Introduction

Refrigeration is ubiquitous in our daily life, either food storage and medical treatment, or air conditioners and all kinds of electronic devices, it can be found almost everywhere1. With the inexorable development of technology and civilization, the consumption of electricity is increasing in an astonishing speed, nearly 25% of which is attributed to the refrigeration field2. The current refrigerants used in this technology are mostly harmful gases like hydrofluorocarbon-which have global warming potentials exceeding 2000 times that of CO2 and hence is unfriendly to our planet3,4. Therefore, there is an urgent need to develop a brand-new environmentally benign and efficient refrigeration technology to address this issue5.

Under such a circumstance, solid-state refrigeration based on caloric effect from phase transition is likely to undertake this arduous task6. Caloric effect can be categorized into barocaloric effect (BCE)7,8,9,10,11,12,13,14, magnetocaloric effect (MCE)15,16,17, electrocaloric effect (ECE)18,19,20,21, and elastocaloric effect (eCE)22,23, among which BCE attracts an increasing attention because of its universality, safety and relative low cost compared with the expensive magnetic field of MCE, the breakdown voltage of ECE and the demand of huge mechanical strength of eCE materials. In contrast, it is relatively easy to obtain a hydrostatic pressure through pressure-transmitting mediums24,25,26. In fact, BCE has been found in a broad range of materials, such as spin-crossover materials27,28,29, solid-liquid phase transition n-alkanes30,31, plastic crystals25,32,33,34,35,36, ferro/ferrielectric materials37,38, ferroelastic materials39, organic-inorganic materials with carbon chains40, and magnetic phase transition alloys41,42,43,44,45.

The past few years have witnessed the thriving of the BCE materials, especially the discovery of organic plastic crystal with barocaloric entropy change (ΔS) more than 500 J kg-1 K-1, which indeed offered a strong impulse in this field32. Moreover, giant BCE with ΔS more than 100 J kg-1 K-1 has been also found in many other materials and ΔS with ~720 J kg-1 K-1 was found in n-alkanes associated with solid–liquid phase transition30,31. However, the materials with huge ΔS are commonly organic ones, which can be more or less toxic and need to be chemically synthesized.

Herein, we exploit H2O as the target candidate, which has been overlooked, for the study of BCE after taking a few merits into account. First, H2O is ubiquitous; second, the latent heat of the ice-water phase transition around 273 K is huge, ~340 kJ/kg from our measurements, and the corresponding entropy change ΔS is ~1200 J kg-1 K-1, also accompanied with a maximal isothermal entropy change ΔSiso∼1050 J kg-1 K-1 at a small pressure of 0.1 GPa, which is hitherto, to the best of our knowledge, the highest value among the reported BCE and the only one more than 1000 J kg-1 K-1. Moreover, reversible barocaloric entropy change as much as 1018 J kg-1 K-1 can be achieved by significantly mitigating supercooling degree through adding a little amount of dopant (1.33 wt% GdCl3). While the reversible refrigeration capacity RCrev which represents the capacity for exchanging heat between hot and cold sink in an ideal cooling cycle can reach 9700 J/kg, at the tier 1 place among the reported BCE materials. H2O is environmentally benign, harmless and non-toxic, hence it is likely to be a satisfactory and potential candidate for BCE refrigeration.

During exploring colossal BCE in H2O associated with the transition between crystalline ice-Ih and disordered water, a few new findings emerged. Our neutron studies presented the first experimental evidence that the main cause of H-bond breakage during ice-water transition is the O-H bending instead of the elongation of O-O distance between neighboring molecules (which was once predicted via simulation46 but no experimental evidence was given so far), from which the critical cutoff value of H-bonds was firstly determined. On the basis, the exact coordination number of H-bonds in ice and water was obtained by combining with DFT-MD calculations, i.e. 4/molecule at ice declines to 3/molecule at water in average, which was validated by our experiments considering the H-bond energy from x-ray absorption spectrum (XAS)47. This result not only explains the colossal BCE from H-bonds in H2O, more importantly, it provides robust enlightenment that H-bond engineering would be a feasible method to produce more attractive colossal entropy change by creating stronger H-bonds and/or increasing the number of them. This is distinct from the mechanism of complicated organic materials, where the changes of conformation ordering and/or molecular orientation are responsible for the colossal BCE. Besides, an important side finding is the direct experimental evidence of the gas clathrate into ice crystal, which infers the probability of creatures’ existence even in ice and delights people to explore new lives in extreme geological environment.

Results

Barocaloric performances

The H2O sample used in the heat flow measurements was sterile double-distilled H2O to confirm its purity and obtain more accurate results. The heat flow results for pure H2O at ambient pressure with a temperature ramping rate of 1 K/min are shown in Fig. 1a. The sample clearly shows a first-order phase transition with sharp heat flow peaks on heating/cooling, with transition temperatures of approximately 275.4 K/257.1 K, accompanied by a hysteresis of approximately 18.3 K (defined as the temperature difference between the heat flow peaks) owing to the supercooling effect (see details given in Supplementary Note S2). The corresponding entropy change related to the phase transition was ~1170 J kg-1 K-1, which is a record-high value to date among all published BCE materials and also larger than the entropy change of vaporization of R1234yf (CF3CH2CF3, 741 J kg-1 K-1)48 and R1234ze(E) (CHF = CHCF3 (trans), 727 J kg-1 K-1)49, which are environmentally harmful hydrofluorocarbons and hydrofluoroolefins used in conventional vapor compression refrigeration technologies (Supplementary Table S5)50. Therefore, with such an enormous entropy change, a superior BCE can be expected from H2O.

