JOURNAL OF MAGNETIC RESONANCE SO,2 14-224 (1988) Theory of Three-Pulse Sequences for Systemsof Single Spins of Z = z MANGALA S. KRISHNAN, * NELSON LEE, AND B. C. SANCTUARY y Department ofchemistry, McGill University, 801 Sherbrooke West, Montreal, P.Q., Canada H3A X6 AND T. K. HALSTEAD Department of Chemistry, Heslington, York YOI 5DD, England Received August 18,1987; revised March 11,1988 The NMR response of a spin-$ system to a variety of three-pulse sequences is examined theoretically for later use to interpret experiments of solid RI. Analytical expressions are obtained for the contributions to the nuclear magnetic signal due to vector and tensor polarizations. Sequences containing up to three pulses are studied and some long-lived echoes identified and classified. Schemes are proposed for the indirect detection of higher- tensor-rank alignments. 8 1988 Academic Ress, Inc. In a previous paper ( I), the response of a spin system of Br (I = i) in crystalline KBr to a series of two- and three-pulse sequences was given, both theoretically and experimentally. In this paper, we extend the approach to a system of spin-g, for exam- ple, that of iodine in crystalline RI, and present theoretical calculations for various pulse schemes. In Ref. ( 1 ), the authors reported the detection of octupole alignments in spin systems. Here, the extension to spin3 has been done, evaluating in similar terms the presence of higher-tensor-rank alignments. Although these have been ob- served previously for three spins of $ which are dipolar coupled (2)) octupole and other tensor alignments in solids with spins greater than 1 give an opportunity for measuring more than one spin-lattice relaxation process. Polarizations up to that of tensor rank 5 are possible in spin-z systems. In this paper we calculate the response of the spin system to the following sequences of radiofrequency pulses and organize the various contributions to the echoes: (i) 90:- 7~-90;--7~--90;-73 (ii) 903-~,-90+~-90+~ (iii) 90:-~,-45+~-45 G-73 (Jeener-Broekaert sequence). * Present address: Department of Chemistry, University of British Columbia, 2036 Main Mall, Vancou- ver, British Columbia, Canada V6T lY6. t To whom correspondence should be addressed. 0022-2364188 $3.00 Copyri&t 0 1988 by Academic Press, Inc. All rights of reproduction in any form reserved. 214