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

Giacomo Baldi, Valentina M. Giordano, Beatrice Ruta, and Giulio Monaco
Phys. Rev. B 93, 144204 – Published 22 April 2016

Abstract

Recent theoretical models for the vibrations in glasses assume that the complex elastic modulus depends on frequency but not on the wave vector, q. This assumption translates in a simple q dependence of the dynamic structure factor, which can be experimentally tested. Following the suggestion of a recent paper [U. Buchenau, Phys. Rev. E 90, 062319 (2014)], we present here a new analysis, performed in q space, of inelastic x-ray scattering data of supercooled silica. The outcome of the analysis is compared to the more common approach in the frequency domain and indicates that the mentioned theoretical assumption is consistent with the data only below the boson peak frequency. At higher frequencies it gives rise to a breakdown of the classical second moment sum rule. This violation arises from the underlying assumption of the presence of a single excitation in the spectra. A comparison with the vibrational dynamics of α-cristobalite suggests, on the contrary, that in the terahertz frequency domain the inelastic spectrum of the glass gains contributions from both acousticlike and opticlike modes. A microscopic theory of the vibrations in glasses cannot neglect the medium range order in their structure, which gives rise to dispersion curves within a pseudo-Brillouin zone.

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  • Received 22 September 2015
  • Revised 25 March 2016

DOI:https://doi.org/10.1103/PhysRevB.93.144204

©2016 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
  1. Physical Systems
Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Giacomo Baldi*

  • IMEM-CNR, Parco Area delle Scienze 37/A, I-43124 Parma, Italy

Valentina M. Giordano

  • Institute of Light and Matter, UMR5306 Université Lyon 1-CNRS, Université de Lyon, F-69622 Villeurbanne Cedex, France; Université Grenoble Alpes, SIMAP, F-38000 Grenoble, France; and CNRS, SIMAP, F-38000 Grenoble, France

Beatrice Ruta

  • ESRF-The European Synchrotron, CS 40220, F-38043 Grenoble Cedex 9, France

Giulio Monaco

  • Dipartimento di Fisica, Università di Trento, I-38123 Povo (Trento), Italy

  • *giacomo.baldi@cnr.it

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Issue

Vol. 93, Iss. 14 — 1 April 2016

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