Effective anisotropy

If the photolysis process is not immediate, but instead has some finite lifetime r, the parent molecule may have time to rotate during dissociation and so wash out the angular distribution. In this case a reduced effective anisotropy parameter (/3eff) is used to characterize the observed angular distribution. The relationship between [3eg and parent lifetime can be expressed as52,54... 

Despite having been the earliest attempted prediction, proton prediction remains relatively poor. The reasons for this have been alluded to earlier but to summarise the proton chemical shift is often highly dependant on through-space effects (anisotropy) and has a very small distribution. There are four main commercial approaches to proton prediction currently Incremental parameters, HOSE code databases, semi-empirical and cib initio methods. 

Another example of the use of HFFMR was a study of granular cermet films, (Fe5oCo5o)x-(Al203)i-x, that are also of interest for data storage. The original measurements at X-band found that the concentration dependence of the effective anisotropy field deviated from the solid solution law. Experiments at 94 GHz showed that this was shown an artefact, due to the low field for resonance at X-band. At 94 GHz the relationship between anisotropy and composition was found98 to be linear for all x. 

Chain orientation effects anisotropy in the expansion in the orientation direction it is considerably lower than across. Moreover the tendency to (irreversible) shrinkage in the orientation direction upon temperature increase should be taken into account. 

Since we have observed that TB increases with tCo the approximation of U= Keff V has been considered. Here Kejf is an effective anisotropy that encompasses all possible contributions, such as intrinsic and surface anisotropies [5],... 

To determine the effective anisotropy constant we need to compare the activation energy of particles with a given size (i.e. D = (d)) with their... 

Figure 6. Size dependence(shown in reciprocal scale of diameters) of the relative effective anisotropy for the different average diameters for AI2O3/C0 and Cu capped AI2O3/C0/CU. multilayers. Lines are guides to the eye.

We conclude in this section that we are dealing with quite spherical, metallic Co nanoparticles with a very narrow size distribution, that give rise to superparamagnetic behavior. The effective anisotropy of the particles increases by one to two orders of magnitude with respect to the bulk with decreasing size. The origin of this anisotropy enhancement can be traced to the anisotropy of the orbital moment and the increase of the absolute orbital moment of the Co surface atoms, at least for (D > 2 nm. 

Figure 4 shows the calculated effective anisotropy energy density of a particle consisting of three crystallites with volume fractions 0.1, 0.2, and 0.7. The three crystallites have perpendicular easy axis and are strongly exchange coupled. Note if the three volumes are the same, no anisotropy occurs. For comparison, Fig. 4. gives the energy density surface for cubic anisotropy. 

Chain element AL located at distance L from the chain end along the contour leads to the average effective anisotropy in the axes of the first element... 

The effective anisotropy coefficient q which characterizes the anisotropy of the whole material is given by ... 

As G. and S, Olive correctly indicated, the definition of the effective anisotropy coefficient q in Eq. (29) is unfortunate because the case q = 1 may be given not only for isotropic foamed polymers but also for anisotropic ones (for example, if... 

Foam type Volume weight 7 Gas-filling factor G (%) Parameter P Longitudinal Wave Velocity Anisotropy coefficients (Eq. 30 a) Effective anisotropy coefficient q (Eq. 29)... 

The analysis of the splitting pattern can afford the isotropic J value and also the value. Furthermore one can consider that the interplay of the quadrupolar, dipolar and indirect coupling also affects the spinning sideband manifolds. Each component of the sextet will have its own effective anisotropy, and, with the same assumption of the perturbation approach, the effective anisotropy evaluated by the analysis of the SSB manifolds affords the ZY value and the value of the quadrupolar coupling constant %. Furthermore, if the Mn-P intemuclear distance is known by X-ray diffraction, the A/ value can be readily extracted [58]. By using the perturbation approach, the interaction of with metal nuclei having spin 5/2 C Mo, Ru) [61,62], 7/2 ( Co) [58] and 9/2 ( Nb) [63] has been investigated. 

There exists also a theory of Maier and Saupe (A , 47) which takes into account the stability of aligned molecules, for instance in the nematic state, due to the anisotropy of the dispersion forces. The Flory theory covers this as well, but in addition it takes into account two further effects anisotropy of the molecular shape, and the influence of that anisotropy on molecular packing. The separability of factors in equation (1) has been well justified by subsequent results (48), (Flory, P.J. private communication to W.Brostow, August 20, 1985). The Flory theory has been applied, among others, to ternary systems of the type rigid rod polymer... 

The effective anisotropy energy of the chain takes the form [320]... 

Yanes R, Chubykalo-Fesenko O, Kachkachi H, Garanin DA, Evans R, Chantrell RW. Effective anisotropies and energy barriers of magnetic nanoparticles with Neel sur-... 

What makes SMMs unique magnetic systems, however, is the coexistence of classical and quantum mechanisms for spin reversal, hi fact, beside the above-described thermally activated process, spin reversal in SMMs may also occur by QT [46,47,54]. Whenever two states lying on opposite sides of the barrier have the same energy and are quantum-mechanically admixed, a direct underbarrier transition is in principle permitted. QT effects are indeed responsible for the stepped hysteresis loops of Mnu-acetate (Fig. 4) and explain why the effective anisotropy barrier probed by relaxation measurements (Ueff) is usually lower than U. Clearly, QT effects are of paramount importance for an accurate description of SMM behavior and their origin is among the most actively investigated topics in molecular nanomagnetism [54]. 

Effective anisotropy strength functions for the H2 Ar potential surface of Table I, corresponding to different (fixed) values of the diatom stretching coordinate Reproduced with permission... 

Table IV. Effective anisotropy strength parameters and predicted widths for the (n,i,v,j,J)=(0,2,l,2,0) levels of H2 Ar, Rr, and Xe implied by the potential energy surfaces of Table I. Results from Refs. (9 and 19).

Last, if such a material were created and then the stress was relaxed, the effective anisotropy of the material s chemistry would drive some kind of interdiffusion as the material reverted to normal this would be an effect in box (8). 

The work of Hong et al.15 discusses the theoretical analysis of the dipolar lineshapes in the limit of rapid, anisotropic motion. The analysis assumes a motionally averaged dipolar coupling tensor, i.e. the average of the tensor over all the sites/orientations visited during the course of the motion, which has an effective anisotropy AD and asymmetry //>... 

Fig. 10. Simulated LG-CP dipolar powder lineshapes for motions with different effective asymmetry, as labelled, and effective anisotropy An.1 5...

Fig. 4.43. Universal hysteresis loop, obtained by plotting M/M, as a function of HD /Hcii, where Hn is the effective anisotropy field (Globus, 1977).

Globus, A., Duplex, P. Guyot, M. (1971). Determination of initial magnetization curve from crystallite size and effective anisotropy held. IEEE Transactions on Magnetics, MAG-7, 617-22. 

As noted for rubbers, micro tests using scaled-down indentor sizes and smaller loads are being used, and special mention should be made of the micro Vickers test [18]. which has been applied successfully to plastics (sec Ref. [19] for a review) in the determination of crystallization effects, anisotropy, the effect of weathering and heat aging, the study of polymer blends, etc. 

Hk< > = effective anisotropy field STEM = scanning transmission... 

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