• Bartels-Rausch, T. et al. Ice structures, patterns, and processes: a view across the icefields. Rev. Mod. Phys. 84, 885–944 (2012).

    ADS 

    Google Scholar
     

  • Fumagalli, L. et al. Anomalously low dielectric constant of confined water. Science 360, 1339–1342 (2018).

    ADS 

    Google Scholar
     

  • Ball, P. Water as an active constituent in cell biology. Chem. Rev. 108, 74–108 (2008).


    Google Scholar
     

  • Wang, Y.-H. et al. In situ Raman spectroscopy reveals the structure and dissociation of interfacial water. Nature 600, 81–85 (2021).

    ADS 

    Google Scholar
     

  • Petrenko, V. F. & Whitworth, R. W. Physics of Ice (OUP Oxford, 1999).

  • Salzmann, C. G. Advances in the experimental exploration of water’s phase diagram. J. Chem. Phys. 150, 060901 (2019).

    ADS 

    Google Scholar
     

  • Rosu-Finsen, A. et al. Medium-density amorphous ice. Science 379, 474–478 (2023).

    ADS 

    Google Scholar
     

  • Xu, P. et al. Elastic ice microfibers. Science 373, 187–192 (2021).

    ADS 

    Google Scholar
     

  • Saunders, C. in Planetary Atmospheric Electricity (eds LeBlanc, F. et al.) 335–353 (Springer, 2008); https://doi.org/10.1007/978-0-387-87664-1_22

  • Dash, J. G., Rempel, A. W. & Wettlaufer, J. S. The physics of premelted ice and its geophysical consequences. Rev. Mod. Phys. 78, 695–741 (2006).

    ADS 

    Google Scholar
     

  • Thiel, D. V. Electromagnetic emission (EME) from ice crack formation: preliminary observations. Cold Reg. Sci. Technol. 21, 49–60 (1992).


    Google Scholar
     

  • Fifolt, D. A., Petrenko, V. F. & Schulson, E. M. Preliminary study of electromagnetic emissions from cracks in ice. Philos. Mag. B 67, 289–299 (1993).

    ADS 

    Google Scholar
     

  • Zubko, P., Catalan, G. & Tagantsev, A. K. Flexoelectric effect in solids. Annu Rev. Mater. Sci. 43, 387–421 (2013).

    ADS 

    Google Scholar
     

  • Lu, H. et al. Mechanical writing of ferroelectric polarization. Science 336, 59–61 (2012).

    ADS 

    Google Scholar
     

  • Deng, Q., Liu, L. P. & Sharma, P. Flexoelectricity in soft materials and biological membranes. J. Mech. Phys. Solids 62, 209–227 (2014).

    ADS 
    MathSciNet 

    Google Scholar
     

  • Narvaez, J., Vasquez-Sancho, F. & Catalan, G. Enhanced flexoelectric-like response in oxide semiconductors. Nature 538, 219–221 (2016).

    ADS 

    Google Scholar
     

  • Yang, M. M., Kim, D. J. & Alexe, M. Flexo-photovoltaic effect. Science 360, 904–907 (2018).

    ADS 

    Google Scholar
     

  • Vasquez-Sancho, F., Abdollahi, A., Damjanovic, D. & Catalan, G. Flexoelectricity in bones. Adv. Mater. 30, 1705316 (2018).


    Google Scholar
     

  • Shu, L. et al. Photoflexoelectric effect in halide perovskites. Nat. Mater. 19, 605–609 (2020).

    ADS 

    Google Scholar
     

  • Torbati, M., Mozaffari, K., Liu, L. & Sharma, P. Coupling of mechanical deformation and electromagnetic fields in biological cells. Rev. Mod. Phys. 94, 025003 (2022).

    ADS 
    MathSciNet 

    Google Scholar
     

  • Peng, W. et al. Flexoelectric polarizing and control of a ferromagnetic metal. Nat. Phys. 20, 450–455 (2024).


