Software for single crystal analysis

Software for this purpose is often developed in laboratories specialized in single crystal measurements, but the programs are not always available. The computer programs listed in Table 3.4 that the authors are aware of contain several steps, (1) to provide the experimental data (g-factors, hyperfine couplings, zero-field splittings, ENDOR or ESEEM frequencies) as function of crystal orientation, (2) to perform a least squares fitting of a theoretical model to the data, and (3) to make an error analysis of the parameter values, i.e. the principal values and direction cosines of the principal axes of the coupling tensors. 

The last step is model independent and similar code can be applied in all cases. The first step usually requires only minor modification depending on the type of data. We refer to the original literature (Table 3.4) for the technical procedures applied in the second step, but consider below some practices that can help to improve the accuracy of the analysis. 

An exact match may be difficult to achieve, experimentally, however. Some programs therefore have a feature for automatic adjustment of the positions of the axes. In crystals of symmetry higher than triclinic, spectra due to different sites that become identical along the crystal axes makes it easier to accurately determine the obtain axes as shown in Fig. 3.10. Another difficulty, related to the Schonland ambiguity then appears, however, as discussed next. 

All observed transitions for different ms and mi quantum numbers can be included simultaneously in the fit. This feature helps to avoid the ambiguity that may occur in the analysis with the Schonland procedure discussed above and in Section 3.2. Error estimates of the parameters are computed. The program also simulates transition frequencies for the rotation planes. The simulation results are automatically stored in files of two columns, field orientation (deg.) and transition frequency (MHz). Both rotation senses ( sites for orthorombic a,b,c and monoclinic crystals) are simulated. The program was developed by A. S0mes, and can be obtained at [http //www.fys.uio.no/biofysikk/eee/esr.htm]. 

TENSOR. A program to determine hyperfine tensors from ESR or ENDOR single crystal data is described. The variation of hyperfine interaction upon rotating the crystal with respect to the static field is studied by a least-squares algorithm which affords various weighting methods. These take into account the fact that the model equations are not linear in the variables, so that equal measurement errors affect the calculation to different extents. An iterative procedure is available which 

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