oxidation of ni-30%cr according to the wagner model

Thibaut DUBÉDATtdubedat@messel.emse.frTutor : Krzysztof WOLSKI

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Pt-30%Ni Ni-30%Cr The oxidation of an alloy

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Alloy

x0

Oxide

0 xΔxmetal

Δxoxide

Initial Situation After oxidation during dt

Alloy

I) Presentation of the Wagner model described for Ni-Pt

II) Analysis of the results obtained by the Wagner model on Ni-30%Pt

III) My experimental study on Ni-30%Cr

Conclusion

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• Theoretical analysis of the diffusion processes.

Published in 1952, under the title :Theoretical Analysis of the Diffusion Processes Determining the

Oxidation Rate of Alloys, by Carl Wagner.

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C. Wagner, “Theoretical Analysis of the Diffusion Process Determining the Oxidation Rate of Alloys”, Journal of the Electrochemical Society, 99 [10] (1952) 369-380.

The diffusion process

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x

Ni-Pt alloyNiO

2e- , Ni2+Ni

Pt

NA(i)

NA(e)

Ni2++2 e- + ½ O2-> NiO

air

NA(b)

The main assumptions of the Wagner model :In the alloy Migration of nickel ions takes place by jumping of nickel ions from

normal lattice sites to adjacent vacant sites. No variation of the interdiffusion coefficient D

In the oxide Thermodynamic equilibrium in the oxide scale The oxidation rate follows a parabolic law :

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The Flux of metal ions :

Equilibrium condition for the reaction 2 Ni (alloy) + O2 (gaz) = 2 NiO :

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(NA(e)is « equilibrium mole fraction «  for a given ambient partial pressure, at the oxide-air interface .)

with aNiO=1 and aNi=NA

The equilibrium of flux of nickel atoms in the interface alloy-oxide gives us :

The Fick’s second law :

We define :

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(1)

(2)

(3)

By (1), we have :

So, I define :

The equation (2) become :

So,

with erf the error function :

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With :

we find :

For NA(i)= 0.22 and NA(b) = 0.3, α=0.99 and γ= 100 :

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(4)

(NA(b) = 0.3 = « bulk mole fraction »)

By (1), we find the molar fraction of nickel at the interface alloy-oxide NA(i) verify :

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(5)

We recall that :

Influence of D or γ (=D/k°c) on the value of NA(i) :At T = 850°C, for Ni-Pt, we have : NA(e)= 6.4. 10-7, K°c= 4.1. 10-12 cm²/sec

and D ≈ 3.1. 10-12 cm²/sec, and γ=0.76.I do vary D from 5.10-14 to 1.10-9 ie γ from 0.012 to 243.

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NA(i) = f(Log(gamma))

Analysis of the oxidation at 950°C of three samples oxidized during 1h, 10h and 100h and quenched in the liquid nitrogen before observation

• Observation in Metallography • Observation of the concentration profile in the SEM by EDX• Observation of the concentration profile by Auger

Spectroscopy ...

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Why we use both EDX and Auger Spectroscopy?

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Analysis by EDX of the μm scaleAnalysis by Auger

Spectroscopyof the nm scale

Oxide Scale

AES + ion eatching

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First results obtained by Metallography

Sample oxidized during 1h x100 Sample oxidized during 10h x100

With the Wagner model, it is possible to obtain the concentration profile of the Chromium in the alloy.

NA(i) strongly depends on the value of diffusion coefficient!

My future study is aimed to validate (or not) the utilization of Wagner model to describe the concentration profile of the Chromium in the alloy.

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Thank you for your attention

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y = 0.3

• Interpretation Mathematics :

• Interpretation Physics :

For γ<10, the diffusion in the alloy is too slow.Each time a Cr atom arrives to the alloy-oxide interface, it diffuses « instantaneously » into the oxide scale…

and