Multiple Echoes in Solids

By the study of the Zeeman resonance of a nucleus having a large quadrupole moment, like iodine, Watkins and Pound have shown that a cubic crystal like KI is never perfect, and that random electrical gradients always exist at the locations of the nuclei. However, by the cw method only a lower and upper limit can be set to the interaction of the quadrupole moment of the nuclei with these gradients. In order to get more information about their distribution, the spin-echo technique, with large rf field, was used. The calculations, performed in the limit of a field much larger that the random quadrupole interaction, show that, if at time $t=0\mathrm{}$ we apply a 90° pulse, and at time $t=\tau$ we apply a $\varphi$ pulse (with an optimum for $\varphi$ around $\frac{\pi }{5}$), we get: three "allowed" echoes, at times $t$ such that $\frac{(t-\tau )}{\tau }=\frac{1}{2}, 1 \mathrm{and} 2$, which are bell-shaped curves; two "forbidden" echoes for $\frac{(t-\tau )}{\tau }=\frac{3}{2} \mathrm{and} 3$, which are derivatives of bell-shaped curves. These predictions are in agreement with the experiment, and from the width of the allowed echoes, an average of the random quadrupole interaction can be determined: this average, expressed in gauss, was found to vary from 18 gauss to 36 gauss in different samples. We could verify, by using this method, that the crushing, as well as the quenching of the crystals increase the magnitude of the random gradients.