Continuous Lattice Research Articles

Structural stability and metallization of orpiment at high pressure

Binary arsenic sulfide compounds have garnered significant attention owing to their wide-ranging physical properties and promising potential in the domains of electronics and optoelectronics. As a naturally abundant and historically significant semiconductor mineral, orpiment (crystalline As2S3) has encountered limited utilization in the realm of optoelectronics due to its considerable bandgap width. For orpiment with its quasi-two-dimensional layered structure, pressure is one of the most effective methods to regulate its crystal structure and physical properties. In this work, the structural behavior, optical and electrical properties of orpiment under high pressure have been investigated systematically utilizing a combination of experimental methods and theoretical calculations. The monoclinic structure of orpiment is stable up to 48 GPa without structural phase transitions involving changes in the space group occurred. The noticeable changes of lattice parameters, axial ratios, and interatomic distances above 20 GPa are ascribed to a transformation from a two-dimensional layered structure to a quasi-three-dimensional crystal framework. Continuous lattice contraction upon compression is accompanied by gradual bandgap narrowing, which leads to metallization of orpiment. The pressure-induced metallization of orpiment occurs above 40 GPa. The structural behavior, optical and electrical properties of orpiment at high pressure exhibit reversible hysteresis upon pressure release. This study offers a high-pressure approach for modulating crystal structure and physical properties of orpiment to expand its potential applications in the fields of electronics and optoelectronics.

Two-dimensional flat-band solitons in superhoneycomb lattices

Abstract Flat-band periodic materials are characterized by a linear spectrum containing at least one band where the propagation constant remains nearly constant irrespective of the Bloch momentum across the Brillouin zone. These materials provide a unique platform for investigating phenomena related to light localization. Meantime, the interaction between flat-band physics and nonlinearity in continuous systems remains largely unexplored, particularly in continuous systems where the band flatness deviates slightly from zero, in contrast to simplified discrete systems with exactly flat bands. Here, we use a continuous superhoneycomb lattice featuring a flat band in its spectrum to theoretically and numerically introduce a range of stable flat-band solitons. These solutions encompass fundamental, dipole, multi-peak, and even vortex solitons. Numerical analysis demonstrates that these solitons are stable in a broad range of powers. They do not bifurcate from the flat band and can be analyzed using Wannier function expansion leading to their designation as Wannier solitons. These solitons showcase novel possibilities for light localization and transmission within nonlinear flat-band systems.

Atomic-scale investigation of the mechanisms of deformation-induced martensitic transformation at ultra-cryogenic temperatures

Liquefied natural gas storage and transportation as well as space propulsion systems have sparked interest in the martensitic transformation and behaviours of 316 L stainless steels (SS) under ultra-cryogenic deformation. In this study, high-resolution transmission electron microscopy (HRTEM) and molecular dynamics (MD) simulations were used to investigate the atomic arrangements and crystalline defects of deformation-induced γ-austenite → ε-martensite → α′-martensite and γ → α′ martensitic transformations in 316 L SS at 15 and 173 K. The γ → ε transformation involves the glide of Shockley partial dislocations on (111)γ planes without a change in atomic spacing. The formation of an α′ inclusion in a single ε-band is achieved by a continuous lattice distortion, accompanied by the formation of a transition zone of α′ and the expansion of the average atomic spacings due to dislocation shuffling. As α′ grows further into γ, the orientation relationship (OR) of the α′ changes by lattice bending. This process follows the Bogers-Burgers-Olson-Cohen model despite it not occurring on intersecting shear bands. Stacking faults and twins can also serve as nucleation sites for α′ at 173 K. We also found that direct transformation of γ → α′ occurs by the glide of 6aγ[112¯]/12 dislocations on every (111)γ plane with misfit dislocations. Overall, this study provides, for the first time, insights into the atomic-scale mechanisms of various two-step and one-step martensitic transformations induced by cryogenic deformation and corresponding local strain, enhancing our understanding of the role of martensitic transformation under ultra-cryogenic-temperature deformation in controlling the properties.

On the diagonal of Riesz operators on Banach lattices

This paper extends the well-known Ringrose theory for compact operators to polynomially Riesz operators on Banach spaces. The particular case of an ideal-triangularizable Riesz operator on an order continuous Banach lattice yields that the spectrum of such operator lies on its diagonal, which motivates the systematic study of an abstract diagonal of a regular operator on an order complete vector lattice E. We prove that the class of regular operators for which the diagonal coincides with the atomic diagonal is always a band in , which contains the band of abstract integral operators. If E is also a Banach lattice, then contains positive Riesz and positive AM-compact operators.

