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Zhang H, Wang X, Zhang J, Yu HB, Douglas JF. Approach to hyperuniformity in a metallic glass-forming material exhibiting a fragile to strong glass transition. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2023; 46:50. [PMID: 37380868 DOI: 10.1140/epje/s10189-023-00308-4] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2023] [Accepted: 06/05/2023] [Indexed: 06/30/2023]
Abstract
We investigate a metallic glass-forming (GF) material (Al90Sm10) exhibiting a fragile-strong (FS) glass-formation by molecular dynamics simulation to better understand this highly distinctive pattern of glass-formation in which many of the usual phenomenological relations describing relaxation times and diffusion of ordinary GF liquids no longer apply, and where instead genuine thermodynamic features are observed in response functions and little thermodynamic signature is exhibited at the glass transition temperature, Tg. Given the many unexpected similarities between the thermodynamics and dynamics of this metallic GF material with water, we first focus on the anomalous static scattering in this liquid, following recent studies on water, silicon and other FS GF liquids. We quantify the "hyperuniformity index" H of our liquid, which provides a quantitative measure of molecular "jamming". To gain insight into the T-dependence and magnitude of H, we also estimate another more familiar measure of particle localization, the Debye-Waller parameter 〈u2〉 describing the mean-square particle displacement on a timescale on the order of the fast relaxation time, and we also calculate H and 〈u2〉 for heated crystalline Cu. This comparative analysis between H and 〈u2〉 for crystalline and metallic glass materials allows us to understand the critical value of H on the order of 10-3 as being analogous to the Lindemann criterion for both the melting of crystals and the "softening" of glasses. We further interpret the emergence of FS GF and liquid-liquid phase separation in this class of liquids to arise from a cooperative self-assembly process in the GF liquid.
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Affiliation(s)
- Hao Zhang
- Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, T6G 1H9, Canada.
| | - Xinyi Wang
- Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, T6G 1H9, Canada
| | - Jiarui Zhang
- Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, T6G 1H9, Canada
| | - Hai-Bin Yu
- Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan, 430074, Hubei, China
| | - Jack F Douglas
- Material Measurement Laboratory, Material Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, MD, 20899, USA.
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Abstract
Transport properties of porous media are intimately linked to their pore-space microstructures. We quantify geometrical and topological descriptors of the pore space of certain disordered and ordered distributions of spheres, including pore-size functions and the critical pore radius δ_{c}. We focus on models of porous media derived from maximally random jammed sphere packings, overlapping spheres, equilibrium hard spheres, quantizer sphere packings, and crystalline sphere packings. For precise estimates of the percolation thresholds, we use a strict relation of the void percolation around sphere configurations to weighted bond percolation on the corresponding Voronoi networks. We use the Newman-Ziff algorithm to determine the percolation threshold using universal properties of the cluster size distribution. The critical pore radius δ_{c} is often used as the key characteristic length scale that determines the fluid permeability k. A recent study [Torquato, Adv. Wat. Resour. 140, 103565 (2020)10.1016/j.advwatres.2020.103565] suggested for porous media with a well-connected pore space an alternative estimate of k based on the second moment of the pore size 〈δ^{2}〉, which is easier to determine than δ_{c}. Here, we compare δ_{c} to the second moment of the pore size 〈δ^{2}〉, and indeed confirm that, for all porosities and all models considered, δ_{c}^{2} is to a good approximation proportional to 〈δ^{2}〉. However, unlike 〈δ^{2}〉, the permeability estimate based on δ_{c}^{2} does not predict the correct ranking of k for our models. Thus, we confirm 〈δ^{2}〉 to be a promising candidate for convenient and reliable estimates of the fluid permeability for porous media with a well-connected pore space. Moreover, we compare the fluid permeability of our models with varying degrees of order, as measured by the τ order metric. We find that (effectively) hyperuniform models tend to have lower values of k than their nonhyperuniform counterparts. Our findings could facilitate the design of porous media with desirable transport properties via targeted pore statistics.
