On the phase transition in KH₂PO₄

Abstract

The dynamical theory of the phase transition in KDP recently developed by Kobayashi (J. Phys. Soc. Japan24 (1968), 497) is modified by taking into account the interaction of the a-polarized transverse acoustic phonon both with the proton tunnelling mode and the transverse optic phonon polarized along thec-axis. The coupled modes of this three-component system are found in the paraelectric phase within the framework of the RPA approximation. The expressions for the sound velocity in the short-circuited (E = 0) crystal and the static susceptibility at constant stress are derived and well known thermodynamic formulae are obtained if the re-normalized elastic constantc ^P₆₆ and the piezoelectric constanta ₃₆ are introduced. It is shown that these so-called “true” constants should in principle exhibit anomalies near the proton ordering temperature. Also the role of the depolarizing energy in the phase transition of KDP is discussed. The shift of the phase transition temperature of a small insulated particle of KDP is shown to be only a few degrees. Finally, it is explained why the domain structure of a short-circuited or insulated crystal should be essentially the same.