Three-dimensional atomic structure and local chemical order of medium- and high-entropy nanoalloys.

Medium- and high-entropy alloys (M/HEAs) mix several principal elements with near-equiatomic composition and represent a model-shift strategy for designing previously unknown materials in metallurgy1-8, catalysis9-14 and other fields15-18. One of the core hypotheses of M/HEAs is lattice distortion5,19,20, which has been investigated by different numerical and experimental techniques21-26. However, determining the three-dimensional (3D) lattice distortion in M/HEAs remains a challenge. Moreover, the presumed random elemental mixing in M/HEAs has been questioned by X-ray and neutron studies27, atomistic simulations28-30, energy dispersive spectroscopy31,32 and electron diffraction33,34, which suggest the existence of local chemical order in M/HEAs. However, direct experimental observation of the 3D local chemical order has been difficult because energy dispersive spectroscopy integrates the composition of atomic columns along the zone axes7,32,34 and diffuse electron reflections may originate from planar defects instead of local chemical order35. Here we determine the 3D atomic positions of M/HEA nanoparticles using atomic electron tomography36 and quantitatively characterize the local lattice distortion, strain tensor, twin boundaries, dislocation cores and chemical short-range order (CSRO). We find that the high-entropy alloys have larger local lattice distortion and more heterogeneous strain than the medium-entropy alloys and that strain is correlated to CSRO. We also observe CSRO-mediated twinning in the medium-entropy alloys, that is, twinning occurs in energetically unfavoured CSRO regions but not in energetically favoured CSRO ones, which represents, to our knowledge, the first experimental observation of correlating local chemical order with structural defects in any material. We expect that this work will not only expand our fundamental understanding of this important class of materials but also provide the foundation for tailoring M/HEA properties through engineering lattice distortion and local chemical order.

Accurate real space iterative reconstruction (RESIRE) algorithm for tomography.

Tomography has made a revolutionary impact on the physical, biological and medical sciences. The mathematical foundation of tomography is to reconstruct a three-dimensional (3D) object from a set of two-dimensional (2D) projections. As the number of projections that can be measured from a sample is usually limited by the tolerable radiation dose and/or the geometric constraint on the tilt range, a main challenge in tomography is to achieve the best possible 3D reconstruction from a limited number of projections with noise. Over the years, a number of tomographic reconstruction methods have been developed including direct inversion, real-space, and Fourier-based iterative algorithms. Here, we report the development of a real-space iterative reconstruction (RESIRE) algorithm for accurate tomographic reconstruction. RESIRE iterates between the update of a reconstructed 3D object and the measured projections using a forward and back projection step. The forward projection step is implemented by the Fourier slice theorem or the Radon transform, and the back projection step by a linear transformation. Our numerical and experimental results demonstrate that RESIRE performs more accurate 3D reconstructions than other existing tomographic algorithms, when there are a limited number of projections with noise. Furthermore, RESIRE can be used to reconstruct the 3D structure of extended objects as demonstrated by the determination of the 3D atomic structure of an amorphous Ta thin film. We expect that RESIRE can be widely employed in the tomography applications in different fields. Finally, to make the method accessible to the general user community, the MATLAB source code of RESIRE and all the simulated and experimental data are available at  https://zenodo.org/record/7273314 .

Three-dimensional atomic packing in amorphous solids with liquid-like structure.

Liquids and solids are two fundamental states of matter. However, our understanding of their three-dimensional atomic structure is mostly based on physical models. Here we use atomic electron tomography to experimentally determine the three-dimensional atomic positions of monatomic amorphous solids, namely a Ta thin film and two Pd nanoparticles. We observe that pentagonal bipyramids are the most abundant atomic motifs in these amorphous materials. Instead of forming icosahedra, the majority of pentagonal bipyramids arrange into pentagonal bipyramid networks with medium-range order. Molecular dynamics simulations further reveal that pentagonal bipyramid networks are prevalent in monatomic metallic liquids, which rapidly grow in size and form more icosahedra during the quench from the liquid to the glass state. These results expand our understanding of the atomic structures of amorphous solids and will encourage future studies on amorphous-crystalline phase and glass transitions in non-crystalline materials with three-dimensional atomic resolution.

Capturing 3D atomic defects and phonon localization at the 2D heterostructure interface.

The three-dimensional (3D) local atomic structures and crystal defects at the interfaces of heterostructures control their electronic, magnetic, optical, catalytic, and topological quantum properties but have thus far eluded any direct experimental determination. Here, we use atomic electron tomography to determine the 3D local atomic positions at the interface of a MoS2-WSe2 heterojunction with picometer precision and correlate 3D atomic defects with localized vibrational properties at the epitaxial interface. We observe point defects, bond distortion, and atomic-scale ripples and measure the full 3D strain tensor at the heterointerface. By using the experimental 3D atomic coordinates as direct input to first-principles calculations, we reveal new phonon modes localized at the interface, which are corroborated by spatially resolved electron energy-loss spectroscopy. We expect that this work will pave the way for correlating structure-property relationships of a wide range of heterostructure interfaces at the single-atom level.

