A study of the band structure in two-dimensional phononic crystals based on plane-wave algorithm

In this paper, the calculating course of the plane-wave algorithm is introduced to solve the sound wave equation and the band structure of phononic crystals. The phononic crystals of two-dimensional binary liquid systems are studied. In conclusion, the CCl4/mercury system is easier to obtain the band-gap than the mercury/CCl4 system. With the increase of the filling fraction (f), the width of the band-gap becomes wider and then narrower. The widest band-gap of CCl4/mercury system appears at f = 0.229, where DeltaOmega(max) = 0.549. While the width of the band-gap in mercury/CCl4 system increases consistently with the filling fraction, when f = 0.554, DeltaOmega(max) = 0.515. Under the same filling fraction, the variation of the cylinder diameter and lattice constant does not affect the band-gap width DeltaOmega.