Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Phonon interpretation of the ‘boson peak’ in supercooled liquids

Nature volume 422, pages 289–292 (2003)Cite this article

Abstract

Glasses1,2 are amorphous solids, in the sense that they display elastic behaviour. In crystalline solids, elasticity is associated with phonons, which are quantized vibrational excitations. Phonon-like excitations also exist in glasses at very high (terahertz; 1012 Hz) frequencies; surprisingly, these persist in the supercooled liquids3. A universal feature of such amorphous systems is the boson peak: the vibrational density of states has an excess compared to the Debye squared-frequency law. Here we investigate the origin of this feature by studying the spectra of inherent structures4 (local minima of the potential energy) in a realistic glass model. We claim that the peak is the signature of a phase transition in the space of the stationary points of the energy, from a minima-dominated phase (with phonons) at low energy to a saddle-point-dominated phase5,6,7 (without phonons). The boson peak moves to lower frequencies on approaching the phonon–saddle transition, and its height diverges at the critical point. Our numerical results agree with the predictions of euclidean random matrix theory8 on the existence of a sharp phase transition9 between an amorphous elastic phase and a phonon-free one.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: The vibrational density of states, g(ω), at low frequencies depends only on the energy of the inherent structure, eIS.
Figure 2: The vibrational density of states g(ω) of the soft-sphere binary mixture at three representative temperatures. (The full set of temperatures was T/TMC = 0.9, 0.83, 0.78, 0.69, 0.61, 0.54 and 0.49; frequencies are given in units of ω0).
Figure 3: Scaling of the position and height of the boson peak near the liquid–phonon transition. (Energies and frequencies are in units of ɛ and ω0, respectively.) a, The position of the boson peak, ωBP, is linear in the control parameter, in this case the energy of the inherent structures eIS.

Similar content being viewed by others

References

  1. Angell, C. A. Formation of glasses from liquids and biopolymers. Science 267, 1924–1935 (1995)

    ADS  CAS  PubMed  Google Scholar 

  2. DeBenedetti, P. G. & Stillinger, F. H. Supercooled liquids and the glass transition. Nature 410, 259–267 (2001)

    Article  ADS  CAS  PubMed  Google Scholar 

  3. Sette, F., Krisch, M. H., Masciovecchio, C., Ruocco, G. & Monaco, G. Dynamics of glasses and glass-forming liquids studied by inelastic X-ray scattering. Science 280, 1550–1555 (1998)

    Article  CAS  Google Scholar 

  4. Stillinger, F. H. A topographic view of supercooled liquids and glass formation. Science 267, 1935–1939 (1995)

    Article  ADS  CAS  PubMed  Google Scholar 

  5. Angelani, L., Di Leonardo, R., Ruocco, G., Scala, A. & Sciortino, F. Saddles in the energy landscape probed by supercooled liquids. Phys. Rev. Lett. 85, 5356–5359 (2000)

    Article  ADS  CAS  PubMed  Google Scholar 

  6. Broderix, K., Bhattacharya, K. K., Cavagna, A., Zippelius, A. & Giardina, I. Energy landscape of a Lennard-Jones liquid: Statistics of stationary points. Phys. Rev. Lett. 85, 5360–5363 (2000)

    Article  ADS  CAS  PubMed  Google Scholar 

  7. Grigera, T. S., Cavagna, A., Giardina, I. & Parisi, G. Geometric approach to the dynamic glass transition. Phys. Rev. Lett. 88, 055502 (2002)

    Article  ADS  PubMed  Google Scholar 

  8. Mézard, M., Parisi, G. & Zee, A. Spectra of euclidean random matrices. Nucl. Phys. B 559, 689–701 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  9. Grigera, T. S., Martín-Mayor, V., Parisi, G. & Verrocchio, P. Vibrations in glasses and Euclidean random matrix theory. J. Phys. Condens. Matter 14, 2167–2179 (2002)

    Article  ADS  CAS  Google Scholar 

  10. Phillips, W. A., Buchenau, U., Nücher, N., Dianoux, A.-J. & Petry, W. Dynamics of glassy and liquid selenium. Phys. Rev. Lett. 63, 2381–2384 (1989)

    Article  ADS  CAS  PubMed  Google Scholar 

  11. Ruocco, G. et al. Relaxation processes in harmonic glasses? Phys. Rev. Lett. 84, 5788–5791 (2000)

    Article  ADS  CAS  PubMed  Google Scholar 

  12. Pilla, O. et al. Transverse acoustic nature of the excess of vibrational states in vitreous silica. Preprint cond-mat/0209519 at 〈http://xxx.lanl.gov〉 (2002).