Subterahertz collective dynamics of polar vortices.

The collective dynamics of topological structures1-6 are of interest from both fundamental and applied perspectives. For example, studies of dynamical properties of magnetic vortices and skyrmions3,4 have not only deepened our understanding of many-body physics but also offered potential applications in data processing and storage7. Topological structures constructed from electrical polarization, rather than electron spin, have recently been realized in ferroelectric superlattices5,6, and these are promising for ultrafast electric-field control of topological orders. However, little is known about the dynamics underlying the functionality of such complex extended nanostructures. Here, using terahertz-field excitation and femtosecond X-ray diffraction measurements, we observe ultrafast collective polarization dynamics that are unique to polar vortices, with orders-of-magnitude higher frequencies and smaller lateral size than those of experimentally realized magnetic vortices3. A previously unseen tunable mode, hereafter referred to as a vortexon, emerges in the form of transient arrays of nanoscale circular patterns of atomic displacements, which reverse their vorticity on picosecond timescales. Its frequency is considerably reduced (softened) at a critical strain, indicating a condensation (freezing) of structural dynamics. We use first-principles-based atomistic calculations and phase-field modelling to reveal the microscopic atomic arrangements and corroborate the frequencies of the vortex modes. The discovery of subterahertz collective dynamics in polar vortices opens opportunities for electric-field-driven data processing in topological structures with ultrahigh speed and density.

Determining the three-dimensional atomic structure of an amorphous solid.

Amorphous solids such as glass, plastics and amorphous thin films are ubiquitous in our daily life and have broad applications ranging from telecommunications to electronics and solar cells1-4. However, owing to the lack of long-range order, the three-dimensional (3D) atomic structure of amorphous solids has so far eluded direct experimental determination5-15. Here we develop an atomic electron tomography reconstruction method to experimentally determine the 3D atomic positions of an amorphous solid. Using a multi-component glass-forming alloy as proof of principle, we quantitatively characterize the short- and medium-range order of the 3D atomic arrangement. We observe that, although the 3D atomic packing of the short-range order is geometrically disordered, some short-range-order structures connect with each other to form crystal-like superclusters and give rise to medium-range order. We identify four types of crystal-like medium-range order-face-centred cubic, hexagonal close-packed, body-centred cubic and simple cubic-coexisting in the amorphous sample, showing translational but not orientational order. These observations provide direct experimental evidence to support the general framework of the efficient cluster packing model for metallic glasses10,12-14,16. We expect that this work will pave the way for the determination of the 3D structure of a wide range of amorphous solids, which could transform our fundamental understanding of non-crystalline materials and related phenomena.

Correlating the three-dimensional atomic defects and electronic properties of two-dimensional transition metal dichalcogenides.

The electronic, optical and chemical properties of two-dimensional transition metal dichalcogenides strongly depend on their three-dimensional atomic structure and crystal defects. Using Re-doped MoS2 as a model system, here we present scanning atomic electron tomography as a method to determine three-dimensional atomic positions as well as positions of crystal defects such as dopants, vacancies and ripples with a precision down to 4 pm. We measure the three-dimensional bond distortion and local strain tensor induced by single dopants. By directly providing these experimental three-dimensional atomic coordinates to density functional theory, we obtain more accurate electronic band structures than derived from conventional density functional theory calculations that relies on relaxed three-dimensional atomic coordinates. We anticipate that scanning atomic electron tomography not only will be generally applicable to determine the three-dimensional atomic coordinates of two-dimensional materials, but also will enable ab initio calculations to better predict the physical, chemical and electronic properties of these materials.

Designing Optimal Perovskite Structure for High Ionic Conduction.

Solid-oxide fuel/electrolyzer cells are limited by a dearth of electrolyte materials with low ohmic loss and an incomplete understanding of the structure-property relationships that would enable the rational design of better materials. Here, using epitaxial thin-film growth, synchrotron radiation, impedance spectroscopy, and density-functional theory, the impact of structural parameters (i.e., unit-cell volume and octahedral rotations) on ionic conductivity is delineated in La0.9 Sr0.1 Ga0.95 Mg0.05 O3- δ . As compared to the zero-strain state, compressive strain reduces the unit-cell volume while maintaining large octahedral rotations, resulting in a strong reduction of ionic conductivity, while tensile strain increases the unit-cell volume while quenching octahedral rotations, resulting in a negligible effect on the ionic conductivity. Calculations reveal that larger unit-cell volumes and octahedral rotations decrease migration barriers and create low-energy migration pathways, respectively. The desired combination of large unit-cell volume and octahedral rotations is normally contraindicated, but through the creation of superlattice structures both expanded unit-cell volume and large octahedral rotations are experimentally realized, which result in an enhancement of the ionic conductivity. All told, the potential to tune ionic conductivity with structure alone by a factor of ≈2.5 at around 600 °C is observed, which sheds new light on the rational design of ion-conducting perovskite electrolytes.

