Imaging surface structure and premelting of ice Ih with atomic resolution.

Ice surfaces are closely relevant to many physical and chemical properties, such as melting, freezing, friction, gas uptake and atmospheric reaction1-8. Despite extensive experimental and theoretical investigations9-17, the exact atomic structures of ice interfaces remain elusive owing to the vulnerable hydrogen-bonding network and the complicated premelting process. Here we realize atomic-resolution imaging of the basal (0001) surface structure of hexagonal water ice (ice Ih) by using qPlus-based cryogenic atomic force microscopy with a carbon monoxide-functionalized tip. We find that the crystalline ice-Ih surface consists of mixed Ih- and cubic (Ic)-stacking nanodomains, forming 19 × 19 periodic superstructures. Density functional theory reveals that this reconstructed surface is stabilized over the ideal ice surface mainly by minimizing the electrostatic repulsion between dangling OH bonds. Moreover, we observe that the ice surface gradually becomes disordered with increasing temperature (above 120 Kelvin), indicating the onset of the premelting process. The surface premelting occurs from the defective boundaries between the Ih and Ic domains and can be promoted by the formation of a planar local structure. These results put an end to the longstanding debate on ice surface structures and shed light on the molecular origin of ice premelting, which may lead to a paradigm shift in the understanding of ice physics and chemistry.

Bevel-edge epitaxy of ferroelectric rhombohedral boron nitride single crystal.

Within the family of two-dimensional dielectrics, rhombohedral boron nitride (rBN) is considerably promising owing to having not only the superior properties of hexagonal boron nitride1-4-including low permittivity and dissipation, strong electrical insulation, good chemical stability, high thermal conductivity and atomic flatness without dangling bonds-but also useful optical nonlinearity and interfacial ferroelectricity originating from the broken in-plane and out-of-plane centrosymmetry5-23. However, the preparation of large-sized single-crystal rBN layers remains a challenge24-26, owing to the requisite unprecedented growth controls to coordinate the lattice orientation of each layer and the sliding vector of every interface. Here we report a facile methodology using bevel-edge epitaxy to prepare centimetre-sized single-crystal rBN layers with exact interlayer ABC stacking on a vicinal nickel surface. We realized successful accurate fabrication over a single-crystal nickel substrate with bunched step edges of the terrace facet (100) at the bevel facet (110), which simultaneously guided the consistent boron-nitrogen bond orientation in each BN layer and the rhombohedral stacking of BN layers via nucleation near each bevel facet. The pure rhombohedral phase of the as-grown BN layers was verified, and consequently showed robust, homogeneous and switchable ferroelectricity with a high Curie temperature. Our work provides an effective route for accurate stacking-controlled growth of single-crystal two-dimensional layers and presents a foundation for applicable multifunctional devices based on stacked two-dimensional materials.

Tracking cubic ice at molecular resolution.

Ice is present everywhere on Earth and has an essential role in several areas, such as cloud physics, climate change and cryopreservation. The role of ice is determined by its formation behaviour and associated structure. However, these are not fully understood1. In particular, there is a long-standing debate about whether water can freeze to form cubic ice-a currently undescribed phase in the phase space of ordinary hexagonal ice2-6. The mainstream view inferred from a collection of laboratory data attributes this divergence to the inability to discern cubic ice from stacking-disordered ice-a mixture of cubic and hexagonal sequences7-11. Using cryogenic transmission electron microscopy combined with low-dose imaging, we show here the preferential nucleation of cubic ice at low-temperature interfaces, resulting in two types of separate crystallization of cubic ice and hexagonal ice from water vapour deposition at 102 K. Moreover, we identify a series of cubic-ice defects, including two types of stacking disorder, revealing the structure evolution dynamics supported by molecular dynamics simulations. The realization of direct, real-space imaging of ice formation and its dynamic behaviour at the molecular level provides an opportunity for ice research at the molecular level using transmission electron microscopy, which may be extended to other hydrogen-bonding crystals.

Disorder-tuned conductivity in amorphous monolayer carbon.

