Interaction Knight shift

Knight shift K s 10 -10 Interaction with conduction electrons via the contact interaction... 

The terms in (la) and (lb) both involve sums of single nuclear spin operators Iz. In contrast, the terms in (lc) involve pairwise sums over the products of the nuclear spin operators of two different nuclei, and are thus bilinear in nuclear spin. If the two different nuclei are still of the same isotope and have the same NMR resonant frequency, then the interactions are homonuclear if not, then heteronuclear. The requirements of the former case may not be met if the two nuclei of the same isotope have different frequencies due to different chemical or Knight shifts or different anisotropic interactions, and the resulting frequency difference exceeds the strength of the terms in (lc). In this case, the interactions behave as if they were heteronuclear. The dipolar interaction is proportional to 1/r3, where r is the distance between the two nuclei. Its angular dependence is described below, after discussing the quadrupolar term. 

Let us now consider the metallic regime, following the discussion of [18]. For nuclei coupled to a mobile system of independent electrons by an isotropic exchange interaction of the form A l S, where I is the nuclear spin and S the electron s spin, the Knight shift can be written as... 

For the metallic regime described above, when the Al S interaction is also responsible for the nuclear relaxation, Korringa [192] showed that the Knight shift and Ti are related by... 

In a sample of bulk Pt metal, all of the nuclei have the same interaction with the conduction electrons and thus see the same local field. The resulting NMR line is quite narrow. However, in our samples of small Pt particles, many of the nuclei are near a surface where the state of the conduction electron is disturbed. This tends to reduce the Knight shift for these nuclei. Since the Pt particles in our samples are of many different sizes and shapes, this reduction in the Knight shift is not the same for every nuclear spin near a surface. Thus, we obtain a broad "smear" of Knight shifts resulting in the lineshapes of Figure 5. 

The absolute chemical shifts of protons in diamagnetic solids are typically near 30 ppm (28), and the Knight shift caused by conduction electrons through contact interaction is estimated to be —31.2 ppm, using the experimental T1T value of 180 JK-sec and the Korringa relation (29) ... 

In organic metals, the nature of the molecular tt orbitals that form the conduction bands leads to a dipolar hyperfine interaction that may be nonnegligible when compared with the contact contribution discussed above [23]. The various terms in the dipolar interaction modify K and Tx 1 in different ways. The dipolar component [3] can be written as a sum of terms, some of which produce anisotropic Knight shifts (or line broadening in powder samples) and contribute to the spin-lattice relaxation rate. 

The way in which this solvent modification occurs is suggested by the pattern of hyperfine constants for (which is one of the few solvated electron species sufficiently stable to obtain its NMR spectrum). The Knight shift of NMR lines is due to the contact Fermi (isotropic) hyperfine interaction of the excess electron with the magnetic nuclei (X) in the solvent molecules it is the measure of spin density, (0) in the r-type atomic orbitals centered on a given nucleus X ... 

This result, seems to indicate the only Korringa-typc spin lattice relaxation for adsorbed hydrogen reported so far. If we assume that it is due to contact interaction with the spins of s-like electrons (by using reasoning similar to that apphed for PdH in Section lll.B), its value gives 200 ppm and places the zero of the Knight shift scale at 115 ppm. Whereas such values cannot be ruled out, it is more hkely that this one-component analysis of shift and relaxation is insufficient. 

If the symmetry of the site is lower than cubic the full tensor form of the electron-nucleus interaction needs to be used, so that in addition to an isotropic term there is an anisotropic contribution. If in the PAS of the Knight shift tensor the components of the tensor are Kx, Ky and Kz, then in the laboratory frame with its orientation in the frame defined by Bo described by the Euler angles 0 and [Pg.49]

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