Skip to main content

Thank you for visiting 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.

Liquid–liquid transition and critical point in sulfur


The liquid–liquid transition (LLT), in which a single-component liquid transforms into another one via a first-order phase transition, is an intriguing phenomenon that has changed our perception of the liquid state. LLTs have been predicted from computer simulations of water1,2, silicon3, carbon dioxide4, carbon5, hydrogen6 and nitrogen7. Experimental evidence has been found mostly in supercooled (that is, metastable) liquids such as Y2O3–Al2O3 mixtures8, water9 and other molecular liquids10,11,12. However, the LLT in supercooled liquids often occurs simultaneously with crystallization, making it difficult to separate the two phenomena13. A liquid–liquid critical point (LLCP), similar to the gas–liquid critical point, has been predicted at the end of the LLT line that separates the low- and high-density liquids in some cases, but has not yet been experimentally observed for any materials. This putative LLCP has been invoked to explain the thermodynamic anomalies of water1. Here we report combined in situ density, X-ray diffraction and Raman scattering measurements that provide direct evidence for a first-order LLT and an LLCP in sulfur. The transformation manifests itself as a sharp density jump between the low- and high-density liquids and by distinct features in the pair distribution function. We observe a non-monotonic variation of the density jump with increasing temperature: it first increases and then decreases when moving away from the critical point. This behaviour is linked to the competing effects of density and entropy in driving the transition. The existence of a first-order LLT and a critical point in sulfur could provide insight into the anomalous behaviour of important liquids such as water.

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.


All prices are NET prices.

Fig. 1: Phase diagram of sulfur around the LLT.
Fig. 2: First-order LLT in sulfur.
Fig. 3: Local order in the LDL and HDL sulfur.

Data availability

The data that support the findings of this study are available from the corresponding author upon request. Source data are provided with this paper.


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

    Article  ADS  CAS  Google Scholar 

  2. Harrington, S., Zhang, R., Poole, P. H., Sciortino, F. & Stanley, H. E. Liquid–liquid phase transition: evidence from simulations. Phys. Rev. Lett. 78, 2409–2412 (1997).

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  4. Boates, B., Teweldeberhan, A. M. & Bonev, S. A. Stability of dense liquid carbon dioxide. Proc. Natl Acad. Sci. USA 109, 14808–14812 (2012).

    Article  ADS  CAS  Google Scholar 

  5. Glosli, J. N. & Ree, F. H. Liquid–liquid phase transformation in carbon. Phys. Rev. Lett. 82, 4659–4662 (1999).

    Article  ADS  CAS  Google Scholar 

  6. Morales, M. A., Pierleoni, C., Schwegler, E. & Ceperley, D. M. Evidence for a first-order liquid–liquid transition in high-pressure hydrogen from ab initio simulations. Proc. Natl Acad. Sci. USA 107, 12799–12803 (2010).

    Article  ADS  CAS  Google Scholar 

  7. Boates, B. & Bonev, S. First-order liquid–liquid phase transition in compressed nitrogen. Phys. Rev. Lett. 102, 015701 (2009).

    Article  ADS  Google Scholar 

  8. Aasland, S. & McMillan, P. F. Density-driven liquid–liquid phase separation in the system Al2O3–Y2O3. Nature 369, 633–636 (1994).

    Article  ADS  CAS  Google Scholar 

  9. Mishima, O. & Stanley, H. E. The relationship between liquid, supercooled and glassy water. Nature 396, 329–335 (1998).

    Article  ADS  CAS  Google Scholar 

  10. Woutersen, S., Ensing, B., Hilbers, M., Zhao, Z. & Angell, C. A. A liquid–liquid transition in supercooled aqueous solution related to the HDA-LDA transition. Science 359, 1127–1131 (2018).

    Article  ADS  CAS  Google Scholar 

  11. Tanaka, H., Hurita, R. & Mataki, H. PRL 92, Liquid–liquid transition in the molecular liquid triphenyl phosphite. Phys. Rev. Lett. 92, 025701–025704 (2004).

    Article  ADS  Google Scholar 

  12. Kurita, R. & Tanaka, H. On the abundance and general nature of the liquid–liquid phase transition in molecular systems. J. Phys. Condens. Matter 17, 293–302 (2005).

