Ultrafast X-ray probing of water structure below the homogeneous ice nucleation temperature

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Water has a number of anomalous physical properties, and some of these become drastically enhanced on supercooling below the freezing point. Particular interest has focused on thermodynamic response functions that can be described using a normal component and an anomalous component that seems to diverge at about 228kelvin (refs 1,2,3 ). This has prompted debate about conflicting theories4, 5, 6, 7, 8, 9, 10, 11, 12 that aim to explain many of the anomalous thermodynamic properties of water. One popular theory attributes the divergence to a phase transition between two forms of liquid water occurring in the ‘no man’s land’ that lies below the homogeneous ice nucleation temperature (TH) at approximately 232kelvin13 and above about 160kelvin14, and where rapid ice crystallization has prevented any measurements of the bulk liquid phase. In fact, the reliable determination of the structure of liquid water typically requires temperatures above about 250kelvin2, 15. Water crystallization has been inhibited by using nanoconfinement16, nanodroplets17 and association with biomolecules16 to give liquid samples at temperatures below TH, but such measurements rely on nanoscopic volumes of water where the interaction with the confining surfaces makes the relevance to bulk water unclear18. Here we demonstrate that femtosecond X-ray laser pulses can be used to probe the structure of liquid water in micrometre-sized droplets that have been evaporatively cooled19, 20, 21 below TH. We find experimental evidence for the existence of metastable bulk liquid water down to temperatures of kelvin in the previously largely unexplored no man’s land. We observe a continuous and accelerating increase in structural ordering on supercooling to approximately 229kelvin, where the number of droplets containing ice crystals increases rapidly. But a few droplets remain liquid for about a millisecond even at this temperature. The hope now is that these observations and our detailed structural data will help identify those theories that best describe and explain the behaviour of water.

At a glance


  1. Coherent X-ray scattering from individual micrometre-sized droplets with a single-shot selection scheme.
    Figure 1: Coherent X-ray scattering from individual micrometre-sized droplets with a single-shot selection scheme.

    a, A train of droplets (Supplementary Information, sectionA.1.1) flows in vacuum perpendicular to ~50-fs-long X-ray pulses. A coherent scattering pattern from a water droplet was recorded when a single droplet was positioned in the interaction region at the time of arrival of a single X-ray pulse. CSPAD stands for, Cornell-SLAC pixel array detector. b, c, Each diffraction pattern is classified (Supplementary Information, sectionA.1.3) either as a water shot exclusively containing pure liquid scattering characterized by a diffuse water ring (b), or as an ice shot characterized by intense and discrete Bragg peaks superposed on the water scattering ring (c).

  2. Time dependence of water crystallization during evaporative cooling.
    Figure 2: Time dependence of water crystallization during evaporative cooling.

    Ice shot fraction (green) and estimated temperature (blue) as functions of travel time in vacuum for droplets of diameter 12µm and speed 10.35ms−1. From the ice shot fraction, shown as mean±s.d. of two to seven individual recordings, we find the onset of ice nucleation to lie between and K. The dashed blue lines represent maximum and minimum temperatures from the Knudsen model, which consistently overlap with experimental data sets from SSRL measured at known absolute temperatures (Supplementary Information, sectionsA.3.2 and B.3.5).

  3. Temperature dependence of water scattering peaks.
    Figure 3: Temperature dependence of water scattering peaks.

    a, Scattering structure factor, S(q), obtained from single-shot diffraction patterns (Supplementary Information, sectionA.3.1). Water temperature decreases from bottom to top (SSRL: 323, 298, 273, 268, 263, 258, 253, 251K; LCLS: 251, 247, 243, 239, 232, 229, 227K). The data reveal a split of the principal S(q) maximum into two well-separated peaks, S1 and S2 (dashed lines). b, Temperature dependence of the S1 and S2 peak positions, calculated from the maxima of local fifth-order polynomial least-squares fits with error bars estimated by shifting the derivatives of the polynomial fits by ±0.05Å (LCLS) and ±0.15Å (SSRL) (Supplementary Information, sectionA.3.1). Green triangles are LCLS data from 12-µm-diameter droplets; red circles are LCLS data from 34- and 37-µm-diameter droplets; and black squares are SSRL data from a static liquid sample. Purple diamonds are LCLS data from 9-µm-diameter droplets measured at a separate LCLS run with separate q-calibration (Supplementary Information, sectionA.1.2). As the temperature decreases in no man’s land, the positions of peaks S1 and S2 approach the characteristic values of LDA ice (dash–dot blue lines) as determined from neutron diffraction22 and clusters of hexagonal ice (iceIh; dashed red lines; Supplementary Information, sectionA.2.3).

