Mean magnetic susceptibility

We carried out a second calculation for BeH at an internuclear distance of 2.67 a.u. corresponding to the minimum of energy.The mean magnetic susceptibility x obtained value, which is equal to -0,86.lO erg.G. mol V, agrees more closely to the value calculated by Fowler and Steiner [5], at the same internuclear distance,which is equal to -0.50 10 erg. G. mol F... 

In Table 7, we reported the mean magnetic susceptibilities X of the BH and CH+ molecules, obtained by G. Berthier et al. [3], using the same SCF ab initio method,... 

Finally, the formula for the mean magnetic susceptibility becomes... 

Derivation van Vleck equation (linear magnetics) or expansion of Brillouin function Restrictions n Bg /kT < 1 - low fields and higher temperatures Formula Curie law Mean magnetic susceptibility... 

The magnetic susceptibility is introduced as a thermodynamic quantity which requires a partial differentiation of the magnetisation according to the applied field. This differential (isothermal) magnetic susceptibility differs from the frequent definition of mean magnetic susceptibility if the behaviour of the magnetic material is nonlinear. 

This derivation, evidently, is well valid for substances obeying a linear dependence of the magnetisation upon the applied magnetic field (paramagnets), and this cannot be overemphasised. Now the expression for the mean magnetic susceptibility is straightforward... 

This is how the limitations of the van Vleck formula can be overcome. The evaluation of the mean magnetic susceptibility is, as above,... 

When the linear approximation to the Brillouin function is not fulfilled, then the mean magnetic susceptibility x = M/H should be substituted by a differential magnetic susceptibility... 

Consequently the magnetic susceptibility is evaluated either via the van Vleck formula (mean magnetic susceptibility) or by differentiating the molar magnetisation (differential magnetic susceptibility). 

Fig. 8.29. Effective magnetic moment based on mean magnetic susceptibility versus temperature for the Tlg term at different magnetic fields B = 0.001 T (solid), fi = 1T (long dashed), fi = 5T (medium dashed), B = 10T (dotted).

Fig. 8.31. Temperature dependence of magnetic susceptibilities for the 4TXg term at different applied fields m—mean magnetic susceptibility d—differential magnetic susceptibility (solid) a— approximate magnetic susceptibility based on the van Vleck equation.

Fig. 8.32. Temperature dependence of effective magnetic moments for the 4Tlg term at different applied fields m—based on the mean magnetic susceptibility d—based on the differential magnetic susceptibility (solid) a—based on the approximate magnetic susceptibility via the van Vleck equation.

For example, the mean magnetic susceptibility for the Sa Sb = 5/2 dimer becomes... 

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