Exploring new materials with unique optical, electrical, and magnetic properties represents a key direction in materials science and is of paramount importance for the development of novel electronic components in industry. Typically, such new materials are obtained by identifying specific structural combinations and particular elemental ratios^［1-2］. However, materials exhibiting anomalous stoichiometries can only exist under extreme conditions, such as high pressure^［3-8］. As previously reported, Na₂Cl and Na₃Cl display unusual bonding and electronic characteristics^［9］. The discovery of materials with anomalous stoichiometries under ambient temperature and pressure conditions would significantly advance materials science. Furthermore, gaining insight into the physical mechanisms and potential interactions of such materials under environmental conditions would contribute to fundamental scientific progress and the identification of new substances.

This paper, based on the cation–π interaction discovered in the 1980s^［10］, employs statistical physics to elucidate the role of water in solution and the adsorption–desorption equilibrium of hydrated cations. It reveals novel two-dimensional crystalline materials such as Na₂Cl, Na₃Cl, and NaCl₂, characterized by anomalous cation–anion ratios (abnormal stoichiometry). In these crystals with abnormal ion ratios, the interactions between cations and anions differ from those in conventional crystals, and their electronic structures also exhibit anomalies^［11］. Taking the two-dimensional crystal Na₂Cl as an example, its Na-to-Cl atomic ratio is 2:1, which results in vacancies at sites that would normally be occupied by Cl atoms, thereby forming periodic single-atom vacancies. This unique structure endows Na₂Cl with exceptional properties, such as an extremely high piezoelectric response. Consequently, these two-dimensional crystals exhibit physical characteristics typically associated with non-conventional valence ions (assuming chemical stability), including conductivity, ferromagnetism, and distinctive structural features. These findings challenge the traditional notion that only transition metals can exhibit ferromagnetism and offer new perspectives for understanding and applying biomagnetism. Finally, this paper discusses the potential ubiquity and possible applications of two-dimensional crystalline materials with anomalous cation–anion ratios.

Aromatic rings are cyclic structures composed of carbon atoms, and chemists recognized early on that they are rich in π electrons^［12］. Although, from the perspective of quantum computation, the interactions between ions and the π electrons in aromatic rings could be calculated quite early, the strong noncovalent bonding interactions between cations and aromatic rings were not experimentally confirmed in the gas phase until 1981 by Sunner et al.^［10］, and were subsequently termed cation–π interactions. In aqueous solutions, ions typically exist as hydrated ions. In 1996, American chemist Dougherty^［13］ pointed out that, considering the hydration effect of cations, the cation–π interactions between cations and aromatic rings are significantly weakened. For example, when a single Na ion interacts with a benzene molecule (a prototypical aromatic ring consisting of a six-membered ring formed by six carbon atoms; Figure 1 a), as illustrated in Figure 1 b^［11］, the average residence time of the hydrated Na ion on the benzene molecule is only 0.2 ns^［14］. Once it leaves the benzene molecule, this Na ion is unlikely to be adsorbed back onto the same surface again, which has led to the long-term underestimation or even neglect of hydrated cation–π interactions since 1996.

