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.
Highlights
Uncovering grain-scale mechanisms that underlie the disorder–order transition in assemblies of dissipative, athermal particles is a fundamental problem with technological relevance
In analogy with equilibrium statistical mechanics, Edwards and co-workers have laid the foundations of a statistical mechanics for amorphous jammed packings[14,15,16,17]
Such a statistical approach hinges on the definition of the space of the possible jammed configurations of grains[16,20]. This space can be considered as the analogue of the phase space in equilibrium thermodynamics
Summary
Uncovering grain-scale mechanisms that underlie the disorder–order transition in assemblies of dissipative, athermal particles is a fundamental problem with technological relevance. Since macroscopic granular packings are dissipative due to friction, it has been argued that the volume of the system and a variable characterizing the mechanical state should replace the energy as key macroscopic descriptors[18,19] Such a statistical approach hinges on the definition of the space of the possible jammed configurations of grains[16,20]. In comparison with classical spatial tessellation techniques (such as Voronoi or Delaunay methods), PH offers a clearer description of the population of cavities and a more comprehensive view of crystallization-driven structural changes It gives us persistence diagrams, akin to a topological phase space, that represent all the grain configurations and patterns within a packing
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
