Liquid–liquid critical point in supercooled silicon

Abstract

A novel liquid–liquid phase transition has been investigated for a wide variety of pure substances, including water, silica and silicon. From computer simulations using the Stillinger–Weber (SW) classical empirical potential, Sastry and Angell1 demonstrated a first order liquid–liquid transition in supercooled silicon at zero pressure, supported by subsequent experimental and simulation studies. Whether the line of such first order transitions will terminate at a critical point, expected to lie at negative pressures, is presently a matter of debate2. Here we report evidence for a liquid–liquid critical point at negative pressures, from computer simulations using the SW potential. We identify Tc1,120±12 K, Pc−0.60±0.15 GPa as the critical temperature and pressure. We construct the phase diagram of supercooled silicon, which reveals the interconnection between thermodynamic anomalies and the phase behaviour of the system as suggested in previous works3,4,5,6,7,8,9,10. We also observe a strong relationship between local geometry (quantified by the coordination number) and diffusivity, both of which change dramatically with decreasing temperature and pressure.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: Equation of state.
Figure 2: Compressibility maxima increase with decrease in temperature.
Figure 3: Coordination number and diffusivity.
Figure 4: Relationship between structure and dynamics.
Figure 5: Phase diagram in PT plane.

References

  1. 1

    Sastry, S. & Angell, C. A. Liquid–liquid phase transition in supercooled silicon. Nature Mater. 2, 739–743 (2003).

  2. 2

    Angell, C. A. Insights into phases of liquid water from study of its unusual glass-forming properties. Science 319, 582–587 (2008).

  3. 3

    Speedy, R. J. & Angell, C. A. Isothermal compressibility of supercooled water and evidence for a thermodynamic singularity at −45 °C. J. Chem. Phys. 65, 851–858 (1976).

  4. 4

    Speedy, R. J. Stability-limit conjecture. An interpretation of the properties of water. J. Phys. Chem. 86, 982–991 (1982).

  5. 5

    Debenedetti, P. G. & D’Antonio, M. C. On the nature of the tensile instability in metastable liquids and its relationship to density anomalies. J. Chem. Phys. 84, 3339–3345 (1985).

  6. 6

    Poole, P. H., Sciortino, F., Essmann, U. & Stanley, H. E. Phase behaviour of metastable water. Nature 360, 324–328 (1992).

  7. 7

    Sastry, S., Debenedetti, P. G., Sciortino, F. & Stanley, H. E. Singularity-free interpretation of the thermodynamics of supercooled water. Phys. Rev. E. 53, 6144–6154 (1996).

  8. 8

    Mishima, O. & Stanley, H. E. Decompression-induced melting of ice IV and the liquid–liquid transition in water. Nature 392, 164–168 (1998).

  9. 9

    Liu, Y., Panagiotopoulos, A. Z. & Debenedetti, P. G. Low-temperature fluid-phase behaviour of ST2 water. J. Chem. Phys. 131, 104508 (2009).

  10. 10

    Saika-Voivod, I., Sciortino, F. & Poole, P. H. Computer simulations of liquid silica: Equation of state and liquid–liquid phase transition. Phys. Rev. E. 63, 011202 (2000).

  11. 11

    Aptekar, L. I. Phase transitions in noncrystalline germanium and silicon. Sov. Phys. Dokl. 24, 993–995 (1979).

  12. 12

    Donovan, E. P., Spaepen, F., Turnbull, D., Poate, J. M. & Jacobson, D. C. Calorimetric studies of crystallisation and relaxation of amorphous Si and Ge prepared by ion implantation. J. Appl. Phys. 57, 1795–1804 (1985).

  13. 13

    Deb, S. K., Wilding, M., Somayazulu, M. & McMillan, P. F. Pressure-induced amorphization and an amorphous–amorphous transition in densified porous silicon. Nature 414, 528–530 (2001).

  14. 14

    Hedler, A., Klaumünzer, S. L. & Wesch, W. Amorphous silicon exhibits a glass transition. Nature Mater. 3, 804–809 (2004).

  15. 15

    Angell, C. A., Borick, S. & Grabow, M. Glass transitions and first order liquid-metal-to-semiconductor transitions in 456 covalent systems. J. Non-Cryst. Solids 205–207, Part 2, 463–471 (1996).

