Despite the amorphous nature of glassy water, x-ray or neutron scattering experiments reveal sharp peaks in the structure factor, indicating the existence of medium-range order (MRO) in the system. However the real space origin of the peaks has yet to be disclosed. Herein, we use a combined approach of molecular dynamics simulations and persistent homology (PH) to investigate two types of glassy water, low-density amorphous (LDA) and high-density amorphous (HDA) ices. We present prominent MRO ring structures in each type of the ices, distinguished by their size and shape as well as the number of their components: MRO rings in HDA are observed smaller, less planar and more membered, compared to those in LDA. The PH-extracted MRO rings successfully reproduce the quantitative features, including the position and width, of the first sharp diffraction peaks in the structure factor, hence suitably serving as the origin of experimental MRO signatures in the amorphous ices. Our study supports that PH is an effective tool to identify hidden MRO in amorphous configurations.
We investigate collective motions of points in 2D systems, orchestrated by Lloyd algorithm. The algorithm iteratively updates a system by minimising the total quantizer energy of the Voronoi landscape of the system. As a result of a tradeoff between energy minimisation and geometric frustration, we find that optimised systems exhibit a defective landscape along the process, where strands of 5- and 7-coordinated dislocations are embedded in the hexatic phase. In particular, dipole defects, each of which is the simplest possible pair of a pentagon and a heptagon, come into the picture of dynamical arrest, as the system freezes down to a disordered hyperuniform state. Moreover, we explore the packing fractions of 2D disk packings associated to the obtained hyperuniform systems by considering the maximum inscribed disks in their Voronoi cells.
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