IOM3 Hume-Rothery Seminar, Derby, 2017-01-18
Process Simulations and Computer Aided Process Development i) Microscopic
Anders Engström
Outline
Introduction
CALPHAD Extensions
Computational tools
Examples
Thermo-Calc Software
Providing computational tools in the field of materials engineering that allow for faster, cheaper and more sustainable innovation, development and production of both materials and components.
We have been supporting material engineers for two decades.
Important and useful tools
In a review of the 2015 literature, Thermo-Calc software products were referenced, mentioned or used in over 1000 publications, distributed on 231 journals, and by organizations from 59 different countries.
The topics range from the macro- to micro-level, from meteorites to platinum jewellery and power plants to nanowire systems.
64 theses published in 16 countries.
In 2015, at a minimum, sixty-four students, 64% at the PhD level, cited Thermo-Calc products.
46 patent citations (with a date of publication in 2015).
Phase Diagrams
Calculated phase diagram of CoCrFeNi-Al by using TCHEA1
Provides stable state, i.e. amount of equilibrium phases. To some extent we can account for non-equilibrium states. e.g. by suspending stable phases, or making certain assumptions on the diffusion rate in liquid vs. solid phases (Scheil-Gulliver). No information about the rate of transformation, nor the microstructure morphology.
The influence of chemistry on microstructure and properties
Heat treating can best be defined as “the controlled application of time, temperature and atmosphere to produce a predictable change in the internal structure (i.e. the microstructure) of a material.” Dan Herring, 100th Column of the “Heat Treat Doctor” published in Industrial Heating magazine
Materials by Design - Cohen’s Reciprocity
Processing
Structure
Properties
Performance
Morris Cohen’s “reciprocity” between the cause/effect logic of science and goal/means logic of engineering.
Cause and effect
Goal/means
The National Academies Press, 2008
Integrated Computational Materials Engineering: A Transformational Discipline for Improved Competitiveness and National Security
ICME
ICME: an approach to design products, the materials that comprise them, and their associated materials processing methods by linking materials models at multiple length scales. Key words are "Integrated", involving integrating models at multiple length scales, and "Engineering", signifying industrial utility.
Need to predict Microstructure evolution during processing and in service
Unfortunately phase transformations is a non-trivial topic.
J. W. Christian, The Theory of Transformations in Metals and Alloys (Pergamon, Oxford, 1981).
MGI - Reinforcing the importance of data
CALPHAD is at the nexus of:
Experiments (on the data assessments are based and validated).
Digital data (databases)
Computational tools (software)
Fundamental databases and tools enabling reduction of the 10-20 years materials creation and deployment cycle by 50% or more.
June 2011
CALPHAD Method
Mobility and Diffusivity
10
2
1
M
M
M
M
9991
191211
DD
DDD
D
Atomic mobility Database
Self-Diffusivity Impurity Diffusivity Intrinsic Diffusivity
Chemical Diffusivity
• (n-1)2 elements in the inter-diffusion matrix. All depending on composition and temperature.
• n mobilities depending on composition and temperature.
J.O. Andersson and J. Ågren, J. Appl. Phys., 72 (1992) 1350.
Atomic Mobility Databases (in a CALPHAD spirit)
Experiments
Diffusion without a chemical gradient:
- Tracer diffusion coefficients
Diffusion under a chemical gradient:
- Chemical interdiffusion coef. - Intrinsic diffusion coefficients
Models
Estimates
- Correlation
Theory
- Ab-initio
Parameter optimization
Storage in mobility database
Applications
Mobility, Diffusivities
),,(ln PTxfRTM B
Ass
ess
me
nt
and
op
tim
izat
ion
P
red
icti
on
Thermodynamic database
𝐷𝑘 = 𝑐𝑘𝑀𝐾
𝜕𝜇𝑘𝜕𝑐𝑘
Modelling of the Atomic Mobility
energyActivationQ
factorFrequencyM
BelementforMobilityM
B
B
B
0
From absolute reaction-rate theory arguments Andersson and Ågren1) suggested:
When treating the composition dependency of the mobility, Jönsson2) found it superior to expand the logarithm of the mobility rather than the value itself, i.e.
