Window glass stiffness and mud ball physics share the same origin

Glass (an amorphous solid) formed by cooling a liquid of melted silica (silicon dioxide) at high temperatures and solidifying it without crystallization is called silica glass, which is widely used as a material for window glass.

Inside silica glass, a tetrahedron with four oxygen atoms covalently bonded around a central silicon atom serves as the basic unit. These tetrahedra share oxygen atoms at their vertices to form a mesh-like network structure. However, exactly how this network generates stiffness (rigidity) has not yet been fully clarified. Squeezing sand in a sandbox with your hands creates a mud ball.

The phenomenon where densely packed sand behaves like a solid is an important fundamental example for understanding the mechanism by which materials acquire rigidity. In physics, this is called a jamming transition and has been studied in the fields of non-equilibrium statistical physics and soft matter physics. Just as people become unable to move inside a packed train, the material becomes less fluid as constraints increase, eventually solidifying.

This balance between degrees of freedom and the number of constraints is thought to apply not only to the packing of sand or people but also to the phenomenon where atoms and molecules form solids.

An international joint research team consisting of Assistant Professor Hideyuki Mizuno of the Graduate School of Arts and Sciences at the University of Tokyo, Assistant Professor Tatsuya Mori of the Department of Materials Science at University of Tsukuba, Professor Emi Minamitani of the Institute of Scientific and Industrial Research at the University of Osaka, and Associate Professor Giacomo Baldi of the University of Trento, Italy, has demonstrated that the origin of the stiffness and brittleness of window glass can be explained by the physics of "sand packing (jamming transition)." The findings were published in PNAS.

The research team precisely reproduced silica glass using molecular dynamics simulations and analyzed its internal network structure in detail. They revealed that the Si-O covalent bond network is in an isostatic state, where the degrees of freedom and the number of constraints (number of bonds) are exactly balanced.

This network lies at the boundary between stability and instability. Considering the covalent bonds alone, it is in a critical state where rigidity is exactly zero. However, in actual silica glass, interactions such as van der Waals forces and Coulomb forces are also at work. These weak interactions stabilize the network and impart finite rigidity.

Therefore, the combination of a critical network structure and stabilization by weak interactions is thought to give rise to both the stiffness and brittleness of window glass. This isostaticity manifests clearly not only in rigidity but also in atomic vibrational excitations.

In silica glass, the occurrence of excess vibrational excitations beyond what is predicted by the Debye theory, the standard theory of solids, has been repeatedly observed through light scattering, inelastic X-ray scattering, and inelastic neutron scattering.

The research team clarified that because silica glass possesses an isostatic network at the boundary between stability and instability, excess soft vibrational excitations occur. This demonstrated that the theoretical framework cultivated in the physics of the jamming transition, observational facts obtained through scattering experiments, and results of computer simulations can be consistently understood under a single, unified picture.

In the future, this work is expected to develop into new methods for designing glass materials from the perspective of isostaticity.

Journal Information
Publication: PNAS
Title: Boson peak in covalent network glasses: Isostaticity and marginal stability
DOI: 10.1073/pnas.2528998123