Five-fold symmetry in liquids

Local Structural Features Elucidate Crystallization of Complex Structures

Complex crystal structures are composed of multiple local environments, and how this type of order emerges spontaneously during crystal growth has yet to be fully understood. We study crystal growth across various structures and along different crystallization pathways, using self-assembly simulations of identical particles that interact via multiwell isotropic pair potentials. We apply an unsupervised machine learning method to features from bond-orientational order metrics to identify different local motifs present during a given structure's crystallization process. In this manner, we distinguish different crystallographic sites in highly complex structures. Tailoring this order parameter to structures of varying complexity and coordination number, we study the emergence of local order along a multistep crystal growth pathway─from a low-density fluid to a high-density, supercooled amorphous liquid droplet and to a bulk crystal. We find a consistent under-coordination of the liquid relative to the average coordination number in the bulk crystal. We use our order parameter to analyze the geometrically frustrated growth of a Frank-Kasper phase and discover how structural defects compete with the formation of crystallographic sites that are more high-coordinated than the liquid environments. The method presented here for classifying order on a particle-by-particle level has broad applicability to future studies of structural self-assembly and crystal growth, and they can aid in the design of building blocks and for targeting pathways of formation of soft-matter structures.

Measuring many-body distribution functions in fluids using test-particle insertion

We derive a hierarchy of equations, which allow a general n-body distribution function to be measured by test-particle insertion of between 1 and n particles. We apply it to measure the pair and three-body distribution functions in a simple fluid using snapshots from Monte Carlo simulations in the grand canonical ensemble. The resulting distribution functions obtained from insertion methods are compared with the conventional distance-histogram method: the insertion approach is shown to overcome the drawbacks of the histogram method, offering enhanced structural resolution and a more straightforward normalization. At high particle densities, the insertion method starts breaking down, which can be delayed by utilizing the underlying hierarchical structure of the insertion method. Our method will be especially useful in characterizing the structure of inhomogeneous fluids and investigating closure approximations in liquid state theory.

A fractal structural feature related to dynamic crossover in metallic glass-forming liquids

The dynamic crossover in supercooled liquids initially predicted by model coupling theory has been widely accepted, but its underlying structural origin is still an open issue for glass-forming liquids. By molecular dynamics simulations of binary CuZr liquids, the present work verifies that high pressure could enhance this crossover, facilitating the studies on the structural features at the crossover temperature T_c. We discover that the topological connectivity of icosahedral clusters is responsible for this dynamic crossover, rather than all clusters. T_c is the temperature at which the connectivity degree between these clusters reaches a maximum and the dynamic heterogeneity begins to keep stable. Below T_c, the fractal topological structures appear in the medium-range order scale. The icosahedral clusters with a certain connectivity pattern can be regarded as a fractal structural unit. By employing the established fractal analysis method, the fractal dimension D of the icosahedral network is calculated. Our results indicate that the D value increases monotonically with increasing pressure and the fractal behavior of the icosahedral network is an inherent feature of metallic glasses. We also find similar fractal behavior in clusters with high local five-fold symmetry. Our findings shed light on the origin of a dynamic crossover in the deep supercooled region of metallic glasses and also demonstrate the important role of icosahedral clusters in uncovering the fractal behavior of metallic glass.

High-Resolution Electron Tomography of Ultrathin Boerdijk-Coxeter-Bernal Nanowire Enabled by Superthin Metal Surface Coating

The rapid advancement of transmission electron microscopy has resulted in revolutions in a variety of fields, including physics, chemistry, and materials science. With single-atom resolution, 3D information of each atom in nanoparticles is revealed, while 4D electron tomography is shown to capture the atomic structural kinetics in metal nanoparticles after phase transformation. Quantitative measurements of physical and chemical properties such as chemical coordination, defects, dislocation, and local strain have been made. However, due to the incompatibility of high dose rate with other ultrathin morphologies, such as nanowires, atomic electron tomography has been primarily limited to quasi-spherical nanoparticles. Herein, the 3D atomic structure of a complex core-shell nanowire composed of an ultrathin Boerdijk-Coxeter-Bernal (BCB) core nanowire and a noble metal thin layer shell deposited on the BCB nanowire surface is discovered. Furthermore, it is demonstrated that a new superthin noble metal layer deposition on an ultrathin BCB nanowire could mitigate electron beam damage using an in situ transmission electron microscope and atomic resolution electron tomography. The colloidal coating method developed for electron tomography can be broadly applied to protect the ultrathin nanomaterials from electron beam damage, benefiting both the advanced material characterizations and enabling fundamental in situ mechanistic studies.

