Experimental Determination of Matrix Axis Orientations

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. 

At first glance, it would appear that all orientation dependence should be lost in the spectrum of a randomly oriented sample and that location of the g- and hyperfine-matrix principal axes would be impossible. While it is true that there is no way of obtaining matrix axes relative to molecular axes from a powder pattern, it is frequently possible to find the orientation of a set of matrix axes relative to those of another matrix. 

Two corollaries stem from this generalization. Since a spin-1/2 nucleus gives only two hyperfine lines, there can be no variation in spacings. Thus powder spectra cannot be analyzed to extract the orientations of hyperfine matrix axes for such important nuclei as 3H, 13C, 19F, 31P, 57Fe, and 103Rh. Secondly, since the observable effects in powder spectra depend on the magnitude of the matrix 

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