Three-dimensional Order Research Articles

Low-dimensional metal-organic frameworks: a pathway to design, explore and tune magnetic structures.

The magnetic structure adopted by a material relies on symmetry, the hierarchy of exchange interactions between magnetic ions and local anisotropy. A direct pathway to control the magnetic interactions is to enforce dimensionality within the material, from zero-dimensional isolated magnetic ions, one-dimensional (1D) spin-chains, two-dimensional (2D) layers to three-dimensional (3D) order. Being able to design a material with a specific dimensionality for the phenomena of interest is non-trivial. While many advances have been made in the area of inorganic magnetic materials, organic compounds offer distinct and potentially more fertile ground for material design. In particular magnetic metal-organic frameworks (mMOFs) combine magnetism with non-magnetic property functionality on the organic linkers within the structural framework, which can further be tuned with mild perturbations of pressure and field to induce phase transitions. Here, it is examined how neutron scattering measurements on mMOFs can be used to directly determine the magnetic structure when the magnetic ions are in a 2D layered environment within the wider 3D crystalline framework. The hydrated formate, in deuterated form, Co(DCOO)2·2D2O, which was one of the first magnetic MOFs to be investigated with neutron diffraction, is reinvestigated as an exemplar case.

Quantum and classical spin dynamics across temperature scales in the S=1/2 Heisenberg antiferromagnet

Using the framework of semiclassical Landau-Lifshitz dynamics (LLD), we conduct a systematic investigation of the temperature-dependent spin dynamics in the S=1/2 Heisenberg square-lattice antiferromagnet (SAFM). By performing inelastic neutron scattering measurements on Zn2VO(PO4)2 (ZVPO) and corresponding finite-temperature spin dynamics simulations based on LLD, we present a comprehensive analysis that bridges quantum and classical spin dynamics over a broad temperature range. First, remarkable agreement between experimental data and LLD simulations is found in the paramagnetic phase of ZVPO, demonstrating the capability of LLD in accurately determining the spin Hamiltonian of S=1/2 systems and capturing the quantum-to-classical crossover of their spin dynamics. Second, by analyzing the discrepancies between the experimental data and the LLD simulations at lower temperatures, we determine the experimental temperature dependence of the quantum effects in the excitation spectrum of the S=1/2 SAFM: the quantum renormalization factor for the magnon energies and the quantum continuum above the one-magnon bands. Notably, the emergence of each quantum effect is found to correlate with the formation of three-dimensional long-range order. This work demonstrates the utility of LLD in gaining experimental insights into the temperature-induced modifications of quantum spin dynamics and their convergence towards classical expectations at higher temperatures. This motivates further applications to more challenging quantum antiferromagnets dominated by stronger quantum fluctuations. Published by the American Physical Society 2024

Evolution mechanism of organic macromolecular structure during lignite pyrolysis

Understanding the mechanisms governing coal pyrolysis reactions, particularly in relation to the coal macromolecular structure, is crucial for improving energy efficiency and facilitating the transition of coal into a clean energy source. This study employs cutting-edge techniques, such as High-Resolution Transmission Electron Microscopy (HRTEM) and Thermogravimetric Analysis coupled with Fourier Transform Infrared Spectroscopy and Mass Spectrometry (TG–FTIR–MS), to analyze lignite and its residual solid samples subjected to pyrolysis across a range of temperatures from 300 °C to 1100 °C. The variational characteristics of the macromolecular structure during coal pyrolysis are examined. Utilizing molecular dynamics simulations, we analyze the evolution mechanism of the macromolecular carbon structure of organic matter during the coal pyrolysis process. The results show that the pyrolysis can be divided into three distinct phases: activation (30–300 °C), pyrolysis (300–650 °C), and condensation (650–1200 °C). During these phases, the coal structure undergoes complex transformations, including folding, twisting, shedding of small molecular side chains, and breaking of macromolecular side chains, ultimately leading to the directional arrangement of structural fragments. The structural units initially undergo decomposition, followed by growth and alignment in a certain direction. The spatial distribution of aromatic structural units evolves from local ordering to complete disordering, culminating in larger-scale, three-dimensional ordering. The order of bond breaking within the macromolecular structure of lignite pyrolysis is: oxygen-containing functional groups (such as C–O and COOH) > aliphatic structure (N–C and C–C) > aromatic structure (CC). By uncovering the reaction intermediates and pathways involved in lignite pyrolysis, this research provides a comprehensive quantitative description of the coal pyrolysis process. These insights offer invaluable theoretical support for the industrial-scale pyrolysis of coal, paving the way for more efficient and sustainable utilization of this crucial energy resource.