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

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

Self-assembly nuclei with a preferred orientation at the extended hydrophobic surface toward textured growth of ZnO nanorods in aqueous chemical bath deposition

Textured growth of ZnO nanorods with no restriction of the substrate material is beneficial to their applications. The approaches to grow ZnO nanorods with texture are based on preparing suitable surface structure on the growth substrate, e.g. using a crystalline substrate with a specific surface structures or pre-depositing seed layers by high-temperature annealing of precursors. In the aqueous nutrient solution of the chemical bath deposition (CBD) process for ZnO growth, the concentration of Zn²⁺ ions at the extended hydrophobic surface is sufficiently high for forming self-assembly nuclei with a preferred orientation, resulting in the subsequent textured growth of ZnO nanorods. In this research, the hydrophobic surface is prepared by modifying Si surface with a self-assembly octadecyltrimethoxysilane (OTMS) monolayer. The formation mechanism of the nuclei on this hydrophobic surface for the textured growth of ZnO nanorods is investigated. It is shown that the nuclei form at the beginning of the CBD process and later transform into the Wurtzite structure to seed ZnO growth. An alternative approach to prepare seed layers is therefore involved in the aqueous CBD process, which is applicable to a range of hydrophobic substrates for textured growth of ZnO nanorods.

Multi-Step Crystallization of Self-Organized Spiral Eutectics

A method for the solidification of metallic alloys involving spiral self-organization is presented as a new strategy for producing large-area chiral patterns with emergent structural and optical properties, with attention to the underlying mechanism and dynamics. This study reports the discovery of a new growth mode for metastable, two-phase spiral patterns from a liquid metal. Crystallization proceeds via a non-classical, two-step pathway consisting of the initial formation of a polytetrahedral seed crystal, followed by ordering of two solid phases that nucleate heterogeneously on the seed and grow in a strongly coupled fashion. Crystallographic defects within the seed provide a template for spiral self-organization. These observations demonstrate the ubiquity of defect-mediated growth in multi-phase materials and establish a pathway toward bottom-up synthesis of chiral materials with an inter-phase spacing comparable to the wavelength of infrared light. Given that liquids often possess polytetrahedral short-range order, our results are applicable to many systems undergoing multi-step crystallization.

Molecular dynamics investigation of the local structure in iron melts and its role in crystal nucleation during rapid solidification

Nucleation process of a bcc crystal after the formation of an MRO cluster.

Sensitive Five-Fold Local Symmetry to Kinetic Energy of Depositing Atoms in Cu-Zr Thin Film Growth

We have investigated the glass formation ability of Cu-Zr alloy by molecular dynamics simulation of the deposition process. The atomistic structures of Zr_xCu_100−x metallic glass films have been systematically examined under the growth conditions of hypereutectic-eutectic, near-eutectic, and hypoeutectic regions by the radial distribution function and simulated X-ray diffraction. The structure analysis using Voronoi polyhedron index method demonstrates the variations of short-range order and five-fold local symmetry in Zr_xCu_100−x metallic glass films with respect to the growth conditions. We manifest that the five-fold local symmetry is sensitive to the kinetic energy of the depositing atoms. There is positive correlation between the degree of five-fold local symmetry and glass forming ability. Our results suggest that sputtering conditions greatly affect the local atomic structures and consequential properties. The glass forming ability could be scaled by the degree of five-fold local symmetry. Our study might be useful in optimizing sputtering conditions in real experiments, as well as promising implications in material design of advanced glassy materials.

A neutron tomography study: probing the spontaneous crystallization of randomly packed granular assemblies

We study the spontaneous crystallization of an assembly of highly monodisperse steel spheres under shaking, as it evolves from localized icosahedral ordering towards a packing reaching crystalline ordering. Towards this end, real space neutron tomography measurements on the granular assembly are carried out, as it is systematically subjected to a variation of frequency and amplitude. As expected, we see a presence of localized icosahedral ordering in the disordered initial state (packing fraction ≈ 0.62). As the frequency is increased for both the shaking amplitudes (0.2 and 0.6 mm) studied here, there is a rise in packing fraction, accompanied by an evolution to crystallinity. The extent of crystallinity is found to depend on both the amplitude and frequency of shaking. We find that the icosahedral ordering remains localized and its extent does not grow significantly, while the crystalline ordering grows rapidly as an ordering transition point is approached. In the ordered state, crystalline clusters of both face centered cubic (FCC) and hexagonal close packed (HCP) types are identified, the latter of which grows from stacking faults. Our study shows that an earlier domination of FCC gives way to HCP ordering at higher shaking frequencies, suggesting that despite their coexistence, there is a subtle dynamical competition at play. This competition depends on both shaking amplitude and frequency, as our results as well as those of earlier theoretical simulations demonstrate. It is likely that this involves the very small free energy difference between the two structures.

