Magneton number

Figure 2. Plot of relative magnetization, a/Os ns a function of H/T. (a) A paramagnetic system Is characterized by an effective magnetic moment, with a Bohr Magneton number vlO per Ion, and by the absence of hysteresis. Paramagnetic saturation occurs at very high "H/T" == 10 Oe K"l. (b) l.angevln curve for S.P. clusters, (c) Part of a ferromagnetic hysteresis curve.

Bohr magneton number, 27 37 self-supported, 27 32, 33 structure, 27 32 Rate constants... 

Fig. 12. Comparison of N6el theory (curve 1) with (open circUs) measured Bohr magneton number ng = extrapo-...

A fairly crude estimate of the magneton number for activated Lu203 and Y203 suggests that only one electron spin per site is active. But for nearly all the other catalysts studied the Bohr magneton number is much larger and it varies widely. 

Two principal unit systems are in use for electromagnetic quantities, the SI and the historic CGS-emu system.11 Whereas the latter system is still being used in the current literature, some quantities can be employed that are identical in value in both unit systems (1) the effective Bohr magneton number /zeff and (2) the magnetic dipole moment m as well as the atomic magnetic dipole moment /za, divided by the Bohr magneton /zB (Tables 3.3 and 3.4). 

The first column gives the room-temperature values of the axial ratio cja for NiAs-type compounds or the corresponding values a/b and lWa/c for MnP-type compounds (taking the smallest axis as b and the largest as c). The second column contains the Bohr magneton number np. 

The molar magnetic susceptibility, xm> is related to a quantity of more interest to the chemist, the Bohr magneton number (or magnetic dipole moment in Bohr magneton units), designated p. The relationship is ... 

N = Avogadro s number a = the diamagnetic constant h the Planck constant (p. 6) p = the Bohr Magneton number k the Boltzmann constant ( =... 

If one defines the "effective Bohr magneton number" as the dimensionless, ueff, we obtain... 

In Table 5.2 are listed several effective Bohr magneton numbers /ieff for iron-group transition ions and rare-earth ions. For the iron-group transition metal ions a second theoretical guess ("spin-only") is also listed ... 

Table 5.2 Effective Bohr Magneton Numbers /xeff (Dimensionless) for Iron-Group Transition Metal and Rare-Earth Ions ...

When some of the Jhighest spin, namely S = Si-fS2 + S3, can lie lowest in energy and hence at very low temperatures the Bohr magneton number n calculated from Eq. (59) will satisfy... 

Xia, K. et al.. The distribution of Cu(ll) on boehmite and sihca surfaces Correlating EPR signal loss with the effective Bohr magneton number of sorbed ions, J. Colloid Interf. Sci., 199, 77, 1998. 

The quantities gQ and g in (77-5) are the gyromagnetic ratios corresponding to the intrinsic angular momentum of the odd particle and to the rotational motion respectively. The former is a characteristic of the state of the odd particle and the latter is theoretically equal to Z/A. Thus the reduced transition probabilities for magnetic transitions are of the order of the square of the nuclear magneton number, while those oi E 2 transitions are of the order of or cm. ... 

The quantity most often quoted to express magnetic properties in metal complexes, the effective Bohr magneton number /Zeff is defined in terms of Xm-... 

Notice that, defined in this way, is a pure number, the Bohr magneton number, which refers to a single molecule. Although often met, it is not strictly correct to call it the effective magnetic moment, and it certainly is incorrect to express it in units of Bohr magnetons, although this is a usage met all too often. 

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)... 

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