Knight shifts in metals

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. 

In systems with unpaired electrons (e.g., metals, radicals, paramagnetic transition metal complexes), a much larger range of chemical shifts is possible. Now the major magnetic interaction is between the nucleus of interest and the unpaired electron(s). The observed shift depends on the excess electron spin population and the coupling constant to the nucleus. The induced contact shifts or Knight shifts (in metals and conductors) often exceed 1000 ppm. 

There is a relationship between l/Tj and the Knight shift in metals that is very sensitive to electron correlation and exchange. To explain this and to derive its implications for expanded alkali metals, we digress briefly to summarize some results of the general theory of nuclear spin relaxation in metals. For noninteracting electrons, the theory of nearly free electrons gives an explicit expression for the integral in Eq. (3.10)... 

Knight Shifts and Metal-Insulator Transition in Doped Silicon... 

Moulson, D. /., and G. A. Styles Knight shifts in liquid binary alloys containing divalent metals. Phys. Letters A 24.4, 438 (1967). 

A simple test of this suggestion is the comparison of a five-layer slab calculation for the Knight shift in platinum (70) with the spectral fits of the layer model (Fig. 48). In both cases the surface resonance is shifted about 4% to low field wuth respect to the bulk signal, and the subsurface signal is found at approximately the halfway point. Another test is qualitatively to compare experimental results for hydrogen chemisorption on platinum (Fig. 55) with a calculation for hydrogen on palladium (175) in both cases an important diminution of the surface LDOS on the metal is found. 

For these CO that are a piece of the metal we should be able to write equations for the (local) Knight shift and relaxation rate, just as for a layer in a metal particle. Writing down the equations is rather easy the local density of states near can be projected on one kind of u-like and two kinds of Ti-like orbitals. It is slightly problematic to write an expression for the orbital relaxation, but it is likely to be dominated by the 7r-like f-LDOS. Assuming that both Ti-like orbitals have the same f-LDOS [the equivalent of setting Rd = 0.2 in Eq. (10) for equal occupation of all five /-like orbitals] and absorbing the orbital Knight shift in the definition of the zero of the shift scale ... 

The results have been reported of a comparative study of the measured electrical resistivities of liquid alkali metals and alloys, and the theoretical predictions for this quantity obtained within the diffraction model.48 The composition dependence of the Knight shifts in Na-Cs, Na-Rb, K-Rb-Cs, and Na-Rb-Cs liquid alloys has also been examined.49 Addition of small quantities of rubidium (0.3—4.51 atom %) to liquid sodium increases the electrical resistivity almost linearly with increasing solute concentration. With increasing temperature from 100 to 1100 °C, the effect of rubidium on the resistivity of sodium progressively diminishes.50 Addition of the solutes Hg, Tl, and Pb increases the resistivity of liquid potassium linearly with both increasing concentration and temperature. The unit increases in resistivity/pfl cm (atom%) , are 8.80, 9.85, and 15.8 for Hg, Tl, and Pb,... 

NMR relaxation and Knight shift In an external field nuclear spins exhibit a Larmor precession with a frequency hyperfine coupling to conduction electrons which leads to spin-flip processes as witnessed by the NMR-relaxation rate and the Knight shift of the resonance frequency Scoq- A review of these important effects for HF superconductors is given by Ton et al. (2003). The relaxation rate is determined by the availability of resonant electron-hole excitations. In the normal state this leads to the Kor-ringa law In the superconducting state the presence of A(k) should lead to a faster... 

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