Double-well potential of SO4 in NH4LiSO4, LiRbSO4, and mixed-crystal LiRb1-xCsxSO4 (x=0.097) studied by x-ray diffraction.

Abstract

The double-well potential of ${\mathrm{SO}}_{4}$ in ${\mathrm{NH}}_{4}$${\mathrm{LiSO}}_{4}$ was estimated at 465 K in its highest-temperature phase on the assumption that each rigid ${\mathrm{SO}}_{4}$ ion executes independent anharmonic oscillation in an effective single-particle potential about the mean position determined in the displacive-type model. The values of potential parameters for the librational motion were estimated by the method of structural analysis using numerical integration of structure factors. The height of the potential barrier is 0.754\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}13}$ erg, about 1.2 times that of the thermal energy ${\mathit{k}}_{\mathit{B}}$T at 465 K. An effective asymmetric potential was also estimated at 457 K in the ferroelectric phase; the stable configuration of the ${\mathrm{SO}}_{4}$ lies near one of two configurations in the disordered phase. ${\mathrm{NH}}_{4}$${\mathrm{LiSO}}_{4}$ was confirmed to undergo an order-disorder phase transition. The potential of ${\mathrm{SO}}_{4}$ in ${\mathrm{LiRbSO}}_{4}$ at 493 K turned out to be also a double-minimum one with barrier height 0.512\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}13}$ erg, about 0.75 times that of ${\mathit{k}}_{\mathit{B}}$T at 493 K. The substitution of Cs for Rb by 9.7 at. % made the potential a shallow broad one. Satisfactory correspondence of the estimated potential with the observed distribution of electron density of oxygen atoms was obtained.