1
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Illing PE, Ono-Dit-Biot JC, Dalnoki-Veress K, Weeks ER. Compression and fracture of ordered and disordered droplet rafts. Phys Rev E 2024; 109:014610. [PMID: 38366516 DOI: 10.1103/physreve.109.014610] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2023] [Accepted: 12/06/2023] [Indexed: 02/18/2024]
Abstract
We simulate a two-dimensional array of droplets being compressed between two walls. The droplets are adhesive due to an attractive depletion force. As one wall moves toward the other, the droplet array is compressed and eventually induced to rearrange. The rearrangement occurs via a fracture, where depletion bonds are quickly broken between a subset of droplets. For monodisperse, hexagonally ordered droplet arrays, this fracture is preceded by a maximum force exerted on the walls, which drops rapidly after the fracture occurs. In small droplet arrays a fracture is a single well-defined event, but for larger droplet arrays, competing fractures can be observed. These are fractures nucleated nearly simultaneously in different locations. Finally, we also study the compression of bidisperse droplet arrays. The addition of a second droplet size further disrupts fracture events, showing differences between ideal crystalline arrays, crystalline arrays with a small number of defects, and fully amorphous arrays. These results are in good agreement with previously published experiments.
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Affiliation(s)
| | | | - Kari Dalnoki-Veress
- Department of Physics & Astronomy, McMaster University, Hamilton, Ontario, L8S 4L8, Canada
- Gulliver, CNRS UMR 7083, ESPCI Paris, University PSL, 75005 Paris, France
| | - Eric R Weeks
- Department of Physics, Emory University, Atlanta, Georgia 30322, USA
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2
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Gramlich JM, Zarif M, Bowles RK. Is there a granular potential? SOFT MATTER 2023; 19:1373-1383. [PMID: 36723165 DOI: 10.1039/d2sm01636b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
Granular materials, such as sand or grain, exhibit many structural and dynamic characteristics similar to those observed in molecular systems, despite temperature playing no role in their properties. This has led to an effort to develop a statistical mechanics for granular materials that has focused on establishing an equivalent to the microcanonical ensemble and a temperature-like thermodynamic variable. Here, we expand on these ideas by introducing a granular potential into the Edwards ensemble, as an analogue to the chemical potential, and explore its properties using a simple model of a granular system. A simple kinetic Monte Carlo simulation of the model shows the effect of mass transport leading to equilibrium and how this is connected to the redistribution of volume in the system. An exact analytical treatment of the model shows that the compactivity and the ratio of the granular potential to the compactivity determine the equilibrium between two open systems that are able to exchange volume and particles, and that mass moves from high to low values of this ratio. Analysis of the granular potential shows that adding a particle to the system increases the entropy at high compactivity, but decreases the entropy at low compactivity. Finally, we demonstrate the use of a small system thermodynamics method for the measurement of granular potential differences.
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Affiliation(s)
- Josh M Gramlich
- Department of Chemistry, University of Saskatchewan, Saskatoon, SK, S7H 0H1, Canada.
| | - Mahdi Zarif
- Department of Physical and Computational Chemistry, Shahid Beheshti University, Tehran 19839-9411, Iran
| | - Richard K Bowles
- Department of Chemistry, University of Saskatchewan, Saskatoon, SK, S7H 0H1, Canada.
- Centre for Quantum Topology and its Applications (quanTA), University of Saskatchewan, SK S7N 5E6, Canada
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3
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Schaller FM, Punzmann H, Schröder-Turk GE, Saadatfar M. Mixing properties of bi-disperse ellipsoid assemblies: mean-field behaviour in a granular matter experiment. SOFT MATTER 2023; 19:951-958. [PMID: 36633168 DOI: 10.1039/d2sm00922f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
The structure and spatial statistical properties of amorphous ellipsoid assemblies have profound scientific and industrial significance in many systems, from cell assays to granular materials. This paper uses a fundamental theoretical relationship for mixture distributions to explain the observations of an extensive X-ray computed tomography study of granular ellipsoidal packings. We study a size-bi-disperse mixture of two types of ellipsoids of revolutions that have the same aspect ratio of α ≈ 0.57 and differ in size, by about 10% in linear dimension, and compare these to mono-disperse systems of ellipsoids with the same aspect ratio. Jammed configurations with a range of packing densities are achieved by employing different tapping protocols. We numerically interrogate the final packing configurations by analyses of the local packing fraction distributions calculated from the Voronoi diagrams. Our main finding is that the bi-disperse ellipsoidal packings studied here can be interpreted as a mixture of two uncorrelated mono-disperse packings, insensitive to the compaction protocol. Our results are consolidated by showing that the local packing fraction shows no correlation beyond their first shell of neighbours in the binary mixtures. We propose a model of uncorrelated binary mixture distribution that describes the observed experimental data with high accuracy. This analysis framework will enable future studies to test whether the observed mean-field behaviour is specific to the particular granular system or the specific parameter values studied here or if it is observed more broadly in other bi-disperse non-spherical particle systems.
