Long-range Translational Order Research Articles

Schramm-Loewner Evolution in 2D Rigidity Percolation.

Amorphous solids may resist external deformation such as shear or compression, while they do not present any long-range translational order or symmetry at the microscopic scale. Yet, it was recently discovered that, when they become rigid, such materials acquire a high degree of symmetry hidden in the disorder fluctuations: their microstructure becomes statistically conformally invariant. In this Letter, we exploit this finding to characterize the universality class of central-force rigidity percolation (RP), using Schramm-Loewner evolution (SLE) theory. We provide numerical evidence that the interfaces of the mechanically stable structures (rigid clusters), at the rigidification transition, are consistently described by SLE_{κ}, showing that this powerful framework can be applied to a mechanical percolation transition. Using well-known relations between different SLE observables and the universal diffusion constant κ, we obtain the estimation κ∼2.9 for central-force RP. This value is consistent, through relations coming from conformal field theory, with previously measured values for the clusters' fractal dimension D_{f} and correlation length exponent ν, providing new, nontrivial relations between critical exponents for RP. These findings open the way to a fine understanding of the microstructure in other important classes of rigidity and jamming transitions.

Two-Dimensional Crystals far from Equilibrium.

When driven by nonequilibrium fluctuations, particle systems may display phase transitions and physical behavior with no equilibrium counterpart. We study a two-dimensional particle model initially proposed to describe driven non-Brownian suspensions undergoing nonequilibrium absorbing phase transitions. We show that when the transition occurs at large density, the dynamics produces long-range crystalline order. In the ordered phase, long-range translational order is observed because equipartition of energy is lacking, phonons are suppressed, and density fluctuations are hyperuniform. Our study offers an explicit microscopic model where nonequilibrium violations of the Mermin-Wagner theorem stabilize crystalline order in two dimensions.

Disordered hyperuniform solid state materials

Disordered hyperuniform (DHU) states are recently discovered exotic states of condensed matter. DHU systems are similar to liquids or glasses in that they are statistically isotropic and lack conventional long-range translational and orientational order. On the other hand, they completely suppress normalized infinite-wavelength density fluctuations like crystals and, in this sense, possess a hidden long-range correlation. Very recently, there have been several exciting discoveries of disordered hyperuniformity in solid-state materials, including amorphous carbon nanotubes, amorphous 2D silica, amorphous graphene, defected transition metal dichalcogenides, defected pentagonal 2D materials, and medium/high-entropy alloys. It has been found that the DHU states of these materials often possess a significantly lower energy than other disorder models and can lead to unique electronic and thermal transport properties, which results from mechanisms distinct from those identified for their crystalline counterparts. For example, DHU states can enhance electronic transport in 2D amorphous silica; DHU medium/high-entropy alloys realize the Vegard's law and possess enhanced electronic bandgaps and thermal transport at low temperatures. These unique properties open up many promising potential device applications in optoelectronics and thermoelectrics. Here, we provide a focused review on these important new developments of hyperuniformity in solid-state materials, taking an applied and “materials” perspective, which complements the existing reviews on hyperuniformity in physical systems and photonic materials. Future directions and outlook are also provided, with a focus on the design and discovery of DHU quantum materials for quantum information science and engineering.

The spikiness of the density of states in quasicrystals

The spikiness of the density of states in quasicrystals The spikiness of the electronic density of states in quasicrystals is believed to be inherent to QCs and so-called approximants (APs) to QCs. Solids have been traditionally divided into two categories: crystalline and amorphous. The dramatic discovery of an icosahedral Al-Mn alloy by Shechtman et al. (1) in 1984 (Shechtman was awarded the 2011 Nobel Prize in Chemistry) extended this dichotomous division by introducing the notion of quasicrystals (QCs). These compounds possess a new type of long-range translational order, quasiperiodicity, and a non-crystallographic orientational order associated with the classically forbidden fivefold, eightfold, tenfold, and twelvefold symmetry axes (2). Whereas there are more than 20 million/tens of thousands known crystalline/amorphous compounds, QCs have hitherto been found in more than a hundred binary and ternary intermetallic systems (3). One of the central problems in condensed matter physics is determining whether quasiperiodicity leads to physical properties that are significantly different from those of crystalline and amorphous materials.

