Evidence for laser-induced homogeneous oriented ice nucleation revealed via pulsed x-ray diffraction

The phenomenon of ice nucleation from supercooled water, which has far-reaching ramifications for the living and nonliving world, commonly involves heterogeneous interfaces. For example, the frost bacterium pseudomonas syringae catalyzes ice nucleation in plants, resulting in wide-scale damage thereto;¹ ice nucleation is of importance for the cryopreservation of tissue;² AgI crystals have been used as promoters of ice nucleation to induce rain precipitation by cloud seeding,³ whereas accretion of ice on airplane wings poses a practical problem.⁴ Homogeneous ice nucleation, i.e., far from a pre-existing interface, on the other hand, has remained a challenge to induce and explore. It involves a stochastic element whereby the initial time and location of nucleation are a priori unknown. Studies that measured freezing temperatures close to theoretical predictions below −30 °C were done with water drops immersed in oil, or injected in the frozen or liquid state into a vacuum chamber.^5–7 Attempts by Stan et al.⁸ to induce homogeneous ice nucleation with an alternating electric field (3 kHz–100 kHz) at 10⁵ V/m were unsuccessful. Insight on homogeneous nucleation indicating that ice-forming nuclei last ∼100 ns has been gleaned from molecular dynamic (MD) simulations.^9,10

Crystal formation has been induced with off-resonance laser pulses for the polymorphic control of glycine¹¹ in supersaturated solutions. The method has been extended to supercooled glacial acetic acid;¹² samples were cooled to −9 °C, but if not nucleated given that glacial acetic acid will freeze at −10 °C, they were removed from the cooling bath and exposed to a pulsed laser beam for several seconds to cause nucleation. Interestingly, focused laser beams, which reached the optical breakdown limit,¹³ readily induced heterogeneous ice nucleation in supercooled water.¹⁴ 

Here, we report homogeneous freezing of supercooled micro-liter water drops via non-focused 532 nm pulsed laser beam illumination at various configurations. This resulted in crystals of hexagonal ice (I_h) at freezing temperatures significantly higher than non-irradiated water drops that froze under heterogeneous conditions. For each of these supercooled water drops soon after their freezing was induced, the orientation of the resulting ice crystallites was determined via a 100 ps synchrotron x-ray pulse impinging on the supercooled drop. Analysis of the resulting x-ray diffraction patterns revealed a clear-cut correlation between the direction and the state of the polarized laser fields and the corresponding crystal alignment (along one axis) or orientation (fixed in three dimensions),¹⁵ which is a key feature of this endeavor. Monitoring the crystal formation also yielded a measure of the time scale of the nucleation process and possible evidence in favor of attachment to one another, i.e., aggregation of similarly oriented neighboring ice crystals following nucleation.

The experimental setup is composed of a cooling chamber (Sec. S1 and Fig. S1) and an optical and pulsed x-ray diffraction setup at the ESRF x-ray synchrotron beamline ID09, shown schematically in Fig. 1(a). The temperature of the chamber is controlled by using two thermoelectric Peltier coolers. At each side of the chamber, there is a view port. On the top cover, another flange is constructed, covered with a rubber septum that allows penetration of a syringe needle for deposition of a water drop (typically with a diameter of 1 mm–2 mm) onto a glass slide. The glass slides, purchased from Cytonix, are coated with a 5 nm thick monolayer of perfluoro-polyether-silane covalently bonded to the glass making it hydrophobic with a 110° contact angle. A corresponding topography AFM image (Fig. S2) reveals an amorphous layer with large aggregates of the polymer, where no lateral periodicity exists. For the temperature measurement, a Pt1000 temperature sensor is used and positioned on a glass slide close to the hydrophobic coated glass slide. To improve temperature homogeneity of the atmosphere surrounding the water drop, an internal copper cage positioned on the chamber floor covers the glass slide. The measured calibration curve to another Pt1000 sensor, which was positioned at the location of the water drop, reveals a shift of only 0.10 °C–0.20 °C between the temperature readings of the two sensors.

