Summary generalized driving force electrochemical

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Unformatted text preview: cs Research Lab. i ziF i Seoul National University Kinetics 8. Component diffusivities and defect diffusivities 8.1. ionic diffusion J A charged component J VA defects J A i J A J A J VA Due to internal equilibria i J A J A DA c A RT D A c A i J VA i i A RT DVA c VA RT A i A VA A A A A VA A A V A A 0 V V 0 A A VA Solid State Ionics Research Lab. A Vi A i A VA A i i i i A A i Seoul National University Kinetics J A D A c A i i RT D A c A i i A i A DVA c VA RT DVA cVA RT RT DA c A DVA c VA i i A RT DA c A A RT VA A DA cA DA cA DVA cVA or A A VA i Solid State Ionics Research Lab. i i Seoul National University Kinetics 8.2. Electronic diffusion Similarly : for electronic carriers J el charged component Jn defects Jp J el J n J p J el el F 2 Due to internal equilibrium el Jn Jp n F n 2 p F 2 p Solid State Ionics Research Lab. e 1 e h e hv c c v el ec h e h c h 0 e c v v v Regular elements Seoul National University Kinetics J el n F 2 n n p F 2 p F 2 p el el n p or Del cel Dncn Dpcp Solid State Ionics Research Lab. Seoul National University Kinetics 9. Diffusion in stoichiometric compounds - System : NaCl + δCaCl2 - Defects : VNa , VCl , Cd Na where [Ca ] given ( ) Na - Defect structure : Charge neutrality : [Ca Na ] [VCl ] [VNa ] Due to internal equilibrium 0 VNa VCl ; Solid State Ionics Research Lab. h [VNa ] [VCl ] K S K S,0 exp s kT Seoul National University Kinetics Solution • Brauwer approximation of the charge neutrality condition • Solution Solid State Ionics Research Lab. Seoul National University Kinetics Piecewise solutions: i) when K S1/2 >>δ (intrinsic regime) [V ][VNa ] K Cl 1/ 2 S ; [Cd ] Na ii) when K S1/2 <<δ (extrinsic regime) [Ca ][VNa ] Na [VCl ] Solid State Ionics Research Lab. KS Seoul National University Kinetics Self-diffusivity i) Intrinsic regime DNa [VNa ]DVNa DNa ; 1 2 VNa V Na 6 g m 2 ao o exp kT DVNa g m g S 2 exp ao o exp kT 2kT s s / 2 s m hS / 2 h m 2 ao exp exp k kT DCl [VCl ]DV Cl s s / 2 s m a exp k 2 o Solid State Ionics Research Lab. hS / 2 h m exp kT Seoul National University Kinetics ii) Extrinsic regime s 2 ]DVNa ao o exp m DNa [VNa k KS DCl [VCl ]DV DV Cl a 2 o o Cl s s s m exp k h S h m exp kT 1 [VNa ] [VCl ] log D+ hm exp kT [VNa ] [Ca ] Na 1 h h m 2s k log D- h m k DNa 1 h h m 2s k h s h m k DCl 1/T Solid State Ionics Research Lab. Seoul National University Kinetics Example: Cation diffusivity of NaCl Solid State Ionics Research Lab. Seoul National University Kinetics 10. Diffusion in nonstoichiometric compounds System : Hypotheti...
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This document was uploaded on 11/26/2013.

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