Internal-stress-induced solid-solid transition involving orientational domains of anisotropic particles

Colloidal particles with anisotropic interaction, such as Janus particles, are important model systems for anisotropic atoms and molecules. Janus particles in a single crystal can rotate collectively and form polycrystalline orientational domains as the temperature increases, while the lattice structure in the translational degree of freedom is preserved. Such an unusual solid-solid transition preserves the long-range translational order but loses the orientational order, and its mechanism is unclear. We find that the transition is induced by internal strains and the orientation-position coupling plays an essential role in the transition. We explain the mechanism using the anisotropic elasticity theory and derive the transition condition and the directions of the domain boundaries by analyzing the strain energy and the stress. The results of the molecular dynamics simulation are consistent with the theoretical analysis. Such a transition mechanism can exist in other anisotropic particle systems.

Metallic glasses and metallic glass nanostructures for functional electrocatalytic applications

This brief review reports the recent advancement of metallic glasses and metallic glass nanostructures for functional electrocatalytic applications. Metallic glasses (MGs) or amorphous metals result from quenching the melts at a high cooling rate (e.g., 106 K/s), bypassing crystallization. Metallic glasses are devoid of long-range translational order, no defects like grain boundaries, and multiple elements included. Due to these unique structural features, MG′s show distinct and valuable mechanical, physical and chemical properties and therefore were widely studied as a structural material for decades. Even though MGs were proposed for catalytic applications earlier, a comprehensive study or attempt to apply these materials successfully in electrocatalytic applications are few since the intrinsic surface area is comparably lesser. A rejuvenated interest among the research community for applying various novel strategies in catalytic applications of MGs is highlighted in the present review. Theoretical approaches using density functional theory (DFT) and high-throughput screening assisted with machine learning paradigm advances the discovery of new MGs, which demonstrated high potential for catalytic applications. We focus on the basic features and recent advances in the MGs for catalytic applications like electrocatalytic water splitting reactions like HER, OER, fuel cell reactions like ORR, alcohol oxidation reactions like MOR, EOR, and degradation of harmful organic dyes from the industrial effluents. The presently advancing strategies for enhancing the performance of these metallic glass electrocatalysts through nanostructuring and high-throughput screening are discussed. The unique atomic-scale structural mechanism of the metallic glasses, which can favor the development of high-performance electrocatalysts even comparable to currently available precious-metal-based catalysts, will be discussed. Finally, we also give future directions on designing novel and superior metallic glass-based advanced catalysts.

Dodecagonal quasicrystals of oil-swollen ionic surfactant micelles

A delicate balance of noncovalent interactions directs the hierarchical self-assembly of molecular amphiphiles into spherical micelles that pack into three-dimensional periodic arrays, which mimic intermetallic crystals. Herein, we report the discovery that adding water to a mixture of an ionic surfactant and n-decane induces aperiodic ordering of oil-swollen spherical micelles into previously unrecognized, aqueous lyotropic dodecagonal quasicrystals (DDQCs), which exhibit local 12-fold rotational symmetry and no long-range translational order. The emergence of these DDQCs at the nexus of dynamically arrested micellar glasses and a periodic Frank-Kasper (FK) σ phase approximant sensitively depends on the mixing order of molecular constituents in the assembly process and on sample thermal history. Addition of n-decane to mixtures of surfactant and water instead leads only to periodic FK A15 and σ approximants with no evidence for aperiodic order, while extended ambient temperature annealing of the DDQC also reveals its transformation into a σ phase. Thus, these lyotropic DDQCs are long-lived metastable morphologies, which nucleate and grow from a stochastic distribution of micelle sizes formed by abrupt segregation of varied amounts of oil into surfactant micelles on hydration. These findings indicate that molecular building block complexity is not a prerequisite for the formation of aperiodic supramolecular order, while also establishing the generic nature of quasicrystalline states across metal alloys and self-assembled micellar materials.

Statistical mechanics of dislocation pileups in two dimensions.

