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Oxidation of Ni-30%Cr according the Wagner Model

Oxidation of Ni-30%Cr according the Wagner Model. Thibaut DUBÉDAT tdubedat@messel.emse.fr Tutor : Krzysztof WOLSKI. What is the Wagner model ?. The diffusion processes determine the oxidation of alloys. Theoretical analysis of the diffusion processes.

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Oxidation of Ni-30%Cr according the Wagner Model

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  1. Oxidation of Ni-30%Cr according the Wagner Model Thibaut DUBÉDAT tdubedat@messel.emse.fr Tutor : Krzysztof WOLSKI

  2. What is the Wagner model ? • The diffusion processes determine the oxidation of alloys. • Theoretical analysis of the diffusion processes. Published in 1952, on the title : TheoreticalAnalysis of the Diffusion ProcessesDetermining the Oxidation Rate of Alloys, by Carl Wagner.

  3. Plan Introduction • Presentation of the Wagner model • Analyze of the results obtained by the Wagner model • Future experimental study Conclusion

  4. Introduction • Ni-30%Cr Pt-30%Ni • The oxidation of an alloy Δxoxide Alloy Oxide x 0 Δxmetal x 0 Initial Situation After oxidation during dt

  5. Presentation of the Wagner model (I/VI) The diffusion process Alloy of Ni-Pt NiO air Ni Ni2+, 2e- Ni2++2 e- + ½ O2-> NiO Pt NA(i) NA(e) x

  6. Presentation of the Wagner model (II/VI) The main hypothesis of the Wagner model : • Migration of nickel ions takes place by jumping of nickel ions from normal lattice sites to adjacent vacant sites. • Migration of electrons occurs by exchange of electrons between divalent and trivalent ions. • Thermodynamic equilibrium in the oxide scale • No variation of interdiffusion coefficient • The oxidation rate follows a parabolic law :

  7. Presentation of the Wagner model (III/VI) • The Flux of metal ions : • Equilibrium condition for the reaction 2 Ni (alloy) + O2 (gaz) = 2 NiO : (aA)4/z Pox =πox (with z=2) (NA(e)is « equilibrium mole fraction «  for a given ambient partial pressure, in the interface oxide-air.).

  8. Presentation of the Wagner model (IV/VI) • The equality of flux of nickel atoms in the interface alloy-oxide give us : • The Fick’s second law: • We define : (1) (2) (3)

  9. Presentation of the Wagner model (IV/VI) • By (1), we have : • So, I define : • The equation (2) become : • So, with erf the error function :

  10. Presentation of the Wagner model (V/VI) With : we find : For NA(i)= 0.22 and NA(b) = 0.3, α=0.99 and γ= 100 : (NA(b) = 0.3 = « bulk mole fraction ») (4)

  11. Presentation of the Wagner model (VI/VI) By (1), we find the molar fraction of nickel at the interface alloy-oxide NA(i) verify : with : (5)

  12. Analyze of the results obtained by the Wagner model (I/I) Influence of D or γ (=D/k°c) on the value of NA(i) : In T = 850°C, for Ni-Pt, we have : NA(e)= 6.4. 10-7, K°c= 4.1. 10-12 cm²/sec et D ≈ 3.1. 10-12 cm²/sec, and γ=0.76. I do vary D from 5.10-14 to 1.10-9ie γ from 0.012 to 243.

  13. Future experimental study (I/II) • Analyze of the oxidation at 950°C of three samples oxidized during 1h, 10h and 100h. • Observation in Metallography • Observation of the profile of concentration in the SCM • Observation of the profile of concentration in EDS and Spectrometry Auger ...

  14. Future experimental study (II/II) • First results obtained by Metallography Sample oxidized during 1h x100 Sample oxidized during 10h x100

  15. Conclusion • With the Wagner model, it is possible to have the concentration profile of the Chromium in the alloy. • But, NA(i) may depend strongly of the value of diffusion coefficient!! • My future study will study validate or not the utilization of Wagner model to describe the concentration profile of the Chromium in the alloy.

  16. Thank you for your attention

  17. Why this abrupt variation of NA(i) for γ ≈ 10 ? • Interpretation Mathematics : and y = 0.3 • Interpretation Physics : • For γ<10, the diffusion in the alloy is too weak. • Each a Cr arrive in alloy-interface, he diffuse « instantaneously » in the oxide scale…

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