Castellanos-Gomez A, Agraït N, Rubio-Bollinger G
Departamento de Física de la Materia Condensada (C-III), Universidad Autónoma de Madrid, Madrid, Spain.
Nanotechnology. 2009 May 27;20(21):215502. doi: 10.1088/0957-4484/20/21/215502. Epub 2009 May 5.
We have performed an experimental characterization of the dynamics of oscillating quartz tuning forks which are being increasingly used in scanning probe microscopy as force sensors. We show that tuning forks can be described as a system of coupled oscillators. Nevertheless, this description requires knowledge of the elastic coupling constant between the prongs of the tuning fork, which has not yet been measured. Therefore, tuning forks have usually been described within the single oscillator or the weakly coupled oscillators approximation that neglects the coupling between the prongs. We propose three different procedures to measure the elastic coupling constant: an opto-mechanical method, a variation of the Cleveland method and a thermal noise based method. We find that the coupling between the quartz tuning fork prongs has a strong influence on the dynamics and the measured motion is in remarkable agreement with a simple model of coupled harmonic oscillators. The precise determination of the elastic coupling between the prongs of a tuning fork allows us to obtain a quantitative relation between the resonance frequency shift and the force gradient acting at the free end of a tuning fork prong.
我们对振荡石英音叉的动力学特性进行了实验表征，这种音叉在扫描探针显微镜中作为力传感器的应用越来越广泛。我们表明，音叉可被描述为一个耦合振荡器系统。然而，这种描述需要了解音叉叉臂之间的弹性耦合常数，而该常数尚未被测量。因此，音叉通常在忽略叉臂之间耦合的单振荡器或弱耦合振荡器近似下进行描述。我们提出了三种不同的方法来测量弹性耦合常数：一种光机械方法、克利夫兰方法的一种变体以及一种基于热噪声的方法。我们发现，石英音叉叉臂之间的耦合对动力学有很大影响，并且测量到的运动与耦合谐波振荡器的简单模型非常吻合。精确确定音叉叉臂之间的弹性耦合，使我们能够获得共振频率偏移与作用在音叉叉臂自由端的力梯度之间的定量关系。