Fig. 1: Barocaloric performance of pure H2O and with 1.33 wt% GdCl3 addition.
figure 1

a Heat flow measured at atmospheric pressure with a temperature ramping rate of 1 K/min for pure H2O and b H2O with GdCl3. c Isothermal entropy change ΔSiso induced by compression (upside) and decompression (downside) of pure H2O and d H2O with GdCl3. e Reversible entropy change ΔSr under various pressures for pure H2O and f H2O with GdCl3. g Reversible adiabatic temperature change from cooling entropy curve at atmospheric pressure and heating entropy curves under applied pressure for pure H2O and h H2O with GdCl3. The extrapolating curves are plotted by dashed lines.

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First, we studied the BCE of pure H2O by high-pressure DSC under various pressures. The peaks of melting/freezing were confirmed to be 275.4 K/257.1 K at atmospheric pressure and 266.1 K/245.0 K at 0.1 GPa with nearly the same thermal hysteresis ~18 K (Fig. S1a). The pressure sensitivity can be deduced to be dTc/dP = −122 K/GPa and −92 K/GPa for cooling and heating, respectively (Fig. S1c), in line with the trend shown in the three-phase diagram (Fig. S25b)51. Accordingly, the entropy change across the solid-liquid phase transition could be extracted for all applied pressures. The entropy change across the phase transition slightly declined from 1170 J·kg-1·K-1 at atmospheric pressure to 1050 J·kg-1·K-1 at 0.1 GPa (Fig. S3a, b) owing to the complexation of H2O with the pressure transmitting gas (Figs. S18 and S19, Supplementary Note S5). Next, the pressurization induced isothermal entropy change (ΔSiso) was calculated according to the equation ΔSiso (T, P1 → P2) = S (T, P2) – S (T, P1), where the atmospheric pressure was set to be the initial and terminal pressure for the compression and decompression procedure, respectively, and the results are plotted in Fig. 1c. The barocaloric entropy change reached a maximum of ΔSiso ∼1050 J·kg-1·K-1 under a small pressure of 0.10 GPa under pressurization and depressurization respectively.

This barocaloric ΔSiso is huge; however, only the reversible parts of the entropy change and adiabatic temperature change, i.e., ΔSr and ΔTr, contribute substantially to practical refrigeration. We further investigated the reversibility of the BCE. The reversible ΔSr was obtained from the overlapping pressurization- and depressurization-induced isothermal entropy change. As shown in Fig. 1c, there was no overlap between the two areas up to 0.1 GPa and no reversible ΔTr; in other words, pure H2O cannot be applied in practical BCE cooling up to 0.1 GPa.

Limited to the pressure of our high-pressure DSC apparatus, we cannot perform heat flow measurement at higher pressures. Fortunately, the dTc/dP of H2O is almost linear (Fig. S1c, d, and Fig. S25, the three-phase diagram of H2O) such that extrapolation can be used to predict ΔSiso at higher pressures, as shown in Fig. S3a, b and Supplementary Note S10 (the dotted lines), from which the reversible ΔSr can be determined (Fig. 1e). Even when the applied pressure reached 0.19 GPa, ΔSr had a tiny value of 160 J·kg-1·K-1 whereas the reversible ΔTr was still zero (Fig. 1g). These BCE performances are likely to be disappointing considering the three-phase diagram of H2O (Fig. S25b)51, where there is an inflection point at approximately 0.22 GPa and the dTc/dP changes to be positive instead of negative, such that the pressure range should not surpass this value to obtain a BCE.

The bottleneck is that the giant entropy change ΔS cannot be reversibly driven owing to the large hysteresis (~18.3 K) caused by the supercooling effect for pure H2O. Fortunately, the supercooling degree, i.e., the hysteresis gap, can be mediated by doping52,53,54. After testing a range of dopants (including monovalence, divalence and trivalence metal ions and insoluble matters), where GdCl3 behaves the best, then a 1.33 wt% ratio of GdCl3 was eventually chosen to further explore the BCE of doped H2O. (Fig. 2 and Supplementary Note S3) The measurement conditions were the same as those used for the pure H2O and the results are illustrated in the right part of Fig. 1. The barocaloric ΔSiso remained the same as that of pure H2O (Fig. 1d) (Supplementary Note S4); however, the thermal hysteresis decreased to ~7.9 K (Fig. 1b, d), which is narrower than that of some well-known plastic crystals such as NPG, PG, and AMP25,32,33 and solid-liquid phase transition n-alkanes30 with huge latent heat ever reported as BCE materials. The relative mechanism of dopants reducing hysteresis can be seen in Supplementary Note S3. From Fig. 1d, it can be seen that there has already been overlapped areas between the pressurization induced ΔSiso at 0.1 GPa and the depressurization caused one at 0.1 GPa. Accordingly, the reversible isothermal entropy change ΔSr is shown in Fig. 1f by extrapolating pressure up to 0.19 GPa, guaranteeing not to surpass the pressure inflection point in three-phase diagram (Fig. S25b)51. ΔSr ~ 1018 J·kg-1·K-1 is obtained at 0.16 GPa, which is hitherto the record-high reversible entropy change among all reported BCE materials. The related adiabatic temperature change was also attained considering the entropy change contribution from the specific heat capacity (see Supplementary Note S1 and Figs. S4–S6). The calculated adiabatic temperature change from the quasi-direct method showed a peak value of ΔTad ∼ -17 K/19 K upon pressurization/depressurization at 0.19 GPa (Fig. S1f), whereas the reversible ones were ΔTr ∼ -9.4 K (Fig. 1h). Moreover, the cooling performances of barocaloric effects can also be assessed by the reversible refrigeration capacity (RCrev = ΔSr,max*ΔTFWHM) which takes into account not only the maximal reversible entropy change ΔSr,max but also the temperature span range ΔTFWHM (the full width at the half maximum of the ΔSr curves) so this parameter would be more comprehensive when evaluating actual performance. RCrev denotes the heat transfer capacity from cold to hot reservoir in a reversible refrigeration cycle. As shown in Fig. S31, the RCrev can reach 9700 J/kg at 0.19 GPa, strongly indicating high potential for actual refrigeration applications. Such a value is quite large after comparing H2O-1.33 wt% GdCl3 with other famous candidates. Moreover, in terms of the RCrev obtained under certain pressure, the parameter RCrev/P of H2O-1.33 wt% GdCl3 is still at the tier 1 place amongst the listed candidates with a high value of 51052 J·kg-1GPa-1 (see Figs. S31, S32, Table 2), further confirming the accessibility of the cooling potential from H2O-1.33 wt% GdCl3.

