Susceptibility formulae

Table 24 Terms of the susceptibility formula in the intermediate crystal field (ge = 2)...

For the 2 2g and 5T2g-terms of the Oh-reference the Griffith theory could be appropriate. In the case of the Cl-interacting terms 3Tig or 4 Tig, the Figgis isotropic Hamiltonian can be applied. These theories offer the magnetic susceptibility formulae in closed forms. However, these approaches... 

As an alternative method for the determination of the cluster size, we analyzed the low-field magnetic moment data from Fig. 2(c) by means of the modified susceptibility formula [24], derived from equation (1) in the low-field limit g B kB(T — Tc) ... 

As this equation is in a certain way the analog of the already tested Eq. (4.112), it has a good chance (although not yet tested) to be a good approximation for y in the whole temperature interval. As we have already ascertained in Section III.A.4, the best interpolation expression for the relaxation time xio to be used in the susceptibility formulas is Eq. (4.105) first introduced in Refs. 71 and 87. 

Terms of the magnetic susceptibility formula for multiplets of intermediate width... 

The corresponding coefficients for the susceptibility formula are collected in Table 8.37 and the product functions XmoiT versus x-1 are displayed in Fig. 8.20. 

In the case of the intermediate field Figgis [5] derived the magnetic susceptibility formula in the form (Table 8.38)... 

Evidently, the exchange coupling constant should be far from zero otherwise the susceptibility formula derived with the help of the perturbation theory diverges. 

The practical link of the diamagnetic susceptibility with atomic radii can be reached performing the stipulated correspondence when from Ihe total number of electrons, N, only the outer (valence) electrons in the atomic systems are considered, while the average becomes Ihe absolute atomic radii itself, R . Therefore, the actual atomic working diamagnetic susceptibility formula in terms of atomic radii becomes (Putz et al., 2003, 2012b,c) ... 

This is the simplest form of the susceptibility formula which was derived by McLachlan in 1962 [61, 62],... 

The susceptibility formula (2.20) can readily be used for calculating the attraction between atoms or molecules, if these particles are replaced by electric dipole oscillators. Let us consider two electric dipole oscillators i and j with elongations u,- and Uj at positions and rj. The electrostatic force exerted on dipole j by a unit moment of dipole i is given by the respective component of the dipole interaction tensor... 

The susceptibility formula Eq. (2.20) can be used to describe the dispersions energy between macroscopic particles 1 and 2 along two alternative routes. We may replace each atom of particles 1 and 2 by a set of dipole oscillators and integrate the dispersion energy between any pair of atoms, or we may treat the particles as a whole as harmonic oscillators. 

The exchange interaction modifies the magnetic susceptibility formula so that at zero temperature... 

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