双旋Y切石英振子模式交替性的分析与研讨

Analysis and Discussing on Modes Interchange of Dual Rotated Y-Cut Quartz Vibrator

本文通过描述固体中弹性声波的christoffel(克里斯托费尔)方程,分析了在石英晶体中,由于其对称性的限制而显示出各向异性的切角范围0≤φ_3≤60°,0≤φ_1≤90°(或0≤φ_3≤30°,-90°≤φ_1≤90°)内,双旋Y切石英振子T模(厚度模)的特性。其中着重分析了30°≤φ_3≤60°,24°≤φ_1≤32°(或0≤φ_3≤30°,-32°≤φ_1≤-24°)这一区域内的T模特性,证实了美国36届频率控制年会报道的“当φ_3在0～10°之间时,存在着b、c摸的交替点”的论述。并得出了两个特定的交替点切角(φ_3°,φ_1°),这在我们所见到的资料中尚未见报道。这些结果对掌握振模的本质,提高石英振子的性能等方面是有实际意义的。

Using Christoffel Equation describng elastic Sound wave, the authors analyzed characteristics of dual rotated Y-Cut quartz vibrator's T mode (thickness mode) of quartz crystal inside its rotate angle range 0≤φ_3≤60°,0≤90°(or 0≤φ_3≤30°,—90°≤φ_1≤90°)where it shows anisotropy because restricted by its symmetry in this paper. Analysis of T mode characteristics for30°≤φ_3≤60°,24°≤φ_1≤32°(or 0≤φ_3≤30°, —32°≤φ_1≤—24°)is emphasized. The discussion on 36th AFCS that'there exist b,c modes interchanging points when φ_3 is between 0 and 10°is verified, and two specific cutting angles (φ_3°φ_1°)were present. These have not been reported in available literature. The results are of practical significance in mastering the nature of vibrating mode, improving performance of quartz crystal vibrator.