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

Abstract

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.