In aqueous solution, ions generally exist as hydrated ions, and ion hydration significantly weakens their interactions with aromatic ring structures. Taking a specific aromatic ring structure—such as the benzene molecule containing only a single six-membered ring—as an example, first-principles calculations show that when the number of water molecules surrounding a K⁺ion increases from 0 to 18, the K⁺–π interaction between K⁺and the benzene molecule decreases from −16.2 kcal/mol to −6.5 kcal/mol (1 kcal/mol = 4.184 kJ/mol). Compared with the vacuum state, the ion–π interaction in aqueous solution is much weaker. Accordingly, the adsorption residence time of ions such as Na⁺and Li⁺on the benzene molecule is very short, often less than one nanosecond. From the perspective of statistical physics, in aqueous solutions containing a large number of ions, the hydrated ion–π interaction should not be evaluated solely based on the adsorption stability of individual ions; instead, the cumulative effects of numerous hydrated ions over time must also be considered. In other words, the macroscopic impact of the hydrated ion–π interaction is inevitably closely related to the ionic concentration of the solution. Still using the benzene molecule as an example, although the residence time of a single ion on a single benzene molecule is brief, after this ion desorbs, other ions will subsequently adsorb onto the same benzene molecule after a certain period. When the ionic concentration in the solution reaches a certain level, this continuous adsorption–desorption dynamic process results in a considerable fraction of time during which ions are present on the surface. The probability of a hydrated ion being adsorbed onto the benzene molecule (considering long-term averaging) is jointly determined by the strength of the hydrated ion–π interaction, the ionic concentration, and the temperature. Numerical simulations indicate that in a NaCl solution at physiological salt concentration, although the average residence time of a single Na⁺ion on the benzene surface is only 0.2 ns, the total duration of Na⁺ion presence on the benzene surface throughout the entire 10-ns simulation reaches 3.8 ns. This means that for nearly 40% of the simulation time, the benzene surface remains bound to Na⁺ions^［14］. Therefore, in many practical processes, the hydrated ion–π interaction often plays a very important, even critical, role. It is worth noting that on surfaces rich in aromatic ring structures, such as graphite and graphene, multiple aromatic rings greatly enhance the hydrated ion–π interaction, leading to substantial ion enrichment on the solid surface (Figure 2)^［15］. When the ionic concentration in the solution is sufficiently high, under the combined effects of electrostatic interactions among ions and thermal fluctuations at room temperature, the large number of ions adsorbed on the surface spontaneously forms ordered structures. Moreover, the differences in the interactions between π electrons and cations versus anions regulate the molar ratios of these adsorbed cations and anions, resulting in two-dimensional crystals with anomalous stoichiometries that differ from those of conventional three-dimensional crystals.

As theory indicates, Na and Cl ions tend to enrich on carbon-based surfaces in unsaturated solutions. Experimental researchers have chosen reduced graphene oxide (rGO) containing certain hydrophilic oxidized functional groups for this purpose, primarily because pristine graphene is hydrophobic and water molecules are difficult to adsorb onto its surface^［16］, which would hinder ion adsorption. In 2018, Shi et al.^［17］ immersed an rGO membrane in an unsaturated NaCl solution under ambient conditions. After 30 minutes, two-dimensional Na–Cl crystals were directly observed on the membrane. Four lines of evidence support the formation of two-dimensional Na–Cl crystals with unconventional stoichiometry on the rGO membrane: (1) the (200) peak in X-ray diffraction (XRD) shifted to approximately 32° relative to the corresponding peak of normal NaCl crystals (Figure 3d–e); (2) energy-dispersive X-ray spectroscopy (EDS) elemental analysis revealed that in selected regions of the rGO membrane, the atomic percentages of Na and Cl were predominantly in the range of 1 to 3, accounting for about 72% of the total (Figure 3f); (3) density functional theory (DFT) calculations predicted the existence of stable two-dimensional Na–Cl crystals, including Na₂Cl and Na₃Cl, at the graphite surface and between bilayer graphene (Figure 3a–c); (4) the experimentally observed shift of the XRD (200) peak to around 32° and its sequence were consistent with the theoretical predictions. Molecular dynamics and DFT calculations demonstrate that the unconventional crystallization of two-dimensional Na–Cl crystals such as Na₂Cl and Na₃Cl arises from cation–π interactions between ions and the π-conjugated system on the graphite surface. Furthermore, molecular orbital analysis combined with residual Mulliken charge calculations indicates charge transfer between the unoccupied valence orbitals of Na⁺ ions and the delocalized π states of aromatic ring structures within the graphene sheets. This charge transfer stabilizes the two-dimensional Na–Cl crystal structures with anomalous stoichiometries at the graphene surface and between layers. Previously, researchers^［18］ generally believed that, under ambient temperature and pressure, solute particles in unsaturated solutions must be very close to a surface to induce surface crystallization. Therefore, this crystallization behavior serves as a supplement to conventional crystallization theory.