The optical setup is aimed to guide the pulsed laser beams (frequency doubled to 532 nm, Nd:YAG, 5 ns FWHM, Ekspla NT342) through 0.5 mm apertures to minimize the angle of the refracted ray in the drop and to impinge upon the water drop either at its upper pole, at its side, or simultaneously in both directions. The tracing of the refracted rays of both laser beams and their intersection with the x-ray beam are illustrated in Figs. 1(b)–1(d). The effective pulse was temporally extended by splitting each pulse to two parts delayed by 10 ns–12.4 ns with respect to each other. Eventually, the magnitude of the electric field of each laser pulse in the volume defined by the intersecting laser beams was about 10⁷ V/m. Under the intensity of the laser pulses, the heating effect is negligible. More details on the calculation of ray tracing and heating effect by the laser pulses are given in Sec. S2.

The pulsed near-monochromatic “pink” x-ray beam (100 ps FWHM, peaked at 18 keV, whose spectrum is shown in the supplementary material, Fig. S3),¹⁶ which passed through the center of the water drop, was always orthogonal to the laser beams (Fig. 1) and synchronized to probe diffraction 100 ns after the laser pulses. The spatial overlap between the x-ray beam spot (100 × 60 μm²) and the spot of each laser beam (500 µm diameter) was verified with a fluorescent screen and a microscope equipped with an optical CCD camera. We also verified that under 6000 x-ray pulses at 10 Hz, no freezing was induced at −18.0 °C.

The sample chamber was flushed and then filled with helium to atmospheric pressure before cooling the chamber below room temperature. Next, we deposited with a syringe a water drop of few microliter on the hydrophobic coated glass slide. The source of the water was an ultra-pure purifier that provides water with specification of electrical resistivity of 18.2 MΩ cm at 25 °C; using this source of water from a quartz bottle filled afresh each time, we deposited a water drop on the hydrophobic glass surface. The sample chamber was mounted on an X, Y, and Z translation stage so that after drop deposition, the water drop could be laterally moved and centered on the laser beam(s).

Once the point of incidence was set, the chamber was cooled directly with the Peltier devices. Our modus operandi was first to cool the chamber to temperatures typically between −10 °C and −13 °C. Then, the chamber was cooled to a specific temperature, and only when the temperature stabilized (±0.1 °C) was the water drop exposed to a train of optical laser pulses (10 Hz repetition rate) during periods of 30 s–180 s. If freezing occurred during this period, laser exposure was stopped; else, the chamber was further cooled, typically in steps of 1 °C–2 °C. After freezing, the same drop was melted and then similarly cooled to freezing under either dark conditions or using another excitation configuration.

The x-ray scattering image from a supercooled water drop (Fig. S4) revealed the broad water peak. The diffraction pattern in Fig. 2(a) from a water drop that had frozen under dark conditions at −27.4 °C displayed Bragg peaks of I_h over a broad azimuthal range, which were hkil-indexed¹⁷ and labeled 1–4 according to the magnitude of their diffraction angles. The cluster of intense (0002) and (10$1¯$0) peaks close to 12- and 9-o’clock (corresponding to an azimuth ϕ of 0° that is almost parallel to the vertical $z^$ axis in the laboratory frame and to 270° in the detector plane), respectively (both circled in red), arose from an assemblage of similarly oriented ice crystals, according to their diffraction vectors with a measured angle of 88 ± 4° therebetween [Fig. 2(b)]; the angle between these two vectors in the I_h crystal structure is 90°. The direction of the vector d^*(0002) indicates that the (0001) crystal plane was parallel to the hydrophobic glass surface, providing evidence of heterogeneous ice nucleation in the dark at the glass surface via the basal {0001} face of ice. Obviously, the hydrophobic amorphous layer on the glass slide (see Sec. II) cannot impose a preferred azimuthal orientation to the ice nucleated heterogeneously on the slide. We note that several {$1$0$1¯$0} reflections in the top right quadrant of Fig. 2(a), all relatively weak, indicate a degree of multi-crystalline formation. For convenience, a drawing is shown of a column-like crystal of I_h [Fig. 2(c)], bounded by the basal {0001}, and primary {10$1¯$0} and secondary {$112¯$0}¹⁸ prismatic, faces, and which also displays the relative orientation of a {10$1¯$0} and {10$1¯$1} face.