Local rotational symmetry in the packing of uniform spheres

Local rotational symmetry (LRS) of a particulate system is important for understanding its structure and phase transition. However, how to properly characterize LRS for this system is still a challenge as the system normally includes both ordered and disordered local structures. Herein, based on the so-called common neighbour subcluster (CNS), we proposed a method to characterize the LRS of uniform spheres packings with the packing fraction ρ ranging within 0.20 and 0.74. It was found that different fold LRSs coexist in most packings, and their maximum degree increases at ρ < 0.64, except for the 2-fold LRS held by 6-sphere CNS that continuously increases to form the fcc crystal at ρ = 0.74. The overall LRS involving all the CNSs monotonically increases with two critical changes at ρ = (0.35-0.40) and 0.64; the evolution of individual LRSs held by specific CNS groups critically changes at ρ ≈ (0.35-0.40), 0.50, 0.55-0.60, and 0.64. The physics corresponding to these critical changes has also been discussed. The findings will significantly enrich the understanding of the structural symmetry of materials including atoms and particles.

Structural evolution and strength change of a metallic glass at different temperatures

The structural evolution of a Zr_64.13Cu_15.75Ni_10.12Al₁₀ metallic glass is investigated in-situ by high-energy synchrotron X-ray radiation upon heating up to crystallization. The structural rearrangements on the atomic scale during the heating process are analysed as a function of temperature, focusing on shift of the peaks of the structure factor in reciprocal space and the pair distribution function and radial distribution function in real space which are correlated with atomic rearrangements and progressing nanocrystallization. Thermal expansion and contraction of the coordination shells is measured and correlated with the bulk coefficient of thermal expansion. The characteristics of the microstructure and the yield strength of the metallic glass at high temperature are discussed aiming to elucidate the correlation between the atomic arrangement and the mechanical properties.

Computer simulations of glasses: the potential energy landscape

We review the current state of research on glasses, discussing the theoretical background and computational models employed to describe them. This article focuses on the use of the potential energy landscape (PEL) paradigm to account for the phenomenology of glassy systems, and the way in which it can be applied in simulations and the interpretation of their results. This article provides a broad overview of the rich phenomenology of glasses, followed by a summary of the theoretical frameworks developed to describe this phenomonology. We discuss the background of the PEL in detail, the onerous task of how to generate computer models of glasses, various methods of analysing numerical simulations, and the literature on the most commonly used model systems. Finally, we tackle the problem of how to distinguish a good glass former from a good crystal former from an analysis of the PEL. In summarising the state of the potential energy landscape picture, we develop the foundations for new theoretical methods that allow the ab initio prediction of the glass-forming ability of new materials by analysis of the PEL.

Evidence for cooling-rate-dependent icosahedral short-range order in a Cu–Zr–Al metallic glass

Samples of Cu47.5Zr47.5Al5metallic glass were prepared at different cooling rate,R. The dependence of the X-ray diffraction patterns onRwas analysed by comparing them with corresponding patterns of computer-simulated models generated at different cooling rates as well. The observed changes in the experimental diffraction patterns are reproduced by the simulations, showing an increasing fraction of icosahedral clusters with decreasing cooling rate. The difference of the fractions of icosahedrally coordinated atoms in mould-cast and rapidly quenched Cu47.5Zr47.5Al5averages to 3 (1)%. Different frozen-in thermal displacements and different density are ruled out as a possible origin for the experimental observations.

Structural signatures of dynamic heterogeneities in monolayers of colloidal ellipsoids

When a liquid is supercooled towards the glass transition, its dynamics drastically slows down, whereas its static structure remains relatively unchanged. Finding a structural signature of the dynamic slowing down is a major challenge, yet it is often too subtle to be uncovered. Here we discover the structural signatures for both translational and rotational dynamics in monolayers of colloidal ellipsoids by video microscopy experiments and computer simulations. The correlation lengths of the dynamic slowest-moving clusters, the static glassy clusters, the static local structural entropy and the dynamic heterogeneity follow the same power-law divergence, suggesting that the kinetic slowing down is caused by a decrease in the structural entropy and an increase in the size of the glassy cluster. Ellipsoids with different aspect ratios exhibit single- or double-step glass transitions with distinct dynamic heterogeneities. These findings demonstrate that the particle shape anisotropy has important effects on the structure and dynamics of the glass.

To establish a structural signature of slow dynamics as a system approaches the glass transition is challenging. Here, the authors identify, by performing video microscopy experiments and simulations, two structural signatures for the rotational and translational dynamics in monolayers of colloidal ellipsoids.

Multistage structural evolution in simple monatomic supercritical fluids: superstable tetrahedral local order

The local order units of dense simple liquid are typically three-dimensional (close packed) clusters: hcp, fcc, and icosahedrons. We show that the fluid demonstrates the superstable tetrahedral local order up to temperatures several orders of magnitude higher than the melting temperature and down to critical density. While the solid-like local order (hcp, fcc) disappears in the fluid at much lower temperatures and far above critical density. We conclude that the supercritical fluid shows the temperature (density)-driven two-stage "melting" of the three-dimensional local order. We also find that the structure relaxation times in the supercritical fluid are much larger than ones estimated for weakly interactive gas even far above the melting line.

