title: Finding the true spin-lattice relaxation time for half-integral nuclei with non-zero quadrupole couplings.
abstract: Measuring true spin-lattice relaxation times T(1) of half-integral quadrupolar nuclei having non-zero nuclear quadrupole coupling constants (NQCCs) presents challenges due to the presence of satellite-transitions (STs) that may lie outside the excitation bandwidth of the central transition (CT). This leads to complications in establishing well-defined initial conditions for the population differences in these multi-level systems. In addition, experiments involving magic-angle spinning (MAS) can introduce spin exchange due to zero-crossings of the ST and CT (or possibly rotational resonance recoupling in the case of multiple sites) and greatly altered initial conditions as well. An extensive comparison of pulse sequences that have been previously used to measure T(1) in such systems is reported, using the (71)Ga (I=3/2) NMR of a Ge-doped h-GaN n-type semiconductor sample as the test case. The T(1) values were measured at the peak maximum of the Knight shift distribution. Analytical expressions for magnetization-recovery of the CT appropriate to the pulse sequences tested were used, involving contributions from both a magnetic relaxation mechanism (rate constant W) and a quadrupolar one (rate constants W(1) and W(2), approximately equal in this case). An asynchronous train of high-power saturating pulses under MAS that is able to completely saturate both CT and STs is found to be the most reliable and accurate method for obtaining the "true T(1)", defined here as (2W+2W1,2)(-)(1). All other methods studied yielded poor agreement with this "true T(1)" value or even resulted in gross errors, for reasons that are analyzed in detail. These methods involved a synchronous train of saturating pulses under MAS, an inversion-recovery sequence under MAS or static conditions, and a saturating comb of pulses on a static sample. Although the present results were obtained on a sample where the magnetic relaxation mechanism dominated the quadrupolar one, the asynchronous saturating pulse train approach is not limited to this situation. The extent to which W(1) and W(2) are unequal does affect the interpretability of the experiment however, particularly when the quadrupolar mechanism dominates. A numerically approximate solution for the I=3/2 recovery case reveals the quantitative effects of any such inequality.
authors.affiliation: Chemistry Division, Naval Research Laboratory, Washington, DC 20375-5342, USA. Electronic address: yesinowski@nrl.navy.mil.
authors.forename: James P
authors.initials: JP
authors.lastname: Yesinowski
keywords: Gallium nitride; Half-integral quadrupolar nuclei; MAS-NMR; Magnetization recovery; Relaxation mechanisms; Spin–lattice relaxation methods; T(1)