Orbital contribution reduction factor

This Section gives an outline of an algebraic calculation of the magnetic properties of a complex ion. The treatment is repeated in more detail in Appendix 10. In real life, the calculations would be carried out by a computer and some of the approximations that will be made here would not be necessary. However, the language of the subject is so wedded to the algebraic treatment that it is essential to study it, at least superficially. 

There is a Boltzmann distribution of molecules over the levels shown on the right-hand side of Fig. 9.2, so that the relative number of molecules occupying a level with energy E is exp( //cT), a quantity which can be used in the expression above provided that we have explicit expressions for the energy levels—and Appendix 10 provides them. The Zeeman part of the calculation provides the value of the magnetic moment for the molecules in a particular level. Having thus obtained a complete expression for this can be related to the quantity usually discussed, the Bohr magneton number because, as was shown in Section 9.2 (eqns 9.4 and 9.5) 

Rather than work with the rather unwieldy equations resulting from the expressions given in Appendix 10 we shall simplify. We ignore the tetragonal 

2 Schematic energy level diagram illustrating the various splittings determining the ground state derived from a t g configuration. 

We can now plot the value of (given by the positive square root of the above expression) against x, or, more conveniently, against 1/x, to give a so-called Kotani plot. This has been done in Fig. 9.3. Also on this figure are indicated the values of C/kT for some d ions at 300 K, C being given the 

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A reduction in the g factor below the value expected for a completely ionic complex is frequently observed and an interpretation is possible in terms of the effect of covalency on the orbital magnetic moment. The delocalization of spin on to the ligands reduces the orbital moment associated with the magnetic cation, and hence any orbital contribution to the g factor. An orbital reduction factor kt) is defined ... 

Equation (5.17) is only available for a compound in which all the 0=Np=0 axes are collinear in the crystal. To apply the present model to the other compound whose crystal consists of plural 0=Np=0 axis directions, it is necessary to consider the individual crystal structures. Nevertheless, the magnetization can be derived in a very simplified manner by ignoring some important problems, such as the validity of the LS-coupling model or the necessity of introducing the orbital reduction factor k (which is needed for correction for the reduction in orbital size caused by covalent contributions), and so on [47]. Another serious problem in the magnetization measurements is the use of polycrystalline samples. According to the present model, the... 

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