Multiple-Time Correlation Functions in Spin-3/2 Solid-State NMR Spectroscopy

From Micro to Macro: Access to Long‐Range Li+ Diffusion Parameters in Solids via Microscopic 6, 7Li Spin‐Alignment Echo NMR Spectroscopy

“…In other words, information about the diffusion pathways the ions choose is obtained. [30,39,94] Regarding the correlation function of Figure 4, at t m = 0.3 s the plateau S 1 (t p ) shows up. In a simple view, for sufficiently long evolution times, it should approximate a value of S 1 (t p !1) = 1/N where N is the number of involved w Q values (see above) provided the different crystallographic sites are uniformly occupied.…”

“…The first two pulses, a 908 pulse followed by 458 pulse whose phase is shifted by 908, generate the so-called spin-alignment state. [30,94] In the ideal case the top of the echo appears at t = t p (see Figure 3, where 7 Li SAE NMR echoes of polycrystalline Li 4 SiO 4 [49] are shown as a function of acquisition time t and for various mixing times t m ). To avoid as much as possible the preparation of, for example, interfering dipolar order, proper pulse phasing is necessary.…”

“…To avoid as much as possible the preparation of, for example, interfering dipolar order, proper pulse phasing is necessary. [39,94] In the case of 7 Li, which is subject to relatively strong dipole-dipole couplings, the preparation time t p usually has to be chosen as short as possible; [37,52,59,62] values smaller than 20 ms are typical. However, this choice depends on the strength of the specific interactions, that is, on the properties of the nucleus under investigation (see below), as well as the coupling constant d Q;i being directly proportional to the EFGs present.…”

“…Similarly, fluctuations of the quadrupole frequencies w Q,i due to Li hopping between electrically non-equivalent sites lead to a decay of the SAE amplitude S 2 (see below), which is the primary observable in SAE NMR spectroscopy. The three-pulse sequence used to sample NMR SAEs is equal to that introduced by Jeener and Broekaert: [94,95] (908) X Àt p À(458) Y Àt m À(458) f Àt To determine Li diffusion parameters such as Li jump rates, [41,96] the stimulated echo, which shows up after the last pulse, is recorded as a function of mixing time t m keeping the evolution (or preparation) time t p constant. The first two pulses, a 908 pulse followed by 458 pulse whose phase is shifted by 908, generate the so-called spin-alignment state.…”

NMR Multi-Time Correlation Functions of Ion Dynamics in Solids

“…2.2.2. In 7 Li NMR, I = 3/2 leads to more complex spin dynamics so that more elaborate pulse sequences can be required to measure MT-CF [1,14]. For the present contribution, it is sufficient to note that the stimulated-echo pulse sequence provides straightforward access to F ss 2 for I = 3/2 nuclei, too, see e.g.…”