Atomic order of rare earth ions in a complex oxide: a path to magnetotaxial anisotropy

Complex oxides offer rich magnetic and electronic behavior intimately tied to the composition and arrangement of cations within the structure. Rare earth iron garnet films exhibit an anisotropy along the growth direction which has long been theorized to originate from the ordering of different cations on the same crystallographic site. Here, we directly demonstrate the three-dimensional ordering of rare earth ions in pulsed laser deposited (EuxTm1-x)3Fe5O12 garnet thin films using both atomically-resolved elemental mapping to visualize cation ordering and X-ray diffraction to detect the resulting order superlattice reflection. We quantify the resulting ordering-induced ‘magnetotaxial’ anisotropy as a function of Eu:Tm ratio using transport measurements, showing an overwhelmingly dominant contribution from magnetotaxial anisotropy that reaches 30 kJ m−3 for garnets with x = 0.5. Control of cation ordering on inequivalent sites provides a strategy to control matter on the atomic level and to engineer the magnetic properties of complex oxides.

Non-thermal phonon dynamics and a quenched exciton condensate probed by surface-sensitive electron diffraction

Interactions among and between electrons and phonons steer the energy flow in photo-excited materials and govern the emergence of correlated phases. The strength of electron–phonon interactions, decay channels of strongly coupled modes and the evolution of three-dimensional order are revealed by electron or X-ray pulses tracking non-equilibrium structural dynamics. Despite such capabilities, the growing relevance of inherently anisotropic two-dimensional materials and functional heterostructures still calls for techniques with monolayer sensitivity and, specifically, access to out-of-plane phonon polarizations. Here, we resolve non-equilibrium phonon dynamics and quantify the excitonic contribution to the structural order parameter in 1T-TiSe2. To this end, we introduce ultrafast low-energy electron diffuse scattering and trace strongly momentum- and fluence-dependent phonon populations. Mediated by phonon–phonon scattering, a few-picosecond build-up near the zone boundary precedes a far slower generation of zone-centre acoustic modes. These weakly coupled phonons are shown to substantially delay overall equilibration in layered materials. Moreover, we record the surface structural response to a quench of the material’s widely investigated exciton condensate, identifying an approximate 30:70 ratio of excitonic versus Peierls contributions to the total lattice distortion in the charge density wave phase. The surface-sensitive approach complements the ultrafast structural toolbox and may further elucidate the impact of phonon scattering in numerous other phenomena within two-dimensional materials, such as the formation of interlayer excitons in twisted bilayers.

Van der Waals epitaxial AlGaN/GaN growth on hexagonal BN via two-dimensional N-induced dislocation slip

We demonstrate the epitaxial growth of nitride heterojunction structures on two-dimensional materials. The growth behavior of Al atoms on hexagonal boron nitride (h-BN) involves preferential adsorption and diffusion along the N-top position, considerably improving AlN formation in the early stage of nucleation. Preferential N adsorption enables h-BN to provide a natural N surface for the substrate. Moreover, the natural N surface provided by h-BN can induce three-dimensional island-like order merging of the upper AlN layer, promoting dislocation slip annihilation. The dislocations annihilation depth of GaN films was shortened to 870 nm, resulting in an order of magnitude decrease in the density of screw dislocations to 5.50 × 107 cm−2 and considerable improvement in the performance of HEMT devices on SiC. Therefore, h-BN films can be used as two-dimensional insertion layers to obtain high-quality van der Waals epitaxial nitride films in GaN-based HEMT devices.

Chiral ground states of ferroelectric liquid crystals.

