Erratum: Static and dynamic properties of the structural phase transitions in NaNbO3

Abstract

The static and dynamic properties which characterize the structural phase transitions in NaNb${\mathrm{O}}_{3}$ have been widely investigated by transient NMR measurements of the ${\mathrm{Na}}^{23}$ and ${\mathrm{Nb}}^{93}$ nuclei in a powdered sample (no large-enough single crystal was available). The temperature range investigated (100-1100 \ifmmode^\circ\else\textdegree\fi{}K) includes both the purely structural transitions associated with the tilting of the Nb${\mathrm{O}}_{6}$ octahedra and the ferroelectric and antiferroelectric transitions associated with the off-center motion of the Nb atoms. The static effects have been investigated through the changes in the free-precession decay of the central line due to second-order quadrupole broadening. The dephasing time of the free-precession decay has been related to the quadrupole coupling constant. The temperature dependence of the rotational displacement of the Nb${\mathrm{O}}_{6}$ octahedra and of the off-center displacement of the Nb ions is then obtained. The variation of the tilt angle $\ensuremath{\phi}$ of the oxygen octahedra near the transition at 641 \ifmmode^\circ\else\textdegree\fi{}C is very rapid and it is not possible to decide whether $\ensuremath{\phi}$ goes to zero continuously or with a small discontinuity. The maximum value of $\ensuremath{\phi}$ in the tetragonal phase, as deduced from a crude estimate of the electric field gradient in a point-charge model, is about 7\ifmmode^\circ\else\textdegree\fi{}. No off-center displacement of the Nb atom is observed, on cooling, before the 480 \ifmmode^\circ\else\textdegree\fi{}C transition. The numerical values for the Nb displacements in the $R$ and $P$ phase ($\ensuremath{\sim}0.11$ \AA{} at 373 \ifmmode^\circ\else\textdegree\fi{}C and $\ensuremath{\sim}0.15$ \AA{} at 315 \ifmmode^\circ\else\textdegree\fi{}C) are in good agreement with previous indications of x-ray diffraction measurements. The dynamic effects have been investigated through nuclear spin-lattice quadrupole relaxation. A theory is developed which relates the relaxation rate to the critical parameters of the central peak in the dynamic cubic-tetragonal phase transition at 641 \ifmmode^\circ\else\textdegree\fi{}C, a value $\ensuremath{\nu}\ensuremath{\simeq}0.6$ for the critical index of the correlation length can be estimated; the rotational fluctuations appear to have a quasiplanar correlation. The experimental results seem to indicate that for $(T\ensuremath{-}{T}_{c})\ensuremath{\sim}4$ \ifmmode^\circ\else\textdegree\fi{}C the slowing down reaches an angular frequency of the order of 300 MHz. Finally, an estimate for the root-mean-square local fluctuating angle near ${T}_{c}$ of about 1.6\ifmmode^\circ\else\textdegree\fi{} is obtained.