Thermo-Calc Software - RWTH Aachen University

Thermo-Calc Software

CALCULATING THERMODYNAMIC PROPERTIES

http://www.thermocalc.com Phone: +46 8 545 959 30E-mail: [email protected] Fax: +46 8 673 3718

Thermo-Calc User Seminar

New version of DICTRA

Aachen, September 11th, 2008

Thermo-Calc SoftwareThe DICTRA SoftwareA 1D finite difference code for simulation of DIffusionControlled TRAnsformations in multi component alloys.

The result of more than 20 years and 60 man-years R&D at:

Emphasis has been placed on linking fundamental models to critically assessed thermodynamic and kinetic data, allowing simulations to be performed with realistic conditions on alloys of practical importance.

Helander et al., ISIJ Int. 37(1997), pp. 1139-45

Example: Interdiffusion in compound

Royal Institute of Technology (KTH) in Stockholm, SwedenMax-Planck Institute für Eisenforschung in Düsseldorf, Germany

Thermo-Calc SoftwareDICTRA - Applied to numerous problemsCarburizing and decarburizationMicrosegregation during solidification Precipitate growth and dissolutionPrecipitate coarseningInterdiffusion in coating/substrate systemsTLP bonding of alloys and much more…

2.60 m

Ball screw for the AirbusA380 aircraft: a martensiticas carburized stainless steel

0,0

0,4

0,8

1,2

1,6

2,0

2,4

2,8

3,2

3,6

4,0

4,4

4,8

0 100 200 300 400 500 600 700 800 900µm

%C

profil carbone calculé en fin d'enrichissement

profil carbone calculé après 3h de diffusion

Fe-12Cr-2Ni-2Mo-0.12C at 955°C::Calculated carbon profile at the end of the enrichment step

Calculated carbon profile after 3h of diffusion

Example: Simulation of carbon evolution in high alloyed steels by Aubert & Duval, France.

Turpin et al., Met. Trans. A 36(2005), pp. 2751-60

Distance from surface (μm)

Carb

on co

ntent

(%)

Thermo-Calc SoftwareKinetic and Thermodynamic input

All simulations depend on assessed kinetic and thermodynamic data that is supplied in databases.

A numerical finite difference scheme is used for solving a system of coupled parabolic partial differential equations.

DATABASESKinetic Thermodynamic

Mobilities Gibbs Energy

Diffusivities

2

2

xG

∂∂

∑ ⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

−∂∂

−=i n

i

j

iikkik

nkj xx

MxxD μμδ )(

Thermo-Calc SoftwareKinetic Databases (in a CALPHAD spirit)

Diffusion without a chemical gradient:

- Tracer diffusion coefficients

Expe

rimen

tsTh

eory

Diffusion under a chemical gradient:

- Chemical interdiffusion coefficients

- Intrinsic diffusion coefficients

Models( ) ),,(ln PTxfRTMB =α

- Ab-initio

- Correlation

Parameter Optimization

Database

Kinetic properties

Thermo-Calc SoftwareWhy a database with mobilities?

[ ]⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=••

••

•

9991

191211

DD

DDD

D

(n-1)2 elements in the inter-diffusion matrix. All depending on composition and temperature.

n mobilities depending on composition and temperature.

The advantage with mobilities become evident when n is large, e.g. for an alloy with 10 components we have only 10 mobilities, but as many as 81 interdiffusion coefficients that we need to model.

From the mobilities we may calculate any diffusion coefficient (i.e. tracer-, individual- or interdiffusion coefficients), provided of course we know the thermodynamics for our system. This relation is verybeneficial during the assessment step.

[ )⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

=•

10

2

1

M

MM

M

Thermo-Calc SoftwareDICTRA Models – overview

α

Matrixβ

Particlerrp 5.1=

vγ α

Single phase

Coarsening

Moving boundary Cell

Disperse system Homogenization

Thermo-Calc SoftwareDICTRA 25

Major improvements:

New approach to diffusion in dispersed systems

Diffusion in complex phases, e.g. ionic

Improved procedure for generation of automatic start-values for activities/potentials at a moving phase interface

Thermo-Calc SoftwareDICTRA 25 - ”Effective phase” multiphase simulations

Flux between slices ”n-1” and ”n”Equilibrium calculationfor each slice

Phase fractionsPhase compositionsChemical potentialsMobilities

”Effective” [Mkxk] from combining rules

[ ] [ ]z

xMxMV

J keffnkk

effnkk

mk Δ

Δ−= −

μ1

1

New approach allow us to account for diffusion in more than one phase

Thermo-Calc SoftwareDICTRA 25 - Calculating effective [Mkxk]

Combining rules are frequently used for determining an “effective”transport property in a multi-phase mixture, from:

1) the transport properties in the individual phases, 2) the fraction of phases, 3) and sometimes also from their geometrical distribution.

Exact knowledge of the geometrical distribution is rarely known for a real case and it may be useful to study limiting cases or bounds.


