Nuclei half-integer

As discussed above, CP involving half-integer quadrupole nucleus is not trivial and 43Ca 1H CP experiments are in general of rather low... 

In addition to studies of sihca supports work has also been carried out focusing on aluminas. However, the appHcation of H —> Al CP-MAS NMR is complicated as compared to H —> Si CP, as this involves transfer between a half-integer nucleus ( H) and a quadmpolar nucleus ( Al). The issues surrounding this have, however, been discussed in depth by a number of workers [183, 185-190]. Despite these challenges, the application of H —> Al CP-MAS NMR to catalytic systems has been successfully demonstrated. The first such study was carried out by Morris and Ellis in 1989 [186] for hydrated y-Al203. However, this was only partially successful as it failed to observe any tetrahedrally coordinated surface aluminum as result of processes which are unfavorable to CP, including fast spin-lattice relaxation [186]. 

To produce an NMR spectrum, a nucleus must possess a nuclear spin. Nuclei with odd mass numbers (e.g. Si, Al) have half-integer spins and are of most interest for solid state NMR. Nuclei with even mass numbers and odd charge (e.g. H, " N) have integer spins, and although subject to difficulties they can still be useful NMR nuclei. Of the 120 nuclei suitable for NMR, 9 have spin I = 1, 31 are spin I = V2, 32 are spin I = /2, 22 are spin I = /2, 18 are spin I = I2 and 8 are spin I =... 

Fig. 5 The effect of magic-angle spinning on the central transition lineshape for a half-integer spin quadrupolar nucleus. Left central transition lineshape under static, i.e., non-spinning conditions. Right the same transition under magic-angle spinning. The asymmetry parameter r is given with each spectrum. Reproduced with permission from [61])...

The work by Frydman et al.41 has some very nice examples of the dynamic effects on half-integer quadrupolar lineshapes. This work examines XO4 anions where X contains a quadrupolar nucleus, 185/187Re, 55Mn and 75As... 

A quick estimate as to the nuclear spin being integer, half integer, or zero can be made from the number of protons (atomic number) and neutrons (atomic mass - atomic number) contained in that nucleus. A summary is given in Table 1.1. 

Figure 3 Energy level splittings and transitions for half-integer quadrupolar nuclei, as illustrated for the example of a spin-3/2 nucleus, (Oy is the NMR transition frequency in the absence of the quadrupolar interaction, Wy is the quadrupolar frequency, and 0 is the angle between the magnetic field and the principal axis of the electric field gradient tensor.

A further characteristic line broadening interaction occurs for nuclei with nuclear spinsf>l/2 in addition to the interactions discussed above [seeEq.(l)]. These nuclei exhibit an electric quadrupole moment that interacts with the electric field gradient at the site of the nucleus. The NMR spectriun of quadrupole nuclei with half-integer nuclear spins (7=3/2,5/2,...) consists of the -hl/2 -1/2 central transition and the so-called satellite transitions ( l/2 3/2, 3/2 quadrupole interaction it is practically impossible to excite the whole spectriun non-selectively, i.e., the central transition is often selectively observed. 

Fig. 3. Line shape function of the central transition of a quadrupole nucleus with a half-integer nuclear spin, calculated for /Jq=0 in the limiting case of rapid magic angle spinning assuming that the electric quadrupole interaction is the dominating line broadening interaction...

For an ensemble of crystallographically equivalent nuclei with spin /, 21 NMR transitions take place. For most elements, the most abundant spin-active isotope is quadrupolar with half-integer spin. For these nuclei, spectro-scopists usually focus on the mj = 1/2 — mi = -1 /2 transition since it is not perturbed by the first-order quadrupolar interaction (i.e., to a first approximation, this transition behaves like that for a spin-1/2 nucleus, see below). Hence, an overview of the theory for half-integer spin quadrupolar nuclei is presented here. For a thorough description of the theory for the quadrupolar interaction, readers are referred to numerous texts and reviews on the topic. ... 

In solution NMR spectroscopy, the receptivity, D, of a nucleus is often used to assess the suitability of a given isotope for NMR studies. D depends on the magnetogyric ratio, 7, of the nucleus and on the natural abundance, C, of the isotope D= y C[I I + 1)]. However, in solid-state NMR spectroscopy of half-integer quadrupolar nuclei, one usually only excites the CT, so that the effective D is less than that observed for NMR of solutions. Although 7 and C are important when considering the suitability of a particular isotope for solid-state NMR studies, many other factors must also be considered. 

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