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Lomba E, Weis JJ, Guisández L, Torquato S. Minimal statistical-mechanical model for multihyperuniform patterns in avian retina. Phys Rev E 2020; 102:012134. [PMID: 32794939 DOI: 10.1103/physreve.102.012134] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2020] [Accepted: 06/22/2020] [Indexed: 11/07/2022]
Abstract
Birds are known for their extremely acute sense of vision. The very peculiar structural distribution of five different types of cones in the retina underlies this exquisite ability to sample light. It was recently found that each cone population as well as their total population display a disordered pattern in which long-wavelength density fluctuations vanish [Jiao et al., Phys. Rev. E 89, 022721 (2014)PLEEE81539-375510.1103/PhysRevE.89.022721]. This property, known as hyperuniformity, is also present in perfect crystals. In situations like the avian retina in which both the global structure and that of each component display hyperuniformity, the system is said to be multihyperuniform. In this work, we aim at devising a minimal statistical-mechanical model that can reproduce the main features of the spatial distribution of photoreceptors in avian retina, namely the presence of disorder, multihyperuniformity, and local heterocoordination. This last feature is key to avoiding local clustering of the same type of photoreceptors, an undesirable feature for the efficient sampling of light. For this purpose, we formulate a minimal statistical-mechanical model that definitively exhibits the required structural properties: an equimolar three-component mixture (one component to sample each primary color: red, green, and blue) of nonadditive hard disks to which a long-range logarithmic repulsion is added between like particles. Interestingly, a Voronoi analysis of our idealized system of photoreceptors shows that the space-filling Voronoi polygons display a rather uniform area distribution, symmetrically centered around that of a regular lattice, a structural property also found in human retina. Disordered multihyperuniformity offers an alternative to generate photoreceptor patterns with minimal long-range concentration and density fluctuations. This is the key to overcoming the difficulties in devising an efficient visual system in which crystal-like order is absent.
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Affiliation(s)
- Enrique Lomba
- Instituto de Química Física Rocasolano, CSIC, Calle Serrano 119, E-28006 Madrid, Spain
| | - Jean-Jacques Weis
- Université de Paris-Saclay, Laboratoire de Physique Théorique, Bâtiment 210, 91405 Orsay Cedex, France
| | - Leandro Guisández
- Instituto de Química Física Rocasolano, CSIC, Calle Serrano 119, E-28006 Madrid, Spain.,IFLYSIB (UNLP, CONICET), 59 No. 789, B1900BTE La Plata, Argentina
| | - Salvatore Torquato
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA.,Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA
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Meyra AG, Zarragoicoechea GJ, Maltz AL, Lomba E, Torquato S. Hyperuniformity on spherical surfaces. Phys Rev E 2019; 100:022107. [PMID: 31574707 DOI: 10.1103/physreve.100.022107] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2018] [Indexed: 11/07/2022]
Abstract
We study and characterize local density fluctuations of ordered and disordered hyperuniform point distributions on spherical surfaces. In spite of the extensive literature on disordered hyperuniform systems in Euclidean geometries, to date few works have dealt with the problem of hyperuniformity in curved spaces. Indeed, some systems that display disordered hyperuniformity, like the spatial distribution of photoreceptors in avian retina, actually occur on curved surfaces. Here we will focus on the local particle number variance and its dependence on the size of the sampling window (which we take to be a spherical cap) for regular and uniform point distributions, as well as for equilibrium configurations of fluid particles interacting through Lennard-Jones, dipole-dipole, and charge-charge potentials. We show that the scaling of the local number variance as a function of the window size enables one to characterize hyperuniform and nonhyperuniform point patterns also on spherical surfaces.
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Affiliation(s)
- Ariel G Meyra
- IFLYSIB (UNLP, CONICET), 59 No. 789, B1900BTE La Plata, Argentina.,Instituto de Química Física Rocasolano, CSIC, Calle Serrano 119, E-28006 Madrid, Spain
| | - Guillermo J Zarragoicoechea
- IFLYSIB (UNLP, CONICET), 59 No. 789, B1900BTE La Plata, Argentina.,Comisión de Investigaciones Científicas de la Provincia de Buenos Aires, Argentina
| | - Alberto L Maltz
- Departamento de Matemática, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, CC 72 Correo Central 1900 La Plata, Argentina
| | - Enrique Lomba
- Instituto de Química Física Rocasolano, CSIC, Calle Serrano 119, E-28006 Madrid, Spain
| | - Salvatore Torquato
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA.,Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA
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Ma Z, Torquato S. Hyperuniformity of generalized random organization models. Phys Rev E 2019; 99:022115. [PMID: 30934260 DOI: 10.1103/physreve.99.022115] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2018] [Indexed: 11/07/2022]
Abstract
Studies of random organization models of monodisperse (i.e., identical) spherical particles have shown that a hyperuniform state is achievable when the system goes through an absorbing phase transition to a critical state. Here we investigate to what extent hyperuniformity is preserved when the model is generalized to particles with a size distribution and/or nonspherical shapes. We begin by examining binary disks in two dimensions and demonstrate that their critical states are hyperuniform as two-phase media, but not hyperuniform nor multihyperuniform as point patterns formed by the particle centroids. We further confirm the generality of our findings by studying particles with a continuous size distribution. Finally, to study the effect of rotational degrees of freedom, we extend our model to noncircular particles, namely, hard rectangles with various aspect ratios, including the hard-needle limit. Although these systems exhibit only short-range orientational order, hyperuniformity is still preserved. Our analysis reveals that the redistribution of the "mass" of the particles rather than the particle centroids is central to this dynamical process. The consideration of the "active volume fraction" of generalized random organization models may help to resolve which universality class they belong to and hence may lead to a deeper theoretical understanding of absorbing-state models. Our results suggest that general particle systems subject to random organization can be a robust way to fabricate a wide class of hyperuniform states of matter by tuning the structures via different particle-size and -shape distributions. This in turn potentially enables the creation of multifunctional hyperuniform materials with desirable optical, transport, and mechanical properties.
