Geometric effects of H-atom disordering in hydrogen-bonded ferroelectrics

Geometric restraints resulting from differences in the electronic structure of the oxygen atoms involved in the -OH...O= hydrogen bonds are analyzed in terms of their consistency with the symmetry requirements in ferroelectric crystals. The interdependence between these restraints and the symmetry combines the effect of H-atom disordering with displacements of all the atoms involved in the hydrogen bond, and it allows one to evaluate the changes induced by phase transitions in dimensions of hydrogen bonds, in the arrangement of molecules and ions or even the anomalous changes in the unit-cell dimensions and strain tensor of the crystal. Characteristic structural features observed in the KDP-type (where KDP is KH₂{PO}₄$) ferroelectric crystals above ${T}c$, like shortening of the O...O distance, or the inclination angle between the O...O direction and the H-atom hopping trajectory, are explained. Consistence of the calculated structural parameters with those measured experimentally by neutron diffraction for several classes of prototypical KDP-type ferroelectric crystals (squaric acid, PbHPO₄, and KH₂{PO}₄$), is structural evidence of the ferroelectric-phase symmetry of the electronic structure in the KDP-type ferroelectric crystals at their paraelectric phase.