Diffusion crystallographic anisotropy

For minerals, if diffusion is anisotropic, the bulk method gives only an average diffusivity for an assumed effective shape, but cannot determine the diffusivity along different crystallographic directions. The profiling method is necessary to quantitatively resolve the anisotropy. 

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. 

Fig. 6.11. (a) Mossbauer spectra of Fe in an aluminium single crystal at 295 and 923 K for different orientations of the gamma-ray beam along the crystallographic directions, (b) Diffusional broadening Fq at 923 K as a function of the observation direction specified by 0, the polar angle the azimuthal angle is 43°. The continuous line is the calculated anisotropy for selfdiffusion and the broken line is for impurity diffusion. (Mullen, 1980.)... 

---