Because iRTMln is often found to have a fairly linear composition dependency
1. Andersson, Ågren, J Appl Phys 72(1992)1350 2. Jönsson, Scand J Metall 24(1995)21
Composition dependency
BBB QMRTrepresentswhere 0ln
In a CALPHAD spirit the composition dependency is represented with a linear combination of the values at each endpoint of the composition space, and a Redlich-Kister expansion, i.e.
NiAl
Al
Al
Al
Ni
Al
,
Engström , Ågren, Z Metallkd 87(1996)92
Ni-Al
Example: FCC Ni-Al
NiAl
Ni
Al
Ni
Ni
Ni
,
Ni Al
-15.0
-14.5
-14.0
-13.5
-13.0
-12.5
-12.0
-11.5
LO
GD
C(F
CC
,AL
,AL
,NI)
0 0.05 0.10 0.15 0.20
Mole-Fraction Al
1573 1523 1473 1423 1373 1323 1273
Ferromagnetic ordering
Jönsson , Z Metallkd 83(1992)349
Activation energy for the mobility in the paramagnetic state
Contribution to the activation energy from magnetic ordering
Fe self-diffusion
Magnetic enthalpy H
Factor of proportionality mag D
2
Chemical ordering
Inspired by Jönssons work on the effect from magnetic ordering, Helander and Ågren suggested:
Activation energy for the mobility in the disordered paramagnetic state
Contribution to the activation energy from magnetic ordering
Contribution to the activation energy from chemical ordering
Contribution to the activation energy from chemical ordering of i-j atoms
Helander, Ågren, Acta Mater 47(1999)1141
Effect from chemical ordering in the Ni-Al system
Helander, Ågren, Acta Mater 47(1999)1141
Ni-0.45Al - pure Ni diffusion couple
Extension to multicomponent systems
0
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
Mass F
racti
on
-1200 -800 -400 0 400 800 1200
Distance (m)
DICTRA (2006-05-09:20.57.50) :
TIME = 3600000
Al Co Cr Fe Mo Nb Ti
2006-05-09 20:57:50.12 output by user anders from NEMO
IN100 IN738
Symbols are experimental
data taken from Campbell et
al, Materials Sci & Eng A
407(2005), pp. 135-146.
Volume and bulk modulus – Pressure dependence
lattice parameter
molar volume
density thermal
expansion coefficient
relative length change
lattice mismatch
The effect of Si content on the densities
of Al-Si alloys
liquid solid Casting shrinkage
0 25 50 75 100
Mass percent Si
250
500
750
1000
1250
1500
Tem
pera
ture
[C
els
ius]
SI in DIAMOND_A4
SI in FCC_A1
SI in LIQUID
SI in DIAMOND_A4
SI in FCC_A1
SI in LIQUID
Liquid
Liquid + SiLiquid + Fcc
Fcc + Si
1 atm
1 GPa
To facilitate linkage among Thermodynamics, Process modelling, and Microstructure evolution Elasticity Elastic constants Young’s modulus Bulk modulus Shear modulus Possion’s ratio Viscosity (and diffusivity) in liquid Thermal conductivity and diffusivity Electric conductivity and resistivity Thermal radiative properties: emissivity, absorptivity, reflectivity, transmissivity
Further CALPHAD Extensions
Properties of interfaces
f(r)
r
Interfacial energy Grain boundary energy Surface tension
Classic or non-classic
thermodynamics
Atomistic modeling -
molecular dynamics
and Monte Carlo
method
First principles
Estimation of interfacial energy
1999Noble, Mater Sci Engr, A266, 80-85
Distribution of Al-Li /d’ interfacial
energy value found in literature
Our first approximation
Ds sc sol
A l
N ZE
N Z
2D sol P ME X X
For a binary matrix and precipitate of the same structure that
can be described by a regular solution model*
Misciblity gap of non-regular solution phase
Matrix and precipitate of different structure
Multicomponent system
D solE
* Based on Becker R. Ann Phys 1938;424:128
Estimation of interfacial energy
System Phases Estimation (J/m2) Literature (J/m2)
Al-Li /d’ 0.011 0.004 to 0.115
Cu-Ti Cu/Cu4Ti 0.035 0.067, 0.031
Ni-Al-Cr g/g’ 0.022 0.023
Co-W-C Co/WC 0.68 0.44 to 1.09
Further investigations:
Entropy effect
Diffusiveness of interface
Incoherency
Size effect
Grain boundary energy
Thermodynamics: Gibbs energy
Diffusion: Mobility
Phase Field Method
Langer-Schwartz
First Principles Calculation
CALPHAD f(r
r
Interfacial energy & Volume & Elastic constants
t
H or S
Towards prediction of microstructure evolution and material properties
CALPHAD-type genomic databases with thermodynamic, thermophysical as well as kinetic properties have been and will be the only feasible source to provide input data for simulation of materials processing and microstructure evolution in multicomponent systems.
