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Sodium under pressure It has recently been shown that, when high pressures are applied, crystals of lithium and sodium undergo a sequence of phase transitions — including (for sodium) a striking and as yet unexplained pressure-induced drop in the melting temperature. Jean-Yves Raty et al . have now identified the cause of this unusual melting behaviour: it emerges because liquid sodium undergoes a series of transitions similar to those seen in the solid state, but at much lower pressures. Intriguingly, one of these transitions is driven by the opening of a 'pseudogap' in the electronic density of states, the first time such an effect has been seen in a liquid metal. When high pressures are applied, crystals of lithium and sodium undergo a sequence of phase transitions, including a striking pressure-induced drop in the melting temperature. The cause of the unusual melting behaviour has now been identified: it emerges because liquid sodium undergoes a series of transitions similar to those seen in the solid state, but at much lower pressures. One of these transitions is driven by the opening of a 'pseudogap' in the electronic density of states. At ambient conditions, the light alkali metals are free-electron-like crystals with a highly symmetric structure. However, they were found recently to exhibit unexpected complexity under pressure 1 , 2 , 3 , 4 , 5 , 6 . It was predicted from theory 1 , 2 —and later confirmed by experiment 3 , 4 , 5 —that lithium and sodium undergo a sequence of symmetry-breaking transitions, driven by a Peierls mechanism, at high pressures. Measurements of the sodium melting curve 6 have subsequently revealed an unprecedented (and still unexplained) pressure-induced drop in melting temperature from 1,000 K at 30 GPa down to room temperature at 120 GPa. Here we report results from ab initio calculations that explain the unusual melting behaviour in dense sodium. We show that molten sodium undergoes a series of pressure-induced structural and electronic transitions, analogous to those observed in solid sodium but commencing at much lower pressure in the presence of liquid disorder. As pressure is increased, liquid sodium initially evolves by assuming a more compact local structure. However, a transition to a lower-coordinated liquid takes place at a pressure of around 65 GPa, accompanied by a threefold drop in electrical conductivity. This transition is driven by the opening of a pseudogap, at the Fermi level, in the electronic density of states—an effect that has not hitherto been observed in a liquid metal. The lower-coordinated liquid emerges at high temperatures and above the stability region of a close-packed free-electron-like metal. We predict that similar exotic behaviour is possible in other materials as well.

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 cells 1 – 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 determination 5 – 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 glasses 10 , 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. A method that achieves atomic-resolution tomographic imaging of an amorphous solid enables detailed quantitative characterization of the short- and medium-range order of the three-dimensional atomic arrangement.

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. Atomic electron tomography is used to determine the three-dimensional atomic structure of monatomic amorphous solids with liquid-like structure, which is characterized by the existence of pentagonal bipyramid networks with medium-range order.

Predicting structure from the attributes of a material's building blocks remains a challenge and central goal for materials science. Isolating the role of building block shape for self-assembly provides insight into the ordering of molecules and the crystallization of colloids, nanoparticles, proteins, and viruses. We investigated 145 convex polyhedra whose assembly arises solely from their anisotropic shape. Our results demonstrate a remarkably high propensity for thermodynamic self-assembly and structural diversity. We show that from simple measures of particle shape and local order in the fluid, the assembly of a given shape into a liquid crystal, plastic crystal, or crystal can be predicted.

Reconfigurable, ordered matter offers great potential for future low-power computer memory by storing information in energetically stable configurations. Among these, skyrmions—which are topologically protected, robust excitations that have been demonstrated in chiral magnets1–4 and in liquid crystals5–7—are driving much excitement about potential spintronic applications8. These information-encoding structures topologically resemble field configurations in many other branches of physics and have a rich history9, although chiral condensed-matter systems so far have yielded realizations only of elementary full and fractional skyrmions. Here we describe stable, high-degree multi-skyrmion configurations where an arbitrary number of antiskyrmions are contained within a larger skyrmion. We call these structures skyrmion bags. We demonstrate them experimentally and numerically in liquid crystals and numerically in micromagnetic simulations either without or with magnetostatic effects. We find that skyrmion bags act like single skyrmions in pairwise interaction and under the influence of current in magnetic materials, and are thus an exciting proposition for topological magnetic storage and logic devices.Structures containing multiple skyrmions inside a larger skyrmion—called skyrmion bags—are experimentally created in liquid crystals and theoretically predicted in magnetic materials. These may have applications in information storage technology.

