agren oxides

7/27/2019 Agren Oxides

1/51

John gren

Dept. of Matls. Sci. & Engg.Royal Institute of TechnologyStockholm, 100 44 Sweden

Acknowledgement: Reza Naraghi, Samuel Hallstrm, Lars Hglund andMalin Selleby

Diffusion in metal oxides and high-

temperature oxidation of metals


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TC users group meetingAccess 6-7 Sept 2012

MGI

ICME

3D-MS

New Research directionsin Materials science and Engineering:


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Content

1. Aim of work

2. Defects and diffusion - Wagners theory3. Krger-Vink method and sublatticeformalism

4. Generalization of Wagners theory using

the sublattice formalism5. Growth of external oxide layers6. Metal diffusion in the iron oxides7. Oxygen diffusion in the iron oxides

8. Divergence of oxygen flux and Kirkendalleffect


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Predict oxidation:- Sharp-interface methods DICTRA- Diffuse-interface methods phase-field

For example:

- Oxidation of steels- Degradation of superalloy coatingsWe need:

- Mathematical expressions for oxidation rate interms of diffusional flux as function of gradientsin composition or chemical potentials.

- Parameters that characterize a given material

1. Aim of work


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TC users group meetingAccess 6-7 Sept 2012 Excellence Relevance - Availability

Issues in modelling of oxidation

Predict: Rate of oxidation

- External (growth of external layers)- Internal (internal oxide particles)

- Grain boundaries in metal and in oxides What oxides form? Porosity

- Kirkendall effect

Jonsson etal. 2006

Giggins andPettit 1971

Internal oxidation of Mn, Si, Cretc during carburization (Holmet al. 2010)


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Combination of CALPHAD thermodynamics anddiffusion kinetics based on atomic mobilities hasbecome a powerful tool to simulate diffusional

transformations in multicomponent metallic alloys e.g.- Ni-base super alloys- Complex steels- Cemented carbides

Allows simulation of , e.g.- Diffusional interactions in joints of dissimilar materials- Homogenization- Precipitation reactions

The method has been extended to cover quitecomplex phases such as stoichiometric phases andphases with ordering reactions, e.g. B2-NiAl.

Now it is being extended to cover oxides.


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cLD

x

cD

x

c

cL

xLJ

:Flux

Kinetic parametersfrom defects

Darkens thermodynamic factor,e.g. from Calphad analysis

Vacancy mechanism!Defects more complicated in oxides.

General approach:


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2. Defects and diffusion - Wagnerstheory

In metallic systems the major mechanism for diffusionis atoms jumping to adjacent vacant lattice sites lattice defects are important.

For oxides Wagner postulated different kind of defectswhere the vacancies are of special importance.

Even for a stoichiometric oxides there will be defects;- Schottky- Frenckel

'

...

Diffusion by vacancy mechanism:

k k Va k k

k k k

J c y M FF


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Diffusion in oxides type M1-xO

Stoichiometric MO (x=0)

MnO, FeO, CoO and NiO: O-2 FCC lattice with cations onoctahedral interstices. For stoichiometric MO only smallamounts of vacancies due to Schottky defects:

Slow diffusion, similar fo M and O.Frenckel defects

Much slower diffusion for O than M.

'''

22 ),)(,(

VaVa yy

VaOVaM

where

2

2 2 2

' ''

( , )( , )( )

where Va M

M Va Va M O

y y


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With sublattice formalism

Content of Schottky defects:

2

2

( 2 ) ( )

2 (1 ) ln((1 ) ln

/ (1 )0

10

(1 )

( )exp

2 ( ) (

m MO Va MVa VaMa MO Va VaVa MVa VaM

E

Va Va Va Va m

m Va

Va

mm

Va Va

MVa VaMa MO

Va

Va VaVa MVa VaM Va VaVa MVa

G G y G G G y G G G

RT y y y y G

d G y

dy

dGG

dy y

G G Gy

y G G G y G G

/ 2

)VaM

RTG


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3. Krger-Vink method and sublatticeformalismNon stoichiometric M1-xO (metal deficit oxide)

))(,,( 232 OVaMM 2/3 MVa yy:neutralityElectro

* ''

2

1( ) 2

2Krger-Vink:

One electron is missing on an site, i.e. there

is a "positive hole". Increased diffusivity for M.