CALPHAD – Bridging Atoms and Microstructure
Computational tools / Products
Software
o Thermodynamics - Thermo-Calc
o Diffusion kinetics - DICTRA
o Precipitation kinetics - TC-PRISMA
o Software Development Kits – SDKs
Databases
o Thermodynamic
Alloys, e.g. Al-, Cu-, Fe-, Mg-, Ni-, Si-, Ti-based
HEA’s, Solders, Cemented Carbides,…
Oxides, slags and ionic solutions
Molten salts
Compounds
Aqueous solutions
o Kinetic
Alloys, e.g. Al-, Cu-, Fe-, Mg-, Ni-, Si-, Ti-based alloys
All simulations depend on assessed kinetic and thermodynamic data, which are stored in databases
A numerical finite difference scheme is used for solving a system of coupled parabolic partial differential equations
DATABASES Kinetic Thermodynamics
Mobilities Gibbs Energy
Diffusivities
Solve Diffusion where
Boundary conditions, etc. (External or Internal)
Diffusion Module (DICTRA)
1D finite difference code for simulation of DIffusion Controlled TRAnsformations in multicomponent alloys.
Diffusion Module (DICTRA)
v g
Moving boundary problems with sharp interface
Ck
z
γ
kJ α
kJα
kc
γ
kc
Sharp interface with
assumption of local
equilibrium
Two proven models for dealing with situations that involves more than a single phase. Program may switch automatically between them.
n-1 Flux Balance Equations:
n-1 unknowns:
n-2 chemical potentials.
Velocity of phase boundary,
F-B Equations solved as:
Case study: Micro-segregation during solidification Te
mpera
ture
% Carbon
0 0.2 0.4 0.6 0.8 11,350
1,400
1,450
1,500
1,550
Liquid
d
A B C D
g
- VESPISM (Virtual Experiments to Solve Problems In Steel Metallurgy).
- Development of phase-field code (MICRESS) linked to Thermo-Calc.
- Solidification experiments were performed for alloys A – D below as one assignment in this project.
Casting / solidification
% Carbon
Tem
per
atu
re
g
Liquid
d
Steel C
Steel C:
Fe - 0.8% Mn – 0.7%Si – 0.03%P – 0.4% C
0.30000.150010.001.500
W%Si
W%P
W%S
W%Mn
µm
0 672.0
P
Mn
Si
Observed micro-segregation in Steel C
Line-scans across the dendrite arms (performed by Corus-UK)
Peak drifting!
Question: Why does the P peak drift away from the Mn and Si peaks?
Casting / solidification
Analysis using DICTRA
l/2
Secondary dendrite arm spacing assumed to be 200 µm.
Liquid
Liquid Bcc
υ
Liquid Bcc
υ Fcc
υ
Liquid Fcc υ
Bcc
Fcc
λ/2 =100 μm
Casting / solidification
Cooling function
Time (seconds)
Tem
per
atu
re
- More advanced cooling functions may of course also be imposed. - Also possible to instead define a condition on the rate of latent heat removal from the system.
Cooling rate assumed to be 0.2 ºC/s
Casting / solidification
Solidification range
Tem
per
atu
re
Fraction Solid
Lever rule
DICTRA
Scheil
L + g
L + d Peritectic reaction
Casting / solidification
Fraction of solid phases
Frac
tio
n S
olid
Time (Seconds)
g
d
Peritectic reaction
Casting / solidification
Carbon profiles during solidification
90 s 135 s
300 s
3000 s
Casting / solidification
90 s
135 s
300 s
3000 s
90 s
135 s
300 s
3000 s
Silicon and Manganese
Casting / solidification
Si Mn
Phosphorus
90 s 135 s
300 s
3000 s
Casting / solidification
Segregation profiles after 610 s (when the last melt disappears)
Mn Si P C
Casting / solidification
Segregation profiles after 1000 and 3000 s
after 1000 s after 3000 s
Mn Si P C
Mn Si P C
Casting / solidification
610 s
1000 s
3000 s
The solution
Mn and Si increase the phosphorus activity.
