Report on the piezoelectric frequency effect in quartz and its   possibility in other piezoelectric materials
  We report the eigen-frequency shift induced by an applied voltage on quartz material. The samples are in the form of commercial 32 KHz quartz tuning forks used in watches. Three vibration modes are studied: one prong oscillates, two prongs oscillate in the same and opposite directions. They all show a parabolic dependence of the eigen-frequency shift on the bias voltage applied across the fork, which is explained owing to the voltage-induced internal stress that varies as the fork oscillates. Thus, this piezoelectric frequency effect is possible to exist in all piezoelectric materials. The average coefficient of the piezoelectric frequency effect is as low as several hundred nano-Hz per millivolt, implying that the most precise (nano-Hz) yet fast-response voltage-controlled oscillators and phase-locked loops can be built. 
Yubin Hou and Qingyou Lu
physics.ins-det