Phase Diagrams with FACTSage · 2020. 10. 10. · GTT-Technologies Annual Workshop and User‘s...

GTT-Technologies Annual Workshop and User‘s Meeting

Herzogenrath-Kohlscheid (Aachen, Germany)

5th July, 2013

Phase Diagrams with FACTSage Speaking different Languages for Thermochemical Properties

Michael Auinger

Outlook

– Motivation

– Thermochemical Properties in Oxides

– Ellingham-Richardson Diagrams

– Stability Diagrams

– Thermochemistry of Oxides and Nitrides

– Nitrides in the System Iron - Chromium - Carbon

– Nitrogen and Oxygen in Iron - Silicon

– Summary

Oxidation Processes in Steels

scale (mainly ‘FeO’)

Grain Boundary Oxidation

Singheiser et.al., Materials & Corrosion 62 (2011) 504

The Problem

pictures from various internet sources and FACTSage

Lost in Translation?

أنا أحب الديناميكا „ “الحرارية

„Μου αρέσει

θερμοδυναμική “

„我喜歡熱力學 “

„나는 열역학을

좋아 “

„Мне нравится

термодинамики “ „আমি তাপগমতমিদ্যা পছন্দ “

An Effective Solution

أنا أحب الديناميكا „ “الحرارية





좋아 “



An Effective Solution

„I like thermo-

dynamics“ أنا أحب الديناميكا „

“الحرارية





좋아 “



Part I

Thermochemical Properties

of Oxides

Ellingham Diagram

Oregon State University at www.oregonstate.edu (dl 02.07.2013)

http://www.oregonstate.edu/

Ellingham Diagram with FACTSage

2 Fe + O2 2 FeO

Tp

pRGGG

o

OOo

T

Feo

T

FeOo

T

22 ln22

,

)(

,

)(

,

)(

Ellingham Diagrams for Oxide Formation

Ellingham Diagram with FACTSage

2 Fe + O2 2 FeO

Stability Diagrams with FACTSage

2 Fe + O2 2 FeO

Comparison

Tp

pRGGG

o

OOo

T

Feo

T

FeOo

T

22 ln22

,

)(

,

)(

,

)(

o

O

Oo

T

Feo

T

FeOo

T

p

p

RT

GGG2

2

ln22

,

)(

,

)(

,

)(

Properties of Oxygen

Oxide Stability

0 250 500 750 1000 1250 1500 1750 20001250

1000

750

500

250

0

3/2 Fe + O2 = 1/2 Fe3

O4 2 Fe + O2 = 2 FeO

4/3 Cr + O2 = 2/3 Cr

2O3

2 Mn + O2 = 2 MnO

Si + O2 = SiO 2

Sta

ndard

fre

e e

nerg

y o

f fo

rmati

on o

f oxid

es

(-

Go =

-R

T l

n(p

O2

) /

kJ

mol-1

Temperature / °C

4/3 Al + O 2 = 2/3 Al

2O 3

0 K

O2

-25

-20

-15

-10

-5

0

Oxygen p

art

ial

pre

ssure

log(p

O2

)

Iron – Manganese – Chromium alloy

Figure: Spatial phase distribution in an Fe, 2 wt-% Mn, 0.8 wt-% Cr alloy after

oxidation at p(O2)= 3·10-22 bar and 700 °C for 120 min and ternary phase diagram.

published in Mater. Sci. Forum 969 (2011) p.76

Part II

Gaseous Nitriding in the system

Fe – Cr – C

Nitriding of Fe, 1 wt-% Cr, 0.10 wt-% C and

Conditions: 48 h at 500 °C

p(NH3) : p(H2) = 100 (KN = 1 000)

Gaseous Nitriding Process

g´-Phase (Fe4N)

e-Phase (Fe2N)

Diffusion Zone

Theoretical Principles

Figure: Lehrer-Diagram of iron nitrides according to literature (left) and calculated

with the programme FactSage (right).

450 500 550 600 650 7000.01

0.1

1

10

-4

-3

-2

-1

0

1

2

g-Iron (fcc)

-Iron (bcc)

g'-Phase (Fe4N)

KN

= p

NH

3

/p1.