Phosphorus diffusion much faster compared to Mn and Si diffusion.
At the late stage further phosphorus redistribution is controlled by slow Mn and Si diffusion.
Distance (microns)
Ph
osp
ho
rus
acti
vity
Casting / solidification
Diffusion Module (DICTRA)
v g
Moving boundary problems with sharp interface
Multiphase problems with/without finite interface
Ck
z
γ
kJ α
kJα
kc
γ
kc
Sharp interface with
assumption of local
equilibrium
Flux between slices “n-1” and “n”
z
xMxMV
J keff
nkkeff
nkkm
kD
D
1
1
“Effective” from combining rules
kk xM
pkN
1nkN n
kN 1nkN1
kN
H. Larsson: CALPHAD 47 (2014) 1-8
Two proven models for dealing with situations that involves more than a single phase. Program may switch automatically between them.
Microsegregation during solidification
Homogenisation treatment
Precipitate growth and dissolution
Precipitate coarsening
Interdiffusion in coating/substrate systems
TLP bonding of alloys and much more…
Micro-segregation during solidification in alloy AA5182
Dissolution of Mg2Si precipitate in alloy A6401
Diffusion Module (DICTRA)
0
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
Mass F
racti
on
-1200 -800 -400 0 400 800 1200
Distance (m)
DICTRA (2006-05-09:20.57.50) :
TIME = 3600000
Al Co Cr Fe Mo Nb Ti
2006-05-09 20:57:50.12 output by user anders from NEMO
IN100 IN738
40
45
50
55
Mo
le-P
erc
en
t N
i
-500 0 500 Position (microns)
Ni
NiAl-coating IN939
Interdiffusion between NiAl
coating and Ni-base superalloy
Multicomponent diffusion
couple
Example of applications:
Materials selections / Lifetime prediction
Yu et al., Mater Sci. Eng. A394 (2005) 43.
Complex problem involving solving multicomponent diffusion problem in multiphase region. Need for multicomponent kinetic data in -NiAl, g and g’
Selected problem: Coating degradation due to interdiffusion
E. Perez, T. Patterson and Y. Sohn, J. Phase Equilibria and Diffusion 27(2006), pp. 659-64.
NiAl-coating / Ni-base superalloy system
NiAl-coating / GTD111
0.97
-
Mo
0.89
-
Ta
0.48
-
C
Bal
Bal
Ni
GTD111
NiAl-Coating
0.97 6.24 16.6 9.5 6.9
- - - - 50.5
W Ti Cr Co Al Temp. 1050°C Time 96h
0
10
20
30
40
50
60
Mo
le-P
erc
en
t A
l
-500 0 500
Position (microns)
30
35
40
45
50
55
60
65
70
Mo
le-P
erc
en
t N
i
-500 0 500
Position (microns)
Al
Symbols are experimental data from E. Perez, T. Patterson and Y. Sohn, J. Phase Equilibria and Diffusion 27(2006), pp. 659-64.
Ni
NiAl GTD111
i
kk
ieff
kk xMfxM
Rule of mixtures
0
0.2
0.4
0.6
0.8
1.0
1.2 M
ole
-Fra
cti
on
of
Ph
as
e
-500 0 500
Position (microns)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Mo
le-F
rac
tio
n o
f P
ha
se
-500 0 500
Position (microns)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Mo
le-F
rac
tio
n o
f P
ha
se
-500 0 500
Position (microns)
0
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
Mo
le-F
rac
tio
n o
f P
ha
se
-500 0 500
Position (microns)
B2 g
g´
Micrograph from E. Perez et al. J. Phase Equilibria and Diffusion 27(2006), pp. 659-64.
NiAl-coating / GTD111
Symbols are experimental data from E. Perez, T. Patterson and Y. Sohn, J. Phase Equilibria and Diffusion 27(2006), pp. 659-64.