* same charge as normal occupancy

' 1 negative charge relative no

O MO g O Va h

M

rmal occupancy

'' 2 negative charges relative normal occupancy

1 positive ...

2 positive ...


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2 2

2

2' 2

'

' 0

'

/


MM M

h h h

O

e e e

i i Va i m

J L

J L

J

J L

L x y M V

Electricpotentialgradient

(Nernst field)


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2 2

2 22 3

2 12

2

2 3

2

2

2 * 2 1

12

2

12

14

2 3

2

'

'

' 0

'

2 2 0

Yields:

MO M O

M O h M O

O O e

M MOM

h h M O MO

O

e e O

M h O e

J L

J L

J

J L

J J J J

Neutral combinations

No net flow of charge:


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2

2

* ''

2

'' 2 1/2

''

'' 1/3 1/6

1( ) 2

2

[ ][ ]

[ ] 2[ ][ ] ( / 4)

Concentration of vacancies: O M

M O

M

M O

O g O Va h

Va h kP

h VaVa k P


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Sublattice formalism M1-xO

2 3

2 2 3 3

3

2 3

2

2 3

2 3 2

1

2

ln ln ln

2 2

1 1 3

(2 3 )(1 3 ) ln(1 3 ) 2 ln 2 ln

(1 )

ln (2

m M M Va VaM M

E

Va Va mM M M M

Va

VaM

VaM M

m M M M Va

E

m

mO m

ref

O O O

G y G y G y G

RT y y y y y y Gy x

y y x

y y y x

G G x G G GRT x x x x x x G

dG G x

dx

RT P

2

3

3 2 2

1/3 1/6

3 2

4

2 ) ln (1 3 )

0

4 exp (2 2 ) /

ref

M M Va O

ref

M M Va O O

x

G G G RT x

x

x G G G RT P


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2 2

3 3

2

2

3

' 2

' 3

' 0

'

/


MM M

MM M

O

e e e

i i Va i m

J L

J L

J

J L

L x y M V

Electricpotentialgradient

(Nernst field)

4. Generalization of Wagners theoryusing the sublattice formalism


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2 2

3 22 3

2 12

2

3 2 3

2

2

2 3 2 1

12

2

1

32

14

2 3

2

'

'' 0

'

2 3 2 0

Yields:

MO M O

M O M O

O O e

M MOM

M M OM

O

e e O

M M O e

J L

J L J

J L

J J J J

Neutral combinations

No net flow of charge:


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Extreme cases

Fully ionic conductor Le >L

OOMMMOMe LLL 2

1/)

2

132(

3232

0 e


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).(etemperaturVerwey

theabovemetalhalf

almostisMagnetite:Example

LL

OFe

e

43

FeFeFe 32

OOO

FeFeFe

LJ

LJ

'

'

2

O

Fe

O

Fe

O

Fe

LL

JJ

00

''


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5. Growth of external oxide layers

Metal a

Oxide b

Atmosphere with O2Oxygen content

Distance

xx


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Flux balances

In lattice-fixed frame of reference, a = metal,b = oxide.

1/

1/

aaaa

bbbb

MeMeOO

OOMeMe

uxxu

uxxu

and:metalin

and:oxidein

variablesionConcentrat

0',0',1,0

''

''

/

/

//

//

aaaa

aba

a

bab

b

ab

aba

a

bab

b

ab

aaa

bbb

ba

FeOFeO

FeFeFe

s

Fe

s

OOO

s

O

s

Mems

Oms

JJuu

JJuV

vu

V

v

JJuV

vu

V

v

xVV

xVV

:interfacephase/At

volumesMolar


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)ofgrowth(Outward

:interface

:ofShrinkage

ofgrowthInward

:interface

b

b

a

b

ba

bb

b

b

b

bbb

a

ba

b

b

ab

'

1,0,0'

/

''

'

/

/

/

/

MeMe

s

gas

O

gas

Me

ga s

Me

MeOMe

s

O

s

JuV

v

uuJ

gas

uJJV

v

JV

v


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Pfeil (1929) If, on the other hand, diffusionoutwards continued for a prolonged period ... ahollow space would form between the scale and the

inner core.

