Vibrational Properties Beyond Debye Model

The vibrational density of states (VDOS, denoted g(ω)) is a fundamental property of solid materials, determining the specific heat and thermal transport. For over 100 years, the Debye model has served the fundamental law for our understanding of the vibrational properties of bulk solid materials which show a low energy relationship of g(ω) ∝ ω², where ω is the frequency and g(ω) is the number of modes within an energy/frequency interval. Upon the transition from solid to liquid phase, the conventional stable phonon vibration modes in solid phase are replaced by more complex instable vibrational modes, called instantaneous normal modes (INM) at the liquid state. The INMs are consequences of the intrinsic anharmonic interaction potentials among the atoms in liquid phase. Due to the complicated potential landscape, it has been very difficult to analytically describe the vibrational phonon density of states (VDOS) of liquids until very recently. Zaccone and Baggioli [1] have recently developed a theoretic model based on overdamped Langevin liquid dynamics. Distinct from the Debye law, g(ω) ∝ ω², for solids, the model for liquids reveals a linear relationship, g(ω) ∝ ω, in the low-energy region. With inelastic neutron scattering, we confirmed this model on real liquid systems including water, liquid metal, and polymer liquids. We have applied this model and extracted the effective relaxation rate for the short time dynamics for these liquids [2].



[1]. A. Zaccone and M. Baggioli, Proc. Natl. Acad. Sci, USA 118, e2022303118 (2021).

[2]. C. Stamper, D. Cortie, Z. Yue, X. L. Wang and D. H. Yu, J. Phys. Chem. Lett. 13, 3105 (2022).