The boson peak (BP) is an excess in the phonon density of states compared to the Debye model that appears in almost all glasses. It has been repeatedly measured in the bulk by a variety of optical, neutron, and thermal measurements but its origin is still highly debated. Here we present for the first time measurements which clearly show evidence of a dispersionless phonon band on the surface which is identified as the BP. Recently a BP was predicted in a molecular dynamics study of the amorphous silica surface [1].
Experimental investigation of the surface dynamics is difficult in general and even more challenging in case of insulator surfaces. However, scattering experiments with neutral helium atoms upon surfaces have proven to be very well suited for studying surface dynamics. The technique is strictly surface sensitive with no penetration into the bulk and the energy of the probing He-atoms is in the range of the lowest-energy phonons, thus especially sensitive to these modes. In the course of the experiment time-of-flight (TOF) data of scattered He-particles were recorded. A typical TOF record looks similar to inelastic neutron scattering bulk data reported by Dove et al. [2]. A dispersionless mode was observed in our experiments at constant beam energy with varying incident angles, i.e., corresponding to different parallel momentum transfer. The mode is at about 4 meV (1 THz = 4.136 meV) in good agreement with the theoretical predictions. As conclusive evidence that the observed mode is really a surface BP we extracted the surface phonon spectral density from the TOF spectra with the use of straight-forward theoretical models [3]. The interaction of the impinging He-atoms with the surface is in the single-phonon regime at the surface temperatures used in the experiments, which is a precondition for applying the theoretical model. At surface temperatures below 170 K the measured Debye-Waller exponent is quite small and the derived mean-square displacement is in reasonable accord with mean-square bulk displacement values obtained by inelastic neutron scattering.
[1] C. Wang, Y. Tamai, and N. Kuzuu, J. of Non-Cryst. Solids 321, 204 (2003)
[2] M. T. Dove et al., Phys. Rev. Lett. 78, 1070 (1997)
[3] J. R. Manson, Phys. Rev. B 43, 6924 (1991) |