Softness arises from hierarchical structures

Why do glass and other amorphous materials deform more easily in certain regions than in others? A research team from the University of Osaka, the National Institute of Advanced Industrial Sciences and Technology (AIST), the University of Okayama and the University of Tokyo discovered the answer.

By applying a mathematical method known as persistent homology, the team has shown that these soft regions are governed by hidden hierarchical structures, where the ordered and disorderly atomic arrangements coexist.

Crystalline solids, such as salt or ice, have atoms carefully arranged in repetitive patterns. Amorphous materials, including glass, rubber and certain plastics, do not have this long -range control. However, they are not completely random: they have subtle and subtle atomic models which extend over a few nanometers.

The MRO has long been suspected of playing an essential role in determining the physical properties of amorphous materials, in particular their mechanical responses. However, due to the complexity of atomic networks, conventional analysis methods could not clarify how the MRO relates to regions which deform more easily than their environment. The structural origins of mechanical sweetness in the amorphous solids therefore remained elusive.

The research team applied persistent homology, a branch of the analysis of topological data which captures the structural characteristics in several scales. In amorphous silicon – a prototypical covalent amorphous material widely used in solar cells and electronic devices – they discovered hierarchical rings structures: smaller rings with irregular edge lengths are nested inside larger rings.

This coexistence of order and disorder means that sweetness emerges not from chance, but constraints imposed by the average order intertwined with a local disorder. The study also revealed that these hierarchical structures are strongly correlated with localized vibrations with low energy, a universal characteristic of glasses known as “Boson peak”.

“This work provides a new path to link the atomic structure of amorphous materials to their mechanical responses”, explains Emi Minamitani of the University of Osaka, the main author of the study published in Nature communications.

“We believe that these ideas will accelerate the design of sustainable glass and other advanced amorphous materials.”

The discovery establishes a clear structural principle: mechanically soft regions occur when the disorder is integrated into the average order.

This counter -intuitive discovery provides a practical directive to develop amorphous solids which are both flexible and strong – the advantageous applications of screens and coatings with energy devices.