5

H2

temperature / °C

e-Phase (Fe2N)

log

10(p

2 NH

3

/p3 H

2

)

http://www.ipsenusa.com (dl 12.10.2010)

http://www.ipsenusa.com/

Iron – Chromium – Carbon alloy

published in HTM J. Heat Treatm. Mat. 66 (2011) p.100

Figure: Spatial phase distribution in an Fe, 1 wt-% Cr, 0.1 wt-% C alloy after gas

nitriding at KN= 2.4 and 500 °C for 48 h and phase stability diagram.

-10

-5

0

5

0.00 0.25 0.50 0.75 1.0010

-9

10-7

10-5

10-3

10-1

101

CrN

Cr2N

Cr 3

C2

Cr 7

C3

K

N =

p0

.5

o p

NH

3

/p1

.5

H2

xCr

/ (xCr

+xC)

Cr 2

3C

6

Fe + C + Cr3C

2

Fe + Cr

+Cr23

C6

Fe + C + CrN

Fe4N + CrN + C

Fe2N + CrN + C

log

10(p

N2

) /

bar

Binary Phase Diagrams

The System Iron – Nitrogen

Figure: Nitrogen Solubility in Iron at 1 bar (left) and binary Iron-Nitrogen phase

diagram, calculated with FACTSage (right).

H. Zitter, L. Habel Arch. Eisenhüttenwes. 44 (1973) 181.





p1





p1 p2

Part III

Gaseous Nitriding and Oxidation in the system Fe – Si

Nitriding of Fe, 1 wt-% Si

Conditions: 20 h at 550 °C (KN = 1 000)

4 h at 550 °C (KO ≈ 0.01)

Stability Diagram of Iron – Silicon

Figure: Stability diagram of an Fe, 1 wt-% Si alloy at 550 °C with respect to the

partial pressures of nitrogen and oxygen (SGTE Pure Substance Database).

10-9

10-7

10-5

10-3

10-1

101

10-10

10-5

100

105

1010

-10 -5 0 5

-45

-40

-35

-30

-25

-20

-15

-10

Fe

2N

Fe3O

4 + SiO

2

Fe3O

4 + Fe

2SiO

4

K

O =

pH

2O

/pH

2

KN = p

NH3

/p1.5

H2

Fe + Si

SiO2

Fe2SiO

4

Fe2O

3 + SiO

2

Si3N

4

Si2ON 2

Fe

4N

log

10(p

O2

) / b

ar

log10

(pN

2

) / bar

Simulation Results with ASTRID

Figure: Spatial phase distribution in Fe, 1 wt-% Si after gaseous nitriding for 20 h at

KN = 1 000 and oxidation for 4 h and KO ≈ 0.01 (ptot= 1 atm, 550 °C) .

Appl. Simul. of Thermodyn. Reactions and Interphase Diffusion

Ternary Phase Diagrams

Conclusions - The Problem


Conclusions – An Effective Solution


Acknowledgements

Dirk and Alexandra Vogel,

Else-Marie Müller-Lorenz,

Monika Nellessen

Prof. H. Danninger

Vera G. Praig, Markus Holzweber,

Kurt Piplits

Dr. D. Paesold

Bernhard Linder, Klaus Rendl,

Andreas Muhr

Funding

www.oberoesterreich.at (dl 03.07.2013)

Backup Slides

Additional Slides for the Presentation

Where we work…

Max-Planck-Institut

für Eisenforschung GmbH

Head: Prof. Dierk Raabe

Founded in 1917 from the “Kaiser Wilhelm Institute”

by Fritz Wüst.

3 Departments:

Computational Materials Design

Interface Chemistry and Surface Engineering

Microstructure Physics and Alloy Design

From where I am

Austria

Area: 83 879 km²

Inhabitants: ~ 8 405 000

Language: German

Capital: Vienna

Fisher’s Model of Diffusion

3

5

56

log3292.0

z

c

t

DDs GB

Whipple – Le Claire equation

3

5

56

log4704.0

z

c

t

DDs GB

Levine – MacCallum equation

I. Kaur “Fundamentals of … Boundary Diffusion” WILEY (1995)

Some Published Works on HT-Corrosion

Programme Algorithm

0.00 0.25 0.50 0.75 1.00-40

-35

-30

-25

-20

-15

-10

Fe2O

3 (hematite) + Al

2O

3

Fe3O

4 + FeAl

2O

4

oxyg

en p

ress

ure

log(

p(O

2)

/ po)

mole fraction aluminium xAl

Fe + Al

Fe + Al2O

3

'FeO' + FeAl2O

4

Fe + FeAl2O

4

Fe3O

4 + Al

2O

3

Al2O

3 + FeAl

2O

4

700 °C

element migration chemical reaction

tx,iTx,i

tx,ic.D=

dt

dcdiv

ASTRID, published in Oxid. Met. 76 (2011) 247

Data Handling

Al - total

Al

Al-Oxide

Figure: Spatial phase distributions of Fe, 2 wt-% Al (4.05 mol-% Al) after oxidation

at p(O2) = 10-22 bar for 60 min at 700 °C.