Fig. 2: Hysteresis of H2O.
figure 2

a after addition of diverse dopants (including monovalence, divalence and trivalence metal ions and insoluble matters) with the same concentration 0.99 wt% and b various mass ratios of GdCl3. Temperature scanning rate is 1 K/min.

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Neutron diffraction

To understand the mechanism of so huge an entropy change during phase transition, neutron diffraction (ND) and pair distribution function (PDF) measurements were performed to unveil the structural evolution and dynamics of the local atomic environment of H2O. To obtain a high signal to noise ratio, H was substituted with D in the ND experiment. From the ND result at 180 K (Fig. 3a and Fig. S2), the structure and lattice parameters of hexagonal ice (P63/mmc) were determined (Supplementary Table S4), consistent with the three-phase diagram51,55,56. As the temperature was increased to 230 K but remained below TC (277 K), the ND pattern remained the same with clearly visible diffraction peaks (Fig. S2d and e). However, at 300 K, above the TC, there were no diffraction peaks but rather a broadened feature (Fig. 3c), which is a typical character of a disordered phase.

Fig. 3: ND results of D2O.
figure 3

a Refinement ND results of bank 6 at 180 K. b Schematic diagram of ice crystal form. c ND raw data at 300 K. d Schematic diagram of liquid water. Red and white balls denote O and H atoms, respectively, while the dotted blue lines mark H-bonds connecting two H2O molecules.

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Pair distribution function (PDF) analysis

To detect the specific molecule movements and dynamics of local atomic environments, we further performed neutron PDF analysis, with the use of Bragg and diffuse scattering. The PDF results, shown in Fig. 4a, reveal a conspicuous difference between the results at 300 K (liquid water) and those at 180 and 230 K (ice form). For d > 5 Å, all sharp peaks once discernable at 180 K and 230 K become invisible at 300 K, reflecting highly disordering of liquid water. To elaborately analyze the specific changes in the atomic local environment from ice to water, we then focused on the first 5 peaks (Fig. 4b), which correspond to the intramolecular and intermolecular (1) O-D, (2) D-D, (3) D-O, (4) D-D, and (5) O-O pairs (Fig. 4b, c). The remarkable decrease of peak intensity and area on transitioning from ice to water, particularly for peaks (3), (4), and (5) from the intermolecular pairs, unambiguously conveys that the coordination number of D2O molecules decreased. It means that the number of neighboring molecules bonded with a certain individual D2O molecule decreased and the local environment became more disordered in liquid water. Specifically, the peak (3) (inter D-O), denoting the H-bond connecting two neighboring D2O molecules, markedly shifted to a higher d value compared with the other 4 peaks (Table 1), which indicates that the H-bonds were markedly elongated in liquid water.

Fig. 4: Pair Distribution Function results obtained from neutron diffraction of D2O.
figure 4

a PDF results obtained at 180, 230, and 300 K. b Enlarged view of the low distance area of a. Illustration of diverse atom pairs marked with different colors in c ice phase and d liquid water. Blue: (3) O-D, yellow: (4) D-D, and purple: (5) O-O. Right side shows four unit cells. (red ball and white ball denote O and H atom, respectively). e Illustration of the dynamics of two neighboring molecules from ice to water.

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Table 1 Peak position at different temperatures in the PDF curves (Fig. 4b).
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More accurately, the positions of peak (3) (inter D-O) in ice and liquid water are 1.765 Å and 1.865 Å, respectively, with an elongation ΔdO-D = 0.1 Å. Meanwhile, the peak (5) (inter O-O) at 2.745 Å in ice, along with the peak (4) (inter D-D) at 2.315 Å, slightly change to 2.755 Å and 2.325 Å respectively in liquid water with an extension of only ΔdO-O = 0.01 Å, 1/10 of the value of the peak (3) (inter D-O). Under such a circumstance to satisfy the geometric relationship, the intra O-D bond needs to rotate around the intra O atom in a molecule when it transforms from ice to liquid water, as illustrated in Fig. 4e, where a non-zero angle θ (defined as the O-O-D angle) emerges in water that was absent in the ice phase. It is mainly due to this rotation of the intra O-D bond instead of the separation of the two neighboring molecules that causes elongation of the nearest O-D distance (i.e., the H-bond between two neighboring H2O molecules), eventually inducing impairment of the H-bonds. That is, the breakage of H-bonds across the ice-water phase transition is caused by rotation of the molecule around its own O atom, which experimentally evidences the long-standing speculations in previous literature46, where Wernet et al. by theoretical simulation predicted that the H-bonds are predominantly broken by bending of a certain H2O molecule rather than by elongation between neighboring molecules, but no experimental evidence was given so far. Moreover, the three atoms O-O-D after rotation form a triangle and the length of three sides can be obtained (Fig. 4e), with rO-O = 2.755 Å, rO-H,inter = 1.865 Å and rO-H,intra = 0.975 Å at 300 K, and then the O-O-D angle θ∼19.55° can be straightforwardly determined. It is noteworthy that these results are obtained via the PDF peak positions accompanied with peak width, which means the uncertainty or fluctuation of the atom pairs involving disorder, reflected by the significant decrease of the peak intensity and broadening of the peak width across ice-water transition, particularly for the intermolecular pairs, i.e. peaks (3), (4) and (5). That is to say, the illustration in Fig. 4e denotes the “average” situation, whereas the real-world environment is more complex and diverse.

