On the ferroelectric behaviour of potassium dihydrogen phosphate

Abstract
In this paper we consider the properties of potassium dihydrogen phosphate (K D P). In the introduction we compare the behaviour of K D P with that of some isomorphous crystals. From this comparison we conclude that the hydrogen bonds play a deciding part in the phase transition, although the magnitude of the polarization seems to be determined by the heavy ions. As a first theoretical approach we apply the first Bethe approximation to an Ising model, based on the hydrogen lattice of K D P. This model contains an additional configurational energy U as compared to Slater’s work. His results are obtained in the limit as U → ∞. We find a phase transition for all positive values of U , but according to whether U is larger than or smaller than a certain value, which is about 3/2 times Slater’s energy parameter, the transition is a first-or a second-order one. After that we consider an ionic model of K D P which we treat as a polar hydrogen lattice with interpenetrating ionic potassium, phosphorus, and oxygen lattices. As far as possible the detailed behaviour of the constituent atoms is taken into account. The rigidity of the hydrogen bond, the effect of the configurational energy of the hydrogen ions about the phosphate tetrahedra, and the displacements of the K, P and O ions from their lattic sites all appear explicitly in the calculations. It is not found possible to choose our parameters in such a way that we can fit the complete temperature dependence of the susceptibility. The combination of a hydrogen triggering mechanism and the neutron diffraction data imply effective changes of opposite sign for the K and P ions, in disagreement with the expected properties of electro-positive atoms. On the other hand, however, our model gives not only a qualitative account of the similarity of the ferroelectric properties of K D P and its isomorphs, but also of the difference in the temperature independent part of the susceptibility in the ferroelectric and paraelectric phases of K D P, respectively.

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