Ferroelectric nematic liquid crystals are formed by achiral molecules with large dipole moments. Their three-dimensional orientational order is described as unidirectionally polar. We demonstrate that the ground state of a flat slab of a ferroelectric nematic unconstrained by externally imposed alignment directions is chiral, with left- and right-handed twists of polarization. Although the helicoidal deformations and defect walls that separate domains of opposite handedness increase the elastic energy, the twists reduce the electrostatic energy and become weaker when the material is doped with ions. This work shows that the polar orientational order of molecules could trigger chirality in soft matter with no chemically induced chiral centers.

Stability Properties of Multi-Order Fractional Differential Systems in 3D

This paper is devoted to studying three-dimensional non-commensurate fractional order differential equation systems with Caputo derivatives. Necessary and sufficient conditions for the asymptotic stability of such systems are obtained.

Photonic Spin Hopfions and Monopole Loops.

Spin textures with various topological orders are of great theoretical and practical interest. Hopfion, a spin texture characterized by a three-dimensional topological order was recently realized in electronic spin systems. Here, we show that monochromatic light can be structured such that its photonic spin exhibits a hopfion texture in the three-dimensional real space. We also provide ways to construct spin textures of arbitrary Hopf charges. When extending the system to four dimensions by introducing a parameter dimension, a new type of topological defect in the form of a monopole loop in photonic spin is encountered. Each point on the loop is a topological spin defect in three dimensions, and the loop itself carries quantized Hopf charges. Such photonic spin texture and defect may find application in control and sensing of nanoparticles, and optical generation of topological texture in motions of particles or fluids.

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.

Discovering a Wigner-like crystal and soft x-ray correlated plasmons and their couplings in a transition metal dichalcogenide

Low-dimensional systems host many exotic physical properties. Using extended resonant soft x-ray scattering supported with theoretical calculations, we observe concomitantly a Wigner-like crystal in a stripe-like QHKL = (001) superlattice with surprisingly long coherence lengths and new soft x-ray correlated plasmons in WS2. A new electronic transition is found at 125 K upon cooling, which is a transition from two-dimensional ordering to three-dimensional ordering, a result of p–d hybridization anisotropy and electronic correlations. Our result shows the importance of the interplay of long-range electron–electron correlation and short-range electronic screening in determining electronics and optical properties of transition metal dichalcogenides.

Quantitative three-dimensional local order analysis of nanomaterials through electron diffraction

Structure-property relationships in ordered materials have long been a core principle in materials design. However, the introduction of disorder into materials provides structural flexibility and thus access to material properties that are not attainable in conventional, ordered materials. To understand disorder-property relationships, the disorder – i.e., the local ordering principles – must be quantified. Local order can be probed experimentally by diffuse scattering. The analysis is notoriously difficult, especially if only powder samples are available. Here, we combine the advantages of three-dimensional electron diffraction – a method that allows single crystal diffraction measurements on sub-micron sized crystals – and three-dimensional difference pair distribution function analysis (3D-ΔPDF) to address this problem. In this work, we compare the 3D-ΔPDF from electron diffraction data with those obtained from neutron and x-ray experiments of yttria-stabilized zirconia (Zr0.82Y0.18O1.91) and demonstrate the reliability of the proposed approach.

Finite-time sliding mode control methods for a class of non-integer-order systems with input saturations and its application

Control and synchronization of chaotic dynamical systems is a key issue in engineering that has numerous applications in the applied sciences. In this research, single input finite-time sliding mode (FTSMC) control algorithms are developed to synchronize and stabilize a class of three-dimensional non-integer order systems where input saturation is present. Using the non-integer version of the Lyapunov stability theory (LST) and the dynamic-free idea, techniques are devised to suppress the improper behavior of the aforementioned fractional-order (FO) chaotic systems without unpleasant chattering phenomena. The proposed FTSMC approach can be utilized to stabilize and synchronize systems that include model uncertainty, external disturbances, and input saturation. The developed single input techniques have the benefits of being model-free, robust to uncertainty, user-friendly, and establishing equilibrium in a finite amount of time. In addition, the efficacy and applicability of the FTSMC approaches are shown by synchronizing two different industrial FO chaotic systems and chaos suppressing of the PMSM chaotic system utilizing these methods.

