Thermo-Calc Software - RWTH Aachen University
Transcript of 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.
Thermo-Calc Software
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
Thermo-Calc Software
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
Thermo-Calc Software
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.
Courtesy of S. Hallström et al, KTH
Thermo-Calc SoftwareFe diffusion in anion-fixed frame of reference
[ ]zV
MyyMyyJ Fe
mFeVaVaFeFeVaFeVaFe ∂
∂+−=
μ1'''''''''''''''
[ ]'''''''''''''''* FeVaFeVaFeVaFeVa
FeFe MyyMyy
uRTD +=
Normal octahedral extra octahedralsites sites
Courtesy of S. Hallström et al, KTH
Thermo-Calc SoftwareOptimization of mobilities, high temperature
Courtesy of S. Hallström et al, KTH
Thermo-Calc SoftwareLow temperature
Calculated bulk tracer diffusion at 500°C compared to experimental values (single crystal).
Courtesy of S. Hallström et al, KTH
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
Courtesy of S. Hallström et al, KTH
Thermo-Calc SoftwareTracer diffusion in Fe1-δO
Experiments from Chen and Peterson, J. Phys. Solids, 36, 1975.
Courtesy of S. Hallström et al, KTH
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
Courtesy of S. Hallström et al, KTH
Thermo-Calc SoftwareOptimization in Fe2O3
Courtesy of S. Hallström et al, KTH
Thermo-Calc Software
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
Courtesy of S. Hallström et al, KTH
Thermo-Calc SoftwareSimulation 1: oxide thicknesses
Magnetite HematiteWustite
27 µm 0.18 µmCalculated: 45 µmExperimental: 21 µm 11 µm 2 µm
Courtesy of S. Hallström et al, KTH
Thermo-Calc Software
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
Courtesy of S. Hallström et al, KTH
Thermo-Calc SoftwareSimulation 2: oxide thicknesses
Magnetite HematiteWustite
Calculated: 45 µm 10 µm 2 µmExperimental: 21 µm 11 µm 2 µm
Courtesy of S. Hallström et al, KTH
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.
Courtesy of S. Hallström et al, KTH
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.
Courtesy of S. Hallström et al, KTH
Thermo-Calc Software
CALCULATING THERMODYNAMIC PROPERTIES
http://www.thermocalc.com Phone: +46 8 545 959 30E-mail: [email protected] Fax: +46 8 673 3718
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