  4. Temperature dependence of the tetrahedrality of liquid water.
    Figure 4: Temperature dependence of the tetrahedrality of liquid water.

    a, Magnitude of the second g(r) peak, g2, as a function of the splitting, Δq, between the S1 and S2 peaks from TIP4P/2005 molecular dynamics simulations (dots). The inset illustrates g2 for g(r) at 340K (red solid line) and 210K (black dashed line). b, Experimental g2 values, derived from measured Δq values (labels as in Fig. 3b) and the fit to molecular dynamics data shown in a, with error bars estimated from the maximum and minimum Δq values allowed by the uncertainty in the S1 and S2 peak positions. Also shown is the fourth-order polynomial least-squares fit to the experimental data (black solid line), where the last (that is, low-T) two data points for the 12-µm-diameter droplets and the last data point for the 9-µm-diameter droplets are ignored owing to high nonlinearity in the detector response, which artificially decreases g2 (Supplementary Information, sectionA.3.1). For comparison, the temperature dependences of g2 for the TIP4P/2005 (red dashed line) and SPC/E (purple dashed line) models are depicted along with the characteristic value of g2 for LDA ice22 (blue dash–dot line). c, The g(r) of TIP4P/2005 water at 220K (black solid line) bears a striking similarity to LDA ice22 (red dashed line), whereas the measured g(r) of room-temperature water24 (blue dash–dot line) shows significantly less structural correlation.


  1. Temperature-dependent S1 and S2 peak positions for the 5-[micro]l static sample
    Extended Data Table 1: Temperature-dependent S1 and S2 peak positions for the 5-µl static sample
  2. Temperature-dependent S1 and S2 peak positions for the 34-37-[micro]m-diameter droplets
    Extended Data Table 2: Temperature-dependent S1 and S2 peak positions for the 34–37-µm-diameter droplets
  3. Temperature-dependent S1 and S2 peak positions for the 12-[micro]m-diameter droplets
    Extended Data Table 3: Temperature-dependent S1 and S2 peak positions for the 12-µm-diameter droplets
  4. Temperature-dependent S1 and S2 peak positions for the 9-[micro]m-diameter droplets
    Extended Data Table 4: Temperature-dependent S1 and S2 peak positions for the 9-µm-diameter droplets


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Author information


  1. SUNCAT Center for Interface Science and Catalysis, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA

    • J. A. Sellberg,
    • T. A. McQueen,
    • M. Beye,
    • C. Chen &
    • A. Nilsson
  2. Department of Physics, AlbaNova University Center, Stockholm University, S-106 91 Stockholm, Sweden

    • J. A. Sellberg,
    • D. Schlesinger,
    • K. T. Wikfeldt,
    • L. G. M. Pettersson &
    • A. Nilsson
  3. Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, PO Box 20450, Stanford, California 94309, USA

    • C. Huang,
    • D. Nordlund,
    • T. M. Weiss &
    • A. Nilsson
  4. Department of Chemistry, Stanford University, Stanford, California 94305, USA

    • T. A. McQueen &
    • C. Chen
  5. PULSE Institute, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA

    • N. D. Loh,
    • H. Laksmono,
    • R. G. Sierra,
    • C. Y. Hampton,
    • D. Starodub &
    • M. J. Bogan
  6. Center for Free-Electron Laser Science, DESY, Notkestrasse 85, 22607 Hamburg, Germany

    • D. P. DePonte,
    • A. V. Martin &
    • A. Barty
  7. Linac Coherent Light Source, SLAC National Accelerator Laboratory, PO Box 20450, Stanford, California 94309, USA

    • D. P. DePonte,
    • C. Caronna,
    • J. Feldkamp,
    • M. M. Seibert,
    • M. Messerschmidt,
    • G. J. Williams &
    • S. Boutet
  8. Institute for Methods and Instrumentation in Synchrotron Radiation Research, Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, Wilhelm-Conrad-Röntgen Campus, Albert-Einstein-Strasse 15, 12489 Berlin, Germany

    • M. Beye
  9. Mineral Physics Institute, Stony Brook University, Stony Brook, New York, New York 11794-2100, USA

    • L. B. Skinner


A.N., C.H. and M.J.B. had the idea for and designed the experiment; S.B., G.J.W., M.M. and M.M.S. operated the coherent X-ray imaging instrument; M.J.B., D.P.D., T.A.M., J.A.S., C.H., R.G.S., C.Y.H., H.L. and D. Starodub developed, tested and ran the sample delivery system; C.H., T.A.M. and T.M.W. performed the SSRL experiment; J.A.S., T.A.M., H.L., R.G.S., C.H., D.N., M.B., D.P.D., D. Starodub, C.Y.H., C. Chen, L.B.S., M.M.S., M.M., G.J.W., S.B., M.J.B. and A.N. performed the LCLS experiments; A.B., J.A.S., N.D.L., A.V.M., G.J.W. and C. Caronna developed data processing software; J.A.S., C.H., N.D.L., H.L., D.N., A.V.M. and J.F. processed, sorted and analysed data; D. Schlesinger, K.T.W. and L.G.M.P. designed and performed the molecular dynamics simulations; D. Schlesinger, J.A.S., C.H., T.A.M., D. Starodub and L.G.M.P. implemented and simulated the Knudsen theory of evaporation; and A.N., C.H., L.G.M.P., J.A.S., D. Schlesinger and N.D.L. wrote the manuscript with input from all authors.

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  1. Supplementary Information (8.4 MB)

    This file contains Supplementary Text, Supplementary Figures 1-22, Supplementary Tables 1-6 and Supplementary References.

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