EPR study of Fe3+in α‐quartz: A reexamination of the so‐calledIcenter

CW-EPR Spectral Simulations: Solid State

This chapter summarizes the core concepts underlying the simulation of EPR spectra from biological samples in the solid state, from a user perspective. The key choices and decisions that have to be made by a user when simulating an experimental EPR spectrum are outlined. These include: the choice of the simulation model (the network of spins and the associated spin Hamiltonian), the dynamic regime (solid, liquid, slow motion), the level of theory used in the simulation (matrix diagonalization, perturbation theory, etc.), the treatment of orientational order and disorder (powder, crystal, partial ordering), the inclusion of the effects of structural disorder (strains), the effects of other line broadening mechanisms (unresolved hyperfine couplings, relaxation), and the inclusion of experimental distortions (field modulation, power saturation, filtering). Additionally, the salient aspects of utilizing least-squares fitting algorithms to aid the analysis of experimental spectra with the help of simulations are outlined. Although drawing from the experience gained from implementing EasySpin and from interacting with EasySpin's user base, this chapter applies to any EPR simulation software.

Higher-order Zeeman and spin terms in the electron paramagnetic resonance spin Hamiltonian; their description in irreducible form using Cartesian, tesseral spherical tensor and Stevens' operator expressions

In setting up a spin Hamiltonian (SH) to study high-spin Zeeman and high-spin nuclear and/or electronic interactions in electron paramagnetic resonance (EPR) experiments, it is argued that a maximally reduced SH (MRSH) framed in tesseral combinations of spherical tensor operators is necessary. Then, the SH contains only those terms that are necessary and sufficient to describe the particular spin system. The paper proceeds then to obtain interrelationships between the parameters of the MRSH and those of alternative SHs expressed in Cartesian tensor and Stevens operator-equivalent forms. The examples taken, initially, are those of Cartesian and Stevens' expressions for high-spin Zeeman terms of dimension BS(3) and BS(5). Starting from the well-known decomposition of the general Cartesian tensor of second rank to three irreducible tensors of ranks 0, 1 and 2, the decomposition of Cartesian tensors of ranks 4 and 6 are treated similarly. Next, following a generalization of the tesseral spherical tensor equations, the interrelationships amongst the parameters of the three kinds of expressions, as derived from equivalent SHs, are determined and detailed tables, including all redundancy equations, set out. In each of these cases the lowest symmetry, [Formula: see text] Laue class, is assumed and then examples of relationships for specific higher symmetries derived therefrom. The validity of a spin Hamiltonian containing mixtures of terms from the three expressions is considered in some detail for several specific symmetries, including again the lowest symmetry. Finally, we address the application of some of the relationships derived here to seldom-observed low-symmetry effects in EPR spectra, when high-spin electronic and nuclear interactions are present.

Interpreting electron-nuclear-magnetic field interactions from a hamiltonian expressed in tensorial notation

The general experimental hamiltonian expressed in tensorial notation is assessed in a way to ensure that the outcomes from such a hamiltonian reflect correctly the electron-nuclear-magnetic field interactions and yields the appropriate parameters. Without such knowledge the use of hamiltonians in tensorial notation to analyse magnetic resonance spectra may lead to questionable or even meaningless results reflected in several publications over the years. Furthermore, the errors that may occur in handling mixed hamiltonians compound the problem.

Low-symmetry spin hamiltonian and crystal field tensors analysis: Fe(3+) in natrolite

Electron paramagnetic resonance study of a natural single crystal of natrolite was carried out at the frequency nu=36.772 GHz at room temperature. The angular dependence of the four symmetry-related spectra of Fe(3+) in the three crystallographic planes was fitted to a spin Hamiltonian (S=5/2) of symmetry C(i). The rank 4 crystal field tensors at tetrahedral sites were calculated using the point-charge model to determine the principal axes orientations of their cubic and trigonal components. The analysis of zero-field splitting tensors and comparison with crystal field ones suggests that Fe(3+) substitutes for Al(3+) with no significant distortion of the coordination tetrahedron in natrolite. Comparison of data for several natural and synthetic crystals reveals that the 4-rank zero-field splitting tensor invariants for Fe(3+) at the tetrahedral oxygen-coordinated sites are distinguishably smaller than those for Fe(3+) at octahedral sites. Such comparative analysis may help to determine the substitutional sites in other crystals.