Random Motion of Deuterons in KD2PO4

Abstract

Magnetic resonance studies of the deuteron in K${\mathrm{D}}_{2}$P${\mathrm{O}}_{4}$ have been conducted which show the existence of deuteron jumping between and within hydrogen bonds. The experimental results help to explain electrical conductivity and ferroelectric phenomena in crystals of this type.Pulse magnetic resonance experiments show that the lifetime ${T}_{\mathrm{XY}}$ against deuteron jumping between $X$- and $Y$-oriented hydrogen bonds is 15 msec at 70\ifmmode^\circ\else\textdegree\fi{}C with a jump activation energy of approximately 0.58 ev. The $c$-axis electrical conductivity of K${\mathrm{D}}_{2}$P${\mathrm{O}}_{4}$ is found to have the same activation energy, with a value of 1.16\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}10}$ ${(\mathrm{ohm}\mathrm{cm})}^{\ensuremath{-}1}$ at 25\ifmmode^\circ\else\textdegree\fi{}C.The $\ensuremath{\Delta}m=1({P}_{1})$ and $\ensuremath{\Delta}m=2({P}_{2})$ deuteron spin-lattice relaxation transition probabilities due to $X\ensuremath{-}Y$ jumps have been calculated from the known values of ${T}_{\mathrm{XY}}$ and the electric field gradient tensors at $X$ and $Y$ deuteron sites. Their magnitudes and the dependences of these magnitudes on magnetic field, temperature, and orientation are in good agreement with experiment.Further measurements of ${P}_{1}$ and ${P}_{2}$ separately give a component of transition probability proportional to $\mathrm{exp}(0.078 \mathrm{ev}/kT)$ and independent of magnetic field. The orientation dependences of ${P}_{1}$ and ${P}_{2}$ for this component indicate quadrupolar relaxation due to deuteron jumps along hydrogen bonds, with a jump time of order ${10}^{\ensuremath{-}11}$ sec at 215\ifmmode^\circ\else\textdegree\fi{}K. The existence of intrabond jumps governed by an activation energy is shown to be consistent with the Slater theory of K${\mathrm{H}}_{2}$P${\mathrm{O}}_{4}$ as modified by Takagi.