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.

Femtosecond X-ray measurement of coherent lattice vibrations near the Lindemann stability limit

Abstract

The study of phase-transition dynamics in solids beyond a time-averaged kinetic description requires direct measurement of the changes in the atomic configuration along the physical pathways leading to the new phase. The timescale of interest is in the range 10-14 to 10-12 s. Until recently, only optical techniques were capable of providing adequate time resolution1, albeit with indirect sensitivity to structural arrangement. Ultrafast laser-induced changes of long-range order have recently been directly established for some materials using time-resolved X-ray diffraction2,3,4,5,6,7,8. However, the measurement of the atomic displacements within the unit cell, as well as their relationship with the stability limit of a structural phase9,10,11, has to date remained obscure. Here we report time-resolved X-ray diffraction measurements of the coherent atomic displacement of the lattice atoms in photoexcited bismuth close to a phase transition. Excitation of large-amplitude coherent optical phonons gives rise to a periodic modulation of the X-ray diffraction efficiency. Stronger excitation corresponding to atomic displacements exceeding 10 per cent of the nearest-neighbour distance—near the Lindemann limit—leads to a subsequent loss of long-range order, which is most probably due to melting of the material.

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

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Figure 1: Geometrical structure factor |S(h, k, l)|2 of bismuth as a function of the distance d of the two basis atoms for diffraction from (111) and (222) lattice planes.
Figure 2: X-ray diffraction efficiency of the (222) reflection as a function of time delay between the optical pump pulse (fluence 6 mJ cm-2) and the X-ray probe pulse.
Figure 3: X-ray diffraction efficiency of the (111) reflection as a function of time delay between the optical pump pulse (fluence 6 mJ cm-2) and the X-ray probe pulse.
Figure 4

References

  1. Bloembergen, N. From nanosecond to femtosecond science. Rev. Mod. Phys. 71, S283–S287 (1999)

    CAS  Article  Google Scholar 

  2. Chin, A. H. et al. Ultrafast structural dynamics in InSb probed by time-resolved X-ray diffraction. Phys. Rev. Lett. 83, 336–339 (1999)

    ADS  CAS  Article  Google Scholar 

  3. Siders, C. W. et al. Detection of non-thermal melting by ultrafast X-ray diffraction. Science 286, 1340–1342 (1999)

    CAS  Article  Google Scholar 

  4. Lindenberg, A. M. et al. Time-resolved X-ray diffraction from coherent phonons during a laser-induced phase transition. Phys. Rev. Lett. 84, 111–114 (2000)

    ADS  CAS  Article  Google Scholar 

  5. Rousse, A. et al. Non-thermal melting in semiconductors measured at femtosecond resolution. Nature 410, 65–68 (2001)

    ADS  CAS  Article  Google Scholar 

  6. Sokolowski-Tinten, K. et al. Femtosecond X-ray measurement of ultrafast melting and large acoustic transients. Phys. Rev. Lett. 87, 225701 (2001)

    ADS  CAS  Article  Google Scholar 

  7. Cavalleri, A. et al. Femtosecond structural dynamics in VO2 during an ultrafast solid-solid phase transition. Phys. Rev. Lett. 87, 237401 (2001)

    ADS  CAS  Article  Google Scholar 

  8. Feurer, T. et al. Femtosecond silicon Kα pulses from laser produced plasmas. Phys. Rev. E 65, 016412 (2002)

    ADS  CAS  Article  Google Scholar 

  9. Lindemann, F. A. Über die Berechnung molekularer Eigenfrequenzen. Phys. Z. 11, 609–612 (1910)

    CAS  MATH  Google Scholar 

  10. Born, M. Thermodynamics of crystals and melting. J. Chem. Phys. 7, 591–603 (1939)

    ADS  CAS  Article  Google Scholar 

  11. Tallon, J. L. A hierarchy of catastrophes as a succession of stability limits for the crystalline state. Nature 342, 658–660 (1989)

    ADS  CAS  Article  Google Scholar 

  12. Madelung, O. (ed.) Semiconductors: Physics of Non-tetrahedrally Bonded Elements and Binary Compounds I in Landolt-Börnstein, New Series, Group III: Crystal and Solid State Physics Vol. 17, Semiconductors, Part a (Springer, Berlin, 1983).

  13. Peierls, R. More Surprises in Theoretical Physics (Princeton Univ. Press, Princeton, 1991)

    Google Scholar 

  14. Shick, A. B., Ketterson, J. B., Novikov, D. L. & Freeman, A. J. Electronic structure, phase stability, and semimetal-semiconductor transitions in Bi. Phys. Rev. B 60, 15484–15487 (1999)

    ADS  CAS  Article  Google Scholar 

  15. Zeiger, H. J. et al. Theory for displacive excitation of coherent phonons. Phys. Rev. B 45, 768–778 (1992)

    ADS  CAS  Article  Google Scholar 

  16. Hunsche, S., Wienecke, K., Dekorsy, T. & Kurz, H. Impulsive softening of coherent phonons in tellurium. Phys. Rev. Lett. 75, 1815–1818 (1995)

    ADS  CAS  Article  Google Scholar 

  17. Garrett, G. A., Albrecht, T. F., Whitaker, J. F. & Merlin, R. Coherent THz phonons driven by light pulses and the Sb problem: what is the mechanism? Phys. Rev. Lett. 77, 3661–3664 (1996)

    ADS  CAS  Article  Google Scholar 

  18. Hase, M., Mizoguchi, K., Harima, H. & Nakashima, S. Dynamics of coherent phonons in bismuth generated by ultrashort light pulses. Phys. Rev. B 58, 5448–5452 (1998)

    ADS  CAS  Article  Google Scholar 

  19. DeCamp, M. F., Reis, D. A., Bucksbaum, P. H. & Merlin, R. Dynamics and coherent control of high-amplitude phonons in bismuth. Phys. Rev. B 64, 092301 (2001)

    ADS  Article  Google Scholar 

  20. Hase, M., Kitajima, M., Nakashima, S. & Mizoguchi, K. Dynamics of coherent anharmonic phonons in bismuth using high density photoexcitation. Phys. Rev. Lett. 88, 067401 (2002)

    ADS  Article  Google Scholar 

  21. Von der Linde, D. et al. ‘Ultrafast’ extended to X-rays: Femtosecond time-resolved X-ray diffraction. Z. Phys. Chem. 215, 1527–1541 (2001)

    CAS  Google Scholar 

Download references

Acknowledgements

Financial support by the Deutsche Forschungsgemeinschaft, the European Community (Research and Training Network XPOSE) and the German Academic Exchange Service (DAAD) is acknowledged.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Klaus Sokolowski-Tinten.

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

Sokolowski-Tinten, K., Blome, C., Blums, J. et al. Femtosecond X-ray measurement of coherent lattice vibrations near the Lindemann stability limit. Nature 422, 287–289 (2003). https://doi.org/10.1038/nature01490

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature01490

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

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