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Affiliation(s)
- F M Schaller
- Friedrich-Alexander Universität Erlangen-Nürnberg, Institut für Theoretische Physik, Staudtstr. 7B, 91058 Erlangen, Germany.
- Karlsruhe Institute of Technology (KIT), Institut für Stochastik, 76131 Karlsruhe, Germany
| | - H Punzmann
- The Australian National University, Research School of Physics, Canberra ACT 2601, Australia
| | - G E Schröder-Turk
- The Australian National University, Research School of Physics, Canberra ACT 2601, Australia
- Murdoch University, College of Science, Technology, Engineering and Mathematics, 90 South St, Murdoch WA 6150, Australia
| | - M Saadatfar
- The Australian National University, Research School of Physics, Canberra ACT 2601, Australia
- The University of Sydney, School of Civil Engineering, NSW 2006, Australia.
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4
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Francois N, Cruikshank R, Herring A, Kingston A, Webster S, Knackstedt M, Saadatfar M. A versatile microtomography system to study in situ the failure and fragmentation in geomaterials. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2022; 93:083704. [PMID: 36050093 DOI: 10.1063/5.0093650] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2022] [Accepted: 07/04/2022] [Indexed: 06/15/2023]
Abstract
This article describes a microtomography experimental platform enabling in situ micro-mechanical study of failure and fragmentation in geomaterials. The system is based on an original high-pressure triaxial flow cell, which is fully integrated into a custom built microtomography scanner equipped with a laboratory x-ray source. The design of the high-precision mechanical apparatus was informed by the concurrent development of advanced tomographic reconstruction methods based on helical scanning and of algorithms correcting for hardware inaccuracies. This experimental system produces very high-quality 3D images of microstructural changes occurring in rocks undergoing mechanical failure and substantial fragmentation. We present the results of two experiments as case studies to demonstrate the capabilities and versatility of this instrumental platform. These experiments tackle various questions related to the onset of rock failure, the hydromechanical coupling and relaxation mechanisms in fractured rocks, or the fragmentation process in geomaterials such as copper ores.
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Affiliation(s)
- N Francois
- ARC Training Centre for M3D Innovation, Research School of Physics, The Australian National University, Canberra ACT 2601, Australia
| | - R Cruikshank
- ARC Training Centre for M3D Innovation, Research School of Physics, The Australian National University, Canberra ACT 2601, Australia
| | - A Herring
- ARC Training Centre for M3D Innovation, Research School of Physics, The Australian National University, Canberra ACT 2601, Australia
| | - A Kingston
- ARC Training Centre for M3D Innovation, Research School of Physics, The Australian National University, Canberra ACT 2601, Australia
| | - S Webster
- ARC Training Centre for M3D Innovation, Research School of Physics, The Australian National University, Canberra ACT 2601, Australia
| | - M Knackstedt
- ARC Training Centre for M3D Innovation, Research School of Physics, The Australian National University, Canberra ACT 2601, Australia
| | - M Saadatfar
- ARC Training Centre for M3D Innovation, Research School of Physics, The Australian National University, Canberra ACT 2601, Australia
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5
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Osang G, Edelsbrunner H, Saadatfar M. Topological signatures and stability of hexagonal close packing and Barlow stackings. SOFT MATTER 2021; 17:9107-9115. [PMID: 34569592 DOI: 10.1039/d1sm00774b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Two common representations of close packings of identical spheres consisting of hexagonal layers, called Barlow stackings, appear abundantly in minerals and metals. These motifs, however, occupy an identical portion of space and bear identical first-order topological signatures as measured by persistent homology. Here we present a novel method based on k-fold covers that unambiguously distinguishes between these patterns. Moreover, our approach provides topological evidence that the FCC motif is the more stable of the two in the context of evolving experimental sphere packings during the transition from disordered to an ordered state. We conclude that our approach can be generalised to distinguish between various Barlow stackings manifested in minerals and metals.