A qualitative demonstration of the laser-induced ice nucleation is provided by the images in Fig. 3 of two neighboring water drops of similar size where only one was subjected to laser irradiation. This drop froze at −14.0 °C, whereas its neighbor froze at −23.1 °C. Sixty experiments conducted over two years mirrored this result. Under dark conditions, different water drops froze at −26 ± 4 °C. Under illumination, the freezing temperatures depended on the configuration, polarization, and intensity of the laser pulses. For those conditions that favored homogeneous ice nucleation, the temperatures were higher by 7 °C–11 °C (Table S1).

Insight on the laser-induced ice nucleation was gained via the x-ray diffraction images in Fig. 4 by different exposures of a water drop to various configurations of the laser beam. Figures 4(a) and 4(b) correspond to illumination by consecutive vertical and horizontal (i.e., double) laser pulses, with 10 ns delay therebetween, which were linearly polarized with orthogonal electric field vectors E₁ and E₂ within the horizontal plane [Fig. 1(a)]. By comparison, Fig. 4(c) refers to horizontal illumination with a train of single circularly polarized E₂ laser pulses.

The hkil diffraction peaks of I_h, {10$1¯0$}, {0002}, and {10$1¯1$}, in Fig. 4, were assigned applying Bragg’s law d^*(hkil) = 2 sin θ/λ (Fig. S1e), where the wavelength λ = 0.681 Å is dominant in the spectral range of the x-ray beam (Fig. S3). We took advantage of this spectral property to obtain diffraction peaks at angles sufficiently close to zero [Fig. 2(a)] to permit a correlation between the orientations of these hkil crystal planes and the orientations defined by the linearly or circularly polarized electric fields. Furthermore, the combination of the spectral width of the x-ray beam and spread in crystal orientation yielded multiple diffraction peaks, which allowed us to assign crystal orientation. The assignment was also verified in Fig. S5 by the onset of the first appearing diffraction peaks in their corresponding azimuth-integrated 2θ radial profiles.

Analysis of the diffraction peaks in these figures indicated oriented I_h crystallites. Specifically, a set of three {$1$0$1¯1$} diffraction peak clusters of comparable intensities, labeled 3α, 3β, 3γ, were observed in Fig. 4(a), which are symmetry-related, assigned (0$11¯1$⁠), (⁠$1$0$1¯1$⁠), and (⁠$11¯$0$1$⁠), given the match between the measured and the I_h structure-derived angles involving their diffraction vectors (Table I), whose derived directions are depicted in Fig. 5(a). Thus, these diffraction peaks arose from an assemblage of similarly aligned ice crystals, the orientation of which was determined from the diffraction vector set. The peak 3β at 12-o’clock corresponds to (⁠$1$0$1¯1$⁠) crystal planes nearly parallel to the horizontal surface. We determined the orientation of these crystals relative to the x-ray beam direction, using the azimuth ϕ of the diffraction vectors d^*_3α(0$11¯1$⁠) and d^*_3γ(⁠$11¯$0$1$⁠). Importantly, the directions of two principal O–H⋯O bonding arrays in the (⁠$1$0$1¯1$⁠) plane are parallel to the two orthogonal electric field vectors E₁ and E₂, as is evident (and emphasized by the pale blue bars) in Fig. 6(a).

In a similar experiment, we again observed a set of three {10$1¯1$} diffraction peaks, where the (⁠$1$0$1¯1$⁠) diffraction peak was found at 12-o’clock, but the other two peaks (⁠$1¯1$0$1$⁠) and (⁠$11¯$0$1¯$⁠) were differently positioned. Likewise, their corresponding diffraction vectors (see Fig. S6) fixed the crystal orientation revealing H-bonded arrays parallel to the electric field vector E₁, whereas E₂ approximately bisects the other two sets of H-bonding arrays (Fig. S6).

