Broadband echo sequence using a pi composite pulse for the pure NQR of a spin I = 32 powder sample

This work presents a numerical approach to optimizing sequences with composite pulses for the pure NQR of a spin I = 32 powder sample. The calculations are based on a formalism developed in a previous paper, which allows a fast powder-averaging procedure to be implemented. The framework of the Cayley-Klein matrices to describe space rotations by 2 x 2 unitary and unimodular complex matrices is used to calculate the pulse propagators. The object of such a study is to design a high-performance echo sequence composed of a single preparation pulse and a three-pulse composite transfer pulse. We mean a sequence leading to a large excitation bandwidth with a good signal-to-noise ratio, a flat excitation profile near the irradiation frequency, and a good linearity of the phase as a function of frequency offset. Such a composite echo sequence is intended to give a better excitation profile than the classical Hahn (θ)-tau-(2θ) echo sequence. It is argued that in pure NQR of a powder sample, the sequence must be optimized as a whole since both the excitation and the reception of the signal depend on the relative orientation of the crystallites with respect to the coil axis. To our knowledge, this is the first time such a global approach is presented. An extensive numerical study of the composite echo sequence described above is performed in this article. The key of the discrimination between the sequences lies in using the first five reduced moments of the excitation profile as well as an estimator of the phase linearity. Based on such information, we suggest that the echo sequence that best fulfills our criterion is (1)(0)-tau-(0.35)(0)(2.1)(pi)(0.35)(0), the pulse angles omega(RF)t(p) being in radians. The subscripts are the relative pulse phases. We outlined the way to implement the spin echo mapping method to reconstruct large spectra with this sequence, and it is shown that it reduces the acquisition time by a factor of 1.7 if compared to the classical Hahn echo. Some other broadband echo sequences are also briefly discussed. We also study the effect of a small delay between the pulses of the composite pulse to take into account the experimental constraint imposed by the spectrometer. To be complete, we give an estimation of the performances of the Hahn echo, the stimulated echo, and the composite echo sequence optimized for a powder sample when applied to a monocrystal. Experiments performed on chloranil at ambient temperature confirm the predicted excitation profiles. Copyright 2000 Academic Press.