Excitation conditions for quantitative determination of quadrupolar spins with one pulse or spin-echo sequences in solid-state NMR

Abstract

One of the major problems concerning quadrupolar spins in solid-state NMR is their quantification. Ir the optimal excitation conditions with one radio-frequency pulse are widespread known now, this is not the case with the spin-echo sequences. This paper reports some theoretical predictions and their limitations concerning quantification with the echo obtained with spin-echo resonances. To realize that, first, the relative line intensity of a transition ( m + 1, m) is defined in order to allow the comparison of results from different authors. Then results concerning one pulse excitation on a spin I= 3/2 are summarized. The condition of short pulse excitation is generalized to higher spins using the Pauli matrices applied to the two extreme cases: hard pulse of non selective excitation, and selective excitation. Finally the same procedure has been foUowed for the spin-echo sequence involving two x-pulses. It was shown that the optimum conditions are: both the pulse length must be sufficiently short, and the interpulse delay should be taken as short as the duration of the FID provided the phase of the second pulse alternates without changing the receiver phase. In these conditions, the relative echo amplitude depends lineady on the first pulse length and quadraticaUy on the second. The limitations are: the homonuclear magnetic dipolar interaction must be much smaller than the heteronuclear case which must be itself much smaller than the amplitude of the pulse. Furthermore, quantification with the echo requires the determination of the spin-spin relaxation time as well.

27Al NMR Studies of Aluminosilicate Glasses

“…Provided that ω 1 ( ω j Q is obeyed for each quadrupolar spin-site j in a multisite structure (where "(" implies that the magnitudes of ω 1 and ω j Q are separated by at least one order of magnitude), all are uniformly excited and the resulting relative NMR intensities quantitatively reflect the various site abundances. However, the CT nutation frequency during the rf pulse is a factor of (S + 1/2) higher than ω 1 [18,126,139,140];…”

“…(35) is of little practical use, as it is only realized under so-called nonselective rf excitation conditions, whereas if the CT signal is selectively excited using weak rf pulses (see Section 7), a factor of (S + 1/2) lower NMR signal intensity is observed [19,[125][126][127]:…”

“…Consequently, we strongly advice against using solid Al-bearing samples for rf pulse calibrations! (ii) ω 1 ( ω Q : This so-called selective excitation regime implies that the rf field only excites one transition, which in practice always constitutes the CT: "CT-selective excitation" [18,[125][126][127]. Provided that ω 1 ( ω j Q is obeyed for each quadrupolar spin-site j in a multisite structure (where "(" implies that the magnitudes of ω 1 and ω j Q are separated by at least one order of magnitude), all are uniformly excited and the resulting relative NMR intensities quantitatively reflect the various site abundances.…”

“…The fractional signal intensity (F m,mÀ1 ) present in the m ! m À 1 transition out of the total À1QC signal intensity is given by [125][126][127] …”

“…In practice, it is the NMR signal strength from a given sample that matters-i.e., the NMR signal sensitivity that R S aims at predicting. For experimentation focussing on CT detection, it should be remembered that only a fraction of the total À1QC NMR signal from a spin-S nucleus resides in the CT and that this fraction reduces as S is increased [19,[125][126][127]:…”