Langevin diamagnetism

We shall now briefly describe the well-known temperature-independent Langevin diamagnetism of closed-shell ions, such as K+ and Cl in KCl and similar Inorganics, such as Si02, AI2O3, and the zeolites, as well as the covalent organic compounds. Since all such... 

Additional evidence on electron-cloud radii is given by diamagnetic susceptibility and by refractive index. For the well-known Larmor-Langevin theory of diamagnetism (11—13) gives for the molecular diamagnetic susceptibility —Xm the formula... 

Weber in 1854 had attributed paramagnetism to the orientation of little permanent magnets in the substance (and diamagnetism to induced currents, as discussed above). A quantitative treatment was developed by Paul Langevin in 1895, by application of the Boltzmann principle. The theory is the same as for the orientation of electric dipoles (see App. IX). It leads to the equation... 

The first term is always negative and is referred to as the diamagnetic contribution or the Langevin term. The second, sum-over-states term is known as the paramagnetic contribution and is always positive or zero for ground states. 

The first term is seen to be positive, corresponding to a diamagnetic contribution to the susceptibility, y,, called the Langevin term. The second is seen to be negative, corresponding to a paramagnetic contribution Xp, called the Van Vleck term. We may obtain these terms directly by multiplying Eq. (5-23) by the electron... 

In spherically symmetric systems the induced diamagnetism depends primarily on the mean square radius of the valence electrons as the small contribution from the inner-shell electron core can usually be neglected 1 ). In the case of molecules with symmetry lower than cubic, the quantum mechanical treatment by Van Vleck 23> indicates that another term must be added to the Larmor-Langevin expression in order to calculate correctly diamagnetic susceptibilities. This second term arises because the electrons now suffer a resistance to precession in certain directions due to the deviations of the atomic potential from centric symmetry. The induced moment will now be dependent on the orientation of the molecule in the applied magnetic field and thus in general the diamagnetic susceptibility will not be an isotropic quantity 19-a8>. 

Normally the TIP contribution (the van Vleck term) is only a minor correction to the underlying diamagnetism (the Langevin term). In complex systems like metalloproteins the diamagnetic contribution may also dominate the temperature-dependent paramagnetism. 

It is often found that the Curie law Eq. (21) is followed by many magnetically dilute substances other than free atoms or ions. There is, in addition, a second-order contribution to the paramagnetic susceptibility, the so-called temperature-independent paramagnetism Not. (also abbreviated TIP, cf. section 1,1.3.6) which arises from states separated from the ground state by an energy k T It follows that the molar susceptibility corrected for diamagnetism may be frequently represented by the Langevin-Debye expression... 

The use of Xo indicates that the so-called Stoner enhancement factor has not been included (the toner theory is a mean-field theory for itinerant electrons). In Equation (3 3), is the averaged value of the varying D over the particles, Xyv is the Van Vleck paramagnetism, and Xdia is the Langevin (or Larmor) diamagnetism. 

In diamagnetic materials, the magnetic susceptibility can be accurately predicted by Langevin s classical theory of electromagnetism as follows ... 

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