Dieckmann and h schmalzried ber bunsenges phys chem

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Unformatted text preview: versity Kinetics - component fluxes O J O LOO A J A L A A x 0 As a consequence, changes as shown in Fig. t O x Solid State Ionics Research Lab. Seoul National University Kinetics 11.2 Chemical diffusion Component flux Charged Component fluxes A1-O O A 0 Defects fluxes O2 - = e- = VA O VA h A2+ x 0 x 0 x D1C1 1 A : J1 1 1 2 RT (z i F) 2 D2 C2 1 O : J2 2 2 2 RT (z i F) 2 e : J 3 Solid State Ionics Research Lab. D3 C3 1 3 3 2 RT (z i F) Seoul National University Kinetics Local equilibrium condition A A z1 z1e O O z2 z 2e ; A 1 z12 ; O 2 z 23 We know that O A due to Gibbs -Duhem equation. But, these partial currents or fluxes should not be independent of each other. No net current or charge neutrality condition. 3 i z i Fji 0 or 1 i 1 z 1F 1 1 2 z 1F ( A z 1 3 ) Solid State Ionics Research Lab. z 2F 2 z 2F 2 3 F ( O z 2 3 ) 3 0 3 F 3 0 Seoul National University Kinetics Solving for 3 3 t1 t A 2 O z1 z2 where z1 = +2 , z2 = -2 In general for any compound t 3 i i* i zi For binary oxide A1-δO , where i* : neutral component i zi : valence of i-ion ti : transference number of i-ion A O t ion t ion 3 A O z1 z2 where tion = t1 + t2 , the ionic transference number of the system. Solid State Ionics Research Lab. Seoul National University Kinetics Charged component fluxes D1C1 J1 1 RT DC = 1 1 ( A z i 3 ) RT D1C1 = (A t ionA ) RT DC 1 1 t el A RT D2C2 J2 t el O RT J 3 z1J1 z 2 J 2 Neutral component fluxes J A LAA J1 J O LOO J 2 Upon comparison, one may recognize that D1C1 D2 C2 LA t el ; LO t el RT RT due to charge neutrality Solid State Ionics Research Lab. Seoul National University Kinetics - Nonstoichiometry of A1-δO 1 1 CA , CO Vm Vm C A CO CO C A C A J O t Vm C A J A t Vm 1 1 CA ; CO Vm Vm C A CO or CO C A Vm Vm Oxygen excess change with time CO CA (J O J A ) J t Vm t t Solid State Ionics Research Lab. Seoul National University Kinetics Nonstoichiometry flux J J O J A (D2C2 D1C1 ) = t el O RT 1 ion 2 = t O t O (if z1 | z 2 |) 2 2 el 2 el (z 1F) (z 1F) (z 2 F) 1 1 2 = 2 2 2 t el O F z1 z2 Solid State Ionics Research Lab. Seoul National University Kinetics -Chemical diffusion coefficient in comparison with Fick’s 1st law J D Vm O O D1C1 D2C2 t D el RT ( / Vm ) 1 O2 if external equilibrium prevails 2 (D C D C ) t 1 ln Po2 D 11 22 el 2 ( / Vm ) -Nernst-Planck type diffusion coefficient -Chemical diffusion coefficient for non-stoichiometry change for A1-δO O ion O D1C1 D2C2 t D 3 ( / V ) 4F 2 t el ( / V ) RT m m Solid State Ionics Research Lab. Seoul National University Kinetics Summary and Generalization (optional) For a general system AO1+ z1 z 2 0 when 1 - Flux of charged component i Di Ci i J...
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