Magnetic dipole interaction parameters

Apart from the determination of nuclear parameters, the Mossbauer transition in Os, especially the 36.2 and 69.6 keV transitions, are suited for chemical applications. As shown below, the 36.2 keV level, in spite of its large half-width, can be well used for the measurement of isomer shifts, whereas the 69.2 keV state is favorable for the characterization of electric quadrupole or magnetic dipole interactions. Both Mossbauer levels are populated equally well by the parent isotope lr, and simultaneous measurement is possible by appropriate geometrical arrangement. 

The last ratio is independent of the parameters, a and 3 and may regarded as a purely group theoretical (kinematic) result. The same result is obtained dynamically without group theory through the Slater-Condon parameters which are integrals of e2/rjj over analytic hydrogenic orbitals. The chain has been interpreted as the sum of a p orbital-p orbital and a spin orbital-spin orbital magnetic dipole interaction. This inteipretation is clearly nonphysical. 

The first term is the Zeeman interaction with the applied field with a mean shielding o for nucleus i, which may differ somewhat from the value in isotropic solvents due to the anisotropy of the shielding tensor. The second term contains the well-known isotropic part of the indirect spin-spin coupling of nuclei i and /. For pairs of protons the Jq are a few hertz. The major contribution to the parameters Dq of the last term derives from the direct (dir) magnetic dipole interactions of pairs of nuclei, which will be denoted by Efjf1. The contribution from the indirect interactions is often negligible and will be discussed below. 

A. The Interspin Magnetic Dipole Interaction and the Zero-Field Splitting Parameters, 209... 

The general formula in Eq. (8) reveals that the magnetic dipole interaction in triplet states depends on the spin density p (electronic effects) and on the distance d (geometrical effects) between the two radical sites. This implicates that aryl substituents, which are known [32-36] to affect the spin density at the benzylic position, should exhibit a measurable influence on the D parameter of the triplet diradicals 9-11. For convenience, we define the simple Eq. (9), in which the relative changes (AD) caused by the... 

Parallel to these three parameters for the magnetic dipole interaction, there are also three for the electric quadrupole interaction, that we shall not discuss. We remark only that on previous theory the values of in eqs. (5), (6) should be equal the... 

Since the di,scovery more than 40 years ago, Mossbauer spectroscopy has become an extremely powerful analytical tool for the investigation of various types of materials. In most cases, only two parameters are needed, viz. the isomer shift and the quadrupole splitting, to identify a specific sample. In case of magnetically ordered materials, the magnetic dipole interaction is a further helpful parameter for characterization. In the following... 

The zero-field splitting parameters D and E measure the magnetic dipole interaction of the unpaired electrons in the absence of an external field [85Kir, 83Poo, 86Wer, 73Ath]. D is a measure of... 

Magnetic dipole interaction between the nuclear magnetic dipole moment and a magnetic field at the nucleus. The observable Mossbauer parameter is the magnetic splitting AEm . This quantity gives information on the magnetic properties of the material under study. 

Equation (4) is valid with high accuracy because induced magnetic dipoles interact only weakly. By contrast, interaction between the induced electric dipoles is strong and produces substantial local field effects which do not allow one to express the dielectric permittivity of the nematic phase in terms of the molecular parameters in a simple way (see, for example, [4]). 

The connection between the rate constants W and molecular parameters is a complex subject that can only be outlined here. Basically, the dipole-dipole interaction is a through-space effect in which one nuclear magnetic dipole interacts with the local field created by a second nucleus. The value of W depends upon the component of this field that fluctuates at the frequency of the transition, that is at 0, (o and 2Larmor frequency. Working out the algebra shows that the cross-relaxation rates are proportional to spectral densities, which are Fourier transforms of time correlation functions that describe molecular motions ... 

Effective radial parameters of the magnetic dipole interaction for the 4d 5s configuration have been derived from the constants A [20] (in MHz) ... 

From experimental A values [2, 15, 28] the effective radial parameters (in MHz) of the magnetic dipole interaction have been derived, parameters being constrained to be equal to ab initio calculated values or to vary in the constant ratio of the spin-orbit constants [45] ... 

The process of spin-lattice relaxation involves the transfer of magnetization between the magnetic nuclei (spins) and their environment (the lattice). The rate at which this transfer of energy occurs is the spin-lattice relaxation-rate (/ , in s ). The inverse of this quantity is the spin-lattice relaxation-time (Ti, in s), which is the experimentally determinable parameter. In principle, this energy interchange can be mediated by several different mechanisms, including dipole-dipole interactions, chemical-shift anisotropy, and spin-rotation interactions. For protons, as will be seen later, the dominant relaxation-mechanism for energy transfer is usually the intramolecular dipole-dipole interaction. 

We have learned from the preceding chapters that the chemical and physical state of a Mossbauer atom in any kind of solid material can be characterized by way of the hyperfine interactions which manifest themselves in the Mossbauer spectrum by the isomer shift and, where relevant, electric quadrupole and/or magnetic dipole splitting of the resonance lines. On the basis of all the parameters obtainable from a Mossbauer spectrum, it is, in most cases, possible to identify unambiguously one or more chemical species of a given Mossbauer atom occurring in the same material. This - usually called phase analysis by Mossbauer spectroscopy - is nondestructive and widely used in various kinds of physicochemical smdies, for example, the studies of... 

---