Theory of Ferroelectric Phase Transition in KH2PO4Type Crystals. I

To explain the large isotope effect on the transition temperature in KH2P04, the tunnel ing motion of the protons in hydrogen bonds is considered and a theory of the phase transi tion is developed under the assumption that the ferroelectric behavior of this substance is due to cooperation of the ionic displacements, the interactions between ions and protons and the tunneling motion of protons. The relation between the present theory and the Slater model or the Blinc model is discussed. § I. Introduction In spite of the considerable amount of investigation made from the theo retical as well as the experimental side, the microscopic mechanism of the phase transition in KH2P04 and isomorphous crystals does not seem to be clearly un derstood. If . we classify the ferroelectric substances roughly into two groups, displacive and order-disorder type ferroelectrics, then KH2P04 will certainly belong to the latter group. However, the experimental data accumulated so far do not really give us a definite molecular picture of the phase transition, but sometimes reveals obvious inconsistencies among observed quantities. The main object of the present paper and a forthcoming one is to organize the somewhat divergent observed facts from the theoretical point of view and to suggest some experiments which might be helpful in attaining a full understanding of the phenomena. The crystal structure of KH2P04 (which will be abbreviated as KDP here after) is the so-called tetragonal diamond type. A characteristic feature of this structure is the existence of hydrogen bonds connecting two P04 tetrahedra, which run almost perpendicularly to the direction of the ferroelectric c axis. In the ferroelectric phase, the magnitude of the saturated polarization Ps is well accounted for by making use of the observed values for the displacements of ions K+I, p+ 5 and o- 2 along the c axis relative to their symmetric positions. 2 ),s) Therefore the hydrogen bonds do not contribute any appreciable dipole moments to the saturated polarization, and hence the essential unit of the dielectric prop erties in this crystal is the dipole moment of the complex [K-P04] as shown in Fig. 1. If KDP is of an " order-disorder " type of ferroelectric, that is, if the phase transition is caused by order-disorder arrangements of the dipole moments, the two configurations of the complex [K-P04] denoted as (A) and