The crystal structure of tetragonal KH₂PO₄and KD₂PO₄as a function of temperature

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The structures of the paraelectric (tetragonal) phase of KH2PO4 (KDP) and 95% deuterated KD2PO4 (DKDP) have been investigated using high-resolution (sin theta bmax/ lambda >1.1 AA-1) single-crystal neutron-diffraction techniques. Full three-dimensional data have been collected at Tc+5K and Tc+ approximately 150K for both KDP and DKDP. It is clearly established that the distribution of H or D in the short H (or D) bonds is very much better described by a two-site anharmonic model (two gaussian functions, delta apart) than a single-site harmonic model. For DKDP it is further shown that the 'observed' D distribution obtained by Fourier synthesis is two-peaked: this is not yet established for H in KDP. Mean temperature derivatives are obtained for important structural dimensions such as the H (or D) bondlength 2R, and the site separation, delta . The variation with temperature of the refined thermal parameters reveals an anomalous temperature dependence for mu 33(P), the mean-square thermal amplitude of the phosphorus along the ferroelectric axis. The absence of any two-site character in the K distribution, and the details of the H (or D) density distribution, appear to be inconsistent with the generally accepted proton-lattice ferroelectric mode if the H (or D) motion in that mode is identified with excursions of the proton (deuteron) between its two sites, delta apart.