A theoretical study of Lifshitz transition for 2H-TaS2.

Lifshitz transition was proposed to explain a change of the topology structure in a Fermi surface induced by continuous lattice deformation without symmetry breaking since 1960. It is well known that the anomalies of the kinetic coefficients (the coefficient of heat conduction and electrical conductivity, viscosity, sound absorption, etc.) are usually closely connected with the Lifshitz transition behavior. 2H-TaS2 is a typical representative to study its anomalies of temperature dependence of heat capacity, resistivity, Hall effect, and magnetic susceptibility. Its geometrical structure of the charge density wave (CDW) phase and layer number dependence of carrier-sign alternation upon cooling in the Hall measurements have not been well understood. The geometrical structure (T-Ts) of the CDW phase was predicted through first principles calculations for bulk and mono-layer 2H-TaS2. Driven by electron-lattice coupling, Ta atoms contract to form a partially gapped CDW phase. The CDW phase has a larger average interlayer separation of S-S atoms in the adjacent two layers compared with the metal phase, which results in a weaker chemical bonding among S-S atoms in the adjacent two layers and then a narrower bandwidth of the energy band. The narrower bandwidth of the energy band leads to a larger density of states (DOS) in the out-of-plane direction above the Fermi level for the CDW phase. As the Fermi level continually drops from the DOS region with a negative slope to that with a positive slope on cooling, the reversal of the p → n type carrier and the pocket-vanishing-type Lifshitz transition occur in the bulk 2H-TaS2. However, the Fermi level slightly drops by 6 meV and happens to be at the positions of pseudo band gaps, so the reduction of in-plane DOS and total DOS is responsible for the always p-type carrier in the mono-layer samples. Our CDW vector of the k-space separation between two saddle points is QSP ≈ 0.62 GK and can provide a theoretical support for the "saddle-point" CDW mechanism proposed by Rice and Scott. Our theoretical explanation gives a new understanding of both Lifshitz transition for symmetry breaking and reversal for the p-n carrier sign in the Hall measurements in various two-dimensional transition metal disulfides.

Causal structure of spacetime and Scott topology

In this paper we establish the spacetime manifold as a partially ordered set via the casual structure. We show that these partially ordered sets are naturally continuous as a suitable way below relation can be established via the chronological order. We further consider those classes of spacetimes on which a lattice structure can be endowed by physically defining the joins and meets. By considering the physical properties of null geodesics on the spacetime manifold we show that these lattices are necessarily distributive. These lattices are then continuous as a result of the equivalence between the way below relation and chronology. This enables us to define the Scott topology on the spacetime manifold and describe it on an equal footing as any other continuous lattice. We further show that the Scott topology is a proper subset of Alexandroff topology, which must be the manifold topology for the strongly causal spacetimes, (and hence a coarser topology than Alexandroff). In the process we find some interesting results on the sobriety of these manifolds. We prove that they are necessarily not sober under the Scott topology but regain their sobriety under Alexandroff topology. We also define a dual Scott topology on these manifolds by endowing them with bicontinuous poset structure and show that the join of the Scott topology with the dual is the Alexandroff topology. We also discuss the previous works done in this topic and how the present work generalises those results to some extent.

Manipulating Lone-Pair-Driven Luminescence in 0D Tin Halides by Pressure-Tuned Stereochemical Activity from Static to Dynamic.

The excellent luminescence properties and structural dynamics driven by the stereoactivity of the lone pair in a variety of low-dimensional ns2 metal halides have attracted growing investigations for optoelectronic applications. However, the structural and photophysical aspects of the excited state associated with the lone pair expression are currently open questions. Herein, zero-dimensional Sn-based halides with static stereoactive 5 s2 lone pairs are selected as a model system to understand the correlations between the distinctive lone pair expression and the excited-state structural relaxation and charge carrier dynamics by continuous lattice manipulation. Lattice compression drives 5 s2 lone pair active switching and self-trapped exciton (STE) redistribution by suppressing excited-state structural deformation of the isolated SnBr4 2- units. Our results demonstrate that the static expression of the 5 s2 lone pair results in a red broadband triplet STE emission with a large Stokes shift, while its dynamic expression creates a sky-blue narrowband emission dominated by the radiative recombination of singlet STEs. Our findings and the photophysical mechanism proposed highlight the stereochemical effects of lone pair expression in controlling light emission properties and offer constructive guidelines for tuning the optoelectronic properties in diverse ns2 metal halides.