On Structure and Properties of Amorphous Materials

Mechanical, optical, magnetic and electronic properties of amorphous materials hold great promise towards current and emergent technologies. We distinguish at least four categories of amorphous (glassy) materials: (i) metallic; (ii) thin films; (iii) organic and inorganic thermoplastics; and (iv) amorphous permanent networks. Some fundamental questions about the atomic arrangements remain unresolved. This paper focuses on the models of atomic arrangements in amorphous materials. The earliest ideas of Bernal on the structure of liquids were followed by experiments and computer models for the packing of spheres. Modern approach is to carry out computer simulations with prediction that can be tested by experiments. A geometrical concept of an ideal amorphous solid is presented as a novel contribution to the understanding of atomic arrangements in amorphous solids.

Structural and entropic insights into the nature of the random-close-packing limit

Disordered packings of equal sized spheres cannot be generated above the limiting density (fraction of volume occupied by the spheres) of rho approximately 0.64 without introducing some partial crystallization. The nature of this "random-close-packing" limit (RCP) is investigated by using both geometrical and statistical mechanics tools applied to a large set of experiments and numerical simulations of equal-sized sphere packings. The study of the Delaunay simplexes decomposition reveals that the fraction of "quasiperfect tetrahedra" grows with the density up to a saturation fraction of approximately 30% reached at the RCP limit. At this limit the fraction of aggregate "polytetrahedral" structures (made of quasiperfect tetrahedra which share a common triangular face) reaches it maximal extension involving all the spheres. Above the RCP limit the polytetrahedral structure gets rapidly disassembled. The entropy of the disordered packings, calculated from the study of the local volume fluctuations, decreases uniformly and vanishes at the (extrapolated) limit rho(Kappa) approximately 0.66 . Before such limit, and precisely in the range of densities between 0.646 and 0.66, a phase separated mixture of disordered and crystalline phases is observed.

Polytetrahedral nature of the dense disordered packings of hard spheres

We study the structure of numerically simulated hard sphere packings at different densities by investigating local tetrahedral configurations of the spheres. Clusters of tetrahedra adjacent by faces present relatively dense aggregates of spheres atypical for crystals. The number of spheres participating in such polytetrahedral configurations increases with densification of the packing, and at the Bernal's limiting density (the packing fraction around 0.64) all spheres of the packing become involved in such tetrahedra. Thus the polytetrahedral packing cannot provide further increase in the density, and alternative structural change (formation of crystalline nuclei) begins henceforth.

Molecular-dynamics study of liquid nickel above and below the melting point

We have investigated the structural and dynamic properties of liquid nickel by means of large-scale molecular-dynamics simulations, using an effective-pair potential derived from the second-order pseudopotential perturbation theory. The model of interactions is assessed on the single-atom as well as collective dynamic properties. The short-range order in the stable and undercooled liquids is also examined. We show that the present model potential gives a description of the local structure in both states in close agreement with first-principles molecular-dynamics simulations.

Atomic packing of the inherent structure of simple liquids

We report a universal inherent packing structure underlying the simple liquids, the normalized distribution functions of which are independent of temperature and density. The inherent packing state, carrying the maximized configurational entropy, has intrinsic connections with the maximally random jammed state of hard spheres.

Icosahedral short-range order in amorphous alloys

We have characterized the icosahedral short-range order in amorphous solids using local environment probes. Such topological local order is pronounced even in an amorphous alloy that does not form quasicrystalline phases upon crystallization, as demonstrated by the extended x-ray absorption fine structure and x-ray absorption near-edge structure of a Ni-Ag amorphous alloy analyzed through reverse Monte Carlo simulations.

Dense packing and symmetry in small clusters of microspheres

When small numbers of colloidal microspheres are attached to the surfaces of liquid emulsion droplets, removing fluid from the droplets leads to packings of spheres that minimize the second moment of the mass distribution. The structures of the packings range from sphere doublets, triangles, and tetrahedra to exotic polyhedra not found in infinite lattice packings, molecules, or minimum-potential energy clusters. The emulsion system presents a route to produce new colloidal structures and a means to study how different physical constraints affect symmetry in small parcels of matter.

Do liquids exhibit local fivefold symmetry at interfaces?

We calculate the layer-resolved local fivefold symmetry of liquids near interfaces using computer simulation of hard sphere fluids on structured substrates. In the first few adjacent liquid layers, the presence of a surface suppresses local icosahedral packing while the magnitude of local fivefold symmetry in the next layers depends on details of the particle-substrate interaction. For a strong particle-substrate attraction, the local fivefold symmetry in these layers is higher than in the bulk liquid.