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Affiliation(s)
- Georg Osang
- Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria
| | - Herbert Edelsbrunner
- Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria
| | - Mohammad Saadatfar
- School of Civil Engineering, The University of Sydney, Sydney, NSW 2006, Australia.
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6
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Ono-Dit-Biot JC, Soulard P, Barkley S, Weeks ER, Salez T, Raphaël E, Dalnoki-Veress K. Mechanical properties of 2D aggregates of oil droplets as model mono-crystals. SOFT MATTER 2021; 17:1194-1201. [PMID: 33336662 DOI: 10.1039/d0sm01165g] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
We investigate the elastic and yielding properties of two dimensional defect-free mono-crystals made of highly monodisperse droplets. Crystals are compressed between two parallel boundaries of which one acts as a force sensor. As the available space between boundaries is reduced, the crystal goes through successive row-reduction transitions. For small compression forces, the crystal responds elastically until a critical force is reached and the assembly fractures in a single catastrophic global event. Correspondingly there is a peak in the force measurement associated with each row-reduction. The elastic properties of ideal mono-crystal samples are fully captured by a simple analytical model consisting of an assembly of individual capillary springs. The yielding properties of the crystal are captured with a minimal bond breaking model.
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Affiliation(s)
| | - Pierre Soulard
- UMR CNRS Gulliver 7083, ESPCI Paris, PSL Research University, 10 rue Vauquelin, 75005 Paris, France
| | - Solomon Barkley
- Department of Physics & Astronomy, McMaster University, Hamilton, ON L8S 4L8, Canada.
| | - Eric R Weeks
- Department of Physics, Emory University, Atlanta, GA 30322, USA
| | - Thomas Salez
- Univ. Bordeaux, CNRS, LOMA, UMR 5798, F-33405 Talence, France and Global Station for Soft Matter, Global Institution for Collaborative Research and Education, Hokkaido University, Sapporo, Japan
| | - Elie Raphaël
- UMR CNRS Gulliver 7083, ESPCI Paris, PSL Research University, 10 rue Vauquelin, 75005 Paris, France
| | - Kari Dalnoki-Veress
- Department of Physics & Astronomy, McMaster University, Hamilton, ON L8S 4L8, Canada. and UMR CNRS Gulliver 7083, ESPCI Paris, PSL Research University, 10 rue Vauquelin, 75005 Paris, France
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7
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Dhiman I, Kimber SAJ, Mehta A, Chatterji T. A neutron tomography study: probing the spontaneous crystallization of randomly packed granular assemblies. Sci Rep 2018; 8:17637. [PMID: 30518966 PMCID: PMC6281579 DOI: 10.1038/s41598-018-36331-1] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2018] [Accepted: 11/20/2018] [Indexed: 11/09/2022] Open
Abstract
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.
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Affiliation(s)
- Indu Dhiman
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, 37831, USA.
| | - Simon A J Kimber
- Université Bourgogne-Franche Comté, Université de Bourgogne, ICB-Laboratoire Interdisciplinaire Carnot de Bourgogne, Bâtiment Sciences Mirande, 9 Avenue Alain Savary, B-P. 47870, 21078, Dijon Cedex, France
| | - Anita Mehta
- Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103, Leipzig, Germany
| | - Tapan Chatterji
- Institut Laue-Langevin, 71 Avenue des Martyrs, 38000, Grenoble, France.
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8
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Wu Y, An X, Qian Q, Wang L, Yu A. Dynamic modelling on the confined crystallization of mono-sized cubic particles under mechanical vibration. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2018; 41:139. [PMID: 30470964 DOI: 10.1140/epje/i2018-11744-2] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/24/2017] [Accepted: 10/16/2018] [Indexed: 06/09/2023]
Abstract
The dynamic crystallization of cubic granular particles under three-dimensional mechanical vibration is numerically investigated by the discrete element method. The effects of operational conditions (vibration, container shape and system size) and particle properties (gravity and friction) on the formation of crystals and defects are discussed. The results show that the formation and growth of clusters with face-to-face aligned cubic particles can be easily realized under vibrations. Especially, a single crystal with both translational and orientational ordering can be reproduced in a rectangular container under appropriate vibrations. It is also found that the gravitational effect is beneficial for the ordering of a packing; the ordering of frictional particles can be improved significantly with an enlarged gravitational acceleration. The flat walls of a rectangular container facilitate the formation of orderly layered structures. The curved walls of a cylindrical container contribute to the formation of ring-like structures, whereas they also cause distortions and defects in the packing centers. Finally, it is shown that the crystallization of inelastic particles is basically accomplished by the pursuit of a better mechanical stability of the system, with decreasing kinetic and potential energies.