Manipulating Lone‐Pair‐Driven Luminescence in 0D Tin Halides by Pressure‐Tuned Stereochemical Activity from Static to Dynamic

AbstractThe excellent luminescence properties and structural dynamics driven by the stereoactivity of the lone pair in a variety of low‐dimensional ns2 metal halides have attracted growing investigations for optoelectronic applications. However, the structural and photophysical aspects of the excited state associated with the lone pair expression are currently open questions. Herein, zero‐dimensional Sn‐based halides with static stereoactive 5 s2 lone pairs are selected as a model system to understand the correlations between the distinctive lone pair expression and the excited‐state structural relaxation and charge carrier dynamics by continuous lattice manipulation. Lattice compression drives 5 s2 lone pair active switching and self‐trapped exciton (STE) redistribution by suppressing excited‐state structural deformation of the isolated SnBr42− units. Our results demonstrate that the static expression of the 5 s2 lone pair results in a red broadband triplet STE emission with a large Stokes shift, while its dynamic expression creates a sky‐blue narrowband emission dominated by the radiative recombination of singlet STEs. Our findings and the photophysical mechanism proposed highlight the stereochemical effects of lone pair expression in controlling light emission properties and offer constructive guidelines for tuning the optoelectronic properties in diverse ns2 metal halides.

Molecular Modeling of Supercritical Processes and the Lattice—Gas Model

The existing possibilities for modeling the kinetics of supercritical processes at the molecular level are considered from the point of view that the Second Law of thermodynamics must be fulfilled. The only approach that ensures the fulfillment of the Second Law of thermodynamics is the molecular theory based on the discrete–continuous lattice gas model. Expressions for the rates of the elementary stage on its basis give a self-consistent description of the equilibrium states of the mixtures under consideration. The common usage today of ideal kinetic models in SC processes in modeling industrial chemistry contradicts the non-ideal equation of states. The used molecular theory is the theory of absolute reaction rates for non-ideal reaction systems, which takes into account intermolecular interactions that change the effective activation energies of elementary stages. This allows the theory to describe the rates of elementary stages of chemical transformations and molecular transport at arbitrary temperatures and reagent densities in different phases. The application of this theory in a wide range of state parameters (pressure and temperature) is considered when calculating the rates of elementary bimolecular reactions and dissipative coefficients under supercritical conditions. Generalized dependencies are calculated within the framework of the law of the corresponding states for the coefficients of compressibility, shear viscosity, and thermal conductivity of pure substances, and for the coefficients of compressibility, self- and mutual diffusion, and shear viscosity of binary mixtures. The effect of density and temperature on the rates of elementary stages under supercritical conditions has been demonstrated for a reaction’s effective energies of activation, diffusion and share viscosity coefficients, and equilibrium constants of adsorption. Differences between models with effective parameters and the prospects for developing them by allowing for differences in size and contributions from the vibrational motions of components are described.

Representation theorems for regular operators

AbstractWe elaborate, strengthen, and generalize known representation theorems by different authors for regular operators on vector and Banach lattices. Our main result asserts, in particular, that every regular linear operator T acting from a vector lattice E with the principal projection property to a Dedekind complete vector lattice F, which is an ideal of some order continuous Banach lattice G, admits a unique representation , where is the sum of an absolutely order summable family of disjointness preserving operators and is an order narrow (= diffuse) operator. Our main contribution is waiver of the order continuity assumption on T. In proofs, we use new techniques that allow obtaining more general results for a wider class of orthogonally additive operators, which has somewhat different order structure than the linear subspace of linear operators.

Robustness, Scott continuity, and computability

AbstractRobustness is a property of system analyses, namely monotonic maps from the complete lattice of subsets of a (system’s state) space to the two-point lattice. The definition of robustness requires the space to be a metric space. Robust analyses cannot discriminate between a subset of the metric space and its closure; therefore, one can restrict to the complete lattice of closed subsets. When the metric space is compact, the complete lattice of closed subsets ordered by reverse inclusion is $\omega$ -continuous, and robust analyses are exactly the Scott-continuous maps. Thus, one can also ask whether a robust analysis is computable (with respect to a countable base). The main result of this paper establishes a relation between robustness and Scott continuity when the metric space is not compact. The key idea is to replace the metric space with a compact Hausdorff space, and relate robustness and Scott continuity by an adjunction between the complete lattice of closed subsets of the metric space and the $\omega$ -continuous lattice of closed subsets of the compact Hausdorff space. We demonstrate the applicability of this result with several examples involving Banach spaces.

