Multiferroic based 2D phononic crystals: Band structure and wave propagations

In the present work the acoustic band structure of a two-dimensional phononic crystal containing an organic ferroelectric (PVDF- polyvinylidene fluoride) and muliferroic material (LiVCuO4) were investigated by the plane-wave-expansion method. A two-dimensional PC with square lattices composed of LiVCuO4 cylindrical rods embedded in the PVDF matrix are studied to find the existence of stop bands for the waves of certain energy. This phononic bandgap - forbidden frequency range - allows sound to be controlled in many useful ways in structures that can act as sonic filters, waveguides or resonant cavities. Phononic band diagram omega = omega(k) for a 2D PC, in which non-dimensional frequencies omega a/2 pi c (c-velocity of wave) were plotted versus the wavevector k along the Gamma-X-M-Gamma path in the square Brillouin zone show four stop bands in the frequency range 0.01-8.0 kHz. The ferroelectric properties of PVDF and unusual properties of multiferroic LiVCuO4 give us the ability to control the wave propagation through the PC in over a wide frequency range.