Molecular dynamics simulations

To make a quantitative characterization on H-bonds responsible for the colossal entropy change across the phase transition, we performed molecular dynamics (MD) simulations of the H-bonds based on density functional theory (DFT) and the outcomes of the above PDF analysis. In fact, the H-bonds in liquid water is continuously broken and reformed, i.e., liquid water is a dynamic system57 and the H2O molecules can form diverse polyhedrons at a certain time and then disintegrate immediately, before constituting another arbitrary polyhedron again58,59. Here, for simplicity, 72 H2O molecules were considered using two independent calculation methods (VASP and CASTEP) to identify the states of the H-bonds. According to Ref. 46, there are three kinds of H-bond states, Double Donor/DD (the two H atoms of a H2O molecule both form H-bonds with two other O atoms of two neighboring H2O molecules), Single Donor/SD (only one H-atom of a H2O molecule forms an H-bond), and Non Donor/ND (none of the H atoms form H-bonds). From numerous calculations of X-ray absorption spectra (XAS) producing the intensities of pre-edge at 535 eV and main-edge at 537 eV for H2O, Wernet et al. gave an empirical formula as a cut-off for formation of H-bond (Supplementary Note S7)46:

$${\rm{r}}({\rm{\theta }})=-0.00044{{\rm{\theta }}}^{2}+{{\rm{r}}}_{\max },$$
(1)

where r(θ) stands for the O-O distance rO-O of two neighboring H2O molecules in units of Å, θ for the O-O-H angle between the two neighboring molecules in units of degrees (Fig. 5a and b), and rmax for the cutoff value for the H-bond at θ = 0. The most essential issue during the simulation is to obtain an accurate rmax, which denotes the boundary between the two areas of intact and broken H-bonds (the vertex of the parabola, also in unit of Å, see Fig. 5a). As detailed above, two basic parameters (rO-O, θ) = (2.755 Å, 19.55°) have been determined from PDF analysis. Substituting the values into the function (1), we can get the closest cutoff rmax∼2.9 Å, which is always a vacancy in previous simulations46. In other words, this rmax used in the simulation can most exactly reflect the situations in realistic liquid water.

Fig. 5: Illustration of criterion parameters, cut off function, and phonon density of states (PDOS) spectra of H2O.
figure 5

a Cut off function r(θ) = −0.00044θ2 + rmax with rmax ≈ 2.9 Å46. The shaded area denotes intact H-bonds and the other region represents broken ones. b Illustration of the (r, θ) between the two neighboring molecules defined in the simulation. The phonon density of states (PDOS) spectra of H2O in c ice and d water at 298 K. e Contribution from O atoms and f from H atoms in PDOS. Green dashed line in d and e indicates the imaginary frequency in the calculation results of liquid water. The PDOS is calculated within the harmonic approximation at 0 K, which eventually leads to the occurrence of an imaginary frequency in the disordered water.

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After exerting arbitrary perturbations on the ideal crystal ice structure for 9000 steps (9 ps) by VASP or CASTEP, we obtained a disordered, asymmetric structure of liquid water, from which the nearest neighboring O-O distances r1 and r2 and the corresponding O-O-H angles θ1 and θ2 illustrated in Fig. 5b were sorted and assigned as intact or broken areas in Fig. 5a. The three kinds of H-bonds were then determined according to the obtained rmax∼2.9 Å above and the criterion mentioned in Supplementary Note S7. Statistics presented the percentage of three types of H-bonds in water as follows: DD = 54.2%, SD = 40.3%, and ND = 5.5% based on VASP, and DD = 58.3%, SD = 37.5% and ND = 4.2% based on CASTEP. According to XAS experiments of H2O47, the energy difference between intact H-bonds in ice and broken H-bonds in water is 1.5 kcal/mol, from which we can calculate the enthalpy change ΔH during the ice-water phase transition. We then surprisingly found that the theoretical ΔH∼357.9 J/g from VASP and ΔH∼320.2 J/g from CASTEP are almost the same as the measured ΔH = 340 J/g by DSC, which strongly suggests the rationality of the obtained percentages of the three types of H-bonds in water. Accordingly, the average number of H-bonds (N = 4 × DD% + 2 × SD% + 0 × ND%) per H2O molecule in liquid water can be determined (VASP: N∼2.974/molecule and CASTEP: N∼3.082/molecule), noting the N = 4 in ice because of the completely intact H-bonds (DD = 100%). That is to say, the coordination number of H-bonds changes from 4/H2O molecule for ice to ∼3/H2O molecule for liquid water, which is the source of the huge entropy change across the ice-water transition. It should be noted that the obtained H-bonds number per H2O molecule is only an equilibrium occasion in liquid water, the real-world circumstance is much more complicated with continuously broken and reformed H-bonds57. Here, for simplification, only the ice-water phase transition was focused ignoring the dynamic process of H-bonds in water.

