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Unformatted text preview: 5-3 Diffusion Mechanisms
5.3 (a) With vacancy diffusion, atomic motion is from one lattice site to an adjacent vacancy. Selfdiffusion and the diffusion of substitutional impurities proceed via this mechanism. On the other hand, atomic motion is from interstitial site to adjacent interstitial site for the interstitial diffusion mechanism. (b) Interstitial diffusion is normally more rapid than vacancy diffusion because: (1) interstitial atoms, being smaller, are more mobile; and (2) the probability of an empty adjacent interstitial site is greater than for a vacancy adjacent to a host (or substitutional impurity) atom. 5-4 Steady-State Diffusion
5.4 Steady-state diffusion is the situation wherein the rate of diffusion into a given system is just equal to the rate of diffusion out, such that there is no net accumulation or depletion of diffusing species--i.e., the diffusion flux is independent of time. 5-6 5.6 This problem calls for the mass of hydrogen, per hour, that diffuses through a Pd sheet. It first becomes necessary to employ both Equations 5.1a and 5.3. Combining these expressions and solving for the mass yields
M = JAt = DAt 'C 'x 0.4 2.0 kg / m3 = (1.7 u 10-8 m2 /s)(0.25 m2 ) (3600 s/h) 3 m 6 u 10 = 4.1 x 10-3 kg/h 5-7 5.7 We are asked to determine the position at which the nitrogen concentration is 0.5 kg/m3. This problem is solved by using Equation 5.3 in the form
C CB J = D A xA xB If we take CA to be the point at which the concentration of nitrogen is 2 kg/m3, then it becomes necessary to solve for xB, as
C C B xB = xA + D A J Assume xA is zero at the surface, in which case 2 kg / m3 0.5 kg / m3 xB = 0 + (1.2 u 10-10 m2 /s) 1.0 u 107 kg / m2 - s = 1.8 x 10-3 m = 1.8 mm ...
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- Spring '08