Inhomogenous linewidth

The double-resonance data (Fig. 40a) show that the signal from Pt in the surface of the particles is symmetric around a center position of approximately 1.096 G/kHz. This is an inhomogeneous linewidth there are many different types of surface Pt, each resonating at a slightly different frequency, and the observed signal is an unresolved superposition of all these elementary resonances. In the NMR layer model (Fig. 48), this idea is expanded further it is supposed that the difference in resonance frequency, and therefore also in LDOS, between all elementary surface resonances is less than the difference between typical surface and subsurface resonances. The important distribution of surface LDOS values has its equivalent in the MAS-NMR of adsorbed CO the MAS does not narrow the signal (Figs. 35c and 35d) because its width is due to a distribution of isotropic shifts rather than to shift anisotropies. 

The spectrum of benzene dissolved in a liquid crystal served as a prototype in the development of the single quantum n.m.r. of complex spin systems in ordered phases, The multiple quantum spectrum of ordered benzene is shown in fig. 2. The resolution is limited by magnetic homogeneity and the inhomogeneous linewidth is proportional to 1 1. 

The overlap integral reflects the requirement of energy conservation in the ET process. Its value is uncertain because the homogeneous linewidth of solid-state spectra can be up to three orders of magnitude smaller than the inhomogeneous linewidth [359]. A value of 8xl021 J 1 has been adopted for the calculation of MD-MD ET in Cs2NaTmCl6 [360]. 

Even for a single radieal the speetial resolution can be enhanced for disordered solid samples if the inhomogeneous linewidth is dominated by unresolved hyperfine interactions. Whereas the h5 erfine line broadening is not field dependent, the anisotropic g-matrix contribution scales linearly with the external field. Thus, if the magnetic field is large enough, i.e. when the condition... 

It is well known, however, that the width of a spectral line, at least in principle, yields information on the dephasing dynamics of the optical transition. Spectral lineshapes of purely electronic transitions in solids unfortunately are seldom determined by dynamic interactions, but, at least at low temperature, quite often by the effects of strain. The observed, named inhomogeneous linewidth is therefore of little interest. In case of vibronic transitions, however, the effect of vibrational relaxation on the lineshape may exceed the inhomogeneous linebroadening. Even so, classical spectroscopy quite often fails to elucidate the nature and strength of the perturbing forces on the optical (homogeneous) lineshape. 

The reduction of the inhomogeneous linewidth follows from Van Vleck s calculation of the second moment (AB ). It states that (AB > is proportional to N is here the number of nuclear spins. In an A - B pair, the number of nuclear spins is doubled in comparison to an isolated molecule. Therefore, the inhomogeneous linewidth is reduced by the factor 1 /-/z. The experimental values in naphthalene confirm this interpretation in the immediate neighbourhood of the A-M - B crossing points (a = 120° in Fig. 7.4), the experimental value for the ratio of the linewidths of the mini-exitons to those of the isolated molecules is ABm/ABab = 1/1.6. The width AB is thus an additional confirmation of the model for a mini-exciton it consists of the two molecules in a unit cell. At higher N-hg concentrations x = 10%), A-A-B and A-B-B mini-excitons have also been observed [4]. 

Related to the issues of crystallinity, order or randomness in silica samples, as reflected in Si MAS linewidths, are the matters of homogeneous and inhomogeneous contributions to the linewidth. The latter results from a superposition/overlap of numerous closely spaced peaks, each representing a specific structural environment that is, inhomogeneous linewidth contributions arise from a degree of randomness in the structure — structural... 

For simplicity we also assume a Lorentzian shape as a result of the inhomogeneous linewidth A ... 

W j, = 2.5MHz as the values of inhomogeneous linewidths. Probe absorption and dispersion are... 

Radicals in Biological Systems. - The ability to resolve two separate lines with g factors gi and g2 depends on the inhomogeneous linewidth AB1/2 (which is often dominated by unresolved hyperfine interactions in biological systems) and is governed by the relationship... 

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