According to the experimental method described above, the mass ratio of total Na and Cl to graphene is only about 5%. Consequently, the resulting two-dimensional Na₂Cl and Na₃Cl crystals cannot fully cover the graphene surface, which significantly limits both the study of the properties of these anomalous crystals and their efficient applications. Recent studies have shown that by applying an appropriate negative voltage to further enhance graphene’s adsorption capacity for sodium ions, the mass fraction of two-dimensional Na₂Cl and Na₃Cl crystals within the graphene membrane can be increased to 20% or even higher^［19］. As a result, certain unique properties, including ultra-high-sensitivity piezoelectric characteristics and ferromagnetism, can be more effectively verified experimentally. As shown in Figure 4a, a three-electrode configuration was used to establish the electrochemical environment, with a potential of −0.6 V applied to the rGO membrane. The negatively charged rGO membrane served as the working electrode and was incubated in a saturated NaCl solution for 1 hour (Figure 4a). Subsequently, it was dried in air under infrared illumination for 30 minutes. Compared with the condition at 0 V, when the potential was set to −0.6 V, the Na atom content of the rGO membrane increased by an order of magnitude (Figure 4b). Such a high atomic concentration of Na existed within the rGO membrane in the form of dense two-dimensional Na–Cl crystals, with lateral dimensions on the order of tens of nanometers (Figure 4a). DFT calculations indicate that at a low negative potential of −0.6 V, the increase in negative charge on the graphene surface enhances its interaction with Na⁺ while weakening the electrostatic repulsion among cations. This not only promotes the formation of two-dimensional Na₂Cl crystals but also contributes to the stabilization of their crystal structure. Furthermore, the square-shaped two-dimensional Na₂Cl crystals exhibit unexpected piezoelectric properties, which can be directly observed using piezoresponse force microscopy (PFM) and membrane bending experiments, as illustrated in Figure 4d. In the rGO membrane, the output voltage of the two-dimensional Na₂Cl crystals increases with the degree of bending. When the rGO membrane is rapidly bent with a periodic bending angle of 150°, the output voltage can reach approximately 180 mV, as shown in Figure 4c, thereby satisfying the voltage requirements of most nanodevices in practical applications. Achieving high-yield synthesis of unconventional stoichiometric two-dimensional crystals on rGO membranes through the application of a negative potential provides new insights into improving synthetic processes. Importantly, this study offers a generalizable research paradigm: by modifying the surface properties of rGO membranes to regulate the ratio of cations to anions, one can achieve controllable preparation of unconventional stoichiometric two-dimensional crystals.

Based on the aforementioned research approach, Yi et al. ^［20］experimentally synthesized under ambient conditions a stable two-dimensional anion-rich interlayer structure NaCl₂crystal (Figure 5a), which was confined within a positively charged graphene oxide (p-GO) membrane (Na-Cl@p-GO). In the experiment, polyethyleneimine (PEI) was added to a graphene oxide (GO) suspension to prepare a p-GO suspension, thereby functionalizing the GO sheets and adjusting the Zeta (ζ) potential of the GO surface from its original negative value to a positive value under neutral conditions. By drop-casting the p-GO suspension and drying it at 70 ℃ for 12 hours, an independent p-GO membrane was fabricated. When the p-GO membrane was immersed in a NaCl solution, the positively charged surface of the p-GO membrane exhibited a stronger attraction to Cl^-ions than to Na⁺ions, resulting in the formation of a stable two-dimensional anion-rich NaCl₂crystal. The crystal structure consists of a positively charged sodium cation layer sandwiched between two negatively charged chloride anion layers. This unconventional two-dimensional anion-rich NaCl₂crystal exhibits ferromagnetism at room temperature (Figure 5b). Using a magnetic measurement system (MPMS-3, Quantum Design), we observed that Na-Cl@p-GO displays strong ferromagnetism with a distinct hysteresis loop (Figure 5c). The saturation magnetization (M _s) of Na-Cl@p-GO is 0.63 emu/g, approximately three times that of p-GO (0.20 emu/g). Theoretical calculations indicate that the room-temperature ferromagnetism of these crystals originates from the spin polarization of electrons in the chlorine atoms. This finding is unexpected, as conventional compounds composed solely of Na and Cl are nonmagnetic. According to spin-polarized band and density-of-states calculations, the spin-down channel near the Fermi level is completely occupied by the p-electrons of chloride ions, whereas the spin-up channel remains empty, which differs from the properties commonly observed in most transition-metal chalcogenide compounds.

