Here we reproduce the fluid-inclusion experiment, performing repeated measurements on a single sample-a method used in meteorology 5 , bioprotection 6 and protein crystallization 7 , but not yet in liquid water under large mechanical tension. The resulting cavitation statistics are characteristic of a thermally activated process, and both the free energy and the volume of the critical bubble are well described by classical nucleation theory when the surface tension is reduced by less than 10%, consistent with homogeneous cavitation. The line of density maxima of water at negative pressure is found to reach 922.8 kg m −3 at around 300 K, which further constrains its contested phase diagram.Owing to the strong cohesion of water, which manifests in its large surface tension, the liquid is expected to withstand pressures in excess of −100 MPa (ref. 8), as predicted for instance by classical nucleation theory 9 (CNT). The only experimental technique for which such large tensions have been reported uses water inclusions in quartz 3 . The magnitude of the tension was also independently confirmed by light scattering 10 . Several other independent experimental techniques report cavitation at much lower tensions 4 , prompting the proposal of a new kind of heterogeneous cavitation involving stabilization of water in an inclusion against nucleation by impurities 11 or surfaces 12 . Agreement between cavitation-pressure measurements and CNT would thus be advantageous.In the work that pioneered the fluid-inclusions technique 3 , a large number of inclusions, covering a wide density range, were studied. However, the cavitation event in each individual inclusion was usually observed only once. One inclusion was observed in repeated runs ''to nucleate randomly in the range 40-47 • C and occasionally not at all'' 3 , which was qualitatively interpreted as evidence for the crossing of the line of density maxima (LDM) of water. In the present work, we chose to focus on only one inclusion, and to perform a large number of cavitation experiments to obtain the statistics of nucleation. We confirm the previous data in terms of cavitation threshold, but in addition, by probing nucleation rates over three decades and using the nucleation theorem 13 , we gain insight into the nanoscopic mechanism underlying bubble nucleation. The results are consistent with CNT with a slightly Equilibrium transitions are given by blue curves. The extrapolation of the EOS measured at positive pressure 21 is used to plot the liquid-vapour spinodal (red), the LDM (black) and the isochore at ρ = 922.8 kg m −3 (green) corresponding to the inclusion studied (see Methods for details).Here the spinodal is re-entrant 14 , but other scenarios suggest that it remains monotonic 9,15 . The LDM has been measured only down to reduced surface tension, related to the small size of the critical bubble. Moreover, the analysis allows us to derive quantitative information on the LDM, which is of paramount importance in the debate about the origin of water anomalies. Indeed, ...

Water anomalies still defy explanation. In the supercooled liquid, many quantities, for example heat capacity and isothermal compressibility κ T , show a large increase. The question arises if these quantities diverge, or if they go through a maximum. The answer is key to our understanding of water anomalies. However, it has remained elusive in experiments because crystallization always occurred before any extremum is reached. Here we report measurements of the sound velocity of water in a scarcely explored region of the phase diagram, where water is both supercooled and at negative pressure. We find several anomalies: maxima in the adiabatic compressibility and nonmonotonic density dependence of the sound velocity, in contrast with a standard extrapolation of the equation of state. This is reminiscent of the behavior of supercritical fluids. To support this interpretation, we have performed simulations with the 2005 revision of the transferable interaction potential with four points. Simulations and experiments are in near-quantitative agreement, suggesting the existence of a line of maxima in κ T (LMκ T ). This LMκ T could either be the thermodynamic consequence of the line of density maxima of water [Sastry S, Debenedetti PG, Sciortino F, Stanley HE (1996) Phys Rev E 53:6144-6154], or emanate from a critical point terminating a liquid-liquid transition [Sciortino F, Poole PH, Essmann U, Stanley HE (1997) Phys Rev E 55:727-737]. At positive pressure, the LMκ T has escaped observation because it lies in the "no man's land" beyond the homogeneous crystallization line. We propose that the LMκ T emerges from the no man's land at negative pressure.scenarios for water | Widom line | Berthelot tube W ater differs in many ways from standard liquids: ice floats on water, and, upon cooling below 48C, the liquid density decreases. In the supercooled liquid, many quantities, for example heat capacity and isothermal compressibility, show a large increase. Extrapolation of experimental data suggested a powerlaw divergence of these quantities at −458C (1). Thirty years ago, the stability-limit conjecture proposed that an instability of the liquid would cause the divergence (2) (Fig. 1A). This is supported by equations of state (EoSs), such as the International Association for the Properties of Water and Steam (IAPWS) EoS (3), fitted on the stable liquid and extrapolated to the metastable regions. Ten years later, the second critical point interpretation, based on simulations (4), proposed that, instead of diverging, the anomalous quantities would reach a peak, near a Widom line (5, 6) that emanates from a liquid-liquid critical point (LLCP) terminating a first-order liquid-liquid transition (LLT) between two distinct liquid phases at low temperature (Fig. 1B). The two scenarios differ in the shape of the line of density maxima (LDM) of water ( Fig. 1 A and B). A recent work (7) has added one point on this line at large negative pressure, but this was not enough to decide between the two scenarios.It has been argued (8) that ...