Dislocation pileups directly impact the material properties of crystalline solids through the arrangement and collective motion of interacting dislocations. We study the statistical mechanics of these ordered defect structures embedded in two-dimensional crystals, where the dislocations themselves form one-dimensional lattices. In particular, pileups exemplify a new class of inhomogeneous crystals characterized by spatially varying lattice spacings. By analytically formulating key statistical quantities and comparing our theory to numerical experiments using an intriguing mapping of dislocation positions onto the eigenvalues of recently studied random matrix ensembles, we uncover two types of one-dimensional phase transitions in dislocation pileups: A thermal depinning transition out of long-range translational order from the pinned-defect phase, due to a periodic Peierls potential, to a floating-defect state, and finally the melting out of a quasi-long-range ordered floating-defect solid phase to a defect liquid. We also find the set of transition temperatures at which these transitions can be directly observed through the one-dimensional structure factor, where the delta function Bragg peaks, at the pinned-defect to floating-defect transition, broaden into algebraically diverging Bragg peaks, which then sequentially disappear as one approaches the two-dimensional melting transition of the host crystal. We calculate a set of temperature-dependent critical exponents for the structure factor and radial distribution function, and obtain their exact forms for both uniform and inhomogeneous pileups using random matrix theory.

The effects of vacancies and their mobility on the dynamic heterogeneity in 1,3-dimethylimidazolium hexafluorophosphate organic ionic plastic crystals.

Organic ionic plastic crystals (OIPCs) are the crystals of electrolytes with a long-range translational order. The rotational modes of ions in OIPCs are, however, activated even in solid phases such that the diffusion of dopants such as lithium ions may be facilitated. OIPCs have been, therefore, considered as good candidates for solid electrolytes. Recent experiments and theoretical studies have suggested that both the translational and the rotational diffusion of ions are quite heterogeneous: the diffusion of some ions are quite fast while other ions of the same kind hardly diffuse, either rotationally or translationally. Such dynamic heterogeneity would be a key to the transport mechanism of dopants in solid state electrolytes. In this work, we investigate the effects of defects on the dynamic heterogeneity of OIPCs. We perform atomistic molecular dynamics simulation of 1,3-dimethylimidazolium hexafluorophosphate ([MMIM][PF6]) with a pair of cation and anion vacancies. At low temperature, vacancies undergo hopping motions toward each other and form a charge-neutral cluster. At high temperature, two vacancies act like a loosely bonded molecule and diffuse together via hopping motions. We find that the translational diffusion of ions is correlated strongly with the vacancy diffusion and becomes heterogeneous when the vacancies hop. The rotation of ions also becomes active when the ions are close to vacancies such that the rotational dynamic heterogeneity strengthens.

Emergent solidity of amorphous materials as a consequence of mechanical self-organisation

Amorphous solids have peculiar properties distinct from crystals. One of the most fundamental mysteries is the emergence of solidity in such nonequilibrium, disordered state without the protection by long-range translational order. A jammed system at zero temperature, although marginally stable, has solidity stemming from the space-spanning force network, which gives rise to the long-range stress correlation. Here, we show that such nonlocal correlation already appears at the nonequilibrium glass transition upon cooling. This is surprising since we also find that the system suffers from giant anharmonic fluctuations originated from the fractal-like potential energy landscape. We reveal that it is the percolation of the force-bearing network that allows long-range stress transmission even under such circumstance. Thus, the emergent solidity of amorphous materials is a consequence of nontrivial self-organisation of the disordered mechanical architecture. Our findings point to the significance of understanding amorphous solids and nonequilibrium glass transition from a mechanical perspective.

Low-Frequency Dynamics and Its Correlation of Nanoscale Structures in Amorphous Solids

Unlike the crystalline solids, the atomic arrangements in amorphous solids lack long-range translational and orientational order. Despite intense research activity on their structures, the details of how the atoms are packed in amorphous solids remain mysterious at present. Here, we propose a structure feature like polymers and estimate the nanoscale of short-range order (SRO) and medium-range order (MRO) in this description according to the boson peak in amorphous solids. The result supports the concepts that (a) the low-frequency local vibrations are defined by the characteristic length of nanoscale clusters and (b) a decisive scale correlation of solvent atoms, SRO and MRO is about 1:3:7 in amorphous solids.