If graphene membranes are immersed in a divalent ion solution (e.g., a CaCl₂ solution), can we also obtain a two-dimensional crystal? Will such a crystal appear in an anomalous stoichiometric ratio as well? Theoretical predictions indicate that not only will a crystal form on the graphene surface, but this crystal exists in the form of CaCl, where the molar ratio of calcium ions to chloride ions is 1:1. This result differs from our conventional understanding. In experiments, the crystal structure can be directly observed using cryo-electron microscopy, as shown in Figure 6. The Ca-to-Cl ion ratio in the crystal is 1:1^［21］. Since graphene itself is neutral, it is reasonable to speculate that calcium ions exhibit the properties of a monovalent ion—one with metallic character and strong paramagnetic response, possibly even room-temperature ferromagnetism. However, there have been no reports of monovalent calcium ions thus far; therefore, it is impossible experimentally to verify whether the calcium ions in the crystal are indeed monovalent. Superconducting quantum interference device (SQUID) measurements yielded hysteresis loops, demonstrating that the CaCl two-dimensional crystal on the graphene membrane does indeed possess ferromagnetic properties. Furthermore, its metallic nature has also been experimentally confirmed. Why do the CaCl two-dimensional crystals on graphene exhibit both ferromagnetism and metallicity? Compared with conventional CaCl₂ crystals, the electronic structures of the cations and anions in the CaCl two-dimensional crystal display anomalies as well. To substantiate this point, X-ray near-edge absorption fine structure (NEXAFS) spectroscopy was performed on dry samples of rGO membranes adsorbing Ca and Cl ions, and the results were compared with those of bulk metallic Ca and conventional three-dimensional CaCl₂ crystals. The L₃ and L₂ edge peaks of Ca in the rGO membrane sample were distinctly different from the peaks corresponding to Ca⁰ in metallic Ca and from those corresponding to Ca²⁺ in conventional three-dimensional CaCl₂ crystals (Figure 7a). Further numerical analysis confirmed that this spectrum could not be a combination of the spectra of metallic Ca and Ca²⁺ in conventional three-dimensional CaCl₂ crystals. This indicates that although the calcium ions in the CaCl two-dimensional crystal on graphene are in ionic form, they are not in the conventional divalent state. For a single calcium ion, the presence of an unbonded valence electron endows it with spin and hence a magnetic moment. The experimentally observed ferromagnetism suggests that the interactions among these ions are sufficiently strong.

Considering that Cu ions in nature exist not only in the divalent state Cu²⁺, but also in the monovalent state Cu⁺. Therefore, based on the method of forming Ca-Cl@rGO crystals within a graphene membrane, the valence states of Cu ions within the graphene membrane (Cu-Cl@rGO) were investigated^［11］. The NEXAFS spectra at the Cu L₃ and L₂ edges are shown in Figure 7b. In the dry sample of the Cu-Cl@rGO membrane, the L₃ and L₂ edge peaks of Cu appear at 925.39 eV and 945.19 eV, respectively (indicated by the red dashed lines), which are consistent with the positions of the corresponding peaks in standard CuCl crystals. This indicates the presence of +1-valent Cu in the Cu-Cl crystals embedded within the rGO membrane. Furthermore, the resulting system exhibits ferromagnetic properties very similar to those of the Ca-based system. It should be noted that, for copper, the monovalent state may arise from inner-shell d electrons, whereas for calcium it can only originate from outer-shell electrons.