High-entropy alloys have exhibited unusual materials properties. The stability of equimolar single-phase solid solution of five or more elements is supposedly rare and identifying the existence of such alloys has been challenging because of the vast chemical space of possible combinations. Herein, based on high-throughput density-functional theory calculations, we construct a chemical map of single-phase equimolar high-entropy alloys by investigating over 658,000 equimolar quinary alloys through a binary regular solid-solution model. We identify 30,201 potential single-phase equimolar alloys (5% of the possible combinations) forming mainly in body-centered cubic structures. We unveil the chemistries that are likely to form high-entropy alloys, and identify the complex interplay among mixing enthalpy, intermetallics formation, and melting point that drives the formation of these solid solutions. We demonstrate the power of our method by predicting the existence of two new high-entropy alloys, i.e. the body-centered cubic AlCoMnNiV and the face-centered cubic CoFeMnNiZn, which are successfully synthesized. The compositional space of potential high-entropy alloys is gigantic and difficult to explore efficiently. Here, the authors use high-throughput first-principles computations to predict what elements can mix to form high-entropy alloys, understanding of the factors favoring their formation.

Moiré superlattices in transition metal dichalcogenide (TMD) heterostructures can host novel correlated quantum phenomena due to the interplay of narrow moiré flat bands and strong, long-range Coulomb interactions 1 – 9 . However, microscopic knowledge of the atomically reconstructed moiré superlattice and resulting flat bands is still lacking, which is critical for fundamental understanding and control of the correlated moiré phenomena. Here we quantitatively study the moiré flat bands in three-dimensional (3D) reconstructed WSe 2 /WS 2 moiré superlattices by comparing scanning tunnelling spectroscopy (STS) of high-quality exfoliated TMD heterostructure devices with ab initio simulations of TMD moiré superlattices. A strong 3D buckling reconstruction accompanied by large in-plane strain redistribution is identified in our WSe 2 /WS 2 moiré heterostructures. STS imaging demonstrates that this results in a remarkably narrow and highly localized K-point moiré flat band at the valence band edge of the heterostructure. A series of moiré flat bands are observed at different energies that exhibit varying degrees of localization. Our observations contradict previous simplified theoretical models but agree quantitatively with ab initio simulations that fully capture the 3D structural reconstruction. Our results reveal that the strain redistribution and 3D buckling in TMD heterostructures dominate the effective moiré potential and the corresponding moiré flat bands at the Brillouin zone K points. Scanning tunnelling spectroscopy and ab initio simulations reveal buckling reconstruction and in-plane strain redistribution in WSe 2 /WS 2 moiré heterostructures.

The limits of dislocation-mediated metal plasticity are studied by using in situ computational microscopy to reduce the enormous amount of data from fully dynamic atomistic simulations into a manageable form. Probing plasticity limits of metals Fully dynamic atomistic simulations of plastic deformation in metals are so computationally demanding that materials physicists have instead developed mesoscale proxies to model dislocation dynamics. In this paper, Vasily Bulatov and colleagues take on the challenge of modelling metal plasticity at the atomic level. Such simulations require models that contain many millions of atoms (the largest simulation in this study contains 268 million atoms), and algorithms are used to process the datasets down to a volume that allows human interpretation. The authors probe ultrahigh-strain-rate deformation in body-centred-cubic tantalum, a model metal, to investigate the limits of metal plasticity. They show that at certain limiting conditions, dislocations can no longer relieve metal loading and twinning takes over. At a strain rate lower than this limit, flow stress and dislocation density achieve a steady state and a sort of metal kneading is observed. The simulations support previous proposals of the maximum dislocation density that can be reached before a metal collapses. Ordinarily, the strength and plasticity properties of a metal are defined by dislocations—line defects in the crystal lattice whose motion results in material slippage along lattice planes 1 . Dislocation dynamics models are usually used as mesoscale proxies for true atomistic dynamics, which are computationally expensive to perform routinely 2 . However, atomistic simulations accurately capture every possible mechanism of material response, resolving every “jiggle and wiggle” 3 of atomic motion, whereas dislocation dynamics models do not. Here we present fully dynamic atomistic simulations of bulk single-crystal plasticity in the body-centred-cubic metal tantalum. Our goal is to quantify the conditions under which the limits of dislocation-mediated plasticity are reached and to understand what happens to the metal beyond any such limit. In our simulations, the metal is compressed at ultrahigh strain rates along its [001] crystal axis under conditions of constant pressure, temperature and strain rate. To address the complexity of crystal plasticity processes on the length scales (85–340 nm) and timescales (1 ns–1μs) that we examine, we use recently developed methods of in situ computational microscopy 4 , 5 to recast the enormous amount of transient trajectory data generated in our simulations into a form that can be analysed by a human. Our simulations predict that, on reaching certain limiting conditions of strain, dislocations alone can no longer relieve mechanical loads; instead, another mechanism, known as deformation twinning (the sudden re-orientation of the crystal lattice 6 ), takes over as the dominant mode of dynamic response. Below this limit, the metal assumes a strain-path-independent steady state of plastic flow in which the flow stress and the dislocation density remain constant as long as the conditions of straining thereafter remain unchanged. In this distinct state, tantalum flows like a viscous fluid while retaining its crystal lattice and remaining a strong and stiff metal.