Three-dimensional atomic scale electron density reconstruction of octahedral tilt epitaxy in functional perovskites.

Octahedral tilts are the most ubiquitous distortions in perovskite-related structures that can dramatically influence ferroelectric, magnetic, and electronic properties; yet the paradigm of tilt epitaxy in thin films is barely explored. Non-destructively characterizing such epitaxy in three-dimensions for low symmetry complex tilt systems composed of light anions is a formidable challenge. Here we demonstrate that the interfacial tilt epitaxy can transform ultrathin calcium titanate, a non-polar earth-abundant mineral, into high-temperature polar oxides that last above 900 K. The comprehensive picture of octahedral tilts and polar distortions is revealed by reconstructing the three-dimensional electron density maps across film-substrate interfaces with atomic resolution using coherent Bragg rod analysis. The results are complemented with aberration-corrected transmission electron microscopy, film superstructure reflections, and are in excellent agreement with density functional theory. The study could serve as a broader template for non-destructive, three-dimensional atomic resolution probing of complex low symmetry functional interfaces.

Artificial two-dimensional polar metal at room temperature.

Polar metals, commonly defined by the coexistence of polar crystal structure and metallicity, are thought to be scarce because the long-range electrostatic fields favoring the polar structure are expected to be fully screened by the conduction electrons of a metal. Moreover, reducing from three to two dimensions, it remains an open question whether a polar metal can exist. Here we report on the realization of a room temperature two-dimensional polar metal of the B-site type in tri-color (tri-layer) superlattices BaTiO3/SrTiO3/LaTiO3. A combination of atomic resolution scanning transmission electron microscopy with electron energy-loss spectroscopy, optical second harmonic generation, electrical transport, and first-principles calculations have revealed the microscopic mechanisms of periodic electric polarization, charge distribution, and orbital symmetry. Our results provide a route to creating all-oxide artificial non-centrosymmetric quasi-two-dimensional metals with exotic quantum states including coexisting ferroelectric, ferromagnetic, and superconducting phases.

Observation of Quasi-Two-Dimensional Polar Domains and Ferroelastic Switching in a Metal, Ca3Ru2O7.

Polar domains arise in insulating ferroelectrics when free carriers are unable to fully screen surface-bound charges. Recently discovered binary and ternary polar metals exhibit broken inversion symmetry coexisting with free electrons that might be expected to suppress the electrostatic driving force for domain formation. Contrary to this expectation, we report the first direct observation of polar domains in single crystals of the polar metal Ca3Ru2O7. By a combination of mesoscale optical second-harmonic imaging and atomic-resolution scanning transmission electron microscopy, the polar domains are found to possess a quasi-two-dimensional slab geometry with a lateral size of ∼100 µm and thickness of ∼10 nm. Electronic structure calculations show that the coexistence of electronic and parity-lifting orders arise from anharmonic lattice interactions, which support 90° and 180° polar domains in a metal. Using in situ transmission electron microscopy, we also demonstrate a strain-tuning route to achieve ferroelastic switching of polar metal domains.

Light-Activated Gigahertz Ferroelectric Domain Dynamics.

Using time- and spatially resolved hard x-ray diffraction microscopy, the striking structural and electrical dynamics upon optical excitation of a single crystal of BaTiO_{3} are simultaneously captured on subnanoseconds and nanoscale within individual ferroelectric domains and across walls. A large emergent photoinduced electric field of up to 20×10^{6} V/m is discovered in a surface layer of the crystal, which then drives polarization and lattice dynamics that are dramatically distinct in a surface layer versus bulk regions. A dynamical phase-field modeling method is developed that reveals the microscopic origin of these dynamics, leading to gigahertz polarization and elastic waves traveling in the crystal with sonic speeds and spatially varying frequencies. The advances in spatiotemporal imaging and dynamical modeling tools open up opportunities for disentangling ultrafast processes in complex mesoscale structures such as ferroelectric domains.

Continuously Tuning Epitaxial Strains by Thermal Mismatch.

