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

http://adsjapan.blogspot.com (dl 10.06.2010)

Figure: Shibuya (渋谷) crossing in Tokyo at night when pedestrian lights are green.

Thermodynamics in normal life

http://www.gettyimages.com (dl 10.06.2010)

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