Inverse projection of axisymmetric orientation distributions

We show that the projection of an axisymmetric three-dimensional orientation distribution to two dimensions can be cast into an Abel transform. Based on this correspondence, we derive an exact integral inverse, which allows for the quantification of three-dimensional uniaxial alignment of rod-like units from two-dimensional sliced images, thus providing an alternative to X-ray or tomographic analysis. A matrix representation of the projection and its inverse is derived, providing a direct relationship between two- and three-dimensional order parameters for both polar and non-polar systems.

MOLECULAR SIMULATION OF WATER STRUCTURE IN NARROW SLITLIKE PORES

The structure of water in narrow slitlike pores has been studied by the methods of molecular dynamics simulation. Pores with interwall distances of 6.2–15.5 Å have been considered. Water structures resulting from spontaneous crystallization upon cooling to T = 300 K have been clarified on the basis of twoand three-dimensional order parameters. It has been shown that the observed structures can be described as sections of FCC or HCP crystals.

A meshfree method for the solution of 2D and 3D second order elliptic boundary value problems in heterogeneous media

We propose a simple meshfree method for two-dimensional and three-dimensional second order elliptic boundary value problems in heterogeneous media based on equilibrated basis functions. The domain is discretized by a regular nodal grid, over which the degrees of freedom are defined. The boundary is also discretized by simply introducing some boundary points over it, independent from the domain nodes, granting the method the ability of application for arbitrarily shaped domains without the drawback of irregularity in the nodal grid. In heterogeneous media, the governing Partial Differential Equation (PDE) has non-constant coefficients for the partial derivatives, preventing Trefftz-based techniques to be applicable. The proposed method satisfies the PDE independent from the boundary conditions, as in Trefftz approaches. Meanwhile, by applying the weak form of the PDE instead of the strong form through weighted residual integration, the inconvenience of variable coefficients shall be resolved, since the bases will not need to analytically satisfy the PDE. The weighting in the weak form integrals is such that the boundary integrals vanish. The boundary conditions are thus collocated over the defined boundary points. Domain integrals break into algebraic combination of one-dimensional pre-evaluated integrals, thus omitting the numerical integration from the solution process. Each node corresponds to a local sub-domain called cloud. The overlap between adjacent clouds ensures integrity of the solution and its derivatives throughout the domain, an advantage with respect to C0 formulations.

Revealing the Structural Organization of Gamma-irradiated Starch Granules Using Polarization-resolved Second Harmonic Generation Microscopy.

Starch is a semi-crystalline macromolecule with the presence of amorphous and crystalline components. The amorphous amylose and crystalline amylopectin regions in starch granules are susceptible to certain physical modifications, such as gamma irradiation. Polarization-resolved second harmonic generation (P-SHG) microscopy in conjunction with SHG-circular dichroism (CD) was used to assess the three-dimensional molecular order and inherent chirality of starch granules and their reaction to different dosages of gamma irradiation. For the first time, the relationship between starch achirality (χ21/χ16 and χ22/χ16) and chirality (χ14/χ16) determining susceptibility tensor ratios has been elucidated. The results showed that changes in the structure and orientation of long-chain amylopectin were supported by the decrease in the SHG anisotropy factor and the χ22/χ16 ratio. Furthermore, SHG-CD illustrated the molecular tilt angle by revealing the arrangement of amylopectin molecules pointing either upward or downward owing to molecular polarity.

