Spectra of Dilute Single Crystals

Spectra of radicals in a dilute single crystal are obtained for various orientations, usually with the field perpendicular to one of the crystal axes. Each spectrum usually can be analyzed as if they were isotropic to obtain an effective g-value and hyperfine coupling constants for that orientation. Since the g- and hyperfine-matrix principal axes are not necessarily the same as the crystal axes, the matrices, written in the crystal axis system, usually will have off-diagonal elements. Thus, for example, if spectra are obtained for various orientations in the crystal vy-plane, the effective g-value is  

A sinusoidal plot of grf 2 vs. p can be analyzed to determine Ku K2, and K3. Exploration of another crystal plane gives another set of Ks that depend on other combinations of the gy, eventually enough data are obtained to determine the six independent values of gy (g is a symmetric matrix so that gy = gy,). The g-matrix is then diagonalized to obtain the principal values and the transformation matrix, elements of which are the direction cosines of the g-matrix principal axes relative to the crystal axes. An analogous treatment of the effective hyperfine coupling constants leads to the principal values of the A2-matrix and the orientation of its principal axes in the crystal coordinate system. 

In their 1967 book, Atkins and Symons6a summarized much of the early ESR work on small inorganic radicals, many of which were produced by photolysis or radiolysis of single crystals of the precursor molecules. A good example of the application of the information that can be obtained from such single-crystal studies is the analysis of the spectrum of N03, produced by y-irradiation of KN03 crystals by Livingston and Zeldes.6b Table 4.1 summarizes the results. 

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We have seen that spectra of dilute single crystals are analyzed in a way that gives the orientations of the g- and hyperfine-matrix principal axes relative to the crystal axes. Historically, most of the information on noncoincident matrix axes is derived from such studies. 

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