Crystalline anisotropy

Here iC is the intrinsic anisotropy constant due to the crystalline anisotropy. After the demagnetization in the longest direction, k is the shape-dependent constant (for an infinite cylinder k = 1.38), M is the exchange constant, and R the particle radius. An infinite cylinder with only shape anisotropy gives... 

Coercivity of Thin-Film Media. The coercivity ia a magnetic material is an important parameter for appHcations but it is difficult to understand its physical background. It can be varied from nearly zero to more than 2000 kA/m ia a variety of materials. For thin-film recording media, values of more than 250 kA / m have been reported. First of all the coercivity is an extrinsic parameter and is strongly iafluenced by the microstmctural properties of the layer such as crystal size and shape, composition, and texture. These properties are directly related to the preparation conditions. Material choice and chemical inborn ogeneties are responsible for the Af of a material and this is also an influencing parameter of the final In crystalline material, the crystalline anisotropy field plays an important role. It is difficult to discriminate between all these parameters and to understand the coercivity origin ia the different thin-film materials ia detail. 

FIG. 6 Morphology diagram. Plotted is the dimensionless supercooling A versus the crystalline anisotropy e. Compact dendritic (CD) and compact seaweed (CS) structure comprise most of the diagram, under the influence of noise, fractal seaweed (FS) and fractal dendrites (FD) are encountered. For details see text and Ref. 108. 

The first one is the bulk magneto crystalline anisotropy field. It depends on the chemical composition and crystallographic structure of the material. For instance, the anisotropy constant is 30 times larger in cobalt ferrite particles than in magnetite particles. 

One can drastically alter the properties of polymers by suitable reactor design during forming of the polymer into its final shape. As examples, crystallinity, anisotropy, and surface characteristics can be tailored by ... 

The crystalline anisotropy and magnetostriction are sensitive to the minority-spin electrons at Fe " ions, especially if this spin is localized and produces a cooperative Jahn-Teller distortion. The Fe ion contribution to these properties arises primarily from dipole-dipole Interactions. 

In contrast, structure-insensitive reactions are those for which turnover frequency under fixed conditions does not depend or depends slightly on the surface crystalline anisotropy of clusters of varying size or of single crystals exposing different faces. For these kinds of reactions, all accessible surface atoms can be considered as equally active sites (Boudart, 1981 and 1995). 

It should be remembered that even for isotropic defects their elastic interaction is anisotropic, due to crystalline anisotropy, equation (3.1.4). A pair of the simplest Frenkel defects - vacancy and an interstitial atom - attract each other in the direction (100), but their interaction becomes repulsive, e.g., along (111) and (101) axes. 

This critical field called coercivity ff. or switching field Ff., is also equal to FF. If a field is applied in between 0 and 90° the coercivity varies from maximum to zero. In the case of this special example the applied field Ha = Hs = Hc = Hk. Based on the classical theory, Stoner-Wohlfarth (33) considered the rotation unison for noninteracted, randomly oriented, elongated particles. The anisotropic axis can be due to the shape anisotropy (depending on the size and shape of the particle) or to the crystalline anisotropy. In the prolate ellipsoids b is the short axis and a the longest axis. The demagnetizing factors are IV (in the easy direction) and The demagnetizing fields can then be calculated by Hda = — Na Ms, and Hdb = — Nb Ms. The shape anisotropy field is Hd = (Na — Nb)Ms. Then the switching field Hs = Hd = (Na — Nb)Ms. 

If, after the material has been magnetically saturated to the value Bs, the field is reduced to zero, the magnetization vectors rotate out of line with the field towards the nearest preferred direction which is determined in part by magnetocrystalline anisotropy. The magnetization is thus prevented from complete relaxation to the virgin curve and hence, for zero field, there is a remanent induction Bx. In order to reduce the induction to zero a reverse field II,. has to be applied. The coercive field or coercivity II,. depends in part on crystalline anisotropy, as might be expected. 

Figure 4. Energy density plots of the crystalline anisotropy in arbitrary units. For every...

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