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Diffusion Solids Fundamentals Diffusion Controlled Solid State Episode 1 Part 3

Tham khảo tài liệu 'diffusion solids fundamentals diffusion controlled solid state episode 1 part 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | References 35 For crystals with triclinic monoclinic and orthorhombic symmetry all three principal diffusivities are different D1 D2 D3 . 2.17 Among these crystal systems only for crystals with orthorhombic symmetry the principal axes of diffusion do coincide with the axes of crystallographic symmetry. For uniaxial materials such as trigonal tetragonal and hexagonal crystals and decagonal or octagonal quasicrystals with their unique axis parallel to the x3-axis we have D1 D2 D3 . 2.18 For uniaxial materials Eq. 2.16 reduces to D D1 sin2 D3 cos2 2.19 where denotes the angle between diffusion direction and the crystal axis. For cubic crystals and icosahedral quasicrystals D1 D2 D3 D and the diffusivity tensor reduces to a scalar quantity see above . The majority of experiments for the measurement of diffusion coefficients in single crystals are designed in such a way that the flow is one-dimensional. Diffusion is one-dimensional if a concentration gradient exists only in the x-direction and both C and dC dx are everywhere independent of y and z. Then the diffusivity depends on the crystallographic direction of the flow. If the direction of diffusion is chosen parallel to one of the principal axis x1 or x2 or x3 the diffusivity coincides with one of the principal diffusivities D1 or D2 or D3. For an arbitrary direction the measured D is given by Eq. 2.16 . For uniaxial materials the diffusivity D is measured when the crystal or quasicrystal is cut in such a way that an angle occurs between the normal of the front face and the crystal axis. For a full characterisation of the diffusivity tensor in crystals with orthorhombic or lower symmetry measurements in three independent directions are necessary. For uniaxial crystals two measurements in independent directions suffice. For cubic crystals one measurement in an arbitrary direction is sufficient. References 1. A. Fick Annalen der Phyik und Chemie 94 59 1855 Philos. Mag. 10 30 1855 36 2 Continuum Theory of Diffusion 2.