indicated by neutron scattering data. The measured dispersion and damping are used to compute the contribution to the vibrational density of states (VDOS) coming from the propagating acousticlike modes. This part of the VDOS accounts only for a fraction of the BP intensity, indicating that other kinds of excitation accumulate in this frequency range. It is consequently not surprising that the BP does not follow the temperature evolution of the Debye frequency, which describes the modification of the continuum medium. Finally we present a comparison between the experimentally accessible quantities and a recently proposed model for the vibrations in glasses, based on the assumption of random spatial variations of the shear modulus [Schirmacher, Europhys. Lett. 73, 892 (2006)].

Thermal conductivity accumulation in amorphous silica and amorphous silicon

“…While experiments on a-SiO 2 show that there is a crossover region for the low-frequency lifetime scaling from ω −2 to ω −4 [25] and then back to ω −2 [25][26][27][28], our present model is not large enough to investigate the mode properties in this crossover region. Because experiments are limited for a-Si thin films [24], we also consider an ω −4 scaling for Eq.…”

“…To evaluate expressions and models for the low-frequency mode lifetimes requires knowledge of how the lifetimes scale with frequency. The scaling for a-SiO 2 has only recently been measured, with evidence of ω −2 , ω −4 , and a second ω −2 regime as the mode frequency ω increases from 3.14 to 6.28 ×10 12 rads/s [25][26][27][28]. For a-Si, the scaling is not well understood, with temperature-dependent and film thickness-varying measurements suggesting both ω −2 and ω −4 scalings [4][5][6][7][8][9]23,24,[29][30][31][32][33][34].…”

“…By using a constant sound speed, the lifetime and diffusivity frequency scalings will be the same. For amorphous materials, the scaling exponent n has been found experimentally and numerically to be between two and four [6][7][8][9][25][26][27][28][41][42][43]. A value of two corresponds to anharmonic scattering [44], while a value of four corresponds to Rayleightype scattering from point defects [45].…”

On the nontrivial wave-vector dependence of the elastic modulus of glasses

“…The S(q,ω) in one phonon approximation can be written in terms of its classical counterpart as [16,32]:…”

“…Below the BP frequency the mean-free path of the sound waves follows the Rayleigh scattering law, being proportional to the inverse of the fourth power of frequency [12][13][14][15][16][17]. Various theoretical models for the vibrations in glasses are based on the idea of the presence of elastic heterogeneities.…”