Half-integer spin nuclei

The opposite extreme regime, when co coq, involves the so-called soft or selective RF pulses. In this case, pulses of long duration and low power can be used to excite just one of the transitions, which is achieved by a suitable choice of the resonance offset (72) and also of the pulse length. The main aspect to be considered here is that each transition has associated with it a specific frequency and a different effective nutation fi equency, which depends on the values of I and m. For selective excitation of a transition between the levels m + and m, it is found that the ideal soft jr/2 pulse must be shorter than the corresponding hard itjl pulse (which excites all transitions) by a factor of -3-1) —m m 1). For excitation of just the central transition (1 /2 -1 /2) for half-integer spin nuclei, the... 

Scenario 2 fermion nuclei (that is, half-integer spin nuclei)... 

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])...

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 quadrupolar nuclei, the situation differs notably the quadrupolar interaction only affects spins with I>% and is created by electric field gradient resulting from the asymmetry of charge distribution around the nucleus of interest. The quadrupolar interaction is characterized by the nuclear quadrupolar coupling constant Cq (from 0 in symmetrical environments to tens or hundreds of MHz) and an asymmetry parameter T]q. NMR spectra are usually recorded when Cq Vl the Larmor frequency of the quadrupolar spin. In such a case, the NMR spectrum can easily be simulated First, the first-order quadrupolar Hamiltonian, which is the quadrupolar interaction Hamiltonian truncated by the Larmor frequency, has to be taken into account. The first-order quadrupolar interaction (or the zeroth-order term in perturbation theory) is an inhomogeneous interaction and is modulated by MAS and does not affect symmetrical transition —m +m. Therefore, in half-integer spins, the single-quantum central transition (CT, i.e., —1/2 +1/2) is not affected by the first-order quadrupolar inter-... 

Non-spherical nuclei with a half-integer spin >1/2 possess a qnadrupole moment Q, which interacts with the electric-field gradient (EFG) generated by their surroundings. The coupling of Q (a property of the nucleus) with an... 

A nucleus of odd mass number 3/2 etc. A will have a half-integer spin... 

Core electrons are the non-valence electrons, found in lower energy orbitals and bound strongly enough to the nucleus that they are little affected by other atoms. Fermions are particles with half-integer spin, such as the electron or proton (both with spin of 1/2) or Cl nucleus (with spin of 3/2). 

When the observed nucleus is itself quadrupolar. Here the quadrupole interaction is dominant, the others being usually very minor in comparison. Normal MAS speeds are much smaller than typical quadrupole couplings (which lie in the MHz range), producing an enormous number of sidebands, except in the case of the central transition of half-integer spins. In this latter case distinctive line broadening effects appear which cannot be completely removed by MAS. Methods to overcome these difficulties will be reviewed. 

The intrinsic spins of stable nuclei have been determined experimentally, and the values have been explained with modem nuclear structure theory. Tables such as that in Appendix E are available for looking up the spin (I value) of a particular nucleus. The mles of angular momentum coupling are an aid in remembering the intrinsic spins of certain common nuclei. For instance, the helium nucleus, with its even number of protons and neutrons, has an integer spin, I = 0. In terms of the number of protons and neutrons, the carbon-12 nucleus is simply three helium nuclei. It should have an even-integer spin, and it also turns out to be an I = 0 nucleus. The carbon-13 nucleus has one more neutron and thereby has a half-integer spin, I = 1/2. 

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]. 

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. 

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