A research group led by Associate Professor Hiroaki Hiraoka and Assistant Professor Takenobu Nakamura of the Advanced Research Institute for Atomic and Molecular Materials (WPI-AIMR), Tohoku University, is in collaboration with the Institute of Statistical Mathematics (ISM) and the Japan Science and Technology Agency (JST). By developing a mathematical method, he announced that he succeeded in elucidating the hierarchical geometric structure contained in glass.
Unlike crystals, glass does not have periodicity in its atomic arrangement, so there is no descriptive method to properly express its structure.Although it is possible to investigate short-range structures in the vicinity of each atom by the conventional method, it is not effective for a system with a disordered three-dimensional atomic arrangement such as glass.
This time, the research group has developed a mathematical method that can describe the medium-range ordered structure contained in the atomic arrangement of glass, and succeeded in extracting the hierarchical geometric structure of glass.This mathematical method uses the concept of "persistent homology" (a field of mathematics that focuses on the properties maintained when the shape of an object is continuously deformed), and the atomic arrangement is a collection of points in space. It enables multi-scale data analysis focusing on "holes" such as rings and cavities contained therein.As a result, for typical examples of oxide glass and metallic glass (SiO1 and CuZr), the atomic arrangement of each substance is constructed using the molecular dynamics method, and the difference in the internal structure between the liquid and glass states is geometrically arranged. I succeeded in characterizing it scientifically.In particular, it was found that in the glass state, there is an ordered structure with a hierarchy in the ring structure of the atomic arrangement.
The mathematical method developed this time has universality that does not specialize in substances, and is expected to have various applications such as the development of new substances and materials in addition to the development of glass such as information storage and solar panels.
