Evolving Einstein: The instability of aperiodic monotile as a polycrystalline microstructure

The recent discovery of the Einstein monotile has enabled the design of a new class of disordered materials with interesting range of physical and mechanical properties. When the characteristic shape of this monotile alters, the properties of the associated disordered materials varies noticeably. Therefore, the applicability of the hat-based disordered material is coupled with the thermodynamic stability of its tiles. Given this significance, the stability of the aperiodic hat-based microstructure is investigated in this work through a thermodynamically consistent multiphase-field approach. The present analysis reveals that the aperiodic hat microstructure, when treated as a polycrystalline system, is inherently unstable, and is progressively evolving towards a conventional grain morphology with straight interfaces, thereby erasing its characteristic topological disorder. The instability is traced to the grain-boundary network of the hat microstructure, characterised by the energetically unfavourable quadruple-junctions and protrusions, which induce a transformation to a lower-energy state. Despite being morphologically identical, during the evolution, the hats yield grains of varied topological feature or face-classes dictated by the neighbours and additionally, their orientation. The exhaustive analysis of the evolution lends itself in predicting the unstable tiles in the polycrystalline hat microstructure before the energy-minimising evolution sets-in. The present work ultimately unravels that, as opposed to conventional polycrystalline systems, grain growth in the aperiodic-monotile microstructure is dictated by orientation, which correspondingly establishes varying neighbours.