School of Physics, Beihang University, Beijing 100191, China.
Fujian Engineering and Research Center of Green and Environment-Friendly Functional Footwear Materials, College of Chemical Engineering and Materials Science, Quanzhou Normal University, Quanzhou 362000, China.
Sensors (Basel). 2023 Apr 12;23(8):3923. doi: 10.3390/s23083923.
Quartz tuning forks (QTFs) are self-sensing and possess a high quality factor, allowing them to be used as probes for atomic force microscopes (AFMs) for which they offer nano-scale resolution of sample images. Since recent work has revealed that utilizing higher-order modes of QTFs can offer better resolution of AFM images and more information on samples, it is necessary to understand the relationship between the vibration characteristics of the first two symmetric eigenmodes of quartz-based probes. In this paper, a model that combines the mechanical and electrical characteristics of the first two symmetric eigenmodes of a QTF is presented. Firstly, the relationships between the resonant frequency, amplitude, and quality factor between the first two symmetric eigenmodes are theoretically derived. Then, a finite element analysis is conducted to estimate the dynamic behaviors of the analyzed QTF. Finally, experimental tests are executed to verify the validity of the proposed model. The results indicate that the proposed model can accurately describe the dynamic properties of a QTF in the first two symmetric eigenmodes either under electrical or mechanical excitation, which will provide a reference for the description of the relationship between the electrical and mechanical responses of the QTF probe in the first two symmetric eigenmodes as well as the optimization of higher modal responses of the QTF sensor.
石英音叉（QTFs）具有自感特性和高品质因数，可作为原子力显微镜（AFMs）的探针使用，从而实现对样品的纳米级分辨率成像。由于最近的研究表明，利用石英基探针的高阶模式可以提供更好的 AFM 图像分辨率和更多有关样品的信息，因此有必要了解石英基探针的前两个对称本征模的振动特性之间的关系。本文提出了一种结合石英音叉前两个对称本征模的力学和电学特性的模型。首先，从理论上推导出了前两个对称本征模之间的共振频率、振幅和品质因数之间的关系。然后，进行有限元分析以估计所分析的 QTF 的动态行为。最后，进行实验测试以验证所提出模型的有效性。结果表明，所提出的模型可以在电或机械激励下准确描述 QTF 在前两个对称本征模中的动态特性，这将为描述 QTF 探针在前两个对称本征模中的电和机械响应之间的关系以及优化 QTF 传感器的高阶模态响应提供参考。