    Google Scholar
     

  • Slater, B. & Michaelides, A. Surface premelting of water ice. Nat. Rev. Chem. 3, 172–188 (2019).


    Google Scholar
     

  • Ribeiro, I. D. A. & Koning, M. D. Grain-boundary sliding in ice Ih: tribology and rheology at the nanoscale. J. Phys. Chem. C 125, 627–634 (2021).


    Google Scholar
     

  • Ma, Q., Wen, X., Lv, L., Deng, Q. & Shen, S. On the flexoelectric-like effect of Nb-doped SrTiO3 single crystals. Appl. Phys. Lett. 123, 082902 (2023).

    ADS 

    Google Scholar
     

  • Zubko, P., Catalan, G., Buckley, A., Welche, P. R. & Scott, J. F. Strain-gradient-induced polarization in SrTiO3 single crystals. Phys. Rev. Lett. 99, 167601 (2007).

    ADS 

    Google Scholar
     

  • Vales-Castro, P. et al. Flexoelectricity in antiferroelectrics. Appl. Phys. Lett. https://doi.org/10.1063/1.5044724 (2018).

  • Ma, W. & Cross, L. E. Flexoelectricity of barium titanate. Appl Phys. Lett. 88, 232902 (2006).

    ADS 

    Google Scholar
     

  • Narvaez, J. & Catalan, G. Origin of the enhanced flexoelectricity of relaxor ferroelectrics. Appl. Phys. Lett. https://doi.org/10.1063/1.4871686 (2014).

  • Mishima, O., Calvert, L. & Whalley, E. ‘Melting ice’I at 77 K and 10 kbar: a new method of making amorphous solids. Nature 310, 393–395 (1984).

    ADS 

    Google Scholar
     

  • Garg, A. K. High-pressure Raman spectroscopic study of the ice Ih → ice IX phase transition. Phys. Status Solidi a 110, 467–480 (1988).

    ADS 

    Google Scholar
     

  • Su, X. C., Lianos, L., Shen, Y. R. & Somorjai, G. A. Surface-induced ferroelectric ice on Pt(111). Phys. Rev. Lett. 80, 1533–1536 (1998).

    ADS 

    Google Scholar
     

  • Sugimoto, T., Aiga, N., Otsuki, Y., Watanabe, K. & Matsumoto, Y. Emergent high-Tc ferroelectric ordering of strongly correlated and frustrated protons in a heteroepitaxial ice film. Nat. Phys. 12, 1063–1068 (2016).


    Google Scholar
     

  • Aiga, N., Sugimoto, T., Otsuki, Y., Watanabe, K. & Matsumoto, Y. Origins of emergent high-Tc ferroelectric ordering in heteroepitaxial ice films: sum-frequency generation vibrational spectroscopy of H2O and D2O ice films on Pt(111). Phys. Rev. B https://doi.org/10.1103/PhysRevB.97.075410 (2018).

  • Shen, S. & Hu, S. A theory of flexoelectricity with surface effect for elastic dielectrics. J. Mech. Phys. Solids 58, 665–677 (2010).

    ADS 
    MathSciNet 

    Google Scholar
     

  • Tagantsev, A. K. & Yurkov, A. S. Flexoelectric effect in finite samples. J. Appl. Phys. 112, 044103 (2012).

    ADS 

    Google Scholar
     

  • Stengel, M. Surface control of flexoelectricity. Phys. Rev. B 90, 201112 (2014).

    ADS 

    Google Scholar
     

  • Narvaez, J., Saremi, S., Hong, J., Stengel, M. & Catalan, G. Large flexoelectric anisotropy in paraelectric barium titanate. Phys. Rev. Lett. 115, 037601 (2015).

    ADS 

    Google Scholar
     

  • Martí, X. et al. Skin layer of BiFeO3 single crystals. Phys. Rev. Lett. 106, 236101 (2011).

