Scattering of elastic waves by periodic arrays of spherical bodies

We develop a formalism for the calculation of the frequency band structure of a phononic crystal consisting of non-overlapping elastic spheres, characterized by Lam\'e coefficients which may be complex and frequency dependent, arranged periodically in a host medium with different mass density and Lam\'e coefficients. We view the crystal as a sequence of planes of spheres, parallel to and having the two dimensional periodicity of a given crystallographic plane, and obtain the complex band structure of the infinite crystal associated with this plane. The method allows one to calculate, also, the transmission, reflection, and absorption coefficients for an elastic wave (longitudinal or transverse) incident, at any angle, on a slab of the crystal of finite thickness. We demonstrate the efficiency of the method by applying it to a specific example.Comment: 19 pages, 5 figures, Phys. Rev. B (in press

Electronic Energies of Interaction of Point Defects with Interfaces and Grain Boundaries

The electronic energies of interaction of a point defect with interfaces and grain boundaries are calculated, as a function of the distance x$\text{}_{03}$ between the point defect and the corresponding planar defect. These interaction energies are shown to have the same type of oscillations as the corresponding local electronic densities. Therefore the electronic interactions more significantly affect the energy of segregation of point defects towards interfaces when x$\text{}_{03}$ is in the near vicinity of these interfaces, while at large distances the contribution of elastic interactions can dominate

Experimental evidence of zero-angle refraction and acoustic wave-phase control in a two-dimensional solid/solid phononic crystal

The square symmetry of the equifrequency contour of longitudinal waves in a solid/solid two-dimensional phononic crystal (PC) is shown through numerical calculations and experiments to lead to peculiar propagation phenomena. A slab of steel/epoxy PC immersed in water refracts incident longitudinal waves by an angle of zero degrees. The waves propagate along the shortest path between the slab faces. This characteristic enables the superposition within the same volume of the PC of waves with different incidence angles. Two incident waves with symmetrical incident angles can interfere constructively or destructively inside the PC depending on their initial phase difference. This phase difference is shown to enable control of wave propagation through the PC

Band gaps in phoXonic silicon crystal slab

International audienc

Locally Resonant Structures for Low Frequency Surface Acoustic Band Gap Applications

International audienc