Average magnetic

Fig. 20. Scaling of channel enthalpy extraction for the various MHD faciUties discussed in text ( ) achieved, and (e) predicted where O is the average gas conductivity in mho/m B, the average magnetic field in T M, the channel Mach number E, the average channel active length, m and P, the average...

Fig. 1. Orientationally averaged magnetic susceptibility of various forms of carbon [21].

Figure 2 Orbital magnetic moments in bcc-Fe Coi-a . The triangles pointing up-and downwards represent the theoretical moments of Fe and Co, respectively, while the concentration weighted sum is given by circles. Full and open symbols stand for results obtained with and without the OP-term included (SOPR- and SPR-KKR-CPA, resp.). Experimental data [15] for the average magnetic moment (bottom) stemming from magneto mechanical and spectroscopic g-factors are given by full squares and diamonds.

From equation 10.34 we immediately find that the average magnetization is... 

For a multi-spin system, where / = 1/2, the rate of change of the average magnetization (M, ) of a spin i coupled by dipole-dipole interactions to a... 

Fig. 6.17 The average magnetic hyperfine field at low temperatures, obtained from Mossbauer spectra of coated and uncoated 8 nm particles of a-Fe203 (Fig. 6.16). The lines are linear fits to the data in accordance with (6.23) and (6.25). (Reprinted with permission from [77] copyright 2006 by the American Physical Society)...

Thus, in the case of fast relaxation between the two canted states the total average magnetic field, which is experienced by the nucleus, is given by [84, 85]... 

Fig. 7.50 Magnetic hyperfine field //hf in Ni-W-alloys at the W-site as a function (a) of the tungsten concentration and (b) of the average magnetic moment (from [238])...

Figure 2 Comparison between the experimental average magnetic moments of Ni clusters measured by Apsel et al.3 (black dots) and the moments calculated by a tight binding method45,4 (light circles). Reproduced with permission from Ref. 44.

Figure 11 Character of the arrangement of the spin magnetic moments, and average magnetic moment, in seven-atom clusters with a pentagonal bipyramid structure and interatomic distances ranging from <4ulk to 80% <4ulk- Reproduced with permission from Ref. 79.

Table 2. Binding Energy Per Atom Eb, Distance D from Atoms to the Cluster Center, and Average Magnetic Moment Per Atom p for Octahedral Six-Atom Clusters. Data Collected from Zhang et al.107... 

Experiments on Rh clusters5,106 reveal an oscillatory pattern of the average magnetic moment, with large values for N = 15, 16, and 19, and local minima for N = 13-14, 17-18, and 20. DFT calculations have been performed for selected clusters in that size range, usually assuming symmetric structures except for the smallest clusters.108-112 The conclusion reached by the various researchers is that the Rh clusters are magnetic. However, different experiments for the same cluster size show a lot of dispersion. 

The average magnetization I is given by (15), where Bj a) is called a Brillouin function, and a by (16). When a 1, Bj(a) may be expanded, and, if we take only the first term, then (17) results. The paramagnetic susceptibility X is inversely proportional to the absolute temperature T. This relation is called the Curie law, and the proportionality constant C is the Curie constant. 

The nuclear spins can interact with the time-averaged magnetic moments via either through-space (dipolar) or through-bond (Fermi-contact) interactions. The Li MAS NMR spectrum of LiMn204 is... 

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