Proton configurations in the hydrogen bonds of KH2PO4 as seen by resonant x-ray diffraction

KH2PO4 (KDP) belongs to the class of hydrogen-bonded ferroelectrics, whose paraelectric to ferroelectric phase transition is driven by the ordering of the protons in the hydrogen bonds. We demonstrate that forbidden reflections of KDP, when measured at an x-ray absorption edge, are highly sensitive to the asymmetry of proton configurations. The change of average symmetry caused by the freezing of the protons during the phase transition is clearly evidenced. In the paraelectric phase, we identify in the resonant spectra of the forbidden reflections a contribution related to the transient proton configurations in the hydrogen bonds, which violates the high average symmetry of the sites of the resonant atoms. The analysis of the temperature dependence reveals a change of relative probabilities of the different proton configurations. They follow the Arrhenius law, and the activation energies of polar and Slater configurations are 18.6 and 7.3 meV, respectively.