Abstract
The purpose of this work is to construct an improved theory to account for the low-temperature dielectric properties of KCl crystals containing substitutional impurities. The statistical mechanics of a pair of dipoles is discussed in order to derive a generalized Langevin function giving the mean moment of such a pair along the direction of an applied field. A hybrid approximation is then developed, in which the interaction of a typical pair of dipoles is treated explicitly while the remaining interactions are treated by means of a modified Onsager-Pirenne approximation. The resulting equations predict a second-order phase transition at , where is the concentration and the dipole moment of the ions. The predicted spontaneous polarization increases continuously below to reach a saturation value of . A thermodynamic analysis indicates that the asymptotic behavior of the model as is essentially in agreement with the third law, and also enables one to show that the critical temperature should be independent of the applied field.
- Received 12 January 1967
DOI:https://doi.org/10.1103/PhysRev.158.562
©1967 American Physical Society