In Fig. 4(b), the two diffraction peak clusters of comparable intensity (circled 1α, 1β) at 9- and 2-o’clock are symmetry-related according to their diffraction vectors, which we assigned d^*(⁠$1¯1$00) and d^*(⁠$1$0$1¯$0), respectively [see Fig. 4(b) and Table I]. Addition of the two diffraction vectors d^*(⁠$1¯1$00) + 2 × d^*(⁠$1$0$1¯$0) = d^*(⁠$112¯$0) is oriented normal to the horizontal surface [see Fig. 5(b)] so that the (⁠$112¯$0) crystal plane is nearly parallel to the plane of the two orthogonal electric field vectors E₁ and E₂. The two diffraction vectors d^*(⁠$1¯1$00) and d^*(⁠$1$0$1¯$0) also fixed the azimuth of the (⁠$112¯$0) plane in the laboratory frame such that the two orthogonal electric field vectors E₁ $(||y^)$ and E₂ $(||x^)$ are parallel to H-bonded arrays along the −a + b and c axes, respectively [Fig. 5(b)]. Note that the (⁠$112¯$0) crystal plane corresponds to the secondary prismatic face of ice [see Fig. 2(c)].

An identical crystal orientation was obtained in an experiment performed at the x-ray synchrotron ID09 beamline a year later, as shown in Fig. S7, in which the diffraction pattern and vectors are also displayed, but the consecutive linearly polarized electric field pulses E′₁ and E′₂ from orthogonal laser beams were both parallel to each other. Thus, rather than considering the horizontal (⁠$112¯$0) plane as a dominant nucleating plane, in this case, we envisage the ensemble of H-bonds with a component along the unique c axis (see Fig. S8), parallel to fields E′₁ and E′₂, as the crystal nucleating entity.

Further indication of the role played by laser polarization on the orientation of the nucleated ice crystal is given by the result of a circularly polarized single-pulsed laser beam that impinged on the supercooled water drop from its side. We anticipated that circular polarization would promote formation of the {0002} bilayer that incorporates a dense O–H⋯O bonding motif with hexagonal symmetry (Fig. S8) aligned perpendicular to the laser beam, as was observed; the (⁠$0002¯$⁠) and (0002) peaks appear at 9:30 and 3:30 h, respectively [Figs. 4(c) and 5(c)], so that the hexagonal c axis of I_h, being in the same direction as diffraction vector d^*(0002), is nearly parallel to the laser beam [Fig. 5(c)].

The additional experiments performed at the x-ray synchrotron ID09 beamline ESRF a year later with slightly different laser illumination parameters display x-ray diffraction patterns (Fig. S9) akin to what has been observed, further demonstrating the correlation between the polarized laser fields and the H-bonding arrays.

The assemblage of diffraction peaks corresponds to separate crystals of similar orientation. For example, see the magnified images of diffraction peaks at t = 700 ms in Fig. 4. Evolution of the two symmetry-related diffraction peaks 3α(0$11¯1$⁠) and 3γ (⁠$11¯$0$1$⁠) [Fig. 4(a)], as shown in Figs. 7(a) and 7(b), reveals a simultaneous onset of diffraction at t = 0 s. The azimuthal broadening of the diffraction peaks up to t = 0.7 s reaches Δϕ = 2.5° [Fig. 7(b)]. With time, these broad peaks along the azimuth coordinate ϕ became narrower and more intense, e.g., on reaching t = 8.0 s, two separate diffraction peaks (that correspond to two separate crystals) are spanned over Δϕ = 1.5°. Eventually, from t ∼ 12 s, a single narrowest peak with Δϕ = 0.5° appears in the azimuth of one of them. This process was accompanied by peak disappearance, suggesting perhaps crystal growth that incorporates particle attachment²⁰ of similarly oriented nuclei.

Substantial evidence that the laser-induced ice nucleation, which appeared to occur in the central region of the drop (Fig. S10 and Sec. S5), was homogenous came from an analysis of the diffraction data. Oriented ice assemblages were nucleated with their (⁠$101¯1$⁠) or (⁠$112¯$0) planes parallel to the plane formed by two orthogonal laser electric fields whose directions were parallel to the H-bonding arrays in the oriented ice crystals; this correlation is also consistent with aligned I_h nucleated by parallel-linear or by circularly polarized electric fields.