    ADS 

    Google Scholar
     

  • Zhang, X. et al. Large flexoelectriclike response from the spontaneously polarized surfaces in ferroelectric ceramics. Phys. Rev. Lett. 121, 057602 (2018).

    ADS 

    Google Scholar
     

  • Pan, D. et al. Surface energy and surface proton order of ice Ih. Phys. Rev. Lett. 101, 155703 (2008).

    ADS 

    Google Scholar
     

  • Michaelson, H. B. The work function of the elements and its periodicity. J. Appl. Phys. 48, 4729–4733 (1977).

    ADS 

    Google Scholar
     

  • Buser, O. & Aufdermaur, A. in Electrical Processes in Atmospheres (eds Dolezalek, H., Reiter, R. & Landsberg, H. E.) 294–301 (Springer, 1976).

  • Mazzega, E., del Pennino, U., Loria, A. & Mantovani, S. Volta effect and liquidlike layer at the ice surface. J. Chem. Phys. 64, 1028–1031 (1976).

    ADS 

    Google Scholar
     

  • Batra, I. P. & Kleinman, L. Chemisorption of oxygen on aluminum surfaces. J. Electron Spectrosc. Relat. Phenom. 33, 175–241 (1984).

    ADS 

    Google Scholar
     

  • Scott, J. F. Ferroelectrics go bananas. J. Phys. Condens. Matter https://doi.org/10.1088/0953-8984/20/02/021001 (2008).

  • Pedroza, L. S., Poissier, A. & Fernandez-Serra, M. V. Local order of liquid water at metallic electrode surfaces. J. Chem. Phys. 142, 034706 (2015).

    ADS 

    Google Scholar
     

  • Sugimoto, T. & Matsumoto, Y. Orientational ordering in heteroepitaxial water ice on metal surfaces. Phys. Chem. Chem. Phys. 22, 16453–16466 (2020).


    Google Scholar
     

  • Poissier, A., Ganeshan, S. & Fernandez-Serra, M. The role of hydrogen bonding in water–metal interactions. Phys. Chem. Chem. Phys. 13, 3375–3384 (2011).


    Google Scholar
     

  • Mizzi, C. A., Lin, A. Y. W. & Marks, L. D. Does flexoelectricity drive triboelectricity? Phys. Rev. Lett. 123, 116103 (2019).

    ADS 

    Google Scholar
     

  • Mizzi, C. A. & Marks, L. D. When flexoelectricity drives triboelectricity. Nano Lett. 22, 3939–3945 (2022).

    ADS 

    Google Scholar
     

  • Qiao, H. et al. Mixed triboelectric and flexoelectric charge transfer at the nanoscale. Adv. Sci. 8, 2101793 (2021).


    Google Scholar
     

  • Kumar, M., Lim, J., Park, J.-Y. & Seo, H. Flexoelectric effect driven colossal triboelectricity with multilayer graphene. Curr. Appl. Phys. 32, 59–65 (2021).

    ADS 

    Google Scholar
     

  • Lin, S., Zheng, M., Xu, L., Zhu, L. & Wang, Z. L. Electron transfer driven by tip-induced flexoelectricity in contact electrification. J. Phys. D 55, 315502 (2022).

    ADS 

    Google Scholar
     

  • Olson, K. P. & Marks, L. D. What puts the ‘tribo’ in triboelectricity? Nano Lett. 24, 12299–12306 (2024).


    Google Scholar
     

  • Sobarzo, J. C. et al. Spontaneous ordering of identical materials into a triboelectric series. Nature 638, 664–669 (2025).


    Google Scholar
     

  • Milbrandt, J. A. & Morrison, H. Prediction of graupel density in a bulk microphysics scheme. J. Atmos. Sci. 70, 410–429 (2013).

    ADS 

    Google Scholar
     

  • Wettlaufer, J. S. & Dash, J. G. Melting below zero. Sci. Am. 282, 50–53 (2000).


