Ultrasonic investigation of the ferroelectric transition region in KH2PO4

The velocity and attenuation of 15-MHz ultrasonic shear waves have been investigated as a function of the temperature and the electric field applied along the polar axis of potassium dihydrogen phosphate single crystals. These data are analyzed to give the free dielectric susceptibility chi(x) and the constant-stress polarization relaxation time r(x). The chi(x) values are in fairly good agreement both above and below T-c with the predictions of the Silsbee-Uehling-Schmidt model. However, the tau(x) values show a temperature dependence which cannot be readily interpreted in terms of the Silsbee-Uehling-Schmidt model. Comparison with comparable data for KD2PO4 strongly suggests that proton tunneling plays an important role in KH2PO4.