  13. Masciovecchio, C. et al. Observation of large-momentum phononlike modes in glasses. Phys. Rev. Lett. 76, 3356–3359 (1996)

    Article  ADS  CAS  PubMed  Google Scholar 

  14. Matic, A. et al. Contrasting behaviour of acoustic modes in network and non-network glasses. Europhys. Lett. 54, 77–83 (2001)

    Article  ADS  CAS  Google Scholar 

  15. Masciovecchio, C. et al. High-frequency propagating modes in vitreous silica at 295 K. Phys. Rev. B 55, 8049–8051 (1997)

    Article  ADS  CAS  Google Scholar 

  16. Benassi, P. et al. Evidence of high frequency propagating modes in vitreous silica. Phys. Rev. Lett. 77, 3835–3838 (1996)

    Article  ADS  CAS  PubMed  Google Scholar 

  17. Fioretto, D. et al. High-frequency dynamics of glass-forming polybutadiene. Phys. Rev. E 59, 4470–4475 (1999)

    Article  ADS  CAS  Google Scholar 

  18. Pilla, O. et al. Nature of the short wavelength excitations in vitreous silica: An X-ray Brillouin scattering study. Phys. Rev. Lett. 85, 2136–2139 (2000)

    Article  ADS  CAS  PubMed  Google Scholar 

  19. Martín-Mayor, V., Mézard, M., Parisi, G. & Verrocchio, P. The dynamical structure factor in topologically disordered systems. J. Chem. Phys. 114, 8068–8081 (2001)

    Article  ADS  Google Scholar 

  20. Grigera, T. S., Martín-Mayor, V., Parisi, G. & Verrocchio, P. Vibrational spectrum of topologically disordered systems. Phys. Rev. Lett. 87, 085502 (2001)

    Article  ADS  CAS  PubMed  Google Scholar 

  21. Götze, W. & Sjorgen, L. Relaxation processes in supercooled liquids. Rep. Prog. Phys. 55, 241–376 (1992)

    Article  ADS  Google Scholar 

  22. Kob, W. & Andersen, H. C. Testing mode-coupling theory for a supercooled binary Lennard-Jones mixture I: The van Hove correlation function. Phys. Rev. E 51, 4626–6241 (1995)

    Article  ADS  CAS  Google Scholar 

  23. Göetze, W. & Mayr, M. Evolution of vibrational excitations in glassy systems. Phys. Rev. E 61, 587–606 (2000)

    Article  ADS  Google Scholar 

  24. Cavagna, A., Giardina, I. & Parisi, G. Role of saddles in mean-field dynamics above the glass transition. J. Phys. A 34, 5317–5326 (2001)

    Article  ADS  Google Scholar 

  25. Bernu, B., Hansen, J.-P., Hiwatari, Y. & Pastore, G. Soft-sphere model for the glass transition in binary alloys: Pair structure and self-diffusion. Phys. Rev. A 36, 4891–4903 (1987)

    Article  ADS  CAS  Google Scholar 

  26. Grigera, T. S. & Parisi, G. Fast Monte Carlo algorithm for supercooled soft spheres. Phys. Rev. E 63, 045102 (2001)

    Article  ADS  CAS  Google Scholar 

  27. Kob, W., Sciortino, F. & Tartaglia, P. Aging as dynamics in configuration space. Europhys. Lett. 49, 590–596 (2000)

    Article  ADS  CAS  Google Scholar 

  28. Engberg, D. et al. Origin of the boson peak in a network glass B2O3 . Phys. Rev. B 59, 4053–4057 (1999)

    Article  ADS  CAS  Google Scholar 

  29. Mamedov, S., Kisliuk, A. & Quitmann, D. Effect of preparation conditions on the low frequency Raman spectrum of glassy As2S3 . J. Mater. Sci. 33, 41–43 (1998)

    Article  ADS  CAS  Google Scholar 

  30. Horbach, J., Kob, W. & Binder, K. The specific heat of amorphous silica within the harmonic approximation. J. Phys. Chem. B 103, 4104–4108 (1999)

    Article  CAS  Google Scholar 

  31. La Nave, E., Stanley, H. E. & Sciortino, F. Configuration space connectivity across the fragile-to-strong transition in silica. Phys. Rev. Lett. 88, 035501 (2002)

    Article  ADS  PubMed  Google Scholar 

Download references

Acknowledgements

We thank O. Pilla, G. Ruocco and G. Viliani for discussions. We are grateful to the RTN3 collaboration for CPU time in their cluster. V.M.M. was supported in part by the European Commission and the Spanish OCYT.

Author information

Author notes

  1. T. S. Grigera

    Present address: Centro di Studi e Ricerche “Enrico Fermi”, via Panisperna, 89/A, 00184, Roma, Italy

  2. V. Martín-Mayor & P. Verrocchio

    Present address: Departamento de Física Teórica I, Universidad Complutense de Madrid, Avenida Complutense, 28040, Madrid, Spain

Authors and Affiliations

  1. Dipartimento di Fisica, Sezione INFN, SMC and INFM unità di Roma 1, Università di Roma “La Sapienza”, Piazzale Aldo Moro 2, I-00185, Roma, Italy

    T. S. Grigera, V. Martín-Mayor & G. Parisi

  2. Dipartimento di Fisica and INFM unità di Trento, Università di Trento, Via Sommarive, 14, 38050, Povo, Trento, Italy

    P. Verrocchio

Authors
  1. T. S. Grigera
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. Martín-Mayor
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. Parisi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. P. Verrocchio
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. Martín-Mayor.

Ethics declarations

Competing interests

The authors declare that they have no competing financial interests.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grigera, T., Martín-Mayor, V., Parisi, G. et al. Phonon interpretation of the ‘boson peak’ in supercooled liquids. Nature 422, 289–292 (2003). https://doi.org/10.1038/nature01475

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature01475

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing