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.
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The data that support the findings of this study are available from the corresponding author upon request. Source data are provided with this paper.
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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.
The authors declare no competing interests.
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
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.
Structure factors (S(Q)) of liquid sulfur collected on decompression along the isothermal path at T = 740 K.
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.
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).
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.
This video provides a visualization of the first-order transition between the low- and high-density forms of liquid sulfur.
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Henry, L., Mezouar, M., Garbarino, G. et al. Liquid–liquid transition and critical point in sulfur. Nature 584, 382–386 (2020). https://doi.org/10.1038/s41586-020-2593-1