Al

Al2O3

FeAl2O4

Detail of a Grain Boundary

Figure: Spatial distribution of chromium oxides Cr2O3 and FeCr2O4 along a grain

boundary in Fe, 3 wt-% Cr after finished cooling from 650 °C.

Diffusion between different Phases

http://adsjapan.blogspot.com and http://www.gettyimages.com

Figures: Shibuya (渋谷) crossing in Tokyo with green and red pedestrian lights.

single phase

cDJ A LJ A

g

g

RTLc

c

RTL oc

cLLJ A

D

general description

http://adsjapan.blogspot.com/

http://www.gettyimages.com/

Modelling Segregation

[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

Calculation of the Oxidation Depth

0 25 50 75

0.000

0.025

0.050

0.075

0.100

Rel

ativ

e ab

un

dan

ce

Oxidation depth in Sample x / µm

µ, s

0 25 50 75 100

0.00

0.25

0.50

0.75

1.00

Data: Data1_C

Model: SLogistic1

Equation:

y = a/(1 + exp(-k*(x-xc)))

Weighting:

y No weighting

Chi^2/DoF = 0.00721

R^2 = 0.99588

a 3.20455 ±0.00818

xc 29.5835 ±0.10386

k 0.22165 ±0.00442

Fra

ctio

n o

f m

etal

lic

Ch

rom

ium

Depth into Steel Sample x / µm

Cr- oxides metallic Cr

Multikomponentensysteme

Abbildung: Phasenverteilung einer industrienahen Legierungszusammensetzung

nach erfolgter Oxidation bei p(O2) = 10-22 bar und einer technischen Abkühlkurve.

Temperature Dependence

Diffusion equation

tx,icT,x,tx,iTx,i

tx,if+c.D=

dt

dcdiv

RT

Q

eD=D o

iTi

1200 1100 1000 900 800 7001E-19

1E-18

1E-17

1E-16

1E-15

1E-14

1E-13

volume diffusion

grain boundary diffusion

Dif

fusi

on c

oef

fici

ent

D /

m²

s-1

Temperatue T / K

Figure: Temperature dependence of phosphorous diffusion in iron.

I. Stloukal, C. Herzig, Z. Metallkd. 93 (2002) 88

Thermodynamic Principles

Figure: State diagram of water [2] (left) and schematic temperature evolution with constant heating (right).

[2] University of Bristol at www.enm.bris.ac.uk (dl 15.10.2010)

melting

boiling

Ice

temperatu

re T

time t

http://www.enm.bris.ac.uk/

Efficiency of the Calculation

Figure: Distribution of Cr2O3 in Fe, 0.67 wt-% Cr at 700 °C after 90 min. Simulation

with InCorr (left) and with self-written programme (right).

300 FEM-points

Calculation time: 90 min

63 000 FEM-points

Calculation time: 120 min

25 µm

Berechnungsaufwand

Abbildung: Abhängigkeit der Rechenzeit zur Simulation des Oxidationsverhaltens

von Fe, 3 wt-% Cr bei verwendetem Kühlprogramm ab 650 °C (B).

bisher Elementarzelle Kanten Algorithmus gekreuzter0

25

50

75

100

Rec

henz

eit

t rel /

%

Algorithmus

Fine grained

C’ – regime B’ – regime A’ – regime

Coarse grained

C – regime B – regime A – regime

Grain Boundary Diffusion Regimes

Figure: Illustration of different diffusion regimes, depending on total diffusion time and ratio of DGB/D.

I. Kaur “Fundamentals of … Boundary Diffusion” WILEY (1995)

Experimental Set-up

N2

Ar

H2

Ar

H2

Dew-Point Sensor

H2O-Dosage

Gas Mixing Chamber

Reaction Chamber Gas Analysis

(H2O, O2-Content)

in Rev. Sci. Instr. (2013), accepted

Selective Decarburisation at 800 °C

Figure: Experimental parameters during selective decarburisation of Fe, 0.8 wt-% C

at 800°C in Ar / 2.5 vol-% H2 / H2O.

