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 (T1) and proton relaxation times along the rf field (T1ρ) have been measured for polycrystalline (NH4)2SO4. T1 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 τc at various temperatures have been obtained for the two inequivalent NH4 ions from the T1 and T1ρ measurements; above Tc and below 170°K, logτc 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. τc 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 proton T1 and T1ρ 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.
The electron paramagnetic resonance ahsorption of ehroniia supported on alumina has been investigated a t X-band (9.5 khfcps.) and K-band (23.9 kMcps.). Spectra of chroinia-alumina reduced in hydrogen a t 500" show two distinct phases: a dispersed (6) phase whic,h predominates a t low concentrations of chromium and a bulk ( B ) phase which is prevalent at, the higher concentrations. 1 he temperature dependence of the intensity of these phases indicates the &phase consists of rather isolated Cr+3 ions not coupled electronically and the p-phtHe consists of clusters of Cr+3 ions with strong exchange roupling of 3d electrons. Intensity calibrations of e.p.r. spectra have been made and these indicate all the chromium present in the rcduced catalysh to be in the trivalent state.A relatively sharp resonance absorption appears upon oxidation of reduced chromia-alumina with oxygen. A spin-Hamiltonian for each of the observed types of resonances is proposed and discussed.Absolute amounts of 6-and @-phase chromium also arc given.
Self-diffusion coefficients and rotational correlation times have been measured in several polar liquids by pulsed nuclear magnetic resonance techniques. Self-diffusion coefficients are reported for CH3OH, CH3NO2, (CH3)2CO, C6H5NO2, and C6H5Cl; proton, deuterium, and chlorine-35 relaxation times are given for these liquids. Deuteron quadrupolar coupling constants for the deuterated molecules were measured directly for the solids at low temperature. Methyl groups in CH3OH, CH3NO2, and (CH3)2CO have correlation times that are considerably shorter than the correlation time for the tumbling of the entire molecule. The Ivanov theory of large amplitude molecular jumps is generalized to the case of two kinds of jump about different axes and an explicit expression for the over-all correlation time is given. The pre-exponential factors of the methyl group correlation times appear to change drastically in CH3OH and CH3NO2 upon melting. Rotational correlation times for molecular tumbling are in good agreement with those calculated from quasilattice random flight model. In methanol there is evidence that rotation of the molecule about the OH bond direction occurs more rapidly than the over-all tumbling of the molecule. Molecular rotation also appears to be anisotropic in nitrobenzene as evidenced by a factor of 2 difference between the nitrogen and deuteron rotational correlation times. The pressure dependence of the intramolecular relaxation rate in C6H5Cl reported by Bull and Jonas is also shown to be in reasonable agreement with the prediction of the quasilattice model.
Coefficients of self-diffusion have been measured by the spin-echo technique for neat NH] and N0 3 from 200 to 298°K. The data are well represented by D = (4.5±O.2)X 10-] exp [-(2.07±O.02)/RT] for NH3 and by D = (6.0±O.3) X 10-3 exp [-(2.31±O.02)/RT] for N0 3 . The difference in activation energy for self-diffusion between NH] and NO] is shown to be consistent with the viscosity measurements of Hutchison and O'Reilly. These results are interpreted by means of a quasilattice model for self-diffusion in the liquid state. Values of the work required to create a molecular vacancy are evaluated from liquid density, isothermal compressibility and the scaled particle theory. The quas~lattice m~del yields pre-exponential factors for self-diffusion that are in reasonable agreement with expenment.
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