Vibrational dynamics of a two-dimensional micro-granular crystal

July 27, 2017
  • Acoustics of granular crystals (ordered arrays of particles interacting via Hertzian contacts) is a rapidly growing field of research, with most experiments conducted with linear chains or arrays of large (mm to cm) spheres.
  • A few years ago we started studying acoustic waves in self-assembled monolayers of micron-sized spheres [1-4]. However, previous experiments were done on samples lacking long-range order.
  • In a recently published paper, we report the first experiment with a fully ordered microscale granular crystal consisting of a hexagonal lattice of 1.5 μm polystyrene spheres on a glass substrate coated with a thin aluminum film.
  • We excite acoustic modes of the structure by two crossed picosecond laser pulses (the period of the interference pattern defines the acoustic wavevector) and detect them via diffraction of a probe laser beam.

  • The measurements reveal rich dynamics involving three kinds of acoustic modes: low-frequency contact-based modes of the granular monolayer, high-frequency branches originating from spheroidal vibrational modes of the microspheres, and surface Rayleigh waves.
  • Dispersion of contact-based and spheroidal modes indicates that those are collective modes of the microgranular crystal controlled by particle-particle contacts.

FIG. 2. (a) Signal waveforms for three different wave vectors and (b) corresponding Fourier spectra. Peaks labeled V and R correspond to the vertical contact resonance mode and SAWs, respectively. Spheroidal modes are labeled S0-S4. (c) Measured dispersion of acoustic modes of the structure; red vertical dashed line corresponds to the BZ boundary. (d) Dispersion of low-frequency contact-based modes. Solid markers represent the predominantly vertical V mode, smaller hollow markers the horizontal-rotational modes.

  • We observe a spheroidal resonance splitting due to the symmetry breaking by the substrate as well as an avoided crossing between the Rayleigh and spheroidal modes.
  • The observations are in agreement with theoretical calculations, with the whole range of phenomena described by two parameters, i.e., particle-substrate and particle-particle contact spring constants.

FIG. 3. (a) Spectral peaks of the spheroidal mode S2 for three wave vectors, showing the mode splitting which becomes apparent at large wave vectors. (b) Dispersion of the S2 mode revealing the mode splitting and the avoided crossing with the Rayleigh surface wave (blue dashed line).



  1. N. Boechler, J. K. Eliason, A. Kumar, A. A. Maznev, K. A. Nelson, and N. Fang, “Interaction of a Contact Resonance of Microspheres with Surface Acoustic Waves,” Phys. Rev. Lett. 111, 036103 (2013).
  2. M. Hiraiwa, M. Abi Ghanem, S. P. Wallen, A. Khanolkar, A. A. Maznev, and N. Boechler, “Complex contact-based dynamics of microsphere monolayers revealed by resonant attenuation of surface acoustic waves,” Phys. Rev. Lett. 116, 198001 (2016).
  3. J. K. Eliason, A. Vega-Flick, M. Hiraiwa, A. Khanolkar, T. Gan, N. Boechler, N. Fang, K. A. Nelson, and A. A. Maznev, “Resonant attenuation of surface acoustic waves by a disordered monolayer of microspheres,” Appl. Phys. Lett. 108, 061907 (2016).