Correlating atomic configurations-specifically, degree of disorder (DOD)-of an amorphous solid with properties is a long-standing riddle in materials science and condensed matter physics, owing to difficulties in determining precise atomic positions in 3D structures1-5. To this end, 2D systems provide insight to the puzzle by allowing straightforward imaging of all atoms6,7. Direct imaging of amorphous monolayer carbon (AMC) grown by laser-assisted depositions has resolved atomic configurations, supporting the modern crystallite view of vitreous solids over random network theory8. Nevertheless, a causal link between atomic-scale structures and macroscopic properties remains elusive. Here we report facile tuning of DOD and electrical conductivity in AMC films by varying growth temperatures. Specifically, the pyrolysis threshold temperature is the key to growing variable-range-hopping conductive AMC with medium-range order (MRO), whereas increasing the temperature by 25 °C results in AMC losing MRO and becoming electrically insulating, with an increase in sheet resistance of 109 times. Beyond visualizing highly distorted nanocrystallites embedded in a continuous random network, atomic-resolution electron microscopy shows the absence/presence of MRO and temperature-dependent densities of nanocrystallites, two order parameters proposed to fully describe DOD. Numerical calculations establish the conductivity diagram as a function of these two parameters, directly linking microstructures to electrical properties. Our work represents an important step towards understanding the structure-property relationship of amorphous materials at the fundamental level and paves the way to electronic devices using 2D amorphous materials.

Measuring phonon dispersion at an interface.

The breakdown of translational symmetry at heterointerfaces leads to the emergence of new phonon modes localized at the interface1. These modes have an essential role in thermal and electrical transport properties in devices, especially in miniature ones wherein the interface may dominate the entire response of the device2. Although related theoretical work began decades ago1,3-5, experimental research is totally absent owing to challenges in achieving the combined spatial, momentum and spectral resolutions required to probe localized modes. Here, using the four-dimensional electron energy-loss spectroscopy technique, we directly measure both the local vibrational spectra and the interface phonon dispersion relation for an epitaxial cubic boron nitride/diamond heterointerface. In addition to bulk phonon modes, we observe modes localized at the interface and modes isolated from the interface. These features appear only within approximately one nanometre around the interface. The localized modes observed here are predicted to substantially affect the interface thermal conductance and electron mobility. Our findings provide insights into lattice dynamics at heterointerfaces, and the demonstrated experimental technique should be useful in thermal management, electrical engineering and topological phononics.

Atomic imaging of the edge structure and growth of a two-dimensional hexagonal ice.

The formation and growth of water-ice layers on surfaces and of low-dimensional ice under confinement are frequent occurrences1-4. This is exemplified by the extensive reporting of two-dimensional (2D) ice on metals5-11, insulating surfaces12-16, graphite and graphene17,18 and under strong confinement14,19-22. Although structured water adlayers and 2D ice have been imaged, capturing the metastable or intermediate edge structures involved in the 2D ice growth, which could reveal the underlying growth mechanisms, is extremely challenging, owing to the fragility and short lifetime of those edge structures. Here we show that noncontact atomic-force microscopy with a CO-terminated tip (used previously to image interfacial water with minimal perturbation)12, enables real-space imaging of the edge structures of 2D bilayer hexagonal ice grown on a Au(111) surface. We find that armchair-type edges coexist with the zigzag edges usually observed in 2D hexagonal crystals, and freeze these samples during growth to identify the intermediate edge structures. Combined with simulations, these experiments enable us to reconstruct the growth processes that, in the case of the zigzag edge, involve the addition of water molecules to the existing edge and a collective bridging mechanism. Armchair edge growth, by contrast, involves local seeding and edge reconstruction and thus contrasts with conventional views regarding the growth of bilayer hexagonal ices and 2D hexagonal matter in general.

Seeded growth of large single-crystal copper foils with high-index facets.

The production of large single-crystal metal foils with various facet indices has long been a pursuit in materials science owing to their potential applications in crystal epitaxy, catalysis, electronics and thermal engineering1-5. For a given metal, there are only three sets of low-index facets ({100}, {110} and {111}). In comparison, high-index facets are in principle infinite and could afford richer surface structures and properties. However, the controlled preparation of single-crystal foils with high-index facets is challenging, because they are neither thermodynamically6,7 nor kinetically3 favourable compared to low-index facets6-18. Here we report a seeded growth technique for building a library of single-crystal copper foils with sizes of about 30 × 20 square centimetres and more than 30 kinds of facet. A mild pre-oxidation of polycrystalline copper foils, followed by annealing in a reducing atmosphere, leads to the growth of high-index copper facets that cover almost the entire foil and have the potential of growing to lengths of several metres. The creation of oxide surface layers on our foils means that surface energy minimization is not a key determinant of facet selection for growth, as is usually the case. Instead, facet selection is dictated randomly by the facet of the largest grain (irrespective of its surface energy), which consumes smaller grains and eliminates grain boundaries. Our high-index foils can be used as seeds for the growth of other Cu foils along either the in-plane or the out-of-plane direction. We show that this technique is also applicable to the growth of high-index single-crystal nickel foils, and we explore the possibility of using our high-index copper foils as substrates for the epitaxial growth of two-dimensional materials. Other applications are expected in selective catalysis, low-impedance electrical conduction and heat dissipation.