Chiral crystals are materials with a lattice structure that has a well-defined handedness due to the lack of inversion, mirror or other roto-inversion symmetries. Although it has been shown that the presence of crystalline symmetries can protect topological band crossings, the topological electronic properties of chiral crystals remain largely uncharacterized. Here we show that Kramers–Weyl fermions are a universal topological electronic property of all non-magnetic chiral crystals with spin–orbit coupling and are guaranteed by structural chirality, lattice translation and time-reversal symmetry. Unlike conventional Weyl fermions, they appear at time-reversal-invariant momenta. We identify representative chiral materials in 33 of the 65 chiral space groups in which Kramers–Weyl fermions are relevant to the low-energy physics. We determine that all point-like nodal degeneracies in non-magnetic chiral crystals with relevant spin–orbit coupling carry non-trivial Chern numbers. Kramers–Weyl materials can exhibit a monopole-like electron spin texture and topologically non-trivial bulk Fermi surfaces over an unusually large energy window.

Silver nanoparticles are susceptible to oxidation and have accordingly received less attention than gold nanoparticles; ultrastable silver nanoparticles are now reported, which can be produced in very large quantities as a single-sized molecular product, and the origins of their enhanced stability are elucidated using a single-crystal X-ray structure and first-principles calculations. Silver nanoparticles as good as gold Noble metals in nanoparticulate form find practical application as catalysts and in optoelectronics, energy conservation and many other fields. Gold nanoparticles, stable and easy to use, have proved much more useful and so have been studied more extensively than silver nanoparticles, which tend to be susceptible to oxidation. Anil Desireddy et al . describe a simple recipe for the large-scale production of single-sized silver nanoclusters, whose electronic structure gives them exceptional chemical stability. With the availability of stable silver nanoparticles, the metal's desirable electrical and physical properties, abundance and comparatively low cost could be harnessed in a wealth of new applications. Noble-metal nanoparticles have had a substantial impact across a diverse range of fields, including catalysis 1 , sensing 2 , photochemistry 3 , optoelectronics 4 , 5 , energy conversion 6 and medicine 7 . Although silver has very desirable physical properties, good relative abundance and low cost, gold nanoparticles have been widely favoured owing to their proved stability and ease of use. Unlike gold, silver is notorious for its susceptibility to oxidation (tarnishing), which has limited the development of important silver-based nanomaterials. Despite two decades of synthetic efforts, silver nanoparticles that are inert or have long-term stability remain unrealized. Here we report a simple synthetic protocol for producing ultrastable silver nanoparticles, yielding a single-sized molecular product in very large quantities with quantitative yield and without the need for size sorting. The stability, purity and yield are substantially better than those for other metal nanoparticles, including gold, owing to an effective stabilization mechanism. The particular size and stoichiometry of the product were found to be insensitive to variations in synthesis parameters. The chemical stability and structural, electronic and optical properties can be understood using first-principles electronic structure theory based on an experimental single-crystal X-ray structure. Although several structures have been determined for protected gold nanoclusters 8 , 9 , 10 , 11 , 12 , none has been reported so far for silver nanoparticles. The total structure of a thiolate-protected silver nanocluster reported here uncovers the unique structure of the silver thiolate protecting layer, consisting of Ag 2 S 5 capping structures. The outstanding stability of the nanoparticle is attributed to a closed-shell 18-electron configuration with a large energy gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital, an ultrastable 32-silver-atom excavated-dodecahedral 13 core consisting of a hollow 12-silver-atom icosahedron encapsulated by a 20-silver-atom dodecahedron, and the choice of protective coordinating ligands. The straightforward synthesis of large quantities of pure molecular product promises to make this class of materials widely available for further research and technology development 14 , 15 , 16 , 17 , 18 .