12th Annual GTT-Technologies Workshop
17th June, 2010
M. Auinger and M. Rohwerder
Grain Boundary Oxidation Processes and High Temperature Corrosion
Overview
• Theoretical Background
• Programme Description (Linking ChemApp with COMSOL)
• Comparison with Experimental Results
• Introducing Chemical Potentials
• Summary
Oxidation Processes
Figure: Schematic process of grain boundary oxidation in steel sheets, fabricatedby the hot-rolling technique.
scale (mainly ‘FeO’)
Oxygen Partial Pressure
Figure: Thermodynamic stability diagram of iron and iron oxides with respect totemperature and oxygen partial pressure according to SGTE Pure Substance Data.
0 250 500 750 1000 1250-100
-75
-50
-25
0
γ-Fe
oxyg
en p
ress
ure
log(
p(O
2)/po)
temperature θ / °C
α-Fe
Fe3O4
Fe2O3 (hematite)
'FeO' (wustite)
Programme Algorithm
0.00 0.25 0.50 0.75 1.00-40
-35
-30
-25
-20
-15
-10Fe2O3 (hematite) + Al2O3
Fe3O4 + FeAl2O4
oxyg
en p
ress
ure
log(
p(O
2) / p
o)
mole fraction aluminium xAl
Fe + Al
Fe + Al2O3
'FeO' + FeAl2O4
Fe + FeAl2O
4
Fe3O4 + Al2O3
Al2O3 + FeAl2O4
700 °C
element migration(COMSOL Multiphysics)
chemical reaction(ChemApp)
( )( ) ( )( )tx,iTx,i
tx,i c.D=dt
dc∇div
Data HandlingAl - total
Al
Al-Oxide
Figure: Spatial phase distributions of Fe, 2 wt-% Al (4.05 mol-% Al) after oxidationat p(O2) = 10-22 bar for 60 min at 700 °C.
Al
Al2O3
FeAl2O4
Calculation of Oxidationdepth - Distribution
0 25 50 750.000
0.025
0.050
0.075
0.100
rela
tive
abun
danc
e
depth x / µm
µ, σ
0 25 50 75 1000.00
0.25
0.50
0.75
1.00
Data: Data1_CModel: SLogistic1Equation: y = a/(1 + exp(-k*(x-xc)))Weighting: y No weighting Chi^2/DoF = 0.00721R^2 = 0.99588 a 3.20455 ±0.00818xc 29.5835 ±0.10386k 0.22165 ±0.00442
Frac
tion
of m
etal
lic C
hrom
ium
depth x / µm
Oxides metallic Cr
Dependencies with Grain Size
Figure: Grain size dependency of the spatial distribution of chromium oxides in Fe, 3 wt-% Cr after finished cooling procedure (dGB = 500 nm).
Comparison with the Experiments
Figure: Simulation of spatial phase distributions of Fe, 1 wt-% Si (1.97 mol-% Si) after oxidation at p(O2) = 10-22 bar for 90 min at 650 °C (left). AES-captions (right).
AES pictures by S. Borodin, MPIE
Ternary Alloy Systems
Figure: Thermodynamic stability (according to SGTE Pure Substance Data) of silicon and aluminium containing oxide phases in an iron alloy at 650 °C.
0.00 0.25 0.50 0.75 1.00-35
-30
-25
-20Fe3O4 + FeAl2O4 + SiO2FeO
Fe + FeAl2O4 + Fe2SiO4
Fe + SiO2 + FeAl2O4FeAl2O4
Fe + Al2O3 + SiAl2O5
SiAl2O5
Fe + SiO2 + SiAl2O5
Fe + Al2O3 + FeSi
Oxy
gen
Parti
al P
ress
ure
log(
p(O
2)/p0)
xSi/(xSi+xAl)
3 w
t-% S
i, 1
wt-%
Al
Fe + Al + FeSi
Atmosphere
Ternary Alloy Systems
Figure: Spatial phase distributions of silicon, aluminium and their oxides in Fe, 3 wt-% Si, 1 wt-% Al after oxidation at p(O2) = 10-22 bar for 110 min at 650 °C.
Si SiO2 Fe2SiO4 SiAl2O5 FeAl2O4 Al2O3 Al
Programme Benchmark
Figure: Spatial phase distributions in a real alloy after oxidation at p(O2) = 10-22 bar in a technical cooling programme.
Fe FeO Fe3O4 Fe2O3 Fe2MnO4 FeCr2O4 FeSiO3 SiFe2O4 FeAl2O4 Fe3C
Mn MnO MnOx Fe2MnO4 SiMn2O4 SiMnO3 MnAl2O4 Mn23C6 Mn7C3
Cr Cr2O3 FeCr2O4 Cr23C6 Cr7C3 Cr3C2
Programme Benchmark
Figure: Spatial phase distributions in a real alloy after oxidation at p(O2) = 10-22 bar in a technical cooling programme.
Si SiO2 FeSiO3 SiFe2O4 SiMn2O4 SiMnO3 SiAl2O5 SiC
Al Al2O3 FeAl2O4 MnAl2O4 SiAl2O5 AlPO4
C Fe3C Mn23C6 Mn7C3 Cr23C6 Cr7C3 Cr3C2 SiC
Programme Benchmark
Figure: Spatial phase distributions in a real alloy after oxidation at p(O2) = 10-22 bar in a technical cooling programme.
C P2O5 AlPO4
Part II
Introducing chemical Potentials
Thermodynamics in normal life
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Figure: Shibuya (渋谷) crossing in Tokyo at night when pedestrian lights are green.
Thermodynamics in normal life
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Figure: Shibuya crossing in Tokyo in the evening when pedestrian lights are red.
Some Formulas
general description
single phasecDJ A ∇−=
μ∇−= LJ A
∑∑ Δ+Δ+Δ−Δ=Δ nzFnTSpVG ϕμ
( )aRTo ln+= μμ
L=
( )cRTo γμ ln+=
⎟⎟⎠
⎞⎜⎜⎝
⎛∇+∇−∇−= γ
γμ RTLc
cRTL oc
cLLJ A ∇∂∂
−=∇−=μμ
( )cRTo ln~ += μ
321D
Simulation Results
[1] Blavette et al. Microsc. Microanal. 13 (2007) 464
Figure: Numerical simulation of segregation (left) and 3D atom probe tomography of segregated boron atoms along the grain boundary in a NiAl superalloy [1] (right).
t = 0
t ∞concentration
Summary
• simulations of (oxide) phase distributions in local thermodynamic equilibrium with ChemApp
• good agreement within experimental error for binary alloys
• some deviations for ternary systems
• concentration gradients alone can not explain interphase transport phenomena
Again in real life…
Figure: Castle Schönbrunn (Vienna, Austria) in the summer time.
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Acknowledgements
Funding
Christian Doppler Forschungs-gesellschaft
voestalpine Stahl GmbH
Academic partners
Institute of Chemical Technologies and Analytics