Oxidation of Ni-30%Cr according the Wagner Model
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Transcript of Oxidation of Ni-30%Cr according the Wagner Model
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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
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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
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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.).
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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)
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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 :
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 »)
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By (1), we find the molar fraction of nickel at the interface alloy-oxide NA(i) verify :
with :
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(5)
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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
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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