Cluster Approximations for Order-Disorder-Type Hydrogen-Bonded Ferroelectrics. II. Application to KH2PO4

A four-particle cluster approximation is worked out for the free energy of ferroelectric K${\mathrm{H}}_2$P${\mathrm{O}}_4$, taking into account the overlap of the protonic wave functions between the two sites in a hydrogen bond as well as short-range and long-range forces and a part of the proton-lattice interactions. The approximation reduces in the classical limit to the Slater-Takagi-Senko-Uehling treatment of the order-disorder transition in this crystal. It is shown that the changes in the Curie temperature, the spontaneous polarization, and the domain-wall mobility on deuteration can be derived from the decrease in the hydrogen overlap between the two sites and the lowering of the zero-point energy in an anharmonic potential.