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Seoul national university kinetics 7 atomistic

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Unformatted text preview: University Kinetics -Rate of vacancy generation/annihilation C v J C eq v v 0 in local defect equilibrium (i.e., C v C v ) t x t generation vacancy generated J v C v t generation x - + vacancy annihilated - So the local lattice moving to annihilate extra vacancies to keep N v ( x, t ) N eq. v 1 ~ ~ N J v Vm L J v ( D1 D2 ) 1 L c x - Lattice reference frame is, thus, moving relative to Fick’s frame - Drift velocity : L J v (c1 c 2 ) v or v - What about the interstitial mech.? Kirkendall effect possible? How? Solid State Ionics Research Lab. Seoul National University Kinetics -How defects (vacancies) Dislocation climb keep equilibrium concentration? -Vacancy sinks and sources: dislocations, grain boundaries, surfaces -Single crystal : no sinks/sources inside Only surface L JV -Poly-crystals Solid State Ionics Research Lab. Seoul National University Kinetics -Things which happen when defect equilibrium violated. When surface is the only side of vacancy Cortour change pores Solid State Ionics Research Lab. JV Seoul National University Kinetics 8. Final summary Chemical diffusivity & Component Diffusivity 1) ~ DA DA 1 2 ; DA S B A RT 6 Directional drift Thermodynamic bias Random jump ~ DB DB 2) ~ D ( N A DB N B D A ) >0 outside spinodal <0 inside spinodal (negative diffusion coefficient) Extreme case : ideal solution ~ 1 : DA DA Solid State Ionics Research Lab. Seoul National University Kinetics 9. (optional) A more general treatment of the Kirkendall effect - Phenomenologically in the regime of the direct effect 9.1 Reference frames to measure J w J i C i (vi w ) # density in # moles cm 3 - mass-fixed reference frame mic ,m J i 0 mi ci vi wmi ci w c ,m m i c i v i c.m. velocity m i c i - Volume –fixed reference frame ViF J i 0 Vi ci vi wF Vi ci wF Vi ci v i i Vi ci i Solid State Ionics Research Lab. V ' Vi ni 1 Vi ni Seoul National University Kinetics - Number-fixed reference frame N J i 0 c i v i w N c i wN c i v i N i vi i c i i : thermo...
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