Can the isotopic shift in KDP be explained by tunneling only?

Abstract

The isotopic shift of the transition temperature in KDP and its isomorphous compounds has so far been related to tunneling only (1). .This interpretation requires too a high value of tunneling energy P , which leads within the framework of the molecularfield theory to serious contradictions with some other experiments (cf. below). Recent measurements (2) of the pressure dependence of the transition point indicate that the ltferroelectric" interaction between the protons is appreciably weaker than between the deuterons. It opens the possibility to attribute a large part of the isotopic shift to changes in "ferroelectric" interaction. The remainder of the shift may then be explained by means of a much smaller P , which removes the above-mentioned difficulty. The purpose of the present note is to re-estimate the influence of tunneling motion on the basis of molecular-field theory, using the results reported 1) in (2).The molecular-field theory gives the following expressions for the susceptibility in the paraelectric phase x , for the transition temperature Tc, and for the spontaneous polarization Ps at 0 K (1): 0 n P -1 4 -Q J ' Tc = arcth where q = 4 w J . Q denotes the tunneling energy, J the interaction constant for H-bond coupling, Po = Np the saturated polarization, and ) i the dipole moment connected with one H bond. The quantities will be specified by sub-o r superscripts H and D for KDP and DKDP, respectively.The tunneling is of no importance at very high temperatures where it can be written 1) In (2) also the molecular-field approximation was used.