Experimental Observation of Hydrogen in a Mixed State of Order-disorder and Displacive Behavior in Squaric Acid

Abstract

H2C4O4 (Squaric acid, henceforth abbreviated by SQA) is one of the most studied hydrogen-bonded anti-ferroelectrics in the KH2PO4 (KDP) family. Here, we report the static hydrogen lineshape which shows a mixed state behavior of order-disorder and a displacive feature in the anti-ferroelctric (AFE)/paraelectric (PE) phase transition of SQA. We obtained the dipolar splitting data from the nonlinear fitting curve of the static hydrogen lineshape. The calculated proton-proton distance showed an increase at temperatures above the transition temperature T-c. As temperature increases through T-c, the inter-atomic distance shows a peculiar S-shape variation. This S-shape variation around T-c is also observed in other NMR reports for SQA, where the chemical shift variation is used to characterize the deformation of the C4O4 squarate group. Here, we used the dipolar interaction, instead of the chemical shift information, to detect the geometrical change of the hydrogen. Below the transition temperature T-c, the proton interactions showed long-range order whereas it showed short range order at temperatures above T-c. The peculiar S-shape variation from the hydrogen lineshape analysis can be understood as another piece of experimental evidence for a mixed state for the phase transition in SQA.