Schonland method

The analysis in Chapter 3 shows that fittings to the quantities G and P as a function of crystal orientation with respect to the magnetic field according to the Schonland method yield the elements of the hyperfine and nuclear quadrupole coupling tensors. A simple method therefore involves separate measurements of G and P from the observed ENDOR frequencies. 

Abstract The analysis of ESR, ENDOR, and ESEEM data to extract the resonance parameters is treated. Free radicals in solution are mainly identified by their hyper-fine couplings (hfc). The analysis of ESR and ENDOR spectra by visual inspection and by computer simulation is discussed. The Schonland method to obtain the principal values and directions of the anisotropic g- and hfc- tensors from single crystal ESR and ENDOR data is presented. The modifications needed when 5 > A or / > A to obtain zero-field splitting ( i) or nuclear quadrupole coupling (nqc) tensors are considered. Examples of simulations to extract g-, hfc-, Tfs-, and n c-tensors from ESR and ENDOR spectra of disordered systems are presented. Simulation methods in pulsed ESR (1- and 2-dimensional ESEEM) studies are exemplified. Internet addresses for down-loading software for the simulation of ESR, ENDOR, and ESEEM spectra are provided. Software for the analysis of single crystal data by the Schonland method is also available. 

Fig. 3.9 Schematic variation of the g-factor with the magnetic field in the xy-, yz-, and zx-planes in the Schonland method to determine the g-tensor. The variation is shown over a 90 = interval for the angle specifying the orientation of the magnetic field in each plane. For a perfect fit the measured g-factor should agree along the , , and axes in the different planes. A sign error for (g )xy occurs if the crystal is unintentionally mounted for rotation about -z in place of +z, see text for methods to resolve this Schonland ambiguity ...

The angle specifying the magnetic field direction in the Schonland method is usually measured relative to the crystal axes (denoted by , , and in Fig. 3.9). These positions must therefore be accurately determined. A satisfactory positioning is indicated in the Schonland method if the spectra obtained with the magnetic field along one of these axes are identical between two planes. 

X32, Schonland type analysis for S > V2. The software is based on the 2nd order perturbation theory by Iwasaki [19] to obtain the principal values and directions of tensors for S > V2 species including zero-field splittings. The program is in obsolete code (Quickbasic), and is not maintained. It has been applied by the authors for the analysis of zero-field splitting tensors which requires a modification of the Schonland method in accordance with Eq. (3.5) that apparently is not implemented in the other programs in Table 3.4. 

Poole and Farach formulation [48] Equations obtained for the special case with S = / — /2 derived by Poole and Farach [48] are useful when both the inner and outer doublet splittings Ti and are observed. In this case thehyperfine coupling tensor can directly be obtained in single crystal measurements by the Schonland method from the relation ... 

The Schonland procedure to obtain the hyperfine coupling tensor differs in some details depending on the magnitude of the coupling and on the applied methods, usually ESR or ENDOR. 

When the g-factor is anisotropic this simple approach fails. A Schonland fitting procedure can be applied when the ENDOR lines for both ms = V2 and -V2 are observable, while non-linear least squares methods are more generally applicable. The latter method can be adopted e.g. to simultaneously determine hyperfine and nuclear quadrupole tensors. Detailed procedures may be obtained from the literature [12, 14]. 

This application may seem redundant, but is motivated e.g. by the so-called Schonland ambiguity in determining the hyperfine coupling tensor from single crystal measurements. It is only very recently that methods to eliminate the ambiguity [17] have been proposed, and the procedures are not always applicable. An investigation to clarify the radical structure of /-alanine is taken as an example in Fig. 3.27. 

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