The temperature and pressure dependences of the nuclear quadrupole coupling frequency of 23Na in NaBrO3 have been measured. The quadrupole frequency is found to range from 886 kHz at 4.1°K to 849 kHz at 300°K at atmospheric pressure. The pressure dependences were determined at 196°, 273°, and 298°K. From the pressure dependences and the compressibility the frequency was found to vary with the volume about as V−2.5 at all three temperatures. The rate of change in frequency with temperature at a constant volume, ν−1(∂ν / ∂T)v, was found to have a positive value and to decrease in magnitude with increasing temperature above 196°K.
The molar specific heat of NaBrO, in the temperature range 4.2-336 K was determined experimentally and compared with the theory developed by Stahl and generalized in this paper. The relationship between the molar specific heat and temperature was explicitly studied and compared with results obtained by other workers. The method developed also produces the Debye temperature, a,,, the maximum angular frequency, w,, and the product Zw: of the BrO, group, where Z is the moment of inertia and w, is the lattice vibration. The relationships between the 79Br NQR frequency and temperature and between the NQR frequency and molar specific heat were obtained.KEY WORDS Pure quadrupole resonance frequency Molar specific heat Temperature dependence NaBrO, Soon after the discovery' of the pure quadrupole splitting of the nuclear spin energy levels in solids, Bayer' proposed a theory in which this nuclear quadrupole resonance (NQR) depended on temperature for a single mode of oscillation. His work was subsequently generalized by Kushida, and Wang4 for more than one mode of oscillation. The result was a theory which was able to describe gross experimental results but which failed in some detailed aspects. For example, it gave incorrect results for the moments of inertia for the BrO, group in NaBr0,' and KBrO, .6 Kushida et aL7 and Gutowsky and Williams* then showed that a correct theory must include a dependence on volume. In addition, Kushida et al. demonstrated the need for the theory to incorporate the Debye model, and Silva and Schemppg noted the theoretical requirement for a T4 term.Therefore, a better NQR theory was needed which showed the dependence on volume (or molar specific heat, which contains this volume dependence) and on temperature, and could be tested experimentally. Stahl" developed such a theory which incorporates the Debye model and satisfies the theoretical requirement for a T4 term. In this theory, the quadrupole resonance frequency for one mode of vibration is given by exp(ho,JkT) -1 X where vQ is the resonance frequency when T = 0 K, N o is Avogadro's number, Z is the moment of inertia, o1 is the angular frequency of the lattice, O, is the maximum angular frequency of the lattice and k is the Boltzmann constant. C , is the molar heat capacity at constant volume and is given by where x = h o JkT, R is the molar gas constant and @d is the Debye temperature. This model assumes that the asymmetry parameter, N = (qxx -q,,,,)/q,, , is zero. Equation (1) is limited to a single mode of oscillation. It can be generalized, following the same process that Kushida, used to generalize the Bayer' theory, to a result which holds for an arbitrary number of modes of oscillation :where I , is the nth moment of inertia and O, is the nth angular frequency of vibration. We measured the NQR frequency of Na7'Br0, as a function of temperature from 4.2 to 336 K. By comparing the data with Eqn (3), we were able to obtain 0, and Zw' and then C , as a function of temperature. For the bromate group, the summation on n in Eqn (3) takes ...
The pure quadrupole resonance frequency of Br79 and Br81 in NaBrO3 has been measured between 4.2° and 77.3°K. The spin—lattice relaxation times have been measured between 4.2° and 16°K. The frequency measurements were compared with the Bayer—Kushida theory. While qualitative agreement with the theory is found over the entire temperature interval investigated, the theory does not fit the data in detail. The spin—lattice relaxation times were compared with the theory developed by Chang for NaClO3. If a linear or parabolic temperature dependence of the Br quadrupole frequency is used, as has been the case in all previous work, the theory can be made to agree with the data by appropriately choosing the Debye temperature. However, if the more nearly correct temperature dependence of the quadrupole frequency given by Bayer is inserted into the theory, it is found that no reasonable adjustment of the Debye temperature gives agreement. Fair agreement with the data can be obtained in this case by adjusting the velocities of the longitudinal and transverse lattice waves. Furthermore, at low temperatures the frequency dependence of Bayer leads to nearly equal contributions to the relaxation of Δm=±1 and Δm=±2 transitions, in contrast to the assumption of a linear or parabolic temperature dependence which leads to negligible contribution by the Δm=±2 transitions.
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