α matrix γ matrixγ

Larsson and Engström, Acta Mat 54(2006), p. 2431

DICTRA 25 - Interdiffusion in Fe-Cr-Ni diffusion couples (I)

α+ γ / γ / γ + αMa

ss F

racti

on of

α-p

hase

Distance (10-4 m)

0

5

10

15

20

25

30

35

40

Mas

s-pe

rcen

t N

i

10 15 20 25 30 35 40 45 50

Mass-percent Cr

1100 ºC•

•

α + γγ

α

Ni

Cr


Cr-profileNi-profile

DICTRA 25 - Interdiffusion in Fe-Cr-Ni diffusion couples (II)

Larsson and Engström,Acta Mat 54(2006), pp. 2431-

Distance (10-4m) Distance (10-4m)

Thermo-Calc SoftwareDICTRA 25 - MCrAl coating / Ni-base superalloy system (I)

Al-profile Cr-profile

2h 1120°C + 24 h 845°C + 250h 950°CExperimental data From KV Dahl, DTU

NiCoating Bal

BalNi-base alloy

Al Co Cr Mo Ta Ti W15.7 33.7 17.6 0.10 0.05 0.10 0.076.14 7.76 17.8 1.15 1.54 5.62 0.9

Coating Ni-base alloy

Distance (μm) Distance (μm)

Coating Ni-base alloy


Coating

DICTRA 25 - MCrAl coating / Ni-base superalloy system (II)

B2-profile

Mole-

Frac

tion

Coating Substrate

Coating Substrate

Mole-

Frac

tion

Distance (μm)

γ’-profile

Distance (μm)

Thermo-Calc SoftwareThe Fe-O system

Calculated from Sundman 1991.

Courtesy of S. Hallström et al, KTH

Thermo-Calc SoftwareMajor contributions to diffusion in magnetite

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

Thermodynamic model (Sundman 1991):

Extra octahedralVaExtra

octahedralFe+2

octahedral fcctetrahedral

Interstitial sites

1/8*8 sites 4 sitesCourtesy of S. Hallström et al, KTH

Thermo-Calc SoftwareExperimental data, magnetite

Dieckmann & Schmalzried 900-1400°C

Peterson et. al. 1200°C

Aggarwal & Dieckmann 1200°C

Becker et. al. 1200-1400°C

Tracer diffusion coefficients in magnetite

Dieckmann, J Phys Chem Solids Vol. 59, No. 4, pp 507-525, 1998.


Thermo-Calc SoftwareFe diffusion in anion-fixed frame of reference

[ ]zV

MyyMyyJ Fe

mFeVaVaFeFeVaFeVaFe ∂

∂+−=

μ1'''''''''''''''

[ ]'''''''''''''''* FeVaFeVaFeVaFeVa

FeFe MyyMyy

uRTD +=

Normal octahedral extra octahedralsites sites


Thermo-Calc SoftwareOptimization of mobilities, high temperature


Thermo-Calc SoftwareLow temperature

Calculated bulk tracer diffusion at 500°C compared to experimental values (single crystal).


Thermo-Calc SoftwareDiffusion in wustite, Fe1-δO

Thermodynamic model

For vacancy mechanism on cation sublattice in the anion fixed frame of reference:

zVMyyJ Fe

mBVaFeVaFe ∂

∂−=

μ1'''

'''* FeVaFeVa

FeFe

MyyuRTD ≅

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


Thermo-Calc SoftwareTracer diffusion in Fe1-δO

Experiments from Chen and Peterson, J. Phys. Solids, 36, 1975.


Thermo-Calc SoftwareDiffusion in hematite

Thermodynamic model:

For vacancy mechanism on interstitial sublattice in the anion fixed frame of reference:

zVMyyJ Fe

mFeVaFeVaFe ∂

∂−=

μ1''''''

''''''* FeVaFeVa

FeFe

MyyuRTD ≅

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


Thermo-Calc SoftwareOptimization in Fe2O3



600°C, P02=0.05, 24h.fgb==δ/D, D grain size, δ≈5Å gb thickness.Dmag ≈ 3µm, Dcor ≈ 0.1µm.Assumption: Activation energy for diffusion in gb is half that of bulk diffusion.Deff=(1- fgb)Dbulk+ fgbDgb

Gb diffusion assumed only in magnetite and hematite.No diffusion of oxygen.

Simulation 1: Fe-O, 600°C

Pure Fe, 600C, dry O2, 24h. Total oxide thickness is 34 μm. The hematite, magnetite and wustite are 2, 11 and 21 μm, respectively.

10 μmFe

Hematite

Magnetite

Wüstite


Thermo-Calc SoftwareSimulation 1: oxide thicknesses

Magnetite HematiteWustite

27 µm 0.18 µmCalculated: 45 µmExperimental: 21 µm 11 µm 2 µm



Conditions almost identical to simulation 1.

Assumption: Activation energy for diffusion in gb is about 1/3 of that of bulk diffusion (instead of ½).

Simulation 2: Fe-O, 600°C


Thermo-Calc SoftwareSimulation 2: oxide thicknesses

Magnetite HematiteWustite

Calculated: 45 µm 10 µm 2 µmExperimental: 21 µm 11 µm 2 µm


Thermo-Calc SoftwareWustite nucleation?

Chen and Yuen 2003

From eutectoid temperature up to about 700°C, oxidation depends a lot on the thermal history and surface condition of the substrate.

At 580-600°C the scales have been reported to contain phase fractions ranging from almost only hematite, to be dominated by wustite with an extremely thin outermost hematite layer.

At temperatures closest to the eutectoid temperature (570-580 °C), wustitesometimes does not form at all for up to 24h, or does not form a uniform layer.


Thermo-Calc SoftwareConclusions

DICTRA can now handle diffusion in complex phases, e.g. oxides.

Cation diffusion in the three iron oxides has been critically assessed.

Moving metal/oxide phase boundary.

Moving oxide/oxide phase boundary.

Moving oxide/gas phase boundary.

Grain boundary diffusion is taken into account in a simplified manner.

Cr and oxygen diffusion is currently being added.



CALCULATING THERMODYNAMIC PROPERTIES

http://www.thermocalc.com Phone: +46 8 545 959 30E-mail: [email protected] Fax: +46 8 673 3718

Save Time ♦ Reduce Costs ♦ Increase Inovation

Thank You!

Documents

Thermo-Calc Software - RWTH Aachen University