Shapes of Inhomogeneously Broadened Resonance Lines in Solids

Inhomogeneous broadening has been observed in resonance lines in solids over the wide range of energies spanned by nuclear magnetic resonance, electron spin resonance, optical, and M\"ossbauer methods. The broadening arises from random strains, electric fields, and other perturbations from the defects in the lattice containing the centre whose transitions are studied. This paper reviews the calculation of the shapes of such resonance lines. The most important method used is the so-called statistical method. This method determines the line shape as a function of the distribution of the defects with respect to the centres studied, the density of the defects, and the perturbation fields of the individual defects. Emphasis is laid on the physical assumptions and approximations in this method and on its relation to other approaches. The theory is applied to a variety of broadening mechanisms, both in the widely used continuum approximation for the lattice containing the defects and in the more realistic discrete-lattice model. Two classes of experimental work are reviewed. The first deals with the ways in which resonance lines are recognised as being inhomogeneously broadened. These methods show that a wide range of phenomena can be used to check the theory of the line shapes. The second discussion of the experimental work compares theory and experiment for each of the various broadening mechanisms. These mechanisms include broadening by the strains from dislocations and point defects, by the electric fields and field gradients from charged defects, and by unresolved hyperfine structure. In each case theory and experiment are compared in detail for the system for which the most complete data are available. The conclusion is that the statistical method provides a satisfactory approach in all cases for which there are adequate data.