Phonons in porous media at intermediate frequencies

Abstract

PACS 43.35.Yb, 63.50.+x Using ultrasonic techniques, the phonon diffusion coefficient and density of states have been measured at intermediate frequencies in a porous solid network of sintered glass beads. A transition to a very strong scattering regime is observed, whereupon the diffusion coefficient becomes independent of frequency. Near crossover, the density of states is enhanced and exhibits a broad maximum. These data are in good overall agreement with a lattice-based percolation model, and give additional insight into the effects of strong scattering on phonon transport in disorderd media. 1 Introduction Porous media form an interesting class of mesoscopic materials, whose structure at length scales between atomic dimensions and bulk dramatically influence their phonon properties. Examples include packed powders, porous sintered particle networks, aerogels and foams [1][2][3][4][5]. In the low frequency, long wavelength limit, the medium appears uniform and the phonons propagate ballistically, but with a reduced velocity that reflects the weakening of the structure due to its porosity. By contrast, at intermediate frequencies where the wavelength is comparable with the pore size, the scattering can become very strong and the nature of wave propagation is substantially modified. Thus, wave propagation is expected to become diffusive, and the phonons may even become localized. In materials such as sinters, where the basic building block of the structure is much larger than atomic dimensions, a third high frequency regime exists at wavelengths less than the particle size, where phonons propagate freely inside the particles and their character is similar to uniform bulk materials.In this paper, we study the intermediate frequency regime, using ultrasonic techniques to investigate the vibrational modes of a model porous material formed from sintered networks of spherical glass particles. We show that very strong scattering is indeed observed, and directly measure the phonon diffusion coefficient over more than a decade in frequency. The transition to the strong scattering regime is marked by the onset of a plateau in the diffusion coefficient, which is found to be remarkably small. To obtain complementary information on the nature of the vibrational modes of these sintered networks, we also investigate the density of states in and above the crossover region using a novel mode counting technique [5]. Insight into these experimental results is provided by numerical simulations of phonon transport in a model 3D lattice percolation system [6,7], originally performed to elucidate the thermal conductivity plateau in glasses, and by the extensive theoretical work on vibrational localization and transport in random media stimulated by the pioneering ideas of Alexander and Orbach [8].

Attenuation of shear sound waves in jammed solids

“…The characteristic frequency ω * heralds a spectral regime of strong scattering characterized by a small and frequency independent energy diffusivity. This feature is also seen in experiments carried out on glasses as well as porous media [22,23].…”

A statistical approach to direct density of states measurements in disordered systems

“…It is reasonable to assume that mode detectability is a random process, based on the observed character of modal responses to changes in the transducer contact points and the measured speckle statistics in similar samples, which show that the wave fields are Gaussian random variables. 20 Therefore, the binomial distribution should be used as a parent distribution for the number of modes observed. 28 The detection probability and total number of modes can then be written in terms of the measured mean = np and standard deviation = ͱ np͑1− p͒:…”

“…Ultrasonics has played an important role in studying these strongly scattering disordered systems. [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] Initial investigations focused on the applicability of the diffusion approximation to describe the transport of energy by multiply scattered waves in pulsed experiments, where a time-dependent "coda" is observed after the initial arrivals due to ballistic transport. 6,7 Even though the diffusion approximation neglects all phase information, it gives a remarkably accurate description of wave transport under a wide variety of experimental conditions, including transmission and reflection ͑coherent backscattering͒ experiments.…”

“…[20][21][22][23] In such experiments, samples are excited using a short, broadband impulse ͑either from a piezoelectric transducer or by a physical impact͒, and the resulting vibration is measured using a transducer in contact with the sample. Since the number of modes increases with system size, the samples must be sufficiently small to enable the individual modes of vibration to be resolved and counted in the Fourier transform of the received signal, yielding the density of states.…”

Ultrasonic investigation of phonon localization in a disordered three-dimensional "mesoglass"

“…Mesoscopic materials, which have internal structures at length scales between atomic dimensions and bulk, form another important class of disordered systems in which very strong scattering may occur, with potentially dramatic changes to phonon transport. Examples of such materials include packed powders, aerogels, sintered particle networks and foams [3][4][5][6][7]. The range of internal length scales in such mesostructures can vary enormously, from nanometers to millimeters, so that access to the intermediate frequency regime, in which strong scattering is expected, can be tuned to facilitate measurements of the phonon properties.…”