tailieunhanh - Kinetics of Materials - R. Balluff_ S. Allen_ W. Carter (Wiley_ 2005) Episode 5

Tham khảo tài liệu 'kinetics of materials - r. balluff_ s. allen_ w. carter (wiley_ 2005) episode 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 160 CHAPTER 7 ATOMIC MODELS FOR DIFFUSION Using the standard thermodynamic relation dG dP r V and realizing that the pressure dependence of lnp will be relatively very small we may write to a good approximation ỡinr 1 1 m dPiT--WV 7-57 If a plot of InT vs. p is now constructed using the experimental data vm can be determined from its slope. Consider small interstitial atoms jumping by the interstitial mechanism in . Fe with the diffusivity D for a time T. a What is the most likely expected total displacement after a large number of diffusional jumps b What is the standard deviation of the total displacement Solution. a The expected total displacement will be zero because there is no correlation between successive jumps after a jump the interstitial loses its memory of its jump and makes its next jump randomly into any one of its nearest-neighbor sites. b The distribution of displacements will be Gaussian Eq. and the standard deviation will be the root-mean-square displacement given by Eq. as VQDt. Suppose the random walking of a diffusant in a primitive orthorhombic crystal where the particle makes 2V1 jumps of length O1 along the Xi axis N2 jumps of length d2 along the X2 axis and Nị jumps of length 03 along the X3 axis. The three axes are orthogonal and aligned along the crystal axes of the orthorhombic unit cell and the diffusivity tensor in this axis system is D Dn 0 0 0 D22 0 0 0 D33 a Find an expression for the mean-square displacement in terms of the numbers of jumps and jump distances. b Find another expression for the mean-square displacement in terms of the three diffusivities in the diffusivity tensor and the diffusion time. Your answer should be analogous to Eq. which holds for the isotropic case. Solution. a Using Eqs. and N R2 . fi Ma N2a2 N3a3 i l b The diffusion equation will have the form of Eq. . By using the method of scaling described in Section based on the scaling relationships in Eq. .

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