Cr
0
5
10
15
20
25
30
35
40
Mo
le-P
erc
en
t C
r
-500 0 500
Position (microns)
Co
0
5
10
15
Mo
le-P
erc
en
t C
o
-500 0 500
Position (microns)
NiAl-coating / GTD111
Co
Symbols are experimental data from E. Perez, T. Patterson and Y. Sohn, J. Phase Equilibria and Diffusion 27(2006), pp. 659-64.
Cr
0
5
10
15
20
25
30
35
40
Mo
le-P
erc
en
t C
r
-500 0 500
Position (microns)
0
5
10
15
Mo
le-P
erc
en
t C
o
-500 0 500
Position (microns)
g
g´
g
g´
NiAl-coating / GTD111
0
1
2
3
4
5
6
7
8
9
10
Mo
le-P
erc
en
t T
i
-500 0 500
Position (microns)
0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Mo
le-P
erc
en
t W
-500 0 500
Position (microns)
Ti
Symbols are experimental data from E. Perez, T. Patterson and Y. Sohn, J. Phase Equilibria and Diffusion 27(2006), pp. 659-64.
W
NiAl-coating / GTD111
Computational tools / Products
Software
o Thermodynamics - Thermo-Calc
o Diffusion kinetics - DICTRA
o Precipitation kinetics - TC-PRISMA
o Software Development Kits – SDKs
Databases
o Thermodynamic
Alloys, e.g. Al-, Cu-, Fe-, Mg-, Ni-, Si-, Ti-based
HEA’s, Solders, Cemented Carbides,…
Oxides, slags and ionic solutions
Molten salts
Compounds
Aqueous solutions
o Kinetic
Alloys, e.g. Al-, Cu-, Fe-, Mg-, Ni-, Si-, Ti-based alloys
A general computational tool for simulating kinetics of diffusion controlled multi-particle precipitation processes in multi-component and multi-phase alloy systems.
Precipitation Module (TC-PRISMA)
TC-PRISMA is based on Langer-Schwartz theory, and it adopts Kampmann-Wagner numerical (KWN) method to compute the concurrent nucleation, growth, and coarsening of dispersed phase(s).
3D, 2006Jou
LS (Langer-Schwartz) and KWN (Kampmann and Wagner Numerical) Approach
,( ) ( , ) ( , )
f r tr f r t j r t
t r
3
00
4,
3C C C C f r t r dr
0
( , )N f r t dr
0
1( , )r f r t rdr
N
3
0
4( , )
3f r t r dr
Continuity equation
Mass balance
Time Integration
0
( , )N f r t dr
10 50 100 Radius, nm
3D, Particle Size Distribution
f, 1/m4
Models: Nucleation Rate
D
kT
GNZJ s
** exp
tJtJ S
exp
*22
1
Z
*2*
4
4 r
a
1
1/
2//
n
i ii
ii
DX
XX
2
23*
3
16
m
m
G
VG
DD
Interfacial energy, Volume
Classic Nucleation Theory (CNT)
Grain size, dislocation density, etc.
kTrN
VZ
A
m
2*2
D
m
m
G
Vr
2*
2004Svoboda
Models: Growth Rate
rMccc iiiiiii /
r
Vmii
2//
Q. C
hen
, J. J
epp
sso
n, J
. Ågr
en, A
cta
Mat
er. 5
6(2
00
8)1
89
0-1
89
6
Advanced – Analytical Flux-balance Approximation
2 mm
VKG
r r
D
Simplified – Pseudo-steady state Approximation
Cross diffusion
high supersaturation
1
2/ /
/
( ) ( )
( )
i i i
i i i
X r X rK
X r M
Scope and data output
Simulate concurrent nucleation, growth and coarsening of second phases in multicomponent systems.
Output
• Particle Size Distribution
• Number Density
• Average Particle Radius
• Volume Fraction
• Matrix composition
• Precipitate composition
• Nucleation rate
• Critical radius
• TTP
Input
• Alloy composition
• Temperature - Time
• Simulation time
• Thermodynamic data
• Kinetic data
• Property data (Interfacial energy, volume, etc.)
• Nucleation sites and related microstructure information
TC-PRISMA
2011
Version 1.0
• Link to Thermo-Calc
and DICTRA
• Multi-component
Nucleation and Growth
• Different Nucleation
types
• Avdanced Model for
Cross Diffusion and
High Supersaturation
• Highly Intuitