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Boson peak in silica glass and physics of the jamming
Prof. Hideyuki Mizuno
University of Tokyo, Japan
In disordered solids such as glasses, in addition to the phonon excitations observed in ordered crystals, one also observes nonphononic excitations, including soft localized vibrations. The vibrational excess beyond the phonons is known as the boson peak, and it has been observed universally across many types of glasses [1]. For example, in covalent glasses, extensive neutron and inelastic X-ray scattering experiments have repeatedly reported the boson peak. The boson peak is closely linked to glass properties spanning thermal and mechanical behavior—such as excess specific heat, low thermal conductivity, nonaffine elasticity, and local plasticity—so understanding it is fundamentally important for glass science.
A variety of theories and ideas have been proposed to explain the boson peak in glasses. Among the most influential is isostaticity [2], which explains rigidity and vibrational states by counting the constraints that restrict the degrees of freedom of the constituent atoms or molecules. Because isostaticity interfaces naturally with network systems, its scope has extended beyond covalent glasses to the physics of jamming in particulate matter [3], leading to new concepts such as rigidity percolation and marginal stability in disordered systems.
In this work, we explain the boson peak of silica glass—a representative covalent network glass—by leveraging isostaticity and the related concept of marginal stability developed in the context of jamming [4]. First, focusing only on the covalent bonding in silica, we show that the system is exactly isostatic, with the number of constraints matching the number of degrees of freedom, which gives rise to floppy modes. Next, upon adding van der Waals and Coulomb interactions, exact isostaticity is broken and the system becomes marginally stable, producing soft localized vibrational modes. Finally, we clarify how isostaticity and marginal stability are reflected in the dynamical structure factor measured in scattering experiments, and how they can be observed.
[1] T. Nakayama, Boson peak and terahertz frequency dynamics of vitreous silica , Reports on Progress in Physics 65, 1195 (2002).[2] M. F. Thorpe, Continuous deformations in random networks , Journal of Non-Crystalline Solids, 57, 355 (1983).
[3] M. Wyart, On the rigidity of amorphous solids , Annales De Physique 30, 1 (2005).
[4] H. Mizuno, T. Mori, G. Baldi, and E. Minamitani, Boson peak in silica glass: Isostaticity and marginal stability, under review.
Acknowledgements: This work was supported by JSPS KAKENHI Grant Numbers 22K03543, 23H04495, 25H01519.
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