  16. 16

    Ashwin, S. S., Waghmare, U. V. & Sastry, S. Metal-to-semimetal transition in supercooled liquid silicon. Phys. Rev. Lett. 92, 175701 (2004).

  17. 17

    Ganesh, P. & Widom, M. Liquid–liquid transition in supercooled silicon determined by first-principles simulation. Phys. Rev. Lett. 102, 075701 (2009).

  18. 18

    Kurita, R., Murata, K. I. & Tanaka, H. Control of fluidity and miscibility of a binary liquid mixture by the liquid–liquid transition. Nature Mater. 7, 647–652 (2008).

  19. 19

    Debenedetti, P. G. Supercooled and glassy water. J. Phys.: Condens. Matter 15, R1669–R1726 (2003).

  20. 20

    Mallamace, F. et al. Evidence of the existence of the low-density liquid phase in supercooled, confined water. Proc. Natl Acad. Sci. USA 104, 424–428 (2007).

  21. 21

    Stillinger, F. H. & Weber, T. A. Computer simulation of local order in condensed phases of silicon. Phys. Rev. B. 31, 5262–5271 (1985).

  22. 22

    Kim, T. H. et al. In situ high-energy X-ray diffraction study of the local structure of supercooled liquid Si. Phys. Rev. Lett. 95, 085501 (2005).

  23. 23

    Beye, M., Sorgenfrei, F., Schlotter, W. F., Wurth, W. & Föhlisch, A. The liquid–liquid phase transition in silicon revealed by snapshots of valence electrons. Proc. Natl Acad. Sci. USA 107, 16772–16776 (2010).

  24. 24

    Sastry, S. Illuminating liquid polymorphism in silicon. Proc. Natl Acad. Sci. USA 107, 17063–17064 (2010).

  25. 25

    ten Wolde, P. R. & Frenkel, D. Enhancement of protein crystal nucleation by critical density fluctuations. Science 277, 1975–1978 (1997).

  26. 26

    Ghiringhelli, L. M., Valeriani, C., Meijer, E. J. & Frenkel, D. Local structure of liquid carbon controls diamond nucleation. Phys. Rev. Lett. 99, 055702 (2007).

  27. 27

    Sciortino, F., Geiger, A. & Stanley, H. E. Network defects and molecular mobility in liquid water. J. Chem. Phys. 96, 3857–3865 (1991).

  28. 28

    Poole, P. H., Saika-Voivod, I. & Sciortino, F. Density minimum and liquid–liquid phase transition. J. Phys.: Condens. Matter 17, L431–L437 (2005).

  29. 29

    Liu, D. et al. Observation of the density minimum in deeply supercooled confined water. Proc. Natl Acad. Sci USA 104, 9570–9574 (2007).

  30. 30

    Saw, S., Ellegaard, N. L., Kob, W. & Sastry, S. Structural relaxation of a gel modeled by three body interactions. Phys. Rev. Lett. 103, 248305 (2009).

  31. 31

    Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117, 1–19 (1995).

  32. 32

    Voronin, G., Pantea, C., Zerda, T., Wang, L. & Zhao, Y. In situ X-ray diffraction study of silicon at pressures up to 15.5 GPa and temperatures up to 1073 K. Phys. Rev. B. 68, 020102 (2003).

Download references

Acknowledgements

We wish to thank C. A. Angell, P. G. Debenedetti, N. Jakse, K. F. Kelton, P. H. Poole, F. Sciortino, F. Spapen, H. E. Stanley, F. Starr, H. Tanaka and M. Widom for many fruitful discussions and comments on the manuscript. We thank CCMS, JNCASR for the computing facilities, and the Department of Science and Technology, India for support. S. Sastry is adjunct faculty at the International Centre for Theoretical Sciences, TIFR.

Author information

S. Sastry conceived the project, performed preliminary simulations and supervised the research. V.V.V. performed simulations and data analysis. S. Saw performed preliminary simulations and assisted in analysis of some of the data. V.V.V. and S. Sastry wrote the paper.

Correspondence to Srikanth Sastry.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 1249 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Vasisht, V., Saw, S. & Sastry, S. Liquid–liquid critical point in supercooled silicon. Nature Phys 7, 549–553 (2011). https://doi.org/10.1038/nphys1993

Download citation

Further reading