Rayleigh surface phonons and other characteristic terahertz dynamics in diamond nanocrystals

The free boundaries of nanocrystals introduce new surface wave solutions, analogous to the seismic waves on Earth, yet the implications of these surface waves on nanocrystals have remained largely unexplored. Here, we use atomistic molecular dynamics simulations and experimental neutron spectroscopy to elucidate mechanical terahertz-scale features in diamond nanocrystals. Our key insight is the observation and assignment of thermally induced Rayleigh surface phonons, which have low group velocity and amplitude that decays exponentially away from the surface. These states are shown to result in a deviation from the standard three-dimensional form of Debye's law, giving a characteristic linear scaling of the low-energy vibrational density of states in nanocrystals. Normalized to the radius, the surface displacement ratio in diamond nanocrystals exceeds that of the largest recorded earthquakes by a factor of 105±1. We explain how these Rayleigh waves coexist with other distinctive features, including confined lattice phonons, the acoustic gap, and Lamb modes, thereby offering a comprehensive framework for the vibrational dynamics of nanocrystals which can be leveraged for quantum sensing, thermal management, and catalysis. The mechanical vibrations of atoms in nano-sized crystals vary greatly from bulk crystals due to their large surface-area-to-volume ratios and confinement effects. This work characterizes the terahertz vibrations of nanodiamonds, revealing the existence of Rayleigh surface phonons, analogous to surface earthquakes. The unique vibrations observed in nanodiamond are likely universal among nanocrystals and critical for understanding their exceptional physical properties.