HRTEM of Hollow nano crystalsof CoO formed by oxidation ofCo nano-particles.Yadong Yin, et al. Science(2004)


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(Fe+2,Fe+3)1 (Fe+2,Fe+3,Va)2 (Va,Fe+2)2 (O-2)4

Thermodynamic model (Sundman 1991):

Extracctahedral

VaExtraoctahedral

Fe+2

octahedral

fcctetrahedral

Interstitial sites

1/8*8 sites 4 sites

6. Metal diffusion in the iron oxides


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Fe diffusion in magnetite

As Le>>L we may neglect the difference between Fe-ions when considering diffusion:

422 ),(),( OFeVaVaFeFe


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'' '' '' ''' ''' '''12

1'

Absolute reaction rate arguments:

Fe Va Fe FeVa Fe Va FeVa Fe

s

J y y M y y M V

Fe diffusion in lattice-fixed frame ofreference

Normal octahedral extra octahedralsites sites

)/exp(2 RTGvRTM kk

FeL


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Experimental information on Fe

tracer diffusion Dieckmann & Schmalzried 900-1400C Peterson et. al. 1200C Aggarwal & Dieckmann 1200C Becker et. al. 1200-1400C

Fe

FeVaVaFeFeVaFeVaFe uMyyMyyRTD

1'''''''''''''''21

*

s.sublatticecontaining-irondifferentthe

betweenrandomlycompletelysdistributetracerThe


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Optimization of Fe mobilities(Hallstrm et al 2011)


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Tpfer et.al. 1995

Alloy elements in magnetite lattice fixedframe of reference

Tpfer et.al. 1995

CrCrVaVaCrCrVaCrVaCr

Cr

s

CrVaVaCrCrVaCrVaCr

uMyyMyyRTD

zVMyyMyyJ

/

1

'

'''''''''''''''

'''''''''''''''

*

Cr content of inwardgrowing spinel will inheritCr content of alloy.


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Chemical diffusivity (diffusion in a

gradient)

Fe

FeFeFe

cRTLD

~


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m2/s

Mole fraction Fe

Calculated chemical diffusivity in spinel

Red line shows stablecomposition range ofspinel.

Triangles show measured

chemical diffusivities at1508K. Blue dots show where the

triangles should be. Values are high, but still

in reasonable agreement

with experiments.


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Diffusion in corundum structure- Fe2O3

-24

-22

-20

-18

-16

-14

-12

log(DFe

)(m2/s)

6 7 8 9 10 11

104/T (1/K)

95010501150125014001550T

Chang &Wagner 1 atm

Hoshino & Peterson 1 atm

Atkinson & Taylor 1 atm

Himmel et. al. 1 atm

Hoshino & Peterson 1 atm

Sabioni 1atm

Amami et. al. 0.6 atm

Lindner 0.2 atm


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- Cr2O3

Q estimated fromdiffusion of Fe inhematite(isostructural).

Lowest values shouldcorrespond to the mostpure material.

Values from Sabioni andTsai (recalculated totracer) used inoptimization.


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Defect structures for oxygen diffusion and resultsWstite (Halite)

2 3 2

1 1( , , ) ( )

Sundman's model:

Fe Fe Va O

' "

* ' "

1

1

i OO Va O OVa

m

i

O Va O OVa

O

J y y M

V z

D y y Mn

Yamagochi et al. 1982 found that oxygen diffusion rateincreases with oxygen potential. Thus oxygen vacancies

cannot be the dominating mechanism. We thuspostulate that oxygen diffuses on interstitial (cation )sites:

7. Oxygen diffusion in the iron oxides


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Oxygen tracer diffusion in Wstite.