M. Auinger, V.G. Praig, et.al., Corros. Sci., submitted


Figure: Mass change during selective decarburisation of Fe, 0.8 wt-% C at 800°C

in Ar / 2.5 vol-% H2 / H2O.

0 20 40 60 80 100 120 140-2.0

-1.5

-1.0

-0.5

0.0

mass c

hange

m / m

g c

m-2

time t / min

measurement from 27.04.2012



Fe, 0.8 wt-%C, 800 °C, Ar/2.5% H2, DP+13°C



Figure: Cross section of Fe, 0.8 wt-% C after oxidation at 800 °C in Ar / 2.5 % H2 /

H2O for 60 min. The cross section was etched with 1 % HNO3 / Ethanol for 15 s.



Figure: Evolution of the decarburised zone depth in Fe, 0.8 wt-% C after oxidation

at 800 °C in Ar / 2.5 % H2 / H2O. The solid lines represent theoretical results.



Figure: Evolution of the mass change in Fe, 0.8 wt-% C during oxidation at 800 °C

in Ar / 2.5 % H2 / H2O. The solid lines represent the theoretical results.


Ellingham – Formulas + FACTSage Pic

Text here

2 Fe + O2 2 FeO

Formation

)(TG

o

OOo

TFe

Feo

TFeO

FeOo

T

p

pRTGaRTGaRTG 22 lnln22ln220

,

)(

,

)(

,

)(

0!

Tp

pRGGG

o

OOo

T

Feo

T

FeOo

T

22 ln22

,

)(

,

)(

,

)(

d

2

)()()(22

O

T

Fe

T

FeO

T

y

FeFeO

o

OOo

T

Feo

T

FeOo

TaRTaRT

p

pRTGGG lnln2ln22 22

,

)(

,

)(

,

)(

ormationo

TG F,

)(

0

Properties of Nitrogen

figures from Landoldt-Börnstein (right) and FACTSage (left)

Nitride Stability

0 250 500 750 1000 1250 1500 1750 2000750

500

250

0

-250

2 Cr2N + N2

= 4 CrN

8 Fe + N2 = 2 Fe4

N

4 Cr + N2 = 2 Cr2

N

8 Mn + N2 = 2 Mn4

N

3/2 Si + N 2 = 1/2 Si 3

N 4

Sta

ndar

d fr

ee e

nerg

y of

for

mat

ion

of n

itri

des

(-

Go =

-R

T ln

(pN

2

) / k

J m

ol-1

Temperature / °C

2 Al + N 2 = 2 AlN

0 K

N2

-15

-10

-5

0

5

Nit

roge

n pa

rtia

l pre

ssur

e lo

g(p

N2

)


0 250 500 750 1000

1E-5

1E-4

1E-3

0.01

0.1

1

10

100

1000

N2 + 3H

2 2 NH

3

Kp =

pN

H3

/ (p

3/2

H2

p1/

2

N2

) p

0

Temperatur / °C

N2 + 3H

2 2 NH

3

3

,

222

1

2

3NHNH Tp

05.1

!

2

3 pp

pK

H

NH

N

0

)(

2 p

KpK

Tp

NN

05.05.1)(

22

3 ppp

pK

NH

NH

Tp

02

1

2

3 !

)()()(223

N

T

H

T

NH

T GGG RT

GGG

Tp

oTN

oTH

oTNH

eK

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

1

2

3

)(


450 500 550 600 650 7002

3

4

5

6

7

102

103

104

105

106

107

g-Eisen (fcc)

-Eisen (bcc)

g'-Phase (Fe4N)

e-Phase (Fe2N)

log

10(p

N2

/p0)

Temperatur / °C

pN

2

/p

0

http://www.ipsenusa.com (dl 12.10.2010)

Figure: Lehrer-Diagram of iron nitrides according to literature (left) and stability

diagram calculated with the programme FactSage (right).

http://www.ipsenusa.com/

Phase Diagrams with FACTSage · 2020. 10. 10. · GTT-Technologies Annual Workshop and User‘s...

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Transcript of Phase Diagrams with FACTSage · 2020. 10. 10. · GTT-Technologies Annual Workshop and User‘s...