Epitaxial growth of a 100-square-centimetre single-crystal hexagonal boron nitride monolayer on copper.

The development of two-dimensional (2D) materials has opened up possibilities for their application in electronics, optoelectronics and photovoltaics, because they can provide devices with smaller size, higher speed and additional functionalities compared with conventional silicon-based devices1. The ability to grow large, high-quality single crystals for 2D components-that is, conductors, semiconductors and insulators-is essential for the industrial application of 2D devices2-4. Atom-layered hexagonal boron nitride (hBN), with its excellent stability, flat surface and large bandgap, has been reported to be the best 2D insulator5-12. However, the size of 2D hBN single crystals is typically limited to less than one millimetre13-18, mainly because of difficulties in the growth of such crystals; these include excessive nucleation, which precludes growth from a single nucleus to large single crystals, and the threefold symmetry of the hBN lattice, which leads to antiparallel domains and twin boundaries on most substrates19. Here we report the epitaxial growth of a 100-square-centimetre single-crystal hBN monolayer on a low-symmetry Cu (110) vicinal surface, obtained by annealing an industrial copper foil. Structural characterizations and theoretical calculations indicate that epitaxial growth was achieved by the coupling of Cu <211> step edges with hBN zigzag edges, which breaks the equivalence of antiparallel hBN domains, enabling unidirectional domain alignment better than 99 per cent. The growth kinetics, unidirectional alignment and seamless stitching of the hBN domains are unambiguously demonstrated using centimetre- to atomic-scale characterization techniques. Our findings are expected to facilitate the wide application of 2D devices and lead to the epitaxial growth of broad non-centrosymmetric 2D materials, such as various transition-metal dichalcogenides20-23, to produce large single crystals.

The effect of surface hydrophobicity and hydrophilicity on ion-ion interactions at water-solid interfaces.

Condensation and arrangement of ions at water-solid interfaces are of great importance in the formation of electrical double layers (EDL) and the transport of ions under a confined geometry. So far, the microscopic understanding of interfacial ion configurations is still far from complete, especially when the local ion concentration is high and ion-ion interactions become prominent. In this study, we directly visualized alkali metal cations within the hydrogen-bonding network of water on graphite and Cu(111)-supported graphene surfaces, using qPlus-based noncontact atomic force microscopy (NC-AFM). We found that the codeposition of the alkali cations and water molecules on the hydrophobic graphite surface leads to the formation of an ion-doped bilayer hexagonal ice (BHI) structure, where the ions are repelled from each other and scattered in a disordered distribution. In contrast, the hydrated alkali cations aggregate in one dimension on the more hydrophilic graphene/Cu(111) surface, forming a nematic state with a long-range order. Such a nematic state arises from the delicate interplay between water-ion and water-water interactions under surface confinement. These results reveal the high sensitivity of ion-ion interactions and ionic ordering to the surface hydrophobicity and hydrophilicity.

Publisher Correction: The effect of hydration number on the interfacial transport of sodium ions.

In this Letter, the links to Supplementary Videos 5, 7, 9 and 10 were incorrect, and there were some formatting errors in the Supplementary Video legends. These errors have been corrected online.

The effect of hydration number on the interfacial transport of sodium ions.

Ion hydration and transport at interfaces are relevant to a wide range of applied fields and natural processes1-5. Interfacial effects are particularly profound in confined geometries such as nanometre-sized channels6-8, where the mechanisms of ion transport in bulk solutions may not apply9,10. To correlate atomic structure with the transport properties of hydrated ions, both the interfacial inhomogeneity and the complex competing interactions among ions, water and surfaces require detailed molecular-level characterization. Here we constructed individual sodium ion (Na+) hydrates on a NaCl(001) surface by progressively attaching single water molecules (one to five) to the Na+ ion using a combined scanning tunnelling microscopy and noncontact atomic force microscopy system. We found that the Na+ ion hydrated with three water molecules diffuses orders of magnitude more quickly than other ion hydrates. Ab initio calculations revealed that such high ion mobility arises from the existence of a metastable state, in which the three water molecules around the Na+ ion can rotate collectively with a rather small energy barrier. This scenario would apply even at room temperature according to our classical molecular dynamics simulations. Our work suggests that anomalously high diffusion rates for specific hydration numbers of ions are generally determined by the degree of symmetry match between the hydrates and the surface lattice.