Proceeding the simulation further, the phonon density of states (PDOS) reflecting the vibration information can be obtained, as illustrated in Fig. 5c-f. Overall, the PDOS spectra of both ice and water can be divided into four main regions: the vibrational/translational band below 500 cm−1, the swagging band around 1000 cm−1, the OH-bending band around 1600 cm−1, and the OH-stretching band around 3000 cm−1, as presented in Movie S2. The spectra are similar in the low frequency range with the spectrum of water being a little broadened with weaker peak intensity (Fig. 5c, d); however, the high wavenumber regions were notably different (2500–3500 cm−1, as shown in Fig. 5c, d, which is also the main Raman spectrum range, as shown in Fig. 6a), where the peaks are more complex in the liquid water than in ice, reflecting that the water becomes more chaotic on transitioning from ice. To discuss the change of PDOS, we would then regard the ice as a network consisting of balls (molecules) with springs (H-bonds) connecting each molecule, with one side of the spring being linked by H and the other by O. As shown in Fig. 5e and f, the PDOS peaks of O and H in water decrease and widen on transitioning from ice, especially in the range of 0–1000 cm−1 for O and the whole range for H, reflecting the substantial change of H-bonds. In the ice form, H2O molecules are tightly bonded with each other with the perfect springs’ connection, i.e., Double Donor species of H-bonds dominate; hence, the location of a certain atom would be accurate, leading to some specific relative atom distances, which represents the corresponding peaks in the PDOS spectrum. In addition, if one molecule in this network is affected, the others would also be more or less influenced, which then would lead to the atoms’ collective phenomenal vibration around a certain position at a similar frequency when a perturbation is applied in the ice system, presenting the pronounced and sharp PDOS intensity. In contrast, the H-bonds/springs are impaired in liquid water, i.e., the Single Donor and Non-Donor species emerge and the coordination number of H-bonds declines to ~3/molecule, so some springs are not capable enough to bind the molecules at a certain location like the situation in ice and the correlation among molecules decreases. Therefore, the partial unbound H2O molecules have a higher freedom; as such, the possible location of an atom would be difficult to determine, that is, numerous relative atom distances emerge, bringing about the broad, flat and messy PDOS spectrum and the bane of which is just the impairment of the numerous H-bonds once intact in original ice form.

Fig. 6: Raman spectra and illustration of the OH-sb.
figure 6

a Raman spectra at four temperatures. b Illustration of symmetric stretching (both bonds elongate/contract simultaneously) and asymmetric stretching (one bond elongates/contracts while the other contracts/elongates), where red and white balls denote O and H atoms, respectively. (see detailed analysis given in Supplementary Note S8 and the last part of Movie S2).

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Raman spectra

In a bit to understand the change of H-bonds during phase transition, we further measured Raman spectra which reflect the bond dynamics between atoms (Fig. 6a). There are three bands for H2O in the Raman spectrum60: the translational bands below 400 cm−1, the OH–bending bands around 1600 cm−1, and the OH–stretching band (denoted as OH–sb) corresponding to the 2900–3700 cm−1 wavenumber region60,61. To simplify the issue, we focused on the OH-sb because this band is the most intense and easily affected by structural change60.

In ice at 243 and 258 K, H bonds are steadily formed and consequently the H2O molecules are more likely to elongate or contract simultaneously, producing isotropic expansion/shrinkage of macroscopic crystalline features, as reflected by the strong symmetric O-H stretching at 3130 cm−1. The inferior asymmetric stretch at around 3350 cm−1 corresponds to anisotropic effects and is almost completely inhibited by the ordering in ice with strong H-bonds (Fig. 6a and b). As the temperature increases across TC, both bands blue shift; however, the increased amplitude of the asymmetric band was much more pronounced than that of the symmetric band. In water at 283 K, the intensity of both become nearly the same, and the asymmetric band surpasses its counterpart at 298 K. This result provides evidence that water molecules become more individual with less correlation, i.e., they become freer and more disordered on account of the decrease in coordination number of H-bonds per molecule compared with those in ice (see detailed analysis given in Supplementary Note S8).

Discussion

The external perturbation driving an ice-water transition can be either temperature or pressure. From the well-accepted three-phase diagram of H2O51,55,56, the boundary between liquid water and hexagonal ice is approximately a straight line, i.e., the temperature and pressure have the same priority for determining the liquid/ice phase over a given temperature and pressure range (T > −100 °C and P < 0.20 GPa). That is, pressure plays the same role as temperature in driving the formation/breakage of H-bonds in H2O, and the nature of the liquid/ice produced by either temperature or pressure is the same. Note that ice has a larger specific volume (1.09 × 10−3 m3/kg) than liquid water (1 × 10−3m3/kg), which creates a negative dTc/dP in our barocaloric outcomes; therefore, applying pressure can drive the ice-water transition and hence produce a huge barocaloric effect.

