Abstract
A reliable quadric formula for frequency turn-over temperatures versus electrode film thicknesses in quarts crystal tuning forks was proposed and the coefficients were determined by the least squares method using the experimental results of 32-kHz and 76-kHz tuning forks. And a new analysis for the Young's modulus of the electrode film was also proposed using a bar flexural vibration frequency equation. It was found that the mass loading theory could not explain the frequency turn-over temperature characteristics versus electrode film thicknesses for quartz crystal tuning forks, while this theory could well explain the experimental results of tuning forks.