Designed growth of large bilayer graphene with arbitrary twist angles.

The production of large-area twisted bilayer graphene (TBG) with controllable angles is a prerequisite for proceeding with its massive applications. However, most of the prevailing strategies to fabricate twisted bilayers face great challenges, where the transfer methods are easily stuck by interfacial contamination, and direct growth methods lack the flexibility in twist-angle design. Here we develop an effective strategy to grow centimetre-scale TBG with arbitrary twist angles (accuracy, <1.0°). The success in accurate angle control is realized by an angle replication from two prerotated single-crystal Cu(111) foils to form a Cu/TBG/Cu sandwich structure, from which the TBG can be isolated by a custom-developed equipotential surface etching process. The accuracy and consistency of the twist angles are unambiguously illustrated by comprehensive characterization techniques, namely, optical spectroscopy, electron microscopy, photoemission spectroscopy and photocurrent spectroscopy. Our work opens an accessible avenue for the designed growth of large-scale two-dimensional twisted bilayers and thus lays the material foundation for the future applications of twistronics at the integration level.

Twist Phase Matching in Two-Dimensional Materials.

Optical phase matching involves establishing a proper phase relationship between the fundamental excitation and generated waves to enable efficient optical parametric processes. It is typically achieved through birefringence or periodic polarization. Here, we report that the interlayer twist angle in two-dimensional (2D) materials creates a nonlinear geometric phase that can compensate for the phase mismatch, and the vertical assembly of the 2D layers with a proper twist sequence generates a nontrivial "twist-phase-matching" (twist-PM) regime. The twist-PM model provides superior flexibility in the design of optical crystals, which can be applied for twisted layers with either periodic or random thickness distributions. The designed crystal from the twisted rhombohedral boron nitride films within a thickness of only 3.2 µm is capable of producing a second-harmonic generation with conversion efficiency of ∼8% and facile polarization controllability that is absent in conventional crystals. Our methodology establishes a platform for the rational design and atomic manufacturing of nonlinear optical crystals based on abundant 2D materials.

Semiclassical Vibrational Spectroscopy of Real Molecular Systems by Means of Cross-Correlation Filter Diagonalization.

We applied the harmonic inversion technique to extract vibrational eigenvalues from the semiclassical initial value representation (SC-IVR) propagator of molecular systems described by explicit potential surfaces. The cross-correlation filter-diagonalization (CCFD) method is used for the inversion problem instead of the Fourier transformation, which allows much shorter propagation time and is thus capable of avoiding numerical divergence issues while getting rid of approximations like the separable one to the pre-exponential factor. We also used the "Divide-and-Conquer" technique to control the total dimensions under consideration, which helps to further enhance the numerical behavior of SC-IVR calculations and the stability of harmonic inversion methods. The technique is tested on small molecules and water trimer to justify its applicability and reliability. Results show that the CCFD method can effectively extract the vibrational eigenvalues from short trajectories and reproduce the original spectra conventionally obtained from long-time ones, with no loss on accuracy while the numerical behavior is much better. This work demonstrates the possibility to apply the combined method of CCFD and SC-IVR to real molecular potential surfaces, which might be a new way to overcome the numerical instabilities caused by the increase of dimensions.

Nuclear Quantum Effects on the Charge-Density Wave Transition in NbX2 (X = S, Se).

Understanding the origin of charge-density wave (CDW) instability is important for manipulating novel collective electronic states. Many layered transition metal dichalcogenides (TMDs) share similarity in the structural and electronic instability, giving rise to diverse CDW phases and superconductivity. It is still puzzling that even isostructural and isoelectronic TMDs show distinct CDW features. For instance, bulk NbSe2 exhibits CDW order at low temperature, while bulk NbS2 displays no CDW instability. The CDW transitions in single-layer NbS2 and NbSe2 are also different. In the classic limit, we investigate the electron correlation effects on the dimensionality dependence of the CDW ordering. By performing ab initio path integral molecular dynamics simulations and comparative analyses, we further revealed significant nuclear quantum effects in these systems. Specifically, the quantum motion of sulfur anions significantly reduces the CDW transition temperature in both bulk and single-layer NbS2, resulting in distinct CDW features in the NbS2 and NbSe2 systems.

Visualizing the Anomalous Catalysis in Two-Dimensional Confined Space.