    Article  ADS  Google Scholar 

  13. Murata, K. & Tanaka, H. Microscopic identification of the order parameter governing liquid–liquid transition in a molecular liquid. Proc. Natl Acad. Sci. USA 112, 5956–5961 (2015).

    Article  ADS  CAS  Google Scholar 

  14. Katayama, Y. et al. First-order liquid–liquid phase transition in phosphorus. Nature 403, 170–173 (2000).

    Article  ADS  CAS  Google Scholar 

  15. Monaco, G., Falconi, S., Crichton, W. A. & Mezouar, M. Nature of the first-order phase transition in fluid phosphorus at high temperature and pressure. Phys. Rev. Lett. 90, 255701 (2003).

    Article  ADS  CAS  Google Scholar 

  16. Katayama, Y. et al. Macroscopic separation of dense fluid phase and liquid phase of phosphorus. Science 306, 848–851 (2004).

    Article  ADS  CAS  Google Scholar 

  17. Steudel, R. & Eckert, B. Solid sulfur allotropes. Top. Curr. Chem. 230, 1–80 (2003).

    Article  CAS  Google Scholar 

  18. Templeton, L. K., Templeton, D. H. & Zalkin, A. Crystal structure of monoclinic sulfur. Inorg. Chem. 15, 1999–2001 (1976).

    Article  CAS  Google Scholar 

  19. Crichton, W. A., Vaughan, G. B. M. & Mezouar, M. In situ structure solution of helical sulfur at 3 GPa and 400C. Z. Kristallogr. 216, 417–419 (2001).

    CAS  Google Scholar 

  20. Sauer, G. E. & Borst, L. B. Lambda transition in liquid sulfur. Science 158, 1567–1569 (1967).

    Article  ADS  CAS  Google Scholar 

  21. Tobolsky, A. V. & Eisenberg, A. Equilibrium polymerization of sulfur. J. Am. Chem. Soc. 81, 780–782 (1959).

    Article  CAS  Google Scholar 

  22. Zheng, K. M. & Greer, S. C. The density of liquid sulfur near the polymerization temperature. J. Chem. Phys. 96, 2175–2182 (1992).

    Article  ADS  CAS  Google Scholar 

  23. Brazhkin, V. V., Popova, S. V. & Voloshin, R. N. Pressure–temperature phase diagram of molten elements: selenium, sulfur and iodine. Physica B 265, 64–71 (1999).

    Article  ADS  CAS  Google Scholar 

  24. Liu, L. et al. Chain breakage in liquid sulfur at high pressures and high temperatures. Phys. Rev. B 89, 174201 (2014).

    Article  ADS  Google Scholar 

  25. Plašienka, D., Cifra, P. & Martoňák, R. Structural transformation between long and short-chain form of liquid sulfur from ab initio molecular dynamics. J. Chem. Phys. 142, 154502–154512 (2015).

    Article  ADS  Google Scholar 

  26. Mezouar, M. et al. Development of a new state-of-the-art beamline optimized for monochromatic single-crystal and powder X-ray diffraction under extreme conditions at the ESRF. J. Synchrotron Rad. 12, 659–664 (2005).

    Article  CAS  Google Scholar 

  27. Eggert, J., Weck, G., Loubeyre, P. & Mezouar, M. Quantitative structure factor and density measurements of high-pressure fluids in diamond anvil cells by X-ray diffraction: argon and water. Phys. Rev. B 65, 174105 (2002).

    Article  ADS  Google Scholar 

  28. Bellissent, R., Descotes, L., Boué, F. & Pfeuty, P. Liquid sulfur: local-order evidence of a polymerization transition. Phys. Rev. B 41, 2135–2138 (1990).

    Article  ADS  CAS  Google Scholar 

  29. Vahvaselkä, K. S. & Mangs, J. M. X-Ray diffraction study of liquid sulfur. Phys. Scr. 38, 737–741 (1988).

    Article  ADS  Google Scholar 

  30. Kalampounias, A. G., Kastrissios, D. T. & Yannopoulos, S. N. Structure and vibrational modes of sulfur around the λ-transition and the glass transition. J. Non-Cryst. Solids 326–327, 115–119 (2003).

