中文摘要：

用超元胞的平面波展开法，计算了存在点缺陷的二维水／水银声子晶体的能带结构和压强分布。通过改变5×5超元胞中心圆柱体的半径而引入缺陷，发现缺陷填充率（Fd）小于或大于正常柱体填充率（F0）一定数值时（如当R=0．35，Fd〈0．10或Fd〉0．50），都将出现缺陷态，且凡对缺陷态的频率有重要影响。还比较了当Fd=0．03和Fd=0．90两种情况下缺陷态的压强分布，计算结果表明压强分布均具有局域性，n的大小对单模缺陷态的局域程度有影响，而对二重简并模无显著影响。

英文摘要：

Using the super-cell plane wave expansion method, we calculate the band structure and pressure distribution of two-dimensional （2D） water/mercury phononic crystals with point defects. The point defect is created by changing the radius of the center cylinder in the 5 × 5 super-cell. It is found that defect states appear when the defect filling fraction （Fd） is larger or less than the regular filling fraction （ F0 ） by a certain value （ e. g. when F0 =0.35, Fd 〈0.10 or Fd 〉0.50）, and the Fd affects the frequency of the defect states significantly. The pressure distributions of the defect states at Fd = 0.03 and Fd = 0.90 are compared. The computed results show that the pressure distributions are all localized around the defects, and the degree of localization is influenced by the Fd for the single defect modes, but not obviously for the double degenerate modes.