Calibration of piezoelectric positioning actuators using a reference   voltage-to-displacement transducer based on quartz tuning forks
  We use a piezoelectric quartz tuning fork to calibrate the displacement of ceramic piezoelectric scanners which are widely employed in scanning probe microscopy. We measure the static piezoelectric response of a quartz tuning fork and find it to be highly linear, non-hysteretic and with negligible creep. These performance characteristics, close to those of an ideal transducer, make quartz transducers superior to ceramic piezoelectric actuators. Furthermore, quartz actuators in the form of a tuning fork have the advantage of yielding static displacements comparable to those of local probe microscope scanners. We use the static displacement of a quartz tuning fork as a reference to calibrate the three axis displacement of a ceramic piezoelectric scanner. Although this calibration technique is a non-traceable method, it can be more versatile than using calibration grids because it enables to characterize the linear and non-linear response of a piezoelectric scanner in a broad range of displacements, spanning from a fraction of a nanometer to hundreds of nanometers. In addition, the creep and the speed dependent piezoelectric response of ceramic scanners can be studied in detail. 
Andres Castellanos-Gomez, Carlos R. Arroyo, Nicol\'as Agra\"it and   Gabino Rubio-Bollinger
physics.ins-det cond-mat.mes-hall