    Google Scholar
     

  • Takahashi, T. Riming electrification as a charge generation mechanism in thunderstorms. J. Atmos. Sci. 35, 1536–1548 (1978).

    ADS 

    Google Scholar
     

  • Gaskell, W. & Illingworth, A. Charge transfer accompanying individual collisions between ice particles and its role in thunderstorm electrification. Q. J. R. Meteorol. Soc. 106, 841–854 (1980).

    ADS 

    Google Scholar
     

  • Williams, E. R. The tripole structure of thunderstorms. J. Geophys. Res. Atmos. 94, 13151–13167 (1989).

    ADS 

    Google Scholar
     

  • Jayaratne, E., Saunders, C. & Hallett, J. Laboratory studies of the charging of soft-hail during ice crystal interactions. Q. J. R. Meteorol. Soc. 109, 609–630 (1983).

    ADS 

    Google Scholar
     

  • Keith, W. & Saunders, C. The effect of centrifugal acceleration on the charging of a riming hailstone. Meteorol. Atmos. Phys. 41, 55–61 (1989).

    ADS 

    Google Scholar
     

  • Caranti, G., Avila, E. & Ré, M. Charge transfer during individual collisions in ice growing from vapor deposition. J. Geophys. Res. Atmos. 96, 15365–15375 (1991).

    ADS 

    Google Scholar
     

  • Avila, E. E. & Caranti, G. M. A laboratory study of static charging by fracture in ice growing by riming. J. Geophys. Res. Atmos. 99, 10611–10620 (1994).

    ADS 

    Google Scholar
     

  • Pereyra, R. G. & Avila, E. E. Charge transfer measurements during single ice crystal collisions with a target growing by riming. J. Geophys. Res. Atmos. 107, AAC 23-21-AAC 23-29 (2002).

  • Luque, M. Y., Nollas, F., Pereyra, R. G., Bürgesser, R. E. & Ávila, E. E. Charge separation in collisions between ice crystals and a spherical simulated graupel of centimeter size. J. Geophys. Res. Atmos. 125, e2019JD030941 (2020).

    ADS 

    Google Scholar
     

  • Gaskell, W. Field and Laboratory Studies of Precipitation Charges (Univ. Manchester, 1979).

  • Pamuk, B., Allen, P. B. & Fernández-Serra, M. V. Electronic and nuclear quantum effects on the ice XI/ice Ih phase transition. Phys. Rev. B 92, 134105 (2015).

    ADS 

    Google Scholar
     

  • Dash, J. & Wettlaufer, J. The surface physics of ice in thunderstorms. Can. J. Phys. 81, 201–207 (2003).

    ADS 

    Google Scholar
     

  • Ordejón, P., Artacho, E. & Soler, J. M. Self-consistent order-N density-functional calculations for very large systems. Phys. Rev. B 53, R10441 (1996).

    ADS 

    Google Scholar
     

  • Soler, J. M. et al. The SIESTA method for ab initio order-N materials simulation. J. Phys. Condens. Matter 14, 2745 (2002).

    ADS 

    Google Scholar
     

  • Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996).

    ADS 

    Google Scholar
     

  • Dion, M., Rydberg, H., Schröder, E., Langreth, D. C. & Lundqvist, B. I. Van der Waals density functional for general geometries. Phys. Rev. Lett. 92, 246401 (2004).

    ADS 

    Google Scholar
     

  • Wang, J., Román-Pérez, G., Soler, J. M., Artacho, E. & Fernández-Serra, M.-V. Density, structure, and dynamics of water: the effect of van der Waals interactions. J. Chem. Phys. 134, 024516 (2011).

    ADS 

    Google Scholar
     

  • Pamuk, B. et al. Anomalous nuclear quantum effects in ice. Phys. Rev. Lett. 108, 193003 (2012).

    ADS 

    Google Scholar
     

  • Wen, X. et al. Flexoelectricity and surface ferroelectricity of water ice. figshare https://doi.org/10.6084/m9.figshare.29378186 (2025).