Experiments fromYamaguchi et al 1982


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Defect structures for oxygen diffusion and resultsMagnetite (Spinel)

O tracer diffusion in spinel (lattice-fixed frameof reference)

T= 1150C

Millot and Niu 1996


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At low oxygen potentials it seems reasonable thatoxygen diffusion is assisted by anion vacancies.The lower the oxygen potential, the higher fractionof vacancies and rate of diffusion.

(Fe+2,Fe+3)1 (Fe+2,Fe+3,Va)2 (Va,Fe+2)2 (O-2, Va)4

Modification of Sundmans thermodynamic model:

octahedralfcc

tetrahedral

Interstitial sites

1/8*8 sites 4 sites


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(Fe+2,Fe+3)1 (Fe+2,Fe+3,Va)2 (Va,Fe+2,O-2)2 (O-2,Va)4


octahedraltetrahedral

Interstitial sites

1/8*8 sites 4 sites

Alternativ 1

At high oxygen potentials this model predicts verylow vacancy fractions . The higher the oxygen

potential, the lower fraction of vacancies and rateof diffusion. This is not in agreement withexperiments!

fcc

Thi k b t i t t i i


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1a a a i i i OO Va O OVa O Va OVa

m

J y y M y y M

V z

This may work but gives too a strong increase invacancy content at high oxygen potentials.It also requires a complete re-assessment of Fe-O!

Schematic diagram

2

12

ln / lnaVa Od y d P

2

12

ln / lniO Od y d P

216ln / lnO Od D d P

(Millot and Niu 1996)

2

12

ln / lnO Od D d P

(Millot and Niu 1996)


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Alternativ 2

(Fe+2,Fe+3)1

(Fe+2,Fe+3,Va)2

(Va,Fe+2)2

(O-2

, Va)4

octahedral fcctetrahedral

Interstitial sites

1/8*8 sites 4 sites

Could the vacancy formation energy be chosen such that:

log aVay


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1073 K 1423 K

"

* "

1

1

a a a i OO O Va OVa Va OVa

m

a a a i

O O Va OVa Va OVaO

J y y M y M

V z

D y RT y M y Mn

At present we have

(Millot and Niu 1996) (Millot and Niu 1996)


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Defect structures for oxygen diffusion and resultsHematite (Corundum)

3 2 3 2

2 1 3( , ) ( , ) ( , )

Kjellqvist et al. 2008

Fe Fe Va Fe O Va

End members andplane of electro neutrality


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*

1

1

a a a OO Va O OVa

m

a a a

O Va O OVa

O

J y y M

V z

D y y Mn

3 2 3 2

2 1 3( , ) ( , ) ( , )Fe Fe Va Fe O Va

We postulate


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Experiments: Amami et al. 1999

8 Divergence of oxygen flux and


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2 2

2

' /

1/

1

( )

Oxygen is substitutional and divergence of

oxygen flux gives Kirkendall effect:

molar volume/mole of atoms

Rate of density ( ) change:

No porosity Strain

mO Om

m

m

m

vJ J x V

V

V

V JV

div

11 22 33

2

1( )

( )(1 )

rate:

Only porosity (volume fraction ):

m m

m

p

p

m

p

V V J V

f

fV J

f

div

div

8. Divergence of oxygen flux andKirkendall effect


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Maruyama et al. 2004

Voids form as a consequence of a divergence in theoxygen flux.


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Schematics of Kirkendall effectin magnetite

Fe

z

Fe

Distance Distance


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Oxygenmob

ility

Distance

Oxygen

flux

Distance


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zJty OVa //

Distance

Pores Pores


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T. Jonsson et al. 2008

FeO

Fe3 O4

Fe2O

3


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Summary

DICTRA can now handle diffusion in oxides allowingprediction of oxidation.

Data base now contains diffusional mobilities ofWstite (Halite): Fe and OMagnetite (spinel): Fe Cr OHematite (Corundum): Fe, Cr, O

Oxygen diffusion may cause Kirkendall effect and porosity.

agren oxides

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