A Study on the F-T Characteristics of Thickness Modes of Doubly Rotated Y-cut Piezoelectric Quartz Crystal

This study describes a method for analyzing the F-T characteristics of the thickness modes of a doubly rotated Y-cut anisotropic quartz crystal, including a-, b-, and c-modes by using the Christoffel equation that describes sound waves in solids. With this method, the F-T characteristics of the independent rotational angles 3/1 can be predicted. Based on the predicted F-T characteristic curve, the potential application of some cut-types as sensors is discussed. Combined with other methods, such as crystal force-frequency characteristic analysis, this method is expected to provide a research platform for studying new cut-types for various applications, such as frequency control and physical, chemical, and biological sensors, etc.