One of the key issues in this work is the largely reduced hysteresis by adding 1.33 wt% GdCl3 in pure H2O. In general, the addition of any dopants, whether it is soluble or not, can reduce the supercooling degree in supercooled water, the mechanism behind is that the external dopants can provide an additional surface or carrier where H2O molecules can adsorb, which can help or accelerate the nucleation process51. In addition, it can also reduce the energy barrier between the metastable supercooled state and stable ice form, just like the catalysis in the chemical reactions62. Specifically, the mechanism of reducing hysteresis in GdCl3 doped H2O can be explained as the Gd3+ and Cl- ion would absorb H2O molecules, or it can be expressed that H2O molecules would adsorb on the surface of these ions, which improves the nucleation or crystal growth probability considerably than pure H2O as well as lowering the energy barrier for freezing. Therefore, the supercooling degree is mediated.

To understand the mechanism of reduced supercooling degree by dopants, we performed sufficient experiments, and answered why we chose GdCl3 as dopants (see details given in Supplementary Note S3). To find out the critical factors that influence supercooling, such as the charge, volume and solubility of the dopants’ ions, we chose diverse dopants including monovalence ones: AgNO3, CsI, and NH4Cl, divalence ones: CaCl2, CoCl2, and MgCl2, trivalence ones: AlCl3, GdCl3, EuCl3, and BiCl3, as well as insoluble dopants: graphite and TiO2 (Fig. 2a), where GdCl3 behaves the best. From detailed experiments and analysis (Supplementary Note S3), we summarized a rough regularity of the ideal dopants for reducing the hysteresis of pure H2O, which may have the characters of larger ion volume, higher ion charge, larger ion magnetic moment and larger ion mass. However, the exact mechanism requires further research in corresponding field.

The colossal entropy change of H2O reported here derives from the numerous H-bonds during the ice-water phase transition, which conveys robust enlightenment that H-bonds would enact an potent role to produce huge entropy change or latent heat in a system with first-order phase transition, even larger than the values observed in organic systems such as plastic crystals and solid-liquid phase transition n-alkanes. Note that the colossal entropy change of these organics is mainly from the changes of conformation ordering and/or molecular orientation. Therefore, H-bonds should be paid some attention in terms of searching for novel colossal BCE besides the well-known carbon chains. H-bond engineering could be used to introduce a potential colossal entropy change into a target BCE product from the perspective of chemical synthesis. In general, to construct more powerful H-bond in a chemical complex, the acceptor side can be chosen to be F atoms because of its strongest electronegativity and hence an enhanced or robust H-bond can be achieved, which may require more external energy to overcome the energy barrier to complete the first-order phase transition and larger latent heat can be expected. Meanwhile, the energy of a H-bond also depends on the carrier or moiety where the acceptor (N, O, or F) and the donor H exist, i.e., the specific construction of the chemical complex such as bond categories, the chemical rings, etc. can also influence the strength of the target H-bonds63,64, so the specific structure of the final product should be also considered to increase the strength. In addition, the idea to increase the number of H-bond in a certain complex during synthesis may also be feasible to create colossal entropy change via introducing more H atoms and corresponding N, O, and F atoms into the product. Combination of these ideas and consideration of these factors in H-bond engineering might lead to the invention of more effective BCE materials for the refrigeration field. Moreover, H-bonds can even be regarded as a certain “degree of freedom” just like others such as carbon chains in organic matters7,8,65, the magnetism freedom in spin-crossover complexes27,28,29,66,67, and the oriental order in plastic crystals32 and so on. If the H-bonds and others co-exist in a system, the colossal entropy change would be further enhanced and the ideal BCE candidates may be born.

To evaluate the BCE properties of doped H2O, we compared other materials that have a giant BCE, and the results are plotted in Fig. 7. The maximal isothermal ΔSiso of doped H2O is absolutely the largest (ΔSiso∼1050 J·kg-1·K-1) among the listed materials whatever they are organic or inorganic, even more than 1.6 times that of the super-high value so far possessed by solid-liquid phase transition n-alkanes (ΔS∼740 J·kg-1·K-1)30. As for the practical-related reversible part, i.e., the reversible entropy change ΔSr of doped H2O is also large among reported BCE materials (Fig. 7b) at ΔSr ∼1018 J kg-1·K-1, which confirms the realistic prospects for its applications. The minimal pressure required to obtain the maximal reversible entropy change of doped H2O is 0.16 GPa. To compare the practical BCE performance, we also define the parameter ΔSr,max/Psat, where Psat is the lowest pressure required to attain the highest reversible entropy change. As shown in Fig. 7a, b, the barocaloric performance of doped H2O (either ΔSiso,max or ΔSr,max or ΔSr,max/Psat) shows an absolute dominance in inorganic materials, and also largely superior to organic materials except the parameter ΔSr,max/Psat of solid-liquid phase transition n-alkanes and PG. As for the reversible refrigeration capacity RCrev, a parameter representing capability to exchange the heat from hot to the cold end in an ideal cooling cycle, doped H2O also shows superior position in either RCrev or RCrev/P among its peers as presented in Table 2 and Fig. S31 and S32. In inorganic materials, the BCE generally originating from crystal structural change is badly inferior to that of organic substances because the advantages of latter with carbon chains can bring about high structure flexibility due to complex conformational types and the ductility possessed by the chains. In contrast, the specific but simple inorganic H2O full of H-bonds gets inverse. The contribution from the breakage/formation of H-bonds across ice-water transition makes H2O show super colossal BCE performances, exceeding that of almost all organic materials and the harmful Freon commonly used in vapor compression refrigeration.

