Phonon spectrum of compact ceramics: two‐dimensional ordered model

Abstract

The low-frequency range of the phonon spectrum of an ordered two-dimensional composite, modeling compact nanoceramics is theoretically investigated by the finite-difference time-domain method. The necessary conditions for the complete gap to arise have been determined.

Acoustic transmission in slabs of compacted composites

“…For a phonon system with two phonon polarizations the lower boundary of the forbidden gap is determined by the largest of the two (for longitudinal and transverse phonons) resonance frequencies, and the upper one depends on the lesser resonance frequency and the volume fraction of the second constituent (Eqs. (3)-(5) from [6]). Figure 2 presents the dependence of the position of the upper and lower boundaries of the forbidden gap in the phonon spectrum of a periodic composite on the grain radius R (on the plasticizer volume fraction f) subject to the condition that the areas of grains 1 and 2 are equal.…”

“…The original system is a 2D periodic structure consisting of two types of grains (1,2 in Fig. 1) of an acoustically hard material separated by a loose interface region of thickness d. In [6] the phonon spectra of such model systems were studied in relation to the grains and interface materials and the geometric parameters by the finite-difference time-domain (FDTD) method. The numerical results were interpreted on the basis of the analytical results of papers [7,8] which studied, in a scalar model, the phonon scattering at spherical shells modeling the interface boundaries in the elastic limit.…”

“…As a basic model we shall use the infinite ordered ceramics model from [6]. The original system is a 2D periodic structure consisting of two types of grains (1,2 in Fig.…”

“…Composites of precisely this composition will be considered in the present paper. In paper [6] the phonon spectrum of an infinite periodic composite was calculated by the FDTD method according to the scheme from [9] which cannot be used in the case of finite systems or systems disordered with respect to the grain size.…”

“…a frequency region where acoustic waves cannot propagate in the material. In a previous paper [6] we have defined the necessary conditions for a gap to arise in the phonon spectrum of an infinite ordered composite modeling compacted ceramics. The present work deals with a more realistic model, in which the phonon spectra of finite systems (slabs) are investigated, and the size distribution of the compact grains is taken into account.…”