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The European Physical Journal Special Topics

, Volume 216, Issue 1, pp 83–93 | Cite as

Vibrational anomalies and marginal stability of glasses

  • Alessia Marruzzo
  • Stephan Köhler
  • Andrea Fratalocchi
  • Giancarlo Ruocco
  • Walter SchirmacherEmail author
Regular Article

Abstract

The experimentally measured vibrational spectrum of glasses strongly deviates from that expected in Debye’s elasticity theory: The density of states deviates from Debye’s ω2 law (“boson peak”), the sound velocity shows a negative dispersion in the boson-peak frequency regime, and there is a strong increase in the sound attenuation near the boson-peak frequency. A generalized elasticity theory is presented, based on the model assumption that the shear modulus of the disordered medium fluctuates randomly in space. The fluctuations are assumed to be uncorrelated and have a certain distribution (Gaussian or otherwise). Using field-theoretical techniques one is able to derive mean-field theories for the vibrational spectrum of a disordered system. The theory based on a Gaussian distribution uses a self-consistent Born approximation (SCBA),while the theory for non-Gaussian distributions is based on a coherent-potential approximation (CPA). Both approximate theories appear to be saddle-point approximations of effective replica field theories. The theory gives a satisfactory explanation of the vibrational anomalies in glasses. Excellent agreement of the SCBA theory with simulation data on a soft-sphere glass is reached. Since the SCBA is based on a Gaussian distribution of local shear moduli, including negative values, this theory describes a shear instability as a function of the variance of shear fluctuations. In the vicinity of this instability, a fractal frequency dependence of the density of states and the sound attenuation ∝ ω1+a is predicted with a ≲ 1/2. Such a frequency dependence is indeed observed both in simulations and in experimental data. We argue that the observed frequency dependence stems from marginally stable regions in a glass and discuss these findings in terms of rigidity percolation.