Fig. 7: Barocaloric performance of H2O-1.33 wt% GdCl3 compared with representative organic and inorganic BCE materials.
figure 7

a Maximal isothermal entropy change upon compression or decompression. b Maximal reversible entropy change and the value divided by the lowest pressure (Psat) that can be applied to obtain it. Materials include n-alkanes C16H34 and C18H3830, carboranes para-carborane75, organic plastic crystals PG, NPG, NPA, TRIS, and AMP25,32,33, the macromolecular substance PEG100007, organic-inorganic hybrid materials (C9H19NH2)2MnCl4 and (C10H21NH2)2MnCl48, spin-crossover materials Fe[HB(tz)3]227, Fe(L)(NCS)267 and Fe3(bntrz)6(tcnset)628, hybrid perovskite [TPrA][Mn(dca)3]76, ferroelectric plastic crystals C7H14NReO438, molecular salts [Cp2Fe][PF6]77, ferromagnetic MnCoGeB0.0378, superionic conductor AgI26, ammonium sulphate (NH4)2SO437, fullerite C6079 and inorganic NH4I80.Details are also listed in Table 2.

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Table 2 Barocaloric performance of H2O-1.33 wt% GdCl3 compared with representative organic and inorganic BCE materials.
Full size table

In conclusion, by resorting to the pressure-DSC, we quasi-directly measured and reported the colossal barocaloric effect in 1.33 wt% GdCl3 doped H2O. The reversible entropy change ΔSr as large as ~1018 J kg-1 K-1 can be attained with a small hysteresis ∼7.9 K under a low pressure of ~0.16 GPa and a value of 728 J kg-1 K-1 is detected at 0.1 GPa, which is so far the empyrean among all the reported barocaloric materials. The reversible refrigeration capacity RCrev and the parameter RCrev/P are also at the tier 1 position. Combining ND and PDF results, DFT-MD simulation, PDOS and Raman spectra measurements, the colossal thermal effect of H2O is indicated from the breakage/formation of H-bonds across the ice-water transition. The coordination number of H-bonds changes from 4 H-bonds/molecule in ice to 3 H-bonds/molecule in liquid water, which essentially renders the conspicuous phase change and also the record-high entropy change; ultimately, super colossal thermal effect can be driven reversibly by low pressure, generating the reversible colossal barocaloric effect. Innately being safe, innocuous, environment-benign and ubiquitous, doped H2O would be likely to be utilized as the coolant in the design strategy of balocaloric cooling system, probably opening a new era in the field of refrigeration in the future. In addition, the hint of the H-bonds bringing about colossal entropy change in H2O also conveys the feasible method of H-bond engineering for the chemical synthesis to produce more attractive colossal entropy change in the target BCE candidates by creating stronger H-bonds and/or increasing the number of them, as well as even combining them with other degrees of freedom.

Methods

Materials

Sterile double-distilled water and the aforementioned dopants (Fig. 2) were all purchased from Maclin, Shanghai, China, and were used without further purification.

To reduce the supercooling degree, i.e., the hysteresis gap (see details given in Supplementary Note S3), doped H2O was prepared as follows: first, a calculated amount pure liquid water, appropriate for the target mass ratio, was extracted with an injector and placed in a small sample vessel. Next, the selected dopants were added to the pure liquid water to generate a series of doped H2O. After this procedure, these samples were measured by DSC to determine their corresponding hysteresis. The GdCl3 doped H2O had the smallest hysteresis (Fig. 2a), and different mass ratios of GdCl3 were further explored to find the optimal concentration by pressure-DSC. The 1.33 wt% GdCl3 doped one performed the best and was used for subsequent experiments (Fig. 2b).

Neutron diffraction (ND) measurements and PDF analysis

Neutron diffraction (ND) measurements were performed on the Time-of-Flight Multiple Physics Instrument (MPI) at the China Spallation Neutron Source (CSNS), which uses beam port 16# of the CSNS target station facing the center of a decoupled water moderator. To reduce the incoherent scattering background caused by H and increase the signal-to-noise ratio of coherent scattering, H2O was substituted with D2O. The MPI standard operating wavelength range was 0.1–4.5 Å. The beam cross-section center was 300 mm from the axis of the chopper. For the PDF measurements, the Q range was extended to a wide range of 0.08–100 Å−1 with a resolution of 0.4% by a physical design and the neutron flux at the sample was 107 s−1 cm−2, thereby covering a multi-degree disorder and a multi-scale material with a good resolution of the PDF in real space. Further details about the MPI have been previously reported68,69. The total neutron scattering data were processed using the Mantid software and Fourier transforms to obtain PDFs with a maximum momentum transfer Qmax = 25 Å−1. The full-profile Rietveld refinements of the ND patterns and the corresponding pair PDF were performed by FullProf and PDFgui software, respectively.

Raman spectra

Raman spectra were collected in backscattering geometry at variable temperatures by a Jobin Yvon T64000 triple spectrometer equipped with a cooled change-couple device. In the spectrometer a long focus objective of 20× magnification was used to focus the laser beam on the sample surface and to collect the scattered light. Raman spectra were excited with 532.0 nm radiation from a coherent solid-state laser. The laser power at the focus spot, approximately 1 μm in diameter, was maintained at 4.8 mW to obtain high quality spectra. A spectral resolution better than 1 cm−1 was obtained from our experimental configuration.

Pressure DSC, specific heat measurements and barocaloric effects

The measurement of heat flow was performed using the high-pressure differential scanning calorimeter (μDSC7 evo microcalorimeter from SETARAM, temperature range: −40∼120 °C, pressure range: 0–0.1 GPa). The temperature ramping rate was set to be 1 K/min during the whole process of the heat flow measurement. High purity N2 gas (99.999%) was used to apply hydrostatic pressure ranging from atmospheric pressure to 0.1 GPa. The specific heat capacity was also measured by the same calorimeter, the corresponding measurement was calibrated and tested against naphthalene (Standard for GC, ≥99.5% GC). In the formal measurement, a large amount of the sample (761 mg) was used to achieve the precise Cp baseline of both ice and water phases at ambient pressure (Supplementary Fig. S4 and Supplementary Note S1).

