Static and dynamic properties of the structural phase transitions in NaNbO3

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 °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 $\varphi$ of the oxygen octahedra near the transition at 641 °C is very rapid and it is not possible to decide whether $\varphi$ goes to zero continuously or with a small discontinuity. The maximum value of $\varphi$ in the tetragonal phase, as deduced from a crude estimate of the electric field gradient in a point-charge model, is about 7°. No off-center displacement of the Nb atom is observed, on cooling, before the 480 °C transition. The numerical values for the Nb displacements in the $R$ and $P$ phase ($\sim 0.11$ Å at 373 °C and $\sim 0.15$ Å at 315 °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 °C, a value $\nu \simeq 0.6$ 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 $(T-T_c)\sim 4$ °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° is obtained.