Under ambient conditions, LiCl is the only known stable form of Li–Cl crystals with a stoichiometric ratio of 1:1, and the corresponding crystal is insulating. Due to the large difference in electronegativity between Li and Cl, a highly ionic bond is formed, making it suitable for use in batteries and capacitors. Understanding the structure and properties of Li–Cl is of great significance for the development of lithium-based electrochemical energy storage and conversion devices. Recently, Li et al.^［22］successfully prepared a novel two-dimensional anomalous Li₂Cl crystal within an ultrathin rGO membrane. The experimental method involved immersing the rGO membrane in a LiCl solution at a concentration far below saturation under ambient conditions. These flat, large-sized, and stable two-dimensional Li₂Cl crystals could be directly observed by freezing the ultrathin rGO membrane in the LiCl solution (Figure 8a), thereby providing electron imaging protection and enabling *in situ* observation of solution crystallization. Through electron diffraction and fast Fourier transform (FFT) analysis (Figure 8a), it was found that the Li–Cl crystal exhibits a square lattice with four first-order maxima at approximately 7.781 nm^-1, and the diffraction spots of the Li₂Cl crystal show excellent agreement between experimental observations and theoretical predictions. Compared with LiCl, these Li₂Cl crystals exhibit metallic rather than insulating properties. In experiments, conductive atomic force microscopy (C-AFM) was used on graphene sheets to confirm the metallic nature of the two-dimensional Li₂Cl crystals. Figure 8b–c presents AFM images and *I*–*V* characteristics of pure graphene sheets and Li₂Cl–graphene sheets deposited on gold-coated quartz substrates. Interestingly, the *I*–*V* curve of dry Li₂Cl–graphene shows a resistance of 2.6×10⁶ Ω, which is only one-third lower than that of pure graphene, indicating the metallic properties of the Li₂Cl crystals. Density functional theory (DFT) calculations revealed that the most stable geometry-optimized structure of Li₂Cl consists of Li ions at the bottom layer and Li and Cl ions at the top layer, ultimately forming a metal Li₂Cl crystal heterostructure (Li₂Cl–rGO) within the membrane. The two-dimensional Li₂Cl crystals are composed of alternately distributed Li and Cl elements; due to the different electrical effects of these two elements under compressive or tensile strain, materials containing these crystals should exhibit piezoelectric-like characteristics. As shown in Figure 8d, the output voltage of the dried Li₂Cl–rGO membrane increases with increasing bending degree, demonstrating distinct piezoelectric behavior. Furthermore, the dried Li₂Cl–rGO membrane is highly sensitive to humidity, generating a corresponding current at each humidity level (Figure 8e). This indicates that the dried Li₂Cl–rGO membrane can serve as a humidity sensor. As the relative humidity rises from 50% to 100%, the resistance of the rGO membrane containing Li₂Cl undergoes a significant change (Figure 8e), and even under 100% high humidity conditions, it still maintains high sensitivity.

KCl, as a highly important inorganic compound, has attracted considerable attention from researchers due to its wide range of applications. The primary fields involved include agriculture, medicine, industry, and scientific research. As a source of potassium, it participates in various chemical reactions, providing crucial support for the development of new materials and pharmaceuticals. Rechargeable potassium-ion batteries (PIBs) represent a novel type of energy storage device that has garnered significant interest in recent years owing to their low cost and broad applicability. However, their poor cycling stability, low specific capacity, and inferior potassium-ion intercalation performance have hindered their large-scale deployment. Zhan et al.^［23］synthesized a freestanding K-Cl-graphene paper electrode composed of K _x Cl crystals with anomalous stoichiometry and proposed a new general design strategy utilizing this K _x Cl crystal-modified freestanding reduced graphene oxide (K _x Cl-rGO) as an electrode to achieve high-performance K-graphene batteries. As shown in Figure 9a, a GO suspension was drop-cast onto a smooth paper substrate and dried to fabricate a freestanding GO film. Subsequently, annealing at 400 ℃ in air enhanced the electrical conductivity of these graphene films. Following immersion in a 0.5 mol/L KCl solution for 3 hours, potassium ion modification was completed, resulting in K _x Cl crystals with anomalous stoichiometry, which collectively exhibit excellent electrical conductivity and potassium storage capability. To investigate the impact of K _x Cl crystals with anomalous stoichiometry on potassium-ion storage, K _x Cl-rGO was tested as a potassium metal anode in a half-cell configuration. First, cyclic voltammetry (CV) was employed to examine the storage behavior of K⁺ ions in both rGO and K _x Cl-rGO, as illustrated in Figure 9b. For rGO, a cathodic peak was observed at approximately 0.60 V during the first cycle, whereas no such peak was detected near the corresponding position in K _x Cl-rGO. Notably, due to the insertion of potassium ions into the graphene layers, K _x Cl-rGO exhibited a broad and robust reduction peak at 0.06 V. The decoration with K _x Cl crystals possessing unconventional stoichiometry not only facilitated potassium-ion insertion but also enhanced the sample’s capacity, thereby manifesting a critical difference in the electrochemical behavior between K _x Cl-rGO and conventional K _x Cl-rGO. Furthermore, at a current density of 20 mA/g, the galvanostatic charge–discharge curves of the K _x Cl-rGO electrode displayed no distinct discharge plateau within the voltage range of 0.5 to 0.01 V, consistent with the anticipated role of the K _x Cl crystals with unconventional stoichiometry during the pre-potassiation process. These findings indicate that, compared with pure GO, GO modified by K _x Cl crystals having unconventional stoichiometry can store a greater amount of potassium ions. Figure 9d presents the galvanostatic charge–discharge curves of a potassium-ion battery employing K _x Cl-rGO as the anode and K₂Fe［Fe（CN）₆］ as the cathode, operated at a current density of 20 mA/g and a voltage window of 1.0 to 4.0 V. The full cell consisting of K₂Fe［Fe（CN）₆］//K _x Cl-rGO demonstrated a charge–discharge capacity of 70.7/46.5 mAh/g, with an initial Coulombic efficiency of 65.8%. These results suggest that modification with K _x Cl crystals exhibiting anomalous stoichiometry can significantly enhance the potassium-ion storage performance of rGO.