On the basis of the heat flow (Q) response of the temperature at variable pressure, the phase transition entropy curves were constructed by integration of the heat flow:

$${S}_{{pt}}(T,P)={\int }_{{T}_{0}}^{T}\frac{1}{{T}^{{\prime} }}\frac{Q({T}^{{\prime} },P)}{\dot{{T}^{{\prime} }}}d{T}^{{\prime} }.$$
(2)

Considering the thermal response besides the latent heat of phase transition, the total entropy curves were constructed including the specific heat capacity contribution, where the specific heat capacity CP at variable small pressures lower than 0.2 GPa was approximated as that for atmosphere pressure24:

$$S\left(T,P\right)={S}_{{pt}}\left(T,P\right)+{\int }_{{T}_{0}}^{T}\frac{{C}_{p}}{{T}^{{\prime} }}d{T}^{{\prime} }.$$
(3)

The barocaloric isothermal entropy change curves (ΔSiso) were obtained quasi-directly by isothermal subtraction of entropy curves at variable pressure: \(\triangle {S}_{{iso}}\left(T,{P}_{0}\to {P}_{1}\right)=S\left(T,{P}_{1}\right)-S\left(T,{P}_{0}\right)\). Specifically, the ΔSiso for the pressurization process (P0 < P1) used Q(T, P) on heating, while the ΔSiso for depressurization (P0 > P1) process used Q(T, P) on cooling. The reversible isothermal entropy change ΔSr is the overlap of ΔSiso between the pressurized and depressurized processes.

Barocaloric adiabatic temperature change curves (ΔTad) were obtained quasi-directly by adiabatic subtraction of entropy curves at variable pressure: \(\triangle {T}_{{ad}}\left(T,{P}_{0}\to {P}_{1}\right)=T\left(S,{P}_{1}\right)-T\left(S,{P}_{0}\right)\). Similar to ΔSiso, the ΔTad for the pressurization process was determined by the entropy curves on heating and the ΔTad for depressurization process determined by the entropy curves on cooling. A reversible adiabatic temperature change ΔTr was obtained from the adiabatic subtraction of the cooling entropy curve at atmospheric pressure and the heating entropy curve at the applied pressure26.

Besides the entropy change involving the phase transition, the additional entropy change ΔS+ caused by conventional thermal expansion and contraction under pressure were evaluated. The actual ΔS under pressure decreased slightly compared with the value, without considering conventional heat capacity. However, the result of the ΔS+ for H2O here is small, (3.7% out of 1170 J K−1kg−1 during heating and 1.3% of 1170 J K−1kg−1 in the cooling process, respectively) and would have little influence on the outcomes of this work. Notably, the water expansion coefficient αwater is nonlinear and up to 5.3×10−4/K at above ~60 °C. Consequently, we evaluated ΔS+ = 50–65 J K−1kg−1 at 60–80°C away from phase transition, the magnitude of which appears to follow the same tread as the latent heat (see detailed analysis provided in Supplementary Note S8).

MD-DFT calculations on H-bonds and PDOS

Molecular dynamics (MD) simulations were carried out using the density functional theory (DFT) as implemented in the Vienna ab initio simulation package (VASP)70 with the local density approximation (LDA)71. The valence states 2s22p4 for O and 1s1 for H are used with an energy cutoff of 800 eV for the plane wave basis set. To yield the water structure, the hexagonal ice structure (a = 4.4975 Å and c = 7.3224 Å from our ND measurements), including four water molecules, was adopted. We performed ab initio molecular dynamics (AIMD) simulations based on VASP code in the canonical (NVT) ensemble with the Nosé thermostat72 (SMASS = 3) at 273 and 298 K. The water structure data were taken over the last 9 ps (9000 steps) with a time step of 1 fs using a 3 × 3 × 2 hexagonal supercell (72 water molecules). All atomic positions are optimized with the conjugate gradient method until the total energy between two ionic steps are less than 10-6 eV and the atomic forces convergence criterion is set to -0.02 eV/Å. Similar AIMD simulations were also performed using the CASTEP code73. Moreover, the phonon density of states (PDOS) for ice with a 1 × 1 × 1 hexagonal cell and water with a 2 × 2 × 2 hexagonal supercell were calculated using the MedeA-phonon code74.

After exerting arbitrary perturbations to the ideal crystal ice structure for 9000 steps (9 ps) by VASP or CASTEP, we obtained the disordered, asymmetric structure of liquid water, from which the nearest neighbor O-O distances r1 and r2 and the corresponding O-O-H angles θ1 and θ2 illustrated in Fig. 5b were sorted and assigned as intact or broken areas in Fig. 5a.

The H-bond coordination number was calculated as follows: After the structure of liquid water was constructed, the information of bond lengths and bond angles were subtracted from the structure. Next, the statistics were sorted and all (rO-O, θO-O-H) datasets were manually assigned to see whether they are in the shaded area, as shown in Fig. 5a. Finally, the three species: double donor/DD, single donor/SD and non-donor/ND were obtained from last step (detailed process, see Supplementary Note S6) and the average H-bond per H2O molecule is calculated via N = 4 × DD% + 2 × SD% + 0 × ND%.