Deuteron Magnetic Resonance and Proton Relaxation Times in Ferroelectric Ammonium Sulfate

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Abstract
The deuteron nuclear magnetic resonance of single crystals of (ND4)2SO4 has been studied from 77° to 300°K and particularly in the region of the first‐order ferroelectric phase transition at 223°K. At high temperatures four closely spaced pairs of lines (10‐G max separation) are observed, which shift abruptly as the crystal is cooled through the transition temperature (Tc ). These lines are assigned to the two inequivalent ND4 + ions (I and II) in a unit cell, which are slightly distorted from the tetrahedral configuration and rapidly reorienting so as to average the quadrupolar splitting to a small value. At 130°K only two pairs of closely spaced lines are observed due to ND4 + (II); at 77°K eight pairs of widely spaced (400‐G max separation) lines are observed corresponding to ND4 + (I). In the transition to the ferroelectric phase the principal coordinate system of the electric‐field gradient (EFG) tensor rotates by about 30° for each ion with little change in the coupling constants or asymmetry parameters. The spontaneous polarization produced by the distorted ions has been calculated from the observed EFG tensors and is in reasonable agreement with the experimental value. Proton spin—lattice relaxation times (T 1) and protonrelaxation times along the rf field (T 1ρ) have been measured for polycrystalline (NH4)2SO4. T 1 versus temperature (T) has two minima, and may be interpreted as due to the two inequivalent NH4 + tetrahedra reorienting at different frequencies and coupled to each other via dipole—dipole interaction. Correlation times τ c at various temperatures have been obtained for the two inequivalent NH4 ions from the T 1 and T 1ρ measurements; above Tc and below 170°K, logτ c is a linear function of T −1, with normal values of pre‐exponential factors. The activation energies change only slightly at the transition, in agreement with recent neutron inelastic scattering data. τ c is, however, anomalously short immediately below Tc due to the volume contraction of the crystal. Correlation times have also been estimated from deuteron resonance linewidths and proton second moments. The results are consistent with those derived from the protonT 1 and T 1ρ data. An order—disorder mechanism is proposed for the phase transition in which NH4 + tetrahedra are disordered with respect to the crystal ab plane. A first‐order transition is described by the molecular field approximation for a sufficiently strong dependence of the interaction parameter on the spontaneous polarization.