The Crystallographic Anisotropy

The first term in expression (1) describes the exchange energy, the second and the third terms give the crystallographic anisotropy energy. 

One SEXAFS specific feature is the polarisation dependence of the amplitude. This derives from the high anisotropy of the surface and of ultrathin interfaces, that we may consider as quasi two dimensional systems. The relative orientation of the X-ray electric vector with respect to the surface (interface) normal does represent a preferential excitation for those atom pairs aligned along the electric vector e.g. with the electric vector perpendicular to the surface (interface) plane the EXAFS amplitude will be maximum for the atom pairs aligned normal, or almost normal to the surface (interface). The electric vector can be also aligned, within the surface plane, along different crystallographic directions. 

In many luminescence centers the intensity is a function of a specific orientation in relation to the crystallographic directions in the mineral. Even if a center consists of one atom or ion, such luminescence anisotropy may be produced by a compensating impurity or an intrinsic defect. In the case of cubic crystals this fact does not disrupt optical isotropy since anisotropic centers are oriented statistically uniformly over different crystallographic directions. However, in excitation of luminescence by polarized fight the hidden anisotropy may be revealed and the orientation of centers can be determined. 

Fig. 18. Temperature dependence of the magnetization of a LuNi2B2C single crystal in a field of 3 T applied along the crystallographic directions c, a and (110), clearly showing an out-of-(tetragonal basal) plane anisotropy as well as an in-plane anisotropy of Hc2 where Hc2(T) is determined by the indicated linear extrapolation (after...

The microstructure of the decomposed Fe-Mo alloy, Fig. 18.136, shows strong alignment of the developing two-phase microstructure along (100) directions. Such alignment is common in cubic crystals, and it arises from the anisotropy of the effective modulus, Y, in the diffusion equation. From Eq. 18.74 it is apparent that the crystallographic directions in which Y is a minimum will correspond to the wavevector of the fastest-growing waves. 

Hardness testing of minerals shows in most cases a considerable difference in hardness according to crystallographic direction. By analogy with the optical anisotropy of crystals, we call this phenomenon hardness anisotropy. Dmitrev (1949) differentiated three kinds of hardness anisotropy ... 

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