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 O 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 K1-xNaxTaO3 and KTa1-yNbyO3, 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 Tc (x-xc)12, as opposed to Tc (x-xc) for the classical case. Second, the inverse dielectric constant varies with temperature as -1 T2 for the quantum-mechanical case, instead of -1T. Finally, the distribution of transition temperatures in a given macroscopic sample with a Gaussian impurity concentration distribution is p(Tc)Tcexp(-Tc4) 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. © 1979 The American Physical Society.