Mapping nanocrystalline disorder within an amorphous metal–organic framework

Intentionally disordered metal–organic frameworks (MOFs) display rich functional behaviour. However, the characterisation of their atomic structures remains incredibly challenging. X-ray pair distribution function techniques have been pivotal in determining their average local structure but are largely insensitive to spatial variations in the structure. Fe-BTC (BTC = 1,3,5-benzenetricarboxylate) is a nanocomposite MOF, known for its catalytic properties, comprising crystalline nanoparticles and an amorphous matrix. Here, we use scanning electron diffraction to first map the crystalline and amorphous components to evaluate domain size and then to carry out electron pair distribution function analysis to probe the spatially separated atomic structure of the amorphous matrix. Further Bragg scattering analysis reveals systematic orientational disorder within Fe-BTC’s nanocrystallites, showing over 10° of continuous lattice rotation across single particles. Finally, we identify candidate unit cells for the crystalline component. These independent structural analyses quantify disorder in Fe-BTC at the critical length scale for engineering composite MOF materials.

Reusability and energy absorption behavior of 4D printed continuous fiber-reinforced auxetic composite structures

This work proposed a strategy for fabricating intelligent continuous fiber-reinforced lattice structures (CFRLSs) for reusable energy absorption applications based on the cold-programming-induced shape memory effect. By integrating the smart material with continuous fiber, the CFRLSs can not only dissipate a considerable amount of energy but also recover their original shape after stimulation. Herein, two auxetic CFRLSs were developed to demonstrate their reusable energy absorption capacity. Specifically, the shape memory mechanism of the fiber-reinforced composites was first revealed, and the mechanical performance, reusability, and energy absorption capacity of the intelligent CFRLSs were investigated comprehensively. The result shows that CFRLSs present a preferable reusability with a shape recovery ratio above 90% in all test cycles and still exhibit a considerable energy absorption capacity compared to the pure Polylactic acid specimen, even after performing six test cycles. This approach provides a feasible way to design reusable protection devices and implementation in multi-functional applications.

Stabilizing a Li–Mn–O Cathode by Blocking Lattice O Migration through a Nanoscale Phase Complex

Among all intercalation cathodes for Li-ion batteries, Li–Mn–O layered oxides offer the highest initial energy density at the lowest cost, due to the joint contribution from cationic and anionic redox chemistry. However, the poor cycling capability, resulting from the continuous lattice O loss at high potentials (>4.5 V), hinders practical applications. Herein, we employed phase complex engineering to obtain a new Li–Mn–O nanohybrid cathode featuring the uniform and coherent integration of layered nanodomains and spinel nanodomains. The combination of DFT calculations, synchrotron-based transmission X-ray microscopy, in situ differential electrochemical mass spectrometry, in situ synchrotron XRD, and electrochemical tests demonstrated that the O migration path in layered nanodomains was blocked by the neighboring spinel nanodomains with a higher oxygen vacancy migration energy, thus effectively suppressing the irreversible lattice O loss at high potentials and enhancing the cycling stability in both capacity and average voltage. The strategy is experimentally demonstrated to be effective and it leads to a new path for developing stable high-energy-density cathode materials.

Core compactness of ordered topological spaces

<abstract><p>In this paper, we investigate the property of core compactness of ordered topological spaces. Particularly, we give a series of characterizations of the core compactness for directed spaces. Several results obtained in this paper are closely related to a long-standing open problem in Open problems in Topology (J. van Mill, G. M. Reed Eds., North-Holland, 1990): Which distributive continuous lattice's spectrum is exactly a sober locally compact Scott space?</p></abstract>

A novel Fe–Cr–Ni–Co–Mo maraging stainless steel with enhanced strength and cryogenic toughness: Role of austenite with core-shell structures

Metastable austenite plays an important role in improving the cryogenic impact toughness of maraging steels by strain-induced martensitic transformations. However, a significant volume fraction of austenite decreases the yield strength of the material. In this study, to overcome the strength-toughness issue in maraging steels, austenite with a compositional core-shell structure and specific volume fraction are designed in Fe–Cr–Ni–Co–Mo maraging stainless steel. The core-shell compositional structure comprises retained austenite with bulk content in the core region and high Ni content reverted austenite layers in the shell region. During tensile testing, a step transformation of austenite with a continuous lattice is observed; herein, the shell regions are preserved. In contrast, the core regions transform to martensite. Close to the impact fracture, the thin austenite shell layers are retained from the martensitic transformation, which further contribute to the impact toughness. Under the combined influence of austenite and nanoprecipitates (Laves phase), the investigated alloy reaches a yield strength >1200 MPa at room temperature with good cryogenic impact toughness (77 K, >90 J), thereby outperforming conventional maraging steels and several high-entropy alloys. The current study demonstrates that the chemical heterogeneity within metastable austenite may create unique mechanical properties in structural materials.

