Medium-range order in amorphous ices revealed by persistent homology

Abstract

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.

Revealing hidden medium-range order in amorphous materials using topological data analysis

“…As such, the advantage of our developed persistent homology-based methodology lies in its applicability to any amorphous system, as it only requires atomic trajectory and radii information, without requirements of prior knowledge of chemical bonding. In comparison to the previous work on persistent homology, this work considerably expands the number of amorphous structures studied by the S PH function (from 3 to 12) (21,23) and provides the first rigorous test of the methodology for a systematic composition variation in a model glass series. As such, we have generalized the use of persistent homology to deconvolute the contribution of various MRO features to the FSDP in oxide glasses.…”

“…Generally, the application of persistent homology to amorphous MRO structures is challenging, as the definition of characteristic regions (i.e., groups of loops) adopted in the original studies (20)(21)(22)(23)31) is not unique; that is, they use an "optimal cycle" for the geometric characterizations. Here, we introduce a self-consistent and rigorous definition of characteristic regions by separating them according to the number of contained atoms (see below for definitions).…”

Persistent Homology Analysis for Materials Research and Persistent Homology Software: HomCloud

“…34,35) Amorphous ice is another example of a network former, where the medium-range order of the hydrogen-bonding network is quantified by PH. 36)…”

“…Of course, other data than materials science is also available. HomCloud has been already used in various scientific researches, including materials science, 17,34,35,37,38,40,[61][62][63][64][65][66][67][68] geology, 20,69) structural biology, 70) and medical image analysis. 71,72) HomCloud has useful functionalities such as visualization, inverse analysis, machine learning.…”

Unsupervised topological learning for identification of atomic structures

“…In this paper, we propose an unsupervised method to analyse structural information, where descriptors from atomic positions are constructed using persistent homology (PH), a classical tool in topological data analysis (TDA) [14]. In MD simulations, PH has been successfully applied as an analysis tool of medium-range structural environments [15] in amorphous solids [16][17][18], ice [19] and complex molecular liquids [20]. However, to the best of our knowledge, PH has never been used as a translational and rotational invariant descriptor to encode local atomic structures.…”