Hs 2 h m exp kt seoul national university kinetics ii

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Unformatted text preview: cal compound A1-δO Defects : Frenkel disorder in the majority ; A , VA ; e, h i Defects structure : External equilibrium 1 O2 O VA 2h O 2 ; 1/ [VA ]p 2 K ox PO22 Internal equilibria A A VA A i 0 e h ; ; [VA ][A ] K F i np K i Charge neutrality condition 2[A ] p 2[VA ] n i Solid State Ionics Research Lab. Seoul National University Kinetics Solution • Brauwer approximations of the charge neutrality condition • Sequence of majority disorder types • 2[A ] p 2[VA ] n i Piecewise solution Solid State Ionics Research Lab. Seoul National University Kinetics i) K F >>K i n 2[A ] i n A log [ ] i VA [VA ] [A ] i 2[VA ] p p -1/6 VA -1/4 1/4 A i n p log Po2 Self-diffusivities DA DA [Ai ] DVA [VA ] g m( A ) 1 2 2 i A A A ao 0,A exp B A RT i i i i i 6 kT i where D A i and DVA gm(VA ) 1 2 2 VA VA VA ao o,VA exp BVA RT 6 kT Solid State Ionics Research Lab. Seoul National University Kinetics Assuming BA BVA i ii) K i >> K F Solid State Ionics Research Lab. Seoul National University Kinetics DA DA [A ] DVA [VA ] i i DA BA RT i i ; DVA BVA RT Assuming BA BVA i Solid State Ionics Research Lab. Seoul National University Kinetics Example: Co1-O -7 1 O 2 (g) O VCo 2h O 2 1/ [VCo ]p 2 K ox PO22 o A 1000 C log (DCo*/cm2sec-1) B 1100oC C 1200oC -8 D 1300oC 1/4 p[VCo ]PO2 1/6 D* PO2 Co -9 D C -10 B -11 A -12 -10 -8 -6 -4 -2 0 Ideal defect model Dieckmann Chen and Peterson Morin Carter and Richardson Chen and Peterson log (Po2/atm) Solid State Ionics Research Lab. Seoul National University Kinetics Example: Fe3-O4 -7 Fe O 1 3 2 O 2 OO VFe 2h 2 4 Fe Fei VFe Fe 3- 4 log DFe*/cm2sec-1 -8 3 2 h FeFe2 , e FeFe3 -9 n p for random magnetite -10 900oC -14 -12 -10 -8 1200oC 1300oC -12 -16 1000oC 1100oC -11 2/ [VFe ] PO23 1400oC -6 -4 -2 [Fei ] PO2/ 3 2 0 log (Po2 / atm) R. Dieckmann and H. Schmalzried, Ber. Bunsenges. Phys. Chem., 81[4] 414-19 (1977) Solid State Ionics Research Lab. Seoul National University Kinetics 11. Chemical Diffusion – Diffusion in concentration gradient in ionic solids 11. 1 Introduction (statement of the problem) Nonstoichiometry of A1-δO where δ is metal-deficit 1 [VA ] [A ] (p n) (T, PO2 ) for pure A1 O 2 i Solid State Ionics Research Lab. Seoul National University Kinetics Initial and boundary conditions Due to Gibbs-Duhem eq’n at const T & P (1 )dA dO dA1 O 0 if 1 1 or from the equil condition, A O 2 AO 2 o A O AO AO if 1 or A O 0 Solid State Ionics Research Lab. or O A Seoul National University Kinetics - suddenly increase O outside 2 A,O A,O 1 O 2 2 A O,O 0 O x where O ( O,o ) 1 2 O 2 Solid State Ionics Research Lab. Seoul National Uni...
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