Theoretical moment

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.

If one now chooses the appropriate induced dipole model, Eqs. 4.1 through 4.3, or a suitable combination of these, with N parameters po, >7, R0,. .., and one has at least N theoretical moment expressions available, an empirical dipole moment may be obtained which satisfies the conditions exactly, or in a least-mean-squares fashion [317, 38]. We note that a formula was given elsewhere that permits the determination of the range parameter, 1/a, directly from a ratio of first and zeroth moments it was used to determine a number of range parameters from a wide selection of measured moments [189]. In early work, an empirical relationship between the range parameter and the root, a, of the potential is assumed, like 1/a 0.11 a. That relationship is, however, generally not consistent with recent data believed to-be reliable. 

A general check of the overall correctness of the predictions in this field is given by the comparison of the theoretical and experimental results in the series caffeine (82), 2-thiocaffeine (83), 6-thiocaffeine (84), and 2,6-dithiocaffeine (85) for which both are known. The theoretical moments are 4.3, 5.7, 4.2, and 5.6 D, respectively, and the experimental ones 3.7, 4.8, 3.8, and 4.6 D, respectively.164 One notes the strong modification of the moment produced by the replacement of the 0 atom linked to C-2 by an S atom and the practical absence of any change on a similar replacement of the 0 atom linked to C-6. 

Romberg consolidated a distinctly theoretical moment in French elite chemistry. The existing theoretical structure of chemistry—the doctrine of five principles—faced a serious threat from changes in analytic methods and philosophical languages. The chemists of the Paris... 

The small differences between experimental and theoretical moments do not necessarily go back to theory problems but might also be explained by the fact that the experimental measurements were carried out on a nonstoichiometric (Mn-rich) compound. 

The Curie temperature 7., spontaneous magnetization Af, at 4.2 and 300 K, theoretical moment for the rare earth ion R and value of the iron moment of the compound RFe,QSiC(, 5. 

Table 1 shows the comparison between theoretical predictions to experimental results. From the comparison, it is shown that theoretical initial stiffness is higher than the experimental results. The ratio of theoretical values to experimental results is in the range of 3.93 to 6.02. On the other hand, theoretical moment resistance is lower than the experimental results. The ratio of theoretical values to experimental results is in the range of 0.54 to 0.96. 

By matching the theoretical moments given in eq. (14.2-16) with the experimental moments, we can obtain the various parameters of the system. 

In principle, by matching the theoretical moments with the corresponding experimental moments, the adsorption and diffusion parameters can be extracted. To facilitate the reliability of the parameter extracted, we can make use of an inert tracer as well as an adsorbing tracer, and carry out experiments for both of them at different flow rates. 

These equations are linear and are susceptible to Laplace transform analysis, from which we can obtain the theoretical moments. The first normalised moment and the second central moment for this model are ... 

---