Temperature Dependence of the Nuclear Quadrupole Resonance Frequency of 79Br in NaBrO3 and KBrO3

Tipsword, R. F.; Stahl, E. A.; Williams, C. D.

doi:10.1063/1.1670436

Cited by 9 publications

(2 citation statements)

References 7 publications

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“…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.…”

Section: Introductionmentioning

confidence: 99%

Nuclear Magnetic Resonance Study of²³Na Nucleus in NaBrO₃Single Crystal

Yeom¹

2015

Journal of Magnetics

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The nuclear magnetic resonance of the 23 Na nucleus in a NaBrO 3 single crystal was investigated at the temperature range of 200 K~410 K. The tendencies of temperature dependence of the nuclear quadrupole coupling for the two magnetically inequivalent Na(I) and Na(II) centers are found to be opposite to each other. The nuclear spin-lattice relaxation mechanism of 23 Na in the NaBrO 3 crystal is investigated, and the result revealed that the Raman process is dominant in the temperature range investigated. The relaxation process of the 23 Na nuclear spins was well described by a single exponential function in time. The T 1 values of the 23 Na nuclei in the NaBrO 3 single crystal decreased with increasing temperature. The calculated activation energy for the 23 Na is 0.032 ± 0.002 eV.

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Section: Introductionmentioning

confidence: 99%

Nuclear Magnetic Resonance Study of²³Na Nucleus in NaBrO₃Single Crystal

Yeom¹

2015

Journal of Magnetics

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“…There have been a number of publications [1][2][3][4][5] dealing with the temperature variation of nuclear quadrupole resonance frequencies in terms of the well-known Bayer-Kushida expression [6][7][8]. The derivation of the Einstein temperature, 0r, for the torsional modes in the solid state have generally involved two-stage trialand-error calculations.…”

Section: Introductionmentioning

confidence: 99%

Direct numerical analysis of the temperature dependence of nuclear quadrupole resonance frequencies

Smith

Temme

1972

Molecular Physics

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INTRODUCTIONThere have been a number of publications [1][2][3][4][5] dealing with the temperature variation of nuclear quadrupole resonance frequencies in terms of the well-known Bayer-Kushida expression [6][7][8]. The derivation of the Einstein temperature, 0r, for the torsional modes in the solid state have generally involved two-stage trialand-error calculations. We wish to point out that as the Bayer-Kushida expression may be differentiated with respect to each of the variables, namely v 0 and 0j in the simple case, a direct approach to the numerical analysis of v(T)n.q.r" data is possible as long as the associated inertia factors are known.Benedek [1] has discussed the importance of the volume dependence in fitting constant pressure data to the Bayer-Kushida expression, although recent results reported by Early et al. [9] for sodium bromate show that its effect may be small. Recent papers by Utton [4,10] have incorporated the temperature dependence of the Einstein temperatures as a second order effect: more involved temperature dependences for the 8 s have been invoked by other workers [11].For constant pressure data, we use a more consistent approach in which the orders of the temperature dependence of the modes are taken as iterative variables ; we neglect any wave vector dependence of the 0 r. The form of the Bayer-Kushida expression indicates that precise Oj. values for]'> 1 will only be obtained when results from the low temperature region are included in the analysis.

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

Stahl

Tipsword

1990

Magnetic Reson in Chemistry

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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 ...

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Temperature Dependence of the Nuclear Quadrupole Resonance Frequency of 79Br in NaBrO3 and KBrO3

Cited by 9 publications

References 7 publications

Nuclear Magnetic Resonance Study of²³Na Nucleus in NaBrO₃Single Crystal

Nuclear Magnetic Resonance Study of²³Na Nucleus in NaBrO₃Single Crystal

Direct numerical analysis of the temperature dependence of nuclear quadrupole resonance frequencies

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

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Temperature Dependence of the Nuclear Quadrupole Resonance Frequency of 79Br in NaBrO3 and KBrO3

Cited by 9 publications

References 7 publications

Nuclear Magnetic Resonance Study of23Na Nucleus in NaBrO3Single Crystal

Nuclear Magnetic Resonance Study of23Na Nucleus in NaBrO3Single Crystal

Direct numerical analysis of the temperature dependence of nuclear quadrupole resonance frequencies

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

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Product

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Nuclear Magnetic Resonance Study of²³Na Nucleus in NaBrO₃Single Crystal

Nuclear Magnetic Resonance Study of²³Na Nucleus in NaBrO₃Single Crystal

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