Effect of various morphology of in situ generated NbC particles on the wear resistance of Fe-based cladding

To improve the wear resistance of Fe-based cladding, NbC particles with different morphology are generated in situ by adding Nb, Cr3C2 and C with different content. The composition of samples and the morphology of NbC particles generated in situ are revealed by XRD, SEM and EDS. The wear resistance is studied by a reciprocating friction and wear testing machine. The wear mode and the wear mechanism of each sample are investigated. The results show that although NbC particles are generated in situ in samples with different Nb, Cr3C2 and C content, the morphology of NbC particles is varied. The wear resistance of samples containing cross-shaped NbC particles is more outstanding than that of samples containing only rectangular NbC particles. In addition, changing Nb, Cr3C2 and C content does not result in a change in wear mode, but leads to the formation of continuous lattice structure of Cr0.19Fe0.7Ni0.11 and Cr23C6 compounds at grain boundaries and a change in the wear resistance. When the additions of Nb, Cr3C2 and C are 11.2 wt%, 8.6 wt% and 0.2 wt% respectively, the coefficient of friction of the sample is the lowest, and the wear resistance is the most outstanding.

High-pressure structural stability and bandgap engineering of layered tin disulfide

Two-dimensional layered metal dichalcogenides have attracted extensive attention because of their diverse physical properties and potential applications in electronics and optoelectronics. As an eco-friendly and earth abundant semiconductor, SnS2 displays limited optoelectronic applications due to its large and indirect bandgap. Pressure is a powerful tool to tune crystal structures and physical properties of materials. Here, we systematically investigate the structural stability and optical properties of 4H-SnS2 under high pressure. The crystal structure of 4H-SnS2 is stable up to 56 GPa without structural transition and layer sliding. Continuous lattice contraction is accompanied by gradual bandgap narrowing, which is reversible after releasing pressure. The continuous and reversible modulation of the crystal structure and bandgap on 4H-SnS2 suggest promising optoelectronic applications in the range of visible light based on two-dimensional layered metal dichalcogenides.

Intrinsic superflat bands in general twisted bilayer systems

Twisted bilayer systems with discrete magic angles, such as twisted bilayer graphene featuring moiré superlattices, provide a versatile platform for exploring novel physical properties. Here, we discover a class of superflat bands in general twisted bilayer systems beyond the low-energy physics of magic-angle twisted counterparts. By considering continuous lattice dislocation, we obtain intrinsic localized states, which are spectrally isolated at lowest and highest energies and spatially centered around the AA stacked region, governed by the macroscopic effective energy potential well. Such localized states exhibit negligible inter-cell coupling and support the formation of superflat bands in a wide and continuous parameter space, which can be mimicked using a twisted bilayer nanophotonic system. Our finding suggests that general twisted bilayer systems can realize continuously tunable superflat bands and the corresponding localized states for various photonic, phononic, and mechanical waves.

Tuning Crystal Plane Orientation in Multijunction and Hexagonal Single Crystalline CsPbBr3 Perovskite Disc Nanocrystals

Two-dimensional-shaped CsPbBr3 platelet nanocrystals are widely studied for their bright high energy emission and self-assembly. These nanostructures are in orthorhombic phase, have a square shape, and have the vertical axis [001] perpendicular to the basal plane. Moreover, these are mostly single-crystalline structures with a continuous lattice and appear like slices of cube nanocrystals. In contrast, herein, multijunction and hexagonal single crystalline 2D discs of CsPbBr3 are reported to have all their vertical axes [100]. These are obtained by using the perovskite derivative of tetragonal Cs3MnBr5 as the parent material and subsequent B-site Pb(II) introduction in the presence of phenacyl bromide at different reaction temperatures. At low temperature, multijunction discs having random orientations of two horizontal axes [010] and [001] from one to another segment are observed. Orientations of planes remained random as both coherent and incoherent twin planes were observed at their boundaries. However, the number of junctions/segments was reduced at higher temperature, and finally hexagonal single crystalline discs remained as the ultimate product. Analysis suggested that the crystal nature of parent Cs3MnBr5 and temperature-dependent variation in the rate of Pb(II) insertions determined the nature of discs having randomly oriented or static planes in the entire nanostructure. Not only in 2D discs but also, 3D nanocrystals having similar segments with different orientations are formed upon Pb(II) exchange with Mn(II) alloyed cubic CsBr. Hexagonal single crystalline and segmented multijunction CsPbBr3 discs remain unique among 2D perovskites nanostructures, and their formation mechanism indeed introduced new fundamentals of the crystallization process of these emerging energy materials.