Ameliorating the carrier dynamics behavior via plasmonic Ag-modified CuBi2O4 inverse opal for the efficient photoelectrocatalytic reduction of CO2 to CO

Low light absorption efficiency and short carrier diffusion length mainly restrict the use of CuBi2O4 as a photocathode for an efficient photoelectrocatalytic CO2 reduction reaction (PEC-CO2 RR). These inadequacies are alleviated by fabricating CuBi2O4 inverse opal photocathode modify with plasmonic Ag nanoparticles (CuBi2O4 IOs-Ag) by using a sacrificing template method. The CuBi2O4 IOs-Ag photocathode exhibits superior PEC-CO2 RR-to-CO performance with a Faraday efficiency (FE) of 92% at 0.2 V versus reversible hydrogen electrode, and this value is roughly 1.6 times that of the pristine CuBi2O4 thin film. Detail characterization and experiments reveal that the exceptional three-dimensional (3D) order structure simultaneously accelerates the mass transfer rates and enhances the light-harvesting efficiency. In addition, the introduction of Ag nanoparticles remarkably improves the surface charge distribution by forming an ohmic contact with CuBi2O4. Consequently, carrier recombination is efficiently inhibited, and the carrier dynamics behavior is improved. This work provides important insights into the design of high-performance photoelectrocatalytic systems for CO2 reduction by engineering the microstructure of catalysts with localized surface plasmon resonance effect.

Effect of magnetic order on longitudinal Tomonaga-Luttinger liquid spin dynamics in weakly coupled spin- 12 chains

The quantum many-body interactions in one-dimensional spin-$\frac{1}{2}$ systems are subject to Tomonaga-Luttinger liquid (TLL) physics, which predict an array of multiparticle excitations that form continua in momentum-energy space. Here we use inelastic neutron spectroscopy to study the TLL spin dynamics in ${\mathrm{SrCo}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}$, a compound which contains weakly coupled spin-$\frac{1}{2}$ chains of Co atoms, at 0.05 K and in a longitudinal magnetic field up to 9.0 T. The measurements were performed above 3.9 T, where the ground-state N\'eel antiferromagnetic (AFM) order is completely suppressed and the multiparticle excitations are exclusively of the TLL type. In this region and below 7.0 T, the longitudinal TLL mode---psinon/antipsinon (P/AP)---is unexpectedly well described by a damped harmonic oscillator (DHO) while approaching the zone center defining the static spin-spin correlations. A non-DHO-type, continuumlike signal is seen at higher fields, but deviations from the ideal one-dimensional TLL still remain. This change in the P/AP mode coincides with the phase transition between the longitudinal spin density wave (LSDW) and transverse AFM order. Inside the LSDW state, the DHO-type P/AP spectral weight increases and the linewidth broadens as the magnetic order parameter decreases. These results reveal the impact of three-dimensional magnetic order on the TLL spin dynamics; they call for beyond-mean-field treatment for the interchain exchange interactions.

Quasi-one-dimensional Ising-like antiferromagnetism in the rare-earth perovskite oxide TbScO3

The rare-earth perovskite TbScO$_3$ has been widely used as a substrate for the growth of epitaxial ferroelectric and multiferroic thin films, while its detailed low-temperature magnetic properties were rarely reported. In this paper, we performed detailed magnetization, specific heat and single crystal neutron scattering measurements, along with the crystalline electric field calculations to study the low-temperature magnetic properties of TbScO$_3$. All our results suggest the magnetic Tb$^{3+}$ has an Ising-like pseudo-doublet ground state at low temperatures. Due to the constrain of local point symmetry, these Tb$^{3+}$ Ising moments are confined in the $ab$ plane with a tilt angle of $\varphi = \pm48^{\mathrm{o}}$ to the $a$ axis. In zero field, the system undergoes an antiferromagnetic phase transition at $T_{\mathrm{N}}=2.53$ K, and forms a $G_xA_y$ noncollinear magnetic structure below $T_{\mathrm{N}}$. We find the dipole-dipole interactions play an important role to determine the magnetic ground state, which are also responsible for the quasi-one-dimensional magnetism in TbScO$_3$. The significant anisotropic diffuse scatterings further confirm the quasi-one-dimensional magnetism along the $c$ axis. The magnetic phase diagram with the field along the easy $b$ axis is well established. In addition to the $G_xA_y$ antiferromagnetic state, there is an exotic field-induced phase emerged near the critical field $B_{\mathrm{c}}\simeq0.7$ T, where three-dimensional magnetic order is suppressed but strong one-dimensional correlations may still exist.