Description
The vibrational density of states (VDOS), g(ω), is a fundamental property governing the specific heat and thermal transport of materials. For more than a century, the Debye model has provided the foundation for understanding lattice vibrations in bulk crystalline solids, predicting a low-energy scaling of g(ω) ∝ ω².
In liquids, however, stable phonon modes are replaced by instantaneous normal modes (INMs) arising from intrinsically anharmonic atomic interactions. Unlike the Debye behaviour, theory predicts a linear low-energy scaling, g(ω) ∝ ω, for liquids. Using inelastic neutron scattering, we experimentally confirmed this prediction in diverse liquid systems, including water, liquid metals, and polymer liquids, providing direct evidence for a universal vibrational law beyond the Debye model [1,2].
A different departure from Debye behaviour emerges under nanoscale confinement. Measurements of the VDOS of amorphous ice confined within graphene oxide membranes reveal a crossover from the Debye ω² scaling to an ω³ dependence at low energies. Molecular dynamics simulations reproduce the experimental observations, while theoretical analysis attributes the ω³ scaling to geometric constraints on the momentum phase space imposed by confinement along one spatial dimension [3].
These results demonstrate that the low-energy vibrational spectrum is governed not only by atomic interactions but also by phase state and dimensionality. Together, they establish universal scaling laws that extend the classical Debye framework and provide new insights into the vibrational dynamics of condensed matter.
[1] A. Zaccone and M. Baggioli, Proc. Natl. Acad. Sci, USA 118, e2022303118 (2021).
[2] C. Stamper et al., J. Phys. Chem. Lett. 13, 3105 (2022).
[3] Y. Yu, et. al, Nature Communications, 13, 3649, (2022).
| I am the presenting author | Yes |
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