Confined nanospaces provide a new platform to promote catalytic reactions. However, the mechanism of catalytic enhancement in the nanospace still requires insightful exploration due to the lack of direct visualization. Here, we report operando investigations on the etching and growth of graphene in a two-dimensional (2D) confined space between graphene and a Cu substrate. We observed that the graphene layer between the Cu and top graphene layer was surprisingly very active in etching (more than 10 times faster than the etching of the top graphene layer). More strikingly, at a relatively low temperature (∼530 °C), the etched carbon radicals dissociated from the bottom layer, in turn feeding the growth of the top graphene layer with a very high efficiency. Our findings reveal the in situ dynamics of the anomalous confined catalytic processes in 2D confined spaces and thus pave the way for the design of high-efficiency catalysts.

Engineering Interlayer Electron-Phonon Coupling in WS2/BN Heterostructures.

In van der Waals (vdW) heterostructures, the interlayer electron-phonon coupling (EPC) provides one unique channel to nonlocally engineer these elementary particles. However, limited by the stringent occurrence conditions, the efficient engineering of interlayer EPC remains elusive. Here we report a multitier engineering of interlayer EPC in WS2/boron nitride (BN) heterostructures, including isotope enrichments of BN substrates, temperature, and high-pressure tuning. The hyperfine isotope dependence of Raman intensities was unambiguously revealed. In combination with theoretical calculations, we anticipate that WS2/BN supercells could induce Brillouin-zone-folded phonons that contribute to the interlayer coupling, leading to a complex nature of broad Raman peaks. We further demonstrate the significance of a previously unexplored parameter, the interlayer spacing. By varying the temperature and high pressure, we effectively manipulated the strengths of EPC with on/off capabilities, indicating critical thresholds of the layer-layer spacing for activating and strengthening interlayer EPC. Our findings provide new opportunities to engineer vdW heterostructures with controlled interlayer coupling.

Direct observation of highly confined phonon polaritons in suspended monolayer hexagonal boron nitride.

Phonon polaritons enable light confinement at deep subwavelength scales, with potential technological applications, such as subdiffraction imaging, sensing and engineering of spontaneous emission. However, the trade-off between the degree of confinement and the excitation efficiency of phonon polaritons prevents direct observation of these modes in monolayer hexagonal boron nitride (h-BN), where they are expected to reach ultrahigh confinement. Here, we use monochromatic electron energy-loss spectroscopy (about 7.5 meV energy resolution) in a scanning transmission electron microscope to measure phonon polaritons in monolayer h-BN, directly demonstrating the existence of these modes as the phonon Reststrahlen band (RS) disappears. We find phonon polaritons in monolayer h-BN to exhibit high confinement (>487 times smaller wavelength than that of light in free space) and ultraslow group velocity down to about 10-5c. The large momentum compensation provided by electron beams additionally allows us to excite phonon polaritons over nearly the entire RS band of multilayer h-BN. These results open up a broad range of opportunities for the engineering of metasurfaces and strongly enhanced light-matter interactions.

Nonadiabatic Dynamics of Photocatalytic Water Splitting on A Polymeric Semiconductor.

To elucidate the nature of light-driven photocatalytic water splitting, a polymeric semiconductor-graphitic carbon nitride (g-C3N4)-has been chosen as a prototype substrate for studying atomistic water spitting processes in realistic environments. Our nonadiabatic quantum dynamics simulations based on real-time time-dependent density functional theory reveal explicitly the transport channel of photogenerated charge carriers at the g-C3N4/water interface, which shows a strong correlation to bond re-forming. A three-step photoreaction mechanism is proposed, whereas the key roles of hole-driven hydrogen transfer and interfacial water configurations were identified. Immediately following photocatalytic water splitting, atomic pathways for the two dissociated hydrogen atoms approaching each other and forming the H2 gas molecule are demonstrated, while the remanent OH radicals may form intermediate products (e.g., H2O2). These results provide critical new insights for the characterization and further development of efficient water-splitting photocatalysts from a dynamic perspective.

Microscopic Kinetics Pathway of Salt Crystallization in Graphene Nanocapillaries.

The fundamental understanding of crystallization, in terms of microscopic kinetic and thermodynamic details, remains a key challenge in the physical sciences. Here, by using in situ graphene liquid cell transmission electron microscopy, we reveal the atomistic mechanism of NaCl crystallization from solutions confined within graphene cells. We find that rock salt NaCl forms with a peculiar hexagonal morphology. We also see the emergence of a transitory graphitelike phase, which may act as an intermediate in a two-step pathway. With the aid of density functional theory calculations, we propose that these observations result from a delicate balance between the substrate-solute interaction and thermodynamics under confinement. Our results highlight the impact of confinement on both the kinetics and thermodynamics of crystallization, offering new insights into heterogeneous crystallization theory and a potential avenue for materials design.