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Affiliation(s)
- Yongli Wu
- School of Metallurgy, Northeastern University, 110004, Shenyang, China
- Laboratory for Simulation and Modelling of Particulate Systems, Department of Chemical Engineering, Monash University, 3800, Melbourne, VIC, Australia
| | - Xizhong An
- School of Metallurgy, Northeastern University, 110004, Shenyang, China.
| | - Quan Qian
- School of Metallurgy, Northeastern University, 110004, Shenyang, China
| | - Lin Wang
- School of Metallurgy, Northeastern University, 110004, Shenyang, China
| | - Aibing Yu
- Laboratory for Simulation and Modelling of Particulate Systems, Department of Chemical Engineering, Monash University, 3800, Melbourne, VIC, Australia
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9
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Rietz F, Radin C, Swinney HL, Schröter M. Nucleation in Sheared Granular Matter. PHYSICAL REVIEW LETTERS 2018; 120:055701. [PMID: 29481202 DOI: 10.1103/physrevlett.120.055701] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2017] [Revised: 12/11/2017] [Indexed: 06/08/2023]
Abstract
We present an experiment on crystallization of packings of macroscopic granular spheres. This system is often considered to be a model for thermally driven atomic or colloidal systems. Cyclically shearing a packing of frictional spheres, we observe a first order phase transition from a disordered to an ordered state. The ordered state consists of crystallites of mixed fcc and hcp symmetry that coexist with the amorphous bulk. The transition, initiated by homogeneous nucleation, overcomes a barrier at 64.5% volume fraction. Nucleation consists predominantly of the dissolving of small nuclei and the growth of nuclei that have reached a critical size of about ten spheres.
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Affiliation(s)
- Frank Rietz
- Max-Planck-Institute for Dynamics and Self-Organization Göttingen, 37077 Göttingen, Germany
- Institute for Multiscale Simulation, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 91052 Erlangen, Germany
- Department of Nonlinear Phenomena, University Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany
- Department of Pattern Formation, University Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany
| | - Charles Radin
- Department of Mathematics, University of Texas at Austin, Austin, Texas 78712, USA
| | - Harry L Swinney
- Center for Nonlinear Dynamics and Department of Physics, University of Texas at Austin, Austin, Texas 78712, USA
| | - Matthias Schröter
- Max-Planck-Institute for Dynamics and Self-Organization Göttingen, 37077 Göttingen, Germany
- Institute for Multiscale Simulation, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 91052 Erlangen, Germany
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10
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Pore configuration landscape of granular crystallization. Nat Commun 2017; 8:15082. [PMID: 28497794 PMCID: PMC5437301 DOI: 10.1038/ncomms15082] [Citation(s) in RCA: 50] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2016] [Accepted: 02/23/2017] [Indexed: 11/08/2022] Open
Abstract
Uncovering grain-scale mechanisms that underlie the disorder–order transition in assemblies of dissipative, athermal particles is a fundamental problem with technological relevance. To date, the study of granular crystallization has mainly focussed on the symmetry of crystalline patterns while their emergence and growth from irregular clusters of grains remains largely unexplored. Here crystallization of three-dimensional packings of frictional spheres is studied at the grain-scale using X-ray tomography and persistent homology. The latter produces a map of the topological configurations of grains within static partially crystallized packings. Using numerical simulations, we show that similar maps are measured dynamically during the melting of a perfect crystal. This map encodes new information on the formation process of tetrahedral and octahedral pores, the building blocks of perfect crystals. Four key formation mechanisms of these pores reproduce the main changes of the map during crystallization and provide continuous deformation pathways representative of the crystallization dynamics. Emergence and growth of crystalline domains in granular media remains under-explored. Here, the authors analyse tomographic snapshots from partially recrystallized packings of spheres using persistent homology and find agreement with proposed transitions based on continuous deformation of octahedral and tetrahedral voids.
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11
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Weis S, Schröter M. Analyzing X-ray tomographies of granular packings. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2017; 88:051809. [PMID: 28571396 DOI: 10.1063/1.4983051] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Starting from three-dimensional volume data of a granular packing, as, e.g., obtained by X-ray Computed Tomography, we discuss methods to first detect the individual particles in the sample and then analyze their properties. This analysis includes the pair correlation function, the volume and shape of the Voronoi cells, and the number and type of contacts formed between individual particles. We mainly focus on packings of monodisperse spheres, but we will also comment on other monoschematic particles such as ellipsoids and tetrahedra. This paper is accompanied by a package of free software containing all programs (including source code) and an example three-dimensional dataset which allows the reader to reproduce and modify all examples given.
