Homogeneous and inhomogeneous lines

Dipolar coupled lines in solids, especially in single crystals, are usually homogeneous, too, but in a different way. In this case, there are separate contributions to different parts of the line but they cannot be so identified because the coupling between the separate parts of the line is so good. The basic lineshape approximates a Gaussian and its width is totally unrelated to 1/T except that it must equal or exceed it. 

An inhomogeneous line is one in which separate parts of the line can be identified as due to separate contributions. The most common example is a powder pattern due to anisotropies such as quadrupolar or chemical shifts in which crystallites with different orientations with the static magnetic field contribute to different parts of the line. 

One way of determining whether the line is broadened homogeneously or inhomogeneously, is to irradiate and saturate a specific spot in the line with a large, coherent H field. Immediately after the irradiation, the line is detected either by cw or pulse FT NMR and an inhomogeneous line will have a hole burned into it (Bloembergen, et al., 1948). 

As the shape of the hole will approximate the shape of a line in a homogeneous part of the magnetic field, it can be used to study natural lineshapes under conditions of poor Hq homogeneity (Schaefer, 1974). If, on the other hand, the line is homogeneously broadened, the attempt to burn a hole in the line will result in a collapse of the entire line. 

How about some other examples of homogeneously broadened lines The application of high radio frequency power to a transition not only causes saturation (if is sufficiently long) but also causes power broadening for the entire system. When a strongly coupled system, coupled by dipolar interactions, permits spin diffusion and the establishment of a common spin temperature, the attempt to burn a hole in the line will also result in a collapse of the entire line. Dipolar interactions, spin diffusion, and spin temperatures are discussed later in this chapter, as well as in III.C.l. and in IV.D. 

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An example is illustrated in Fig. 2. In case 1, there are two mechanisms operating one in the fast modulation limit, and one in the slow modulation limit. This is the classic case of combined homogeneous and inhomogeneous line broadening. In case 2, there is a single mechanism, but it is in the intermediate modulation region. The Raman hnewidths are identical... 

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