Quadrupolar Echoes in Solids

In a classic paper, Solomon showed that the presence of inhomogeneous, first-order quadrupolar interactions leads to the formation of extra "allowed" spin echoes in nuclei for which the spin I=5/2. We demonstrate (both theoretically and experimentally) that shifting the rf phase of the second pulse by 90^∘{} (in a spin-5/2 system) enhances the extra allowed echoes by a factor of almost 5 in amplitude over the unshifted case. Using the density-matrix formulation (and assuming no magnetic inhomogeneities), we have derived, for a 90^∘{} phase shift, the amplitude and shape dependence on the second-pulse turning angle of the 3/2τ, 2τ, and 3τ echoes. Experimental echo amplitudes and shapes (for both 0^∘{} and 90^∘{} phase shifts) were obtained, at room temperature, on ¹²⁷I in a fused sample of KI, and these show good agreement with the calculations. Because of the enhancement, this technique affords a much easier separation of the respective distributions arising from the 3/2↔5/2 and from the 1/2↔3/2 satellite transitions than is possible in the unshifted case. Another feature of the phase-shifted case is that, in favorable circumstances, the 3τ echo may be observed although the 2τ echo is obscured by the receiver recovery time. Preliminary data on quadrupole distributions at Al sites in NiAl and AuAl₂ intermetallic compounds are presented. Spin-spin relaxation of the satellite transitions is noted. Results expected for systems which have spin values other than I=5/2 (both integral and half-integral) are mentioned.