Domain misalignment

Figure 3.20 Planar defects in solids (a) boundaries between slightly misaligned regions or domains b) stacking mistakes in solids built of layers, such as the micas or clays (c) ordered planar faults assimilated into a crystal to give a new structure and unit cell (shaded).

The exponent m cannot be regarded as a fitting parameter but depends on the symmetry of the system. In most cases, m = 3/2 [16, 140, 158, 166, 167, 174, 175], but m = 2 for highly symmetric systems, such as aligned Stoner-Wohlfarth particles. In particular, the m = 3/2 law is realized for misaligned Stoner-Wohlfarth particles and for most domain-wall pinning mechanisms [5], Experimental values of m tend to vary between 1.5 to 2 [136, 158]. Linear laws, where m = 1, are sometimes used in simplified models, but so far it hasn t been possible to derive them from physically reasonable energy landscapes [5, 16, 176]. The same is true for dependences such as /H- l/H0 [177], where series expansion yields an m = 1 power law. 

Crystals may not be too perfect The condition for Bragg139 reflection, Eq. (8.3.2), is also the condition for total internal reflection. Thus, an absolutely perfect millimeter-sized crystal will reflect internally almost all of the X-ray beam, even at the Bragg angles. However, each crystal contains crystalline domains, 1-10 pm in size, which are slightly misaligned with each other (by seconds or a few minutes of a degree) this is what permits the observation of X-ray diffraction peaks. If the diffracted intensity is unacceptably low, a quick thermal shock to the crystal may help micro-shatter the crystal and form those domains. 

Fig. 15. Diagram illustrating different organizations of partially oriented rods. Although the overall degree of preferred orientation is similar for both diagrams, in (a) the rods are misoriented independently of their relative positions, whilst in (b) they are perfectly aligned within domains, the macroscopic degree of orientation being dependent on the misalignment...

Other complications may also exist in relating the surface magnetization direction with the bulk. Such complications may include misalignment of the in-plane components of the surface and bulk magnetization, the domain structures and the existence of out-of-plane magnetization components for both the surface and bulk. Such complications cannot be... 

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