The Knight Shift

The Knight Shift. — In metals, an additional perturbation to the Larmor frequency must be considered, namely that from the conduction electrons which become polarized by H0 and therefore create a separate magnetic field at the nucleus, giving rise to a further displacement in i 0, which is called the Knight shift and can well be several orders of magnitude greater than the chemical shift. Since the Knight shift is restricted to metals, its relevance to this review has been in the study of finely divided, supported metal catalysts. 

A more detailed discussion of the chemical shift and the Knight shift can be obtained in Slichter s book.3 

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Despite this similarity with chemical shift, the Knight shift is grouped with the electron hyperfine term in (lb) to reflect the fact that both terms arise from the influence of the spin or orbital angular momentum of unpaired electrons. The distinction between the two is that for the electron hyperfine term the electron spin (or hole, as the absence of an electron can be described, e.g., in the case of d9 Cu++) is localized on a paramagnetic defect such as a deep-level transition metal ion. 

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... 

It should be pointed out that a somewhat different expression has been given for the Knight shift [32] and used in the analysis of PbTe data that in addition to the g factor contains a factor A. The factor A corresponds to the I PF(0) I2 probability above except that it can be either positive or negative, depending upon which component of the Kramers-doublet wave function has s-character, as determined by the symmetry of the relevant states and the mixing of wavefunctions due to spin-orbit coupling. 

In this approach to quantitatively analyzing the distribution of carrier concentrations, it was noted that the spatial length scale of dopant concentration fluctuations was an area for future exploration [207]. It is certainly clear that if each crystallite possessed a different dopant and thus carrier concentration, then this approach would be valid to the extent that the Knight shift followed an nj3 functional dependence as expected for a parabolic band. 

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. 

In solid-state NMR [1,51-64], the magnetic coupling between the fullerene anions has to be taken into accoimt. In the case of metal intercalated fullerides that have metallic properties a contribution from the conduction electrons must be added, a phenomenon called the Knight shift . Even if this additional shift affects the C-chemical resonance, the correspondence between extended and discrete systems of comparable Cjq oxidation state is quite close [1]. 

T. J. Bastow and S. Celotto, Temperature variation of the Knight shift for Mg in magnesium metal. Solid State Commun., 1999,110, 271-273. 

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