Magnetisation molar

In a linear isotropic material B = where p, is the permeability of the material. The relative permeability p-r = p./po or = 1 + x is a measure of how much magnetisation a material will generate. The molar and specific susceptibilities are also quoted in the literature. 

In practical experiments, the magnetometer is normally calibrated such that the experimentally determined magnetisation can be converted into the molar magnetic susceptibility (xm) through multiplication by the ratio of the molecular weight to the sample weight and dividing by the applied... 

Analogous relationships hold true among the (volume) magnetisation, mass magnetisation and molar magnetisation, hence... 

The individual constituents of the last expression have their dimensions as follows /i,0 [JA 2m 1], H [Am-1] and M [Am 1] then the expression has the dimension of [J m 3] which refers to the volume energy. If M refers to the molar magnetisation, A/moI[Am2mor1], then the product dw = ix0H dM has the dimension of the molar energy [J mol-1]. It is assumed hereafter that the other energy quantities (17, E, F, G, TS, CT) possess the same dimension. 

Statistical thermodynamics brings the result that the thermal average of the (molar) magnetisation can be evaluated through the formula... 

As a result of the experiment, the discrete function x° versus Tt is obtained. The mass susceptibility or magnetisation is converted to the molar susceptibility and subjected to the corrections for the underlying diamagnetism and eventually for the temperature-independent paramagnetism, yielding Xmol.i =f(Td-... 

Then the molar magnetisation is given through the Brillouin function (introduced in Section 6.1) as... 

Fig. 8.1. Molar magnetisation versus magnetic field for paramagnets (a) for T = 4.2 K individual curves correspond to S = 1/2 (solid), 1 (long dashed), 3/2 (medium dashed), 2 (short dashed) and 5/2 (dotted) (b) for S = 5/2 individual curves correspond to T = 4.2 K (solid), 77 K (long dashed) and 300 K (medium dashed).

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

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