Center for Nanotechnology (CeNTech) and Institute of Physics, University of Münster (WWU), Heisenbergstrasse 1, 48149 Münster, Germany ; Institute of Applied Physics (IAP), Justus-Liebig-University Gießen, Germany.
Center for Nanotechnology (CeNTech) and Institute of Physics, University of Münster (WWU), Heisenbergstrasse 1, 48149 Münster, Germany.
Beilstein J Nanotechnol. 2014 Apr 23;5:507-16. doi: 10.3762/bjnano.5.59. eCollection 2014.
Quartz tuning forks are being increasingly employed as sensors in non-contact atomic force microscopy especially in the "qPlus" design. In this study a new and easily applicable setup has been used to determine the static spring constant at several positions along the prong of the tuning fork. The results show a significant deviation from values calculated with the beam formula. In order to understand this discrepancy the complete sensor set-up has been digitally rebuilt and analyzed by using finite element method simulations. These simulations provide a detailed view of the strain/stress distribution inside the tuning fork. The simulations show quantitative agreement with the beam formula if the beam origin is shifted to the position of zero stress onset inside the tuning fork base and torsional effects are also included. We further found significant discrepancies between experimental calibration values and predictions from the shifted beam formula, which are related to a large variance in tip misalignment during the tuning fork assembling process.
石英音叉作为非接触原子力显微镜中的传感器越来越受到重视，尤其是在“qPlus”设计中。在这项研究中，使用了一种新的、易于应用的设置，以确定音叉叉齿上几个位置的静态弹簧常数。结果显示，与用梁公式计算的值有显著偏差。为了理解这种差异，我们使用有限元方法模拟对完整的传感器设置进行了数字重建和分析。这些模拟提供了音叉内部应变/应力分布的详细视图。如果将梁原点移动到音叉基座内的零应力起始位置，并包括扭转效应，模拟结果与梁公式具有定量一致性。我们还发现实验校准值与偏移梁公式的预测值之间存在显著差异，这与音叉装配过程中尖端不对齐的较大变化有关。