Keywords

Shear Modulus European Physical Journal Special Topic Sound Attenuation Boson Peak Nuclear Inelastic Scat 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    W.A. Phillips, J. Low Temp. Phys. 7, 351 (1972)CrossRefADSGoogle Scholar
  2. 2.
    S.R. Elliott, The Physics of Amorphous Materials (Longman, New York, 1984)Google Scholar
  3. 3.
    K. Binder, W. Kob, Glassy Materials and Disordered Solids: An Introduction (World Scientific, London, 2011)Google Scholar
  4. 4.
    J. Wuttke, W. Petry, G. Coddens, F. Fujara, Phys. Rev. E 52, 4026 (1995)CrossRefADSGoogle Scholar
  5. 5.
    R. Rüffer, A.I. Chumakov, Hyperfine Interactions 128, 255 (2000)CrossRefADSGoogle Scholar
  6. 6.
    S.N. Taraskin, S.R. Elliott, Phys. Rev. B 55, 117 (1997)CrossRefADSGoogle Scholar
  7. 7.
    R.O. Pohl, X. Liu, E. Thompson. Rev. Mod. Phys. 74, 991 (2002)CrossRefADSGoogle Scholar
  8. 8.
    W. Schirmacher, Europhys. Lett. 73, 892 (2006)CrossRefADSGoogle Scholar
  9. 9.
    F. Sette, M.H. Krisch, C. Masciovecchio, G. Ruocco, G. Monaco, Science 280, 1550 (1998)CrossRefGoogle Scholar
  10. 10.
    G. Monaco, V.M. Giordano, PNAS 106, 3659 (2009)CrossRefADSGoogle Scholar
  11. 11.
    G. Baldi, V.M. Giordano, G. Monaco, B. Ruta, Phys. Rev. Lett. 104, 195501 (2010)CrossRefADSGoogle Scholar
  12. 12.
    B. Ruta, G. Baldi, V.M. Giordano, L. Orsingher, S. Rols, F. Scarponi, G. Monaco, J. Chem. Phys. 113, 041101 (2010)CrossRefADSGoogle Scholar
  13. 13.
    G. Baldi, V.M. Giordano, G. Monaco, Phys. Rev. B 83, 174203 (2011)CrossRefADSGoogle Scholar
  14. 14.
    H. Shintani, H. Tanaka, Nat. Mater. 7, 870 (2008)CrossRefADSGoogle Scholar
  15. 15.
    G. Monaco, S. Mossa, PNAS 106, 16907 (2009)CrossRefADSGoogle Scholar
  16. 16.
    A. Marruzzo, W. Schirmacher, A. Fratalocchi, G. Ruocco, Nature Scientific Reports (to be published) (2012)Google Scholar
  17. 17.
    W. Schirmacher, J. Noncryst. Sol. 1, 1 (2010)Google Scholar
  18. 18.
    U. Buchenau, Yu.M. Galperin, V.L. Gurevich, H.R. Schober, Phys. Rev. B 43, 5039 (1991)CrossRefADSGoogle Scholar
  19. 19.
    V.L. Gurevich, H.R. Schober, Phys. Rev. B 57, 295 (1998)Google Scholar
  20. 20.
    V.L. Gurevich, D.A. Parshin, H.R. Schober, Phys. Rev. B 67, 094203 (2003)CrossRefADSGoogle Scholar
  21. 21.
    E. Duval, A. Mermet, L. Saviot, Phys. Rev. B 75, 024201 (2007)CrossRefADSGoogle Scholar
  22. 22.
    W. Schirmacher, G. Diezemann, C. Ganter, Phys. Rev. Lett. 81, 136 (1998)CrossRefADSGoogle Scholar
  23. 23.
    W. Götze, M.R. Mayr, Phys. Rev. E 61, 587 (2000)CrossRefADSGoogle Scholar
  24. 24.
    J.W. Kantelhardt, et al., Phys. Rev. B 63, 064302 (2001)CrossRefADSGoogle Scholar
  25. 25.
    W. Schirmacher, G. Ruocco, T. Scopigno, Phys. Rev. Lett. 98, 025501 (2007)CrossRefADSGoogle Scholar
  26. 26.
    S.N. Taraskin, S. Elliott, Y.H. Loh, G. Nataranjan, Phys. Rev. Lett. 86, 1255 (2001)CrossRefADSGoogle Scholar
  27. 27.
    A.I. Chumakov, et al., Phys. Rev. Lett. 106, 225501 (2011)CrossRefADSGoogle Scholar
  28. 28.
    S. Caponi, et al., Phys. Rev. Lett. 102, 027402 (2009)CrossRefADSGoogle Scholar
  29. 29.
    J. Horbach, W. Kob, K. Binder, Eur. Phys. J. B 19, 531 (2001)CrossRefADSGoogle Scholar
  30. 30.
    F. Léonforte, et al., Phys. Rev. B 72, 224206 (2005)CrossRefADSGoogle Scholar
  31. 31.
    F. Léonforte, et al., Phys. Rev. Lett. 97, 055501 (2006)CrossRefADSGoogle Scholar
  32. 32.
    S.G. Mayr, Phys. Rev. B 79, 060201 (2009)CrossRefADSGoogle Scholar
  33. 33.
    P. Derlet, et al., Eur. J. Phys. B 1, 1 (2012)Google Scholar
  34. 34.
    E. Akkermans, R. Maynard, Phys. Rev. B 32, 7850 (1985)CrossRefADSGoogle Scholar
  35. 35.
    S.R. Elliott, Europhys. Lett. 19, 201 (1992)CrossRefADSGoogle Scholar
  36. 36.
    C. Ganter, W. Schirmacher, Phys. Rev. B 1, 1 (2011)Google Scholar
  37. 37.
    D. Srolovitz, et al., Philos. Mag. A 41, 847 (1981)CrossRefADSGoogle Scholar
  38. 38.
    T. Egami, D. Srolovitz, J. Phys. F: Met. Phys. 12, 2141 (1982)CrossRefADSGoogle Scholar
  39. 39.
    E. Vidal Russell, N.E. Israeloff, Nature 408, 695 (2000)CrossRefADSGoogle Scholar
  40. 40.
    H. Wagner, et al., Nature Materials 10, 439 (2011)CrossRefADSGoogle Scholar
  41. 41.
    M. Tsamados, A. Tanguy, C. Goldenberg, J.-L. Barrat, Phys. Rev. E 80, 026112 (2009)CrossRefADSGoogle Scholar
  42. 42.
    W. Schirmacher, E. Maurer, M. Pöhlmann, Phys. Stat. Sol. (c) 1, 1 (2003)Google Scholar
  43. 43.
    S. John, H. Sompolinky, M.J. Stephen, Phys. Rev. B 28, 5592 (1983)CrossRefADSGoogle Scholar
  44. 44.
    B. Schmid, C. Tomaras, W. Schirmacher, Phys. Rev. B 1, 1 (2010)Google Scholar
  45. 45.
    S.K. Sarkar, G.S. Matharoo, A. Pandey, Phys. Rev. Lett. 92, 215502 (2004)CrossRefADSGoogle Scholar
  46. 46.
    S. Köhler, Diploma thesis (University of Mainz, Mainz, 2011)Google Scholar
  47. 47.
    S. Köhler, W. Schirmacher, G. Ruocco (unpublished)Google Scholar
  48. 48.
    W. Götze, Liquids, freezing and the glass transition (Amsterdam, Elsevier, 1990)Google Scholar
  49. 49.
    W. Wyart, Ann. Phys. (Paris) 30, 1 (2005)Google Scholar

Copyright information

© EDP Sciences and Springer 2013

Authors and Affiliations

  • Alessia Marruzzo
    • 1
    • 2
  • Stephan Köhler
    • 3
  • Andrea Fratalocchi
    • 2
  • Giancarlo Ruocco
    • 1
  • Walter Schirmacher
    • 1
    • 3
    Email author
  1. 1.Dipartimento di Fisica, Universitá di Roma “La Sapienza”RomaItaly
  2. 2.PRIMALIGHT, Faculty of Elect. Engeneering; Applied Mathematics and Computational ScienceKing Abdullah University of Science and Technology (KAUST)ThuwalSaudi Arabia
  3. 3.Institut für PhysikUniversität MainzMainzGermany

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