We have provided CCD images and x-ray diffraction patterns of ice nucleation that occurred at significantly higher temperatures only under the effect of the laser pulses. Our analysis of the first appearance of the diffraction peaks following ice nucleation revealed in all cases H-bonded arrays parallel to the electric fields of the pulsed laser beams. This result is in accordance with a 1064 nm laser-induced formation of two-dimensional crystals of a peptidic β-sheet bilayer on the water surface, in which the N–H⋯O=C bonds were parallel to the linearly polarized electric field of the laser beam, reported by Birman et al.²¹ Furthermore, we observed horizontal orientation of the {10$1¯1$} and {11$2¯$0} planes of I_h, each with their H-bonded arrays parallel to the orthogonal electric fields of the pulsed laser beams. We claim this correlation indicates that ice nucleation was induced within the bulk water drop, specifically in the volume element where the two orthogonal laser beams intersected in the central region of the water drop. Indeed, 100 ns after the ice-inducing laser pulse, the first appearing diffraction peaks that are symmetry related and evolve to become sharper and more intense (as illustrated in Figs. 7 and 4) indicate that ice nucleation in this volume element was detected at an early stage. We thus attribute these findings to laser-induced ice nucleation that takes place in a homogeneous water environment.

This general conclusion, however, prompted the question whether the nucleation within the water drop could not have occurred heterogeneously via ice nucleation particles immersed in the water drop. In addition, we are faced with the question of the mechanism that has led the laser pulses to induce oriented ice nucleation, on which we shall now elaborate.

Ice nucleating materials such as mineral dust samples of K-feldspar²² and kaolinite,²³ amphiphilic alcohol C_nH_2n+1OH monolayers,²⁴ cracks on the side faces of crystalline R,S alanine,²⁵ glass panes and other substrates that support snow crystals with sixfold symmetry,²⁶ and the crystal surface of lithium tantalate²⁷ and the hydrophobic glass surface on which the water drops froze in the dark as described above, all nucleate ice via its basal {0001} face, except for K-feldspar, which nucleates ice via its primary prismatic {10$1¯$0} face. Therefore, the ${101¯1}$ and {$112¯$0} planes would not be faces ice is commonly nucleated from at an ice nucleating particle. We cannot, however, dismiss the possibility that the ice nuclei were induced heterogeneously at the helium–water interface for the one case where the circularly polarized laser beam impinged on the water drop from the side, promoting formation of ice nuclei whose {0002} bilayers (Fig. S8) were nearly perpendicular to the laser beam.

As for additional arguments that would disfavor heterogeneous nucleation, the three x-ray diffraction images [see Figs. 4(a)–4(c)] each indicate that several similarly oriented nuclei were induced with an average angular Δϕ spread of 6 ± 4°. This extent of crystal orientation is, in the main, consistent with the angular spread of the refracted laser rays [see Figs. 1(b)–1(d)] rather than being nucleated by different ice nucleating particles with similar orientations. Another consideration involves the concentration of ice nucleating particles as dictated by the specification of the milli-pore water we used or by a review on nonhomogeneous freezing of “pure” water.²⁸ Each case would correspond to an average of less than one ice nucleating particle in the interaction volume (100 × 60 × 500 µm³) of the x-ray beam with the two orthogonal laser beams. We also exclude the possibility of diffusing particles into this region in view of the high viscosity of supercooled water,²⁹ which is predicted to be essentially immobile.³⁰ 

In conclusion, we found an unambiguous correlation between the direction and the state of the polarized laser fields and the corresponding ice crystal alignment or orientation, where the nucleation appeared to be homogeneously induced at temperatures higher by at least 15 °C than the reported values.^5–7 

