Thibaut DUBÉDATtdubedat@messel.emse.frTutor : Krzysztof WOLSKI

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• The diffusion processes determine the oxidation of alloys.

• Theoretical analysis of the diffusion processes.

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

Oxidation Rate of Alloys, by Carl Wagner.

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Introduction

I) Presentation of the Wagner model

II) Analyze of the results obtained by the Wagner model

III) Future experimental study

Conclusion

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Ni-30%Cr Pt-30%Ni

The oxidation of an alloy

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Alloy

x0

Oxide

0 xΔxmetal

Δxoxide

Initial Situation

After oxidation during dt

The diffusion process

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x

Alloy of Ni-PtNiO

Ni2+, 2e-

Ni

Pt

NA(i) NA(e)

Ni2++2 e- + ½ O2-> NiO

air

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 :

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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)

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

The equality of flux of nickel atoms in the interface alloy-oxide give 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 :

with :

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(5)

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 1.10-9 ie γ from 0.012 to 243.

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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...

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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 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.

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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 weak.Each a Cr arrive in alloy-interface, he diffuse « instantaneously » in the oxide scale…

and