In recent years, under ambient conditions, two-dimensional crystals with anomalous stoichiometries, including Na₂Cl, Na₃Cl, and CaCl, have been formed on GO membranes and rGO membranes. These materials have attracted considerable attention due to their unique electronic structures. The fabrication process of these two-dimensional crystals is remarkably simple: it merely requires immersing a GO or rGO membrane substrate into the corresponding unsaturated solution under ambient conditions. For main-group elements such as Na, Ca, and Cl, since their inner-shell electrons are fully occupied, the crystals they form with anomalous stoichiometric ratios typically exhibit distinctive outer-shell (e.g., valence electron) electronic structures. Such structures are inherently unstable—previously observed only under extreme conditions like high pressure—and simultaneously display unique orbital electron configurations, thereby giving rise to extraordinary physical properties. For example, the two-dimensional NaCl₂crystal exhibits room-temperature ferromagnetism with a pronounced hysteresis loop and a transition temperature exceeding 320 K, which is attributed to spin polarization of electrons in the Cl element. Meanwhile, the two-dimensional CaCl crystal grown on an rGO membrane demonstrates unexpected metallic conductivity, room-temperature ferromagnetism, coexistence of graphene–CaCl heterojunctions, piezoelectricity, and metallic behavior, as well as unique hydrogen storage and release capabilities under ambient conditions. Furthermore, freestanding GO electrodes decorated with K _x Cl crystals exhibit excellent K-ion storage performance, featuring high capacity and good rate capability. These properties fundamentally challenge the conventional understanding that ferromagnetism is exclusively associated with transition metals, holding significant application potential across materials science, electronic components, biology, chemistry, and physics.

Currently, research on two-dimensional crystals with anomalous stoichiometry under ambient conditions has only just begun. It is anticipated that each metallic element may possess unique properties, such as room-temperature ferromagnetism, by forming corresponding anomalous two-dimensional crystals containing metal ions with unpaired valence electrons. Furthermore, given the widespread abundance of metal cations and carbon on Earth, these nanoscale “special” compounds exhibiting previously unrecognized properties may be ubiquitous in nature. The pressing task at hand is to address the synthesis challenges in order to unlock the full application potential of these two-dimensional crystals and their derivatives. Applying a negative electric potential to rGO membranes to achieve high-yield synthesis of Na₂Cl crystals represents a promising strategy for enhancing both crystal size and yield. However, further refinement of the synthesis protocol is required to obtain larger, higher-yielding two-dimensional crystals. Another critical issue is the development of reproducible and controllable synthesis methods, as the performance of these two-dimensional crystals is highly dependent on the structure of their nanoscale building blocks, which often leads to non-reproducible experimental outcomes. Regardless of the future direction of research on two-dimensional crystals with anomalous stoichiometry under ambient conditions, it is certain that the unique properties they exhibit will continue to fuel ongoing scientific inquiry.