Different mechanisms were invoked to explain the laser-induced nucleation under off-resonance laser pulses with intensities of the order of 10⁷ W/cm², which correspond to an electrical field of 10⁷ V/m, or equivalently to 1 mV/Å.³¹ The first mechanism to consider is the optical Kerr effect. Its low magnitude relative to the thermal energy renders the optical Kerr effect irrelevant for our case and also for clusters of molecules that can be relevant only at a much higher laser intensity.³² Another mechanism, dielectric polarizability³¹ relies on the difference in the relative permittivity of a continuous homogeneous dielectric medium surrounding a solid particle. We rule out this mechanism as the difference in the relative permittivity of the pre-nucleus ice, and the surrounding liquid water is surely negligible. We thus hypothesize a model that relies on the attractive interaction between laser-induced dipoles³³ that has a strong dependence on the interdipole distance $1r3$ and the size of the pre-nucleus. Artamonov and Seideman³⁴ simulated the self-assembly of ethylene molecules in saturated vapor. They found that when the intermolecular distance reduces to 3.9 Å–5 Å, the interaction between laser-induced dipoles becomes relevant for the molecular self-assembly and can reduce the potential energy by 900 meV, but for laser pulses with a much higher intensity (110 TW) than those applied in our type of experiments.

Our models to account for the laser-induced nucleation of ice rely in part on the classical picture.⁷ In one scenario, we assume that a nucleus with a pre-critical size is formed in the bulk of the supercooled water drop, which is randomly oriented. The pulsed laser beams will reduce the barrier for ice nucleation by promoting the formation of H-bonded arrays in the nucleus preferably along polarized laser fields, provided the nucleus be(comes) appropriately oriented vis-a-vis the electric fields. In an alternative scenario, rather than enhancing an already formed randomly oriented pre-critical nucleus, the laser beam(s) play a more prominent role by inducing formation of an oriented or aligned early stage ice nucleus. Indeed, this model is in agreement with the observation of an assemblage of similarly oriented ice crystals in keeping with the angular beam spread. Moreover, the fact that we did not observe in any of the above-mentioned experiments diffraction peaks indicating additional and thus different crystal orientations, is consistent with this model.

We are also of the opinion that advantage is taken of the polarizability of the water molecules along their O–H⋯O bonds and of the centrosymmetric proton-disordered crystal structure of I_h such that neighboring antiparallel O–H⋯O bonds may be subject to an attractive interaction between laser-induced dipoles.³⁴ An open question remains whether there is a build-up of H-bonded arrays during the train of laser pulses, finally sensed via x-ray diffraction, or is the barrier for nucleation only overcome by the critical laser pulse following which diffraction from I_h crystals appear, in which case the nucleation time would be <100 ns.

We plan next to investigate in a manner akin to what was done on hexagonal ice, the laser-induced nucleation of crystalline formamide, which melts at +2.5 °C. The structure of crystalline formamide embodies molecular layers in which linear H-bonded arrays are perpendicular to each other. One objective that eluded us in our nucleation study of ice is to induce alignment of the H-bonded layers at a precise Bragg angle appropriate for 100 ps pulsed diffraction to obtain a measure of the size of the crystal nucleus of formamide.

See the supplementary material for additional details on the cooling chamber, assignment of x-ray diffraction vectors, AFM images of the hydrophobic monolayer, details on geometry of the water drop to trace the refracted laser rays, estimation of heating by the laser pulses, spectrum of the pulsed (“pink”) x-ray beam, x-ray scattering image from a liquid water drop, azimuth-integrated 2θ radial profiles of the first appearing diffraction peaks, disordered H-atoms in I_h, additional x-ray diffraction data, a drawing of the H-bonding arrangement in I_h, and CCD images of the water drop at different stages of freezing, and Table listing ice freezing temperatures under various laser polarization conditions and the corresponding nucleated hkil planes of ice.

The data that support the findings of this study are available within the article (and its supplementary material).

The authors are deeply indebted to Gilad Haran and Leeor Kronik of the Weizmann Institute of Science. Gilad, as former Dean of the Faculty of Chemistry, provided the authors with a fund of 40 000$ to initiate and conduct the experiments at a time when I.N., S.J., and L.L. started with was a cartoon of the ice nucleation process. Leeor, as head of the Department of Materials and Interfaces, provided funds to help cover salary requirements. I.N. thanks Ayelet Teitelboim, a former student in the laboratory of D.O., for technical assistance with the opto-mechanical elements and the operation of the laser, and Yeruham (Yuri) Shimoni, Guy Han, and Rostyslav Baron from the department of complex systems at the WIS for technical assistance. The authors thank Wolfgang Reichenbach from the ID09 beamline staff in ESRF for his technical assistance in constructing the setup for the experiments with the pulsed x-ray beam.