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Quadrupolar Tensor Conventions

Contents: [Quadrupolar interaction] - [Quadrupolar tensor]
[References]

 

Quadrupolar Interaction

A quadrupolar nucleus S, with nuclear spin S > 1/2, is subject to an interaction of the nuclear quadrupole moment, eQ, with the component of the electric field gradient (EFG) along a particular direction, Vii = eqii. The Laplace equation requires that the trace of the EFG tensor is zero. In addition, the EFG tensor is symmetric, hence consists only of 5 independent components. In its principal axis system (PAS), XYZ, the EFG tensor is diagonal and can be characterized by the three principal components VXX, VYY, VZZ. In nuclear quadrupole resonance (NQR), the principal components are labelled according to this convention:

   |VZZ| >= |VYY| >= |VXX|

Quadrupolar Tensor

Because of the trace of zero, only two independent parameters are required to characterize the magnitudes of the principal components, and these are usually chosen to be VZZ and the dimensionless asymmetry parameter h. The product of VZZ and the nuclear quadrupole moment is known as the quadrupolar coupling constant, c:

Quadrupolar coupling constant: chi

Asymmetry parameter: eta

Thus, h is constrained to values between 0 and 1. The quadrupolar coupling constant should not be mixed up with the quadrupolar frequency, observed in NQR experiments.

My programs use this convention!

Some parameters can be evaluated on my page on Quadrupolar Parameters. Also, I recommend visiting Pascal Man's page an Quadrupole Coupling in NMR.

Most authors are in agreement with this convention:

Conventions that differ can be found in:

The program SIMPSON by M. Bak uses the convention where qxx >= qyy, different from the NQR community. To compensate this, one can add 90 deg to one of the Euler angles, alpha or gamma, depending on the actual situation.

References

[1]  A. Abragam, Principles of Nuclear Magnetism; Clarendon Press, Oxford (1961).
[2]  E. A. C. Lucken, Nuclear Quadrupole Coupling Constants; Academic Press, London (1969).
[3]  M. H. Cohen, F. Reif, In Solid State Physics; Vol. 5, p 321; F. Seitz, D. Turnbull, Eds.; Academic Press, New York (1957).
[4]  T. P. Das, E. L. Hahn, In Solid State Physics; Suppl. 1, p. 1; F. Seitz, D. Turnbull, Eds.; Academic Press, New York (1958).
[5]  P. P. Man, In Encyclopedia of Nuclear Magnetic Resonance; D. M. Grant, R. K. Harris, Eds.; John Wiley & Sons, Chichester, UK (1996); p. 3838.
[6]  A. C. Olivieri, L. Frydman, L. E. Diaz, J. Magn. Reson. 1987, 75, 50.
[7]  R. K. Harris, A. C. Olivieri, Prog. NMR Spectrosc. 1992, 24, 435.
[8]  H. W. Spiess, In NMR Basic Principles and Progress; Vol. 15, p. 55; P. Diehl, E. Fluck, R. Kosfeld, Eds.; Springer-Verlag, Berlin (1978).
[9]  A. J. Vega, In Encyclopedia of Nuclear Magnetic Resonance; D. M. Grant, R. K. Harris, Eds.; John Wiley & Sons, Chichester, UK (1996); p. 3869.

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