Electron Spin Resonance in the Study of Radiation Damage 249 



In simple cases where single crystals can be prepared, it should be possible 

 to measure (1//'^>av for the interaction of an electron in atomic orbital of 

 atom B interacting with the nucleus of another atom A. Such applications 

 are made later in the discussion. If (1//'^>av~* is greater than the interatomic 

 distance, the electron may be in a hybridized orbital of B which projects 

 away from A. If it is less than the atomic distance, the electron may be in 

 a hybridized orbital which projects toward A. In some instances {\lr^)A\ 

 may be so large that the field of the electron at the nucleus may be greater 

 than the applied field. The nucleus would not then necessarily precess about 

 the direction of H, and the above fommla would not hold for all values of 0. 

 It should still hold when equals zero or 90°, for then the field of the electron 

 at the location of the nucleus would have, on the average, the same direction 

 as H. If the cloud of the electron is symmetrical about the bond axis between 

 A and B, the angle 6 would, in effect, measure the orientation of the bond 

 axis in the field H. For this case (3 cos^ d — 1)av equals 2 for (? = (bond 

 axis parallel to //), and (3 cos^ — l)^^ equals — 1 for = 90° (bond axis 

 perpendicular to H). Thus the A// should have twice the value for equal 

 to zero as that for d equal to 90°. The dipole-dipole interaction of the electron 

 with the nucleus averages to zero when the electron is entirely outside the 

 nucleus and is moving in such a manner that its averaged density achieves 

 spherical symmetry about the nucleus during its lifetime in a spin state. 



Nuclear hyperfine structure of any type becomes independent of the mag- 

 netic field strength after the field becomes sufiiciently strong to achieve the 

 Paschen-Back case, which is assumed in the above treatment. Thus nuclear 

 hyperfine structure can be readily distinguished from the splitting wliich arises 

 from anisotropy in the g factor, discussed below, if measurements are made 

 at two or more frequencies, both with strong fields. Although the direct- 

 dipole type interaction with the nucleus varies with orientation in the field, 

 it does not vary with the magnitude of the field after the strong field case is 

 reached. 



Figure 2 shows the type of hyperfine structure theoretically predicted for 

 the strong field case for various radicals with equally coupling nuclei having 

 spins of I {H or F, for example). Figure 3 illustrates a few cases where the 

 coupling of one or two of the nuclei differs from that of the others. It is appa- 

 rent that these cases are easily distinguishable. 



2. Residual Spin-Orbit Coupling 



If the odd-electron density of a radical is largely concentrated on a non-5 

 orbital of a single atom of a radical or is shared mainly by only two atoms, as 

 it is on the — N — N — group of diphenyl picryl hydrazyl (DPPH), effects of 

 spin-orbit interaction are not entirely negligible. The orbital momentum will 

 be oriented by the strong electrical force of the chemical bond and will not be 

 free to precess about the applied field. Bond-oriented orbital components will 

 give rise to an observable anisotropy in the magnetic susceptibility and thus in 

 the observed g factor. If the odd electron wave function is symmetric about a 

 particular bond as in DPPH, the observed g factor will reflect this symmetry: 

 if all such bonds in a given sample were oriented along the applied H, the ^n 

 factor would differ from the g^^ observed when the bonds are all oriented 



