Quantum ferroelectricity in K/sub 1-x/Na/sub x/TaO3 and KTa/sub 1-y/Nb/sub y/O3

The effect known as ferroelectricity arises when forces between polarizable ions in a solid produce a spontaneous displacement of these ions which results in a lattice polarization below some characteristic (Curie) temperature. Fluctuations in this polarization may be thermally induced as in the case of classical ferroelectrics, or if the Curie temperature is near 0 K, the fluctuations can be due to quantum-mechanical zero-point motion. The term ''quantum ferroelectric'' is applied to those systems where fluctuations in the polarization result from the zero-point motion. Experimental determinations of variations in the dielectric constant, spontaneous polarization, and elastic compliance as a function of temperature and impurity concentration are reported for K/sub 1-x/Na/sub x/TaO3 and KTa/sub 1-y/Nb/sub y/O3, and these results show that the physical properties of quantum ferroelectrics differ from those of classical ferroelectrics in the following ways: First, for a quantum ferroelectric, the transition temperature depends on impurity concentration (i.e., on an effective order parameter) as T/sub c/ proportional (x-x/sub c/)/sup 1/2/, as opposed to T/sub c/ proportional (x-x/sub c/) for the classical case. Second, the inverse dielectric constant varies with temperature as epsilon-1 proportional T2 for the quantum-mechanical case, instead of epsilon-1 proportional T. Finally, the distribution of transition temperatures in a given macroscopic sample with a Gaussian impurity concentration distribution is p (T/sub c/) proportional T/sub c/ exp(-αT/sup ts4//sub c/) for the quantum ferroelectric, as opposed to a Gaussian for the classical situation. These results are in agreement with previous theoretical predictions of some of the distinguishing characteristics of quantum ferroelectricity