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Affiliation(s)
- Simon Weis
- Institut für Theoretische Physik I, Friedrich-Alexander-Universität, 91058 Erlangen, Germany
| | - Matthias Schröter
- Institute for Multiscale Simulation, Friedrich-Alexander-Universität, 91052 Erlangen, Germany
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12
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Saadatfar M, Takeuchi H, Hanifpour M, Robins V, Francois N, Hiraoka Y. Granular compaction and the topology of pore deformation. EPJ WEB OF CONFERENCES 2017. [DOI: 10.1051/epjconf/201714016009] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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13
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Tong H, Tan P, Xu N. From Crystals to Disordered Crystals: A Hidden Order-Disorder Transition. Sci Rep 2015; 5:15378. [PMID: 26483326 PMCID: PMC4613360 DOI: 10.1038/srep15378] [Citation(s) in RCA: 43] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2015] [Accepted: 09/24/2015] [Indexed: 11/09/2022] Open
Abstract
To distinguish between order and disorder is of fundamental importance to understanding solids. It becomes more significant with recent observations that solids with high structural order can behave like disordered solids, while properties of disordered solids can approach crystals under certain circumstance. It is then imperative to understand when and how disorder takes effect to deviate the properties of a solid from crystals and what the correct factors are to control the behaviours of solids. Here we answer these questions by reporting the finding of a hidden order-disorder transition from crystals to disordered crystals for static packings of frictionless spheres. While the geometric indicators are mostly blind to the transition, disordered crystals already exhibit properties apart from crystals. The transition approaches the close packing of hard spheres, giving rise to the singularity of the close packing point. We evidence that both the transition and properties of disordered crystals are jointly determined by the structural order and density. Near the transition, the elastic moduli and coordination number of disordered crystals show particular pressure dependence distinct from known behaviours of both crystals and jammed solids. The discovery of the transition therefore reveals some unknown aspects of solids.
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Affiliation(s)
- Hua Tong
- CAS Key Laboratory of Soft Matter Chemistry, Hefei National Laboratory for Physical Sciences at the Microscale, and Department of Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Peng Tan
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, People's Republic of China
| | - Ning Xu
- CAS Key Laboratory of Soft Matter Chemistry, Hefei National Laboratory for Physical Sciences at the Microscale, and Department of Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
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14
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Hanifpour M, Francois N, Robins V, Kingston A, Allaei SMV, Saadatfar M. Structural and mechanical features of the order-disorder transition in experimental hard-sphere packings. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:062202. [PMID: 26172700 DOI: 10.1103/physreve.91.062202] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2015] [Indexed: 06/04/2023]
Abstract
Here we present an experimental and numerical investigation on the grain-scale geometrical and mechanical properties of partially crystallized structures made of macroscopic frictional grains. Crystallization is inevitable in arrangements of monosized hard spheres with packing densities exceeding Bernal's limiting density ϕ(Bernal)≈0.64. We study packings of monosized hard spheres whose density spans over a wide range (0.59<ϕ<0.72). These experiments harness x-ray computed tomography, three-dimensional image analysis, and numerical simulations to access precisely the geometry and the 3D structure of internal forces within the sphere packings. We show that clear geometrical transitions coincide with modifications of the mechanical backbone of the packing both at the grain and global scale. Notably, two transitions are identified at ϕ(Bernal)≈0.64 and ϕ(c)≈0.68. These results provide insights on how geometrical and mechanical features at the grain scale conspire to yield partially crystallized structures that are mechanically stable.
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Affiliation(s)
- M Hanifpour
- Department of Physics, University of Tehran, Tehran 14395-547, Iran
- School of Physics, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5531, Iran
| | - N Francois
- Department of Applied Mathematics, Research School of Physics and Engineering, Australian National University, Canberra, Australia
| | - V Robins
- Department of Applied Mathematics, Research School of Physics and Engineering, Australian National University, Canberra, Australia
| | - A Kingston
- Department of Applied Mathematics, Research School of Physics and Engineering, Australian National University, Canberra, Australia
| | - S M Vaez Allaei
- Department of Physics, University of Tehran, Tehran 14395-547, Iran
- School of Physics, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5531, Iran
| | - M Saadatfar
- Department of Applied Mathematics, Research School of Physics and Engineering, Australian National University, Canberra, Australia
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