Consensus formation in continuous opinion dynamics on quasiperiodic lattices

We studied the Biswas–Chatterjee–Sen (BCS) consensus formation model, also known as the Kinetic Continuous Opinion Dynamics (KCOD) model on quasiperiodic lattices by using Kinetic Monte Carlo simulations and Finite Size Scaling technique. Our results are consistent with a continuous phase transition, controlled by an external noise. We obtained the order parameter [Formula: see text], defined as the averaged opinion, the fourth-order Binder cumulant [Formula: see text] and susceptibility [Formula: see text] as functions of the noise parameter. We estimated the critical noises for Penrose and Ammann–Beenker lattices. We also considered seven-fold and nine-fold quasiperiodic lattices and estimated the respective critical noises as well. Irrespective of rotational and translational long-range order of the lattice, the system falls in the same universality class of the two-dimensional Ising model. Quasiperiodic order is irrelevant and it does not change any critical exponents for BCS model.

Long-wavelength fluctuations and anomalous dynamics in 2-dimensional liquids

In 2-dimensional systems at finite temperature, long-wavelength Mermin-Wagner fluctuations prevent the existence of translational long-range order. Their dynamical signature, which is the divergence of the vibrational amplitude with the system size, also affects disordered solids, and it washes out the transient solid-like response generally exhibited by liquids cooled below their melting temperatures. Through a combined numerical and experimental investigation, here we show that long-wavelength fluctuations are also relevant at high temperature, where the liquid dynamics do not reveal a transient solid-like response. In this regime, these fluctuations induce an unusual but ubiquitous decoupling between long-time diffusion coefficient D and structural relaxation time τ, where [Formula: see text], with [Formula: see text] Long-wavelength fluctuations have a negligible influence on the relaxation dynamics only at extremely high temperatures in molecular liquids or at extremely low densities in colloidal systems.

Gelation of Lyotropic Liquid-Crystal Phases-The Interplay between Liquid Crystalline Order and Physical Gel Formation.

We present a systematical investigation of gelled lyotropic liquid crystals (LLCs). This new class of soft materials combines the anisotropy of LLCs with the mechanical stability of a physical gel. The studied LLC system consists of sodium dodecyl sulfate as a surfactant, n-decanol as a cosurfactant, and water as a solvent. At room temperature, four liquid crystalline phases (lamellar Lα, nematic Nd and Nc, and hexagonal H1) are formed depending on the composition. We were successful in gelling the lyotropic lamellar phase with the low-molecular-weight organogelator 12-hydroxyoctadecanoic acid (12-HOA). The obtained gelled lamellar phase shows optical birefringence, elastic response, and no macroscopic flow. However, we were not able to obtain gels with hexagonal or nematic structure. These findings can be explained twofold. When gelling the hexagonal phase, the long-range hexagonal order was destroyed and an isotropic gel was formed. The reason might be the incompatibility between the gel fiber network and the two-dimensional long-range translational order of the cylindrical micelles in the hexagonal phase. Otherwise, the lyotropic nematic phase was transformed into an anisotropic gel with the lamellar structure during gelation. Evidently, the addition of the gelator 12-HOA to the lyotropic system considerably widens the lamellar regime because the integration of the surface-active 12-HOA gelator molecules into the nematic micelles flattens out the micelle curvature. We further investigated the successfully gelated Lα phase to examine the impacts of the gel network and the remaining monomeric gelator on both the structure and properties of the gelled lamellar phase. Small-angle X-ray scattering results showed an arrested lamellar layer spacing in the gelled state, which indicates a higher translational order for the gelled lamellar phases in comparison with their gelator-free counterparts.

Tunable assembly of truncated nanocubes by evaporation-driven poor-solvent enrichment

Self-assembly of nanocrystals is extensively used to generate superlattices with long-range translational order and atomic crystallographic orientation, i.e. mesocrystals, with emergent mesoscale properties, but the predictability and tunability of the assembly methods are poorly understood. Here, we report how mesocrystals produced by poor-solvent enrichment can be tuned by solvent composition, initial nanocrystal concentration, poor-solvent enrichment rate, and excess surfactant. The crystallographic coherence and mesoscopic order within the mesocrystal were characterized using techniques in real and reciprocal spaces, and superlattice growth was followed in real time by small-angle X-ray scattering. We show that formation of highly ordered superlattices is dominated by the evaporation-driven increase of the solvent polarity and particle concentration, and facilitated by excess surfactant. Poor-solvent enrichment is a versatile nanoparticle assembly method that offers a promising production route with high predictability to modulate and maximize the size and morphology of nanocrystal metamaterials.