Strain engineering of thin films is a conventionally employed approach to enhance material properties and to energetically prefer ground states that would otherwise not be attainable. Controlling strain states in perovskite oxide thin films is usually accomplished through coherent epitaxy by using lattice-mismatched substrates with similar crystal structures. However, the limited choice of suitable oxide substrates makes certain strain states experimentally inaccessible and a continuous tuning impossible. Here, we report a strategy to continuously tune epitaxial strains in perovskite films grown on Si(001) by utilizing the large difference of thermal expansion coefficients between the film and the substrate. By establishing an adsorption-controlled growth window for SrTiO3 thin films on Si using hybrid molecular beam epitaxy, the magnitude of strain can be solely attributed to thermal expansion mismatch, which only depends on the difference between growth and room temperature. Second-harmonic generation measurements revealed that structure properties of SrTiO3 films could be tuned by this method using films with different strain states. Our work provides a strategy to generate continuous strain states in oxide/semiconductor pseudomorphic buffer structures that could help achieve desired material functionalities.

Terahertz Emission from Hybrid Perovskites Driven by Ultrafast Charge Separation and Strong Electron-Phonon Coupling.

Unusual photophysical properties of organic-inorganic hybrid perovskites have not only enabled exceptional performance in optoelectronic devices, but also led to debates on the nature of charge carriers in these materials. This study makes the first observation of intense terahertz (THz) emission from the hybrid perovskite methylammonium lead iodide (CH3 NH3 PbI3 ) following photoexcitation, enabling an ultrafast probe of charge separation, hot-carrier transport, and carrier-lattice coupling under 1-sun-equivalent illumination conditions. Using this approach, the initial charge separation/transport in the hybrid perovskites is shown to be driven by diffusion and not by surface fields or intrinsic ferroelectricity. Diffusivities of the hot and band-edge carriers along the surface normal direction are calculated by analyzing the emitted THz transients, with direct implications for hot-carrier device applications. Furthermore, photogenerated carriers are found to drive coherent terahertz-frequency lattice distortions, associated with reorganizations of the lead-iodide octahedra as well as coupled vibrations of the organic and inorganic sublattices. This strong and coherent carrier-lattice coupling is resolved on femtosecond timescales and found to be important both for resonant and far-above-gap photoexcitation. This study indicates that ultrafast lattice distortions play a key role in the initial processes associated with charge transport.

Sub-wavelength modulation of χ(2) optical nonlinearity in organic thin films.

Modulating the second-order nonlinear optical susceptibility (χ(2)) of materials at the nanoscale represents an ongoing technological challenge for a variety of integrated frequency conversion and nonlinear nanophotonic applications. Here we exploit the large hyperpolarizability of intermolecular charge transfer states, naturally aligned at an organic semiconductor donor-acceptor (DA) interface, as a means to control the magnitude and sign of χ(2) at the nanoscale. Focusing initially on a single pentacene-C60 DA interface, we confirm that the charge transfer transition is strongly aligned orthogonal to the heterojunction and find that it is responsible for a large interfacial nonlinearity probed via second harmonic generation that is sufficient to achieve d33>10 pm V-1, when incorporated in a non-centrosymmetric DA multilayer stack. Using grating-shadowed oblique-angle deposition to laterally structure the DA interface distribution in such multilayers subsequently enables the demonstration of a χ(2) grating with 280 nm periodicity, which is the shortest reported to date.

Interfacial Octahedral Rotation Mismatch Control of the Symmetry and Properties of SrRuO3.

Epitaxial strain can be used to tune the properties of complex oxides with perovskite structure. Beyond just lattice mismatch, the use of octahedral rotation mismatch at heterointerfaces could also provide an effective route to manipulate material properties. Here, we examine the evolution of the structural motif (i.e., lattice parameters, symmetry, and octahedral rotations) of SrRuO3 films grown on substrates engineered to have the same lattice parameters, but different octahedral rotations. SrRuO3 films grown on SrTiO3 (001) (no octahedral rotations) and GdScO3-buffered SrTiO3 (001) (with octahedral rotations) substrates are found to exhibit monoclinic and tetragonal symmetry, respectively. Electrical transport and magnetic measurements reveal that the tetragonal films exhibit higher resistivity, lower magnetic Curie temperatures, and more isotropic magnetism as compared to those with monoclinic structure. Synchrotron-based quantification of the octahedral rotation network reveals that the tilting pattern in both film variants is the same (albeit with slightly different magnitudes of in-plane rotation angles). The abnormal rotation pattern observed in tetragonal SrRuO3 indicates a possible decoupling between the internal octahedral rotation and lattice symmetry, which could provide new opportunities to engineer thin-film structure and properties.

Does the Dirac cone exist in silicene on metal substrates?

Absence of the Dirac cone due to a strong band hybridization is revealed to be a common feature for epitaxial silicene on metal substrates according to our first-principles calculations for silicene on Ir, Cu, Mg, Au, Pt, Al, and Ag substrates. The destroyed Dirac cone of silicene, however, can be effectively restored with linear or parabolic dispersion by intercalating alkali metal atoms between silicene and the metal substrates, offering an opportunity to study the intriguing properties of silicene without further transfer of silicene from the metal substrates.