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Affiliation(s)
- Zheng Ma
- Department of Physics, Princeton University and Princeton, New Jersey 08544, USA
| | - Salvatore Torquato
- Department of Chemistry, Department of Physics, Princeton Institute for the Science and Technology of Materials, and Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA
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Middlemas TM, Stillinger FH, Torquato S. Hyperuniformity order metric of Barlow packings. Phys Rev E 2019; 99:022111. [PMID: 30934256 DOI: 10.1103/physreve.99.022111] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2018] [Indexed: 06/09/2023]
Abstract
The concept of hyperuniformity has been a useful tool in the study of density fluctuations at large length scales in systems ranging across the natural and mathematical sciences. One can rank a large class of hyperuniform systems by their ability to suppress long-range density fluctuations through the use of a hyperuniformity order metric Λ[over ¯]. We apply this order metric to the Barlow packings, which are the infinitely degenerate densest packings of identical rigid spheres that are distinguished by their stacking geometries and include the commonly known fcc lattice and hcp crystal. The "stealthy stacking" theorem implies that these packings are all stealthy hyperuniform, a strong type of hyperuniformity, which involves the suppression of scattering up to a wave vector K. We describe the geometry of three classes of Barlow packings, two disordered classes and small-period packings. In addition, we compute a lower bound on K for all Barlow packings. We compute Λ[over ¯] for the aforementioned three classes of Barlow packings and find that, to a very good approximation, it is linear in the fraction of fcc-like clusters, taking values between those of least-ordered hcp and most-ordered fcc. This implies that the value of Λ[over ¯] of all Barlow packings is primarily controlled by the local cluster geometry. These results highlight the special nature of anisotropic stacking disorder, which provides impetus for future research on the development of anisotropic order metrics and hyperuniformity properties.
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Affiliation(s)
- T M Middlemas
- Department of Chemistry, Princeton University, New Jersey 08544, USA
| | - F H Stillinger
- Department of Chemistry, Princeton University, New Jersey 08544, USA
| | - S Torquato
- Department of Chemistry, Department of Physics, Princeton Institute for the Science and Technology of Materials, and Program in Applied and Computational Mathematics, Princeton University, New Jersey 08544, USA
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Torquato S. Perspective: Basic understanding of condensed phases of matter via packing models. J Chem Phys 2018; 149:020901. [DOI: 10.1063/1.5036657] [Citation(s) in RCA: 73] [Impact Index Per Article: 12.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Affiliation(s)
- S. Torquato
- Department of Chemistry, Department of Physics, Princeton Center for Theoretical Science, Princeton Institute for the Science and Technology of Materials, and Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA
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Chen D, Lomba E, Torquato S. Binary mixtures of charged colloids: a potential route to synthesize disordered hyperuniform materials. Phys Chem Chem Phys 2018; 20:17557-17562. [DOI: 10.1039/c8cp02616e] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
A new route to fabricate large samples of 2D disordered hyperuniform materials via self-assembly of mixtures of charged colloids.
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Affiliation(s)
- Duyu Chen
- Department of Chemistry
- Princeton University, Princeton
- USA
| | - Enrique Lomba
- Department of Chemistry
- Princeton University, Princeton
- USA
- Instituto de Química Física Rocasolano
- CSIC
| | - Salvatore Torquato
- Department of Chemistry
- Princeton University, Princeton
- USA
- Department of Physics
- Princeton University
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