    Article  Google Scholar 

  31. Braune, H. & Moller, O. The specific heat of liquid sulfur. Z. Naturforsch. B 9a, 210–217 (1954).

    Article  ADS  CAS  Google Scholar 

  32. Kuballa, M. & Schneider, G. Differential thermal analysis under high pressure I: investigation of the polymerisation of liquid sulfur. Ber. Bunsenges. Phys. Chem 75, 513–516 (1971).

    Article  CAS  Google Scholar 

  33. Steudel, R. Liquid sulfur. Top. Curr. Chem. 230, 81–116 (2003).

    Article  CAS  Google Scholar 

  34. Zhao, G. et al. Anomalous phase behavior of first-order fluid–liquid phase transition in phosphorus. J. Chem. Phys. 147, 204501 (2017).

    Article  ADS  CAS  Google Scholar 

  35. Holten, V. & Anisimov, M. A. Entropy-driven liquid–liquid separation in supercooled water. Sci. Rep. 2, 713 (2012).

    Article  ADS  CAS  Google Scholar 

  36. Vasisht, V. V., Saw, S. & Sastry, S. Liquid–liquid critical point in supercooled silicon. Nat. Phys. 7, 549–553 (2011).

    Article  CAS  Google Scholar 

  37. Zhao, G. et al. Phase behavior of metastable liquid silicon at negative pressure: ab initio molecular dynamics. Phys. Rev. B 93, 140203 (2016).

    Article  ADS  Google Scholar 

Download references


We acknowledge the European Synchrotron Radiation Facility for provision of synchrotron beamtime at beamline ID27, the Agence Nationale de la Recherche for financial support under grant number ANR 13-BS04-0015 (MOFLEX) and Almax easy Lab for providing the diamond cylinders.

Author information

Authors and Affiliations



The original idea was conceived by M.M. The experiments were performed by L.H., G.G., D.S. and M.M. with equal contributions. The data were analysed and the figures produced by L.H. with contributions from all the co-authors. The manuscript was written by M.M. and F.D. with contributions from all the co-authors.

Corresponding author

Correspondence to Mohamed Mezouar.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature thanks Yoshio Kono, Wenge Yang and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Density discontinuity at 740 K.

a, Raw datasets of isothermal X-ray absorption profiles I/I0 (where I0 and I are the incident and transmitted intensities, respectively) collected on decompression at 740 K. The black arrow indicates the density jump. b, Resulting isothermal density curve of sulfur (red) and density variation of NaCl pressure standard (blue). Error bars indicate 1 s.d.

Source data

Extended Data Fig. 2 Structure factors.

Structure factors (S(Q)) of liquid sulfur collected on decompression along the isothermal path at T = 740 K.

Source data

Extended Data Fig. 3 Isothermal density discontinuity.

Density of liquid sulfur as a function of temperature along isobaric paths P9 at 0.4 GPa (left) and P10 at 1.3 GPa (right). Error bars indicate 1 s.d.

Source data

Extended Data Fig. 4 LLCP in sulfur.

a, b, X-ray absorption profiles I/I0 in the horizontal (a) and vertical (b) directions in the vicinity of the critical point. During the measurements, the X-ray beam was stopped by the upper and lower anvils of the Paris–Edinburgh press. c, d, Horizontal X-ray absorption profiles at temperatures below (c; 950 K) and above (d; 1,090 K) the critical point. The red arrow in c indicates the I/I0 discontinuity at the LLT. No I/I0 discontinuity is observed at temperatures above the critical point (d).

Supplementary information

Supplementary Information

This file contains Supplementary Figures 1-16 and Supplementary Table 1. The figures and related text provide important information regarding the employed experimental method and data analysis procedure. The Supplementary Table provides absolute density values of liquid sulfur.

Video 1

This video provides a visualization of the first-order transition between the low- and high-density forms of liquid sulfur.

Source data

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Henry, L., Mezouar, M., Garbarino, G. et al. Liquid–liquid transition and critical point in sulfur. Nature 584, 382–386 (2020).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


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.


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