Shear deformation determined by short-range configuration of atoms in topologically close-packed crystal

Dislocation behaviors, which determine mechanical properties of materials, are generally believed to be controlled by long-range lattice translational order. For intermetallic compounds, however, their structures are often closely related to atomic environments, with the short-range configurations possibly deviating from the long-range translational order. Thus, how dislocations move in these crystals is obscure. Here, we resolve the shear deformation, dominated by atomic-environment polyhedra, in a representative topologically close-packed phase with (Cr,Ni,Al)2Nb stoichiometry, using aberration-corrected scanning transmission electron microscopy combining with atomic-resolution energy dispersive X-ray spectroscopy. Dislocations there have Burgers vectors deviating from slip planes and surprisingly move by switching between two different slip planes. Long-range diffusion and local composition variation assist the dislocation motion, as demonstrated by high temperature quasi-static and room temperature impact deformations. These discoveries demonstrate the defining role of short-range configuration in the deformation of complex structured intermetallics and shed light on the novel behavior of dislocations.

Molecular Electron Density Distribution and X-Ray Diffraction Patterns of Smectic A Liquid Crystals - A Simulation Study.

X-ray diffraction (XRD) is one of the most important methods to assess the long-range translational order in smectic A (SmA) liquid crystals. Nevertheless, the knowledge about the influence of the molecular electron density distribution (MEDD) on the XRD pattern is rather limited because it is not possible to vary the orientational order, the translational order and the MEDD independently in an experiment. We here present a systematic simulation study in which we examine this effect and show that the MEDD indeed has a major impact on the general appearance of the XRD pattern. More specifically, we find that the smectic layer peaks and the intensity ratios thereof strongly depend on the width of the MEDD. The classic approach by Leadbetter et al. to determine the smectic translational order parameter from XRD intensities works if the MEDD is quite narrow. In all other cases the influence of the MEDD has to be taken into account.

Order versus disorder: In situ high-pressure structural study of highly polymerized three-dimensional C60 fullerite

The structure of highly polymerized three-dimensional (3D) fullerite C60 was studied by energy-dispersive x-ray diffraction up to a pressure of 11 GPa. The results show that this phase combines the features of an amorphous sp2–sp3 covalent network and a crystallographically ordered phase with long-range translational order associated with the modulation of atomic density inherited from the initial C60 molecules. Crystal reflections can be described in the framework of the face-centered cubic structure with an initial atmospheric pressure parameter of 11.718 ± 0.003 Å, although this is probably the effect of averaging the x-ray scattering data. The bulk modulus of highly polymerized 3D C60 (280 ± 9 GPa) was determined from the pressure-induced change in the lattice parameter and agrees with the measured density and crystallographic density along with the first coordination number (N1 ≈ 3.6) determined from the radial distribution function according to theoretical calculations. The value of N1 indicates that approximately 60% of carbon atoms are in sp3-hybridized states, and a high degree of polymerization was achieved due to the formation of an average of three covalent bonds between neighboring molecules. The correlation between density and bulk modulus is discussed for a wide range of carbon phases.

Lithium Storage Property of Graphite/AlCuFe Quasicrystal Composites

Quasicrystals have long-range quasi-periodic translational ordering and non-crystallographic rotational symmetry. Al–Cu–Fe quasicrystals have great potential for lithium storage because of their high Al content and a large number of defects in the structure. In our previous study (J. Alloys Compd. 805 (2019) 942) we showed that Al–Cu–Fe quasicrystals have good initial capacity whereas its cycle stability is poor. In the present study, graphite/AlCuFe is prepared by the mechanical alloying method. The results show that graphite/AlCuFe quasicrystal composites are successfully synthesized by planetary ball milling at 550 rpm for 80 h. The quasicrystal particle size decreases and the amorphous graphite forms onion-like carbon (OLC) when the two phases mix evenly. OLC forms on the surface of the Al–Cu–Fe quasicrystalline powder. Charge and discharge tests show that graphite/AlCuFe quasicrystal composites have high-stability capacity of 480 mAh/g after 20 cycles, which is larger than the sum of capacities of graphite and Al–Cu–Fe quasicrystals.

Isotope Effects Reveal the Template Influence on the Crystal Growth of a Metal–Halide Network

Crystallization requires the organization of matter into structures with long-range translational order. However, because crystal growth exhibits non-Arrhenius kinetics, it is not possible to apply...