Seoul national university kinetics nonstoichiometry of

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Unformatted text preview: i i =i 2 RT (z i F ) (i 1, 2, 3) - Internal equilibrium condition (ionization) i i* z i 3 where i* neutral component i - Charge neutrality condition i z i Fji 0 3 i Solid State Ionics Research Lab. i t1 i* zi ( i = ionic species ) Seoul National University Kinetics - Gibbs-Duhem equation as a consequence of the local thermodynamic equilibrium i i* 0 i - For a binary A O where z2 z1 t ion t ion t1 t2 3 A O A O z1 z2 z1 z2 D1C1 D1C1 JA ( A z13 ) t el A RT RT D2C2 D2C2 JO (O z 23 )= t el O RT RT Solid State Ionics Research Lab. Seoul National University Kinetics Nonstoichiometry change of AO1+ CO C 1 CA = ; CA or CO A Vm Vm Vm Vm ( / Vm ) 1 1 J O J A J O J A t J J O 1 JA D2C2 DC A t el O 1 1 t el RT RT 1 A O DC D C 2 2 21 1 t el O RT RT 1 D1C1 D2C2 2 t el O RT Solid State Ionics Research Lab. Seoul National University Kinetics 1 1 2 J 2 t O 2 2 el (z1F) (z 2F) z 2 2 1 t el O 1 2 2 z 2 (z1F) (z 2F) ion (z i F) 2 t el O O A where ion z1 z 2 F Solid State Ionics Research Lab. 2 z2 z1 t elA Seoul National University Kinetics 11.3 Meaning of the thermodynamic factors O - Definition f ( ) ( / Vm ) - Thermodynamic meaning (ii) G M A AO (i) O M O G M A o G RTlnaO O O (i) For the larger change of δ, the smaller change in O : f , small (ii) For the smaller charge of δ, the larger charge in O : f , large Solid State Ionics Research Lab. Seoul National University Kinetics 12. Oxygen non-stoichiometry re-equilibration kinetics – An example -BaTiO3-δ -Defect structure V , A C O log[ ] p -1/4 f - Redox equilibrium 1 O2 VO O 2h ; O 2 2 p 1 K OX PO/22 [VO ] 1/4 i - Intrinsic electronic excitation n 0 e h ; np K i - Charge neutrality 2[VO ] p n [A ] C log PO2 1 1 ] (n p) [V ] [AC 2 2 O Solid State Ionics Research Lab. Seoul National University Kinetics -Nonstoichiometry re-equilibration kinetics DOCO O JO t el ( / Vm ) RT ( / Vm ) D ( / V ) 0 VO e f O L 0 m ( / Vm ) J O DO( / Vm ) t For small δ change, one may assume that DOconstant. 2 DO 2 t x Solid State Ionics Research Lab. I.C. (0 x L, 0) 0 B.C. (0,t) (L, t) f Seoul National University Kinetics Solution: ( 2 j 1)2 2 DOt f 4 1 (2 j 1) x sin exp 0 f j 0 ( 2 j 1) L L2 ( 2 j 1)2 2 DOt f 8 1 2 exp or 2 0 f j 0 ( 2 j 1) L2 Measurement: 1 2 n 1 2 e f f 0 f 0 f Solid State Ionics Research Lab. : Conductivity relaxation technique Seoul National University Kinetics 13. Oxygen Permeation - What would happen under an oxygen potential gradient: PO2 (annihilation) 1 AO O 2 (g) A( ) 2 1 O( ) O 2 (g) 2 Solid State Ionics Research Lab. A A1-δO PO2 O A O (new lattice molecule forms) 1 A( ) O 2 (g) AO 2 (oxygen permeation) 1 O 2 (g) O() 2 Seoul National University Kinetics - Oxygen permeation (assuming t1≈0) d ln PO2 DO CO d O 1 O JO t el t RT 2 el RT dx 2 4F dx J O2 L 0 d ln PO2 1 RT JO O t el 2 2 16F dx RT J O2 dx 16F 2 PO2 PO2 O t el d ln PO 2 or Permeation flux J O2 PO2 RT PO2 RT 2 PO 2 O teld ln PO2 16F2L O tel ln PO 2 16F L Solid State Ionics Research Lab. Seoul National University...
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This document was uploaded on 11/26/2013.

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