Thibaut DUBÉDAT
tdubedat@messel.emse.fr
Tutor : Krzysztof WOLSKI
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

Pt-30%Ni
Ni-30%Cr
The oxidation of an alloy
Δxoxide
Alloy
Oxide
0
x
Initial Situation
0
Alloy
Δxmetal
x
After oxidation during dt
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I)
II)
III)
Presentation of the Wagner model
described for Ni-Pt
Analysis of the results obtained by the
Wagner model on Ni-30%Pt
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.
C. Wagner, “Theoretical Analysis of the Diffusion Process
Determining the Oxidation Rate of Alloys”,
Journal of the Electrochemical Society, 99 [10] (1952) 369-380.
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The diffusion process
air
NiO
2e- , Ni2+
Ni2++2 e- + ½ O2-> NiO
Ni-Pt alloy
Ni
NA(b)
Pt
NA(i)
NA(e)
x
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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 :
with aNiO=1 and aNi=NA

(NA(e)is « equilibrium mole fraction « for a given
ambient partial pressure, at the oxide-air
interface .)
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
The equilibrium of flux of nickel atoms in the
interface alloy-oxide gives us :
(1)

The Fick’s second law :
(2)

We define :
(3)
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
By (1), we have :

So, I define :

The equation (2) become :

So,
with erf the error function :
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With :
(NA(b) = 0.3 = « bulk mole fraction »)
we find :
(4)
For
NA(i)= 0.22 and NA(b) = 0.3,
α=0.99 and γ= 100
:
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By (1), we find the molar fraction of nickel at
the interface alloy-oxide NA(i) verify :
(5)
We recall that :
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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))
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•
•
•
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?
Oxide
Scale
AES +
ion eatching
Analysis by Auger
Spectroscopy
of the nm scale
Analysis by EDX of the μm scale
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
First results obtained by Metallography
Sample oxidized during 1h x100
Sample oxidized during 10h x100
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


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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• Interpretation Mathematics :
and
y = 0.3
• 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…
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