Dependence of the pure quadrupole resonance frequency on temperature and molar specific heat for NaBrO₃

Abstract

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 ...

Nuclear Magnetic Resonance Study of23Na Nucleus in NaBrO3Single Crystal

“…Several nuclear quadrupole resonances of NaBrO 3 crystals [6][7][8][9] have been studied for many years. Nuclear magnetic resonance (NMR) is a good technique for the investigation of microscopic information on the materials.…”

Dependence of the pure quadrupole resonance frequency on temperature for KBrO3

“…The proposed theory satisfies the theoretical requirement for a T 4 term. According to this theory, the quadrupole resonance frequency for an arbitrary number of modes of vibration is given by 22 …”

“…For example, it gave incorrect results for the moments of inertia for the BrO 3 group in NaBrO 3 4 and KBrO 3 . 5 Kushida et al 6 21,22 will be compared with experiments in which the NQR frequency was measured as function of temperature holding the pressure constant. The proposed theory satisfies the theoretical requirement for a T 4 term.…”