Frustration and Sound Attenuation in Structural Glasses

Abstract

Three classes of harmonic disorder systems (Lennard-Jones like glasses, percolators above threshold, and spring disordered lattices) have been numerically investigated in order to clarify the effect of different types of disorder on the mechanism of high frequency sound attenuation. We introduce the concept of frustration in structural glasses as a measure of the internal stress, and find a strong correlation between the degree of frustration and the exponent α that characterizes the momentum dependence of the sound attenuation Γ(Q)≃Q α . In particular, α decreases from ≈d+1 in lowfrustration systems (where d is the spectral dimension), to ≈2 for high frustration systems like the realistic glasses examined.PACS numbers: 63.50.+x, 61.43.Fs The nature of collective excitations in disordered solids has been one of the major problems of condensed matter physics during the last decades; the recent devolopment of a high-resolution inelastic X-ray scattering (IXS) facility [1] made Brillouin-like experiments possible in the region of mesoscopic exchanged momenta Q=1÷10 nm −1 , which led to the realization that propagating sound-like excitations exist in glasses up to the Terahertz frequency region. The quantity that characterizes the collective excitations, and which has been determined experimentally in many glasses [2] and liquids [3], is the dynamic structure factor S(Q, ω). Although specific quantitative differences exist among systems, the following qualitative characteristics are common to all the investigated materials: i) there exist propagating acoustic-like excitations for Q values up to Q m , with Q m /Q o ≈0.1÷0.5 (where Q o is the position of the maximum in the static structure factor), which show up as more-or-less well defined Brillouin peaks at Ω(Q) in S(Q, ω), the specific value of Q m /Q o is correlated with the fragility of the glass; ii) the slope of the (almost) linear Ω(Q) vs Q dispersion relation in the Q→0 limit extrapolates to the macroscopic sound velocity; iii) the width of the Brillouin peaks, Γ(Q), follows a power law, Γ(Q)=DQ α , with α≈2 whithin the statistical uncertainties; iv) the value of D does not depend significantly on temperature, indicating that the broadening (i.e. the sound attenuation) in the high frequency region does not have a dynamic origin, but that it is due to disorder [4]. These general features of S(Q, ω) have been confirmed by numerical calculations on simulated glasses [5], obtained within the framework of the mode coupling theory [6], and, more recently, ascribed to a relaxation process associated to the topological disorder [7]. However, except for the simple 1-dimensional case [8], the widespread finding Γ(Q)=DQ 2 , has not yet been explained on a microscopic basis.To this end in this Letter we investigate, in the harmonic approximation, systems showing disorder of different characteristics, and the role played by the latter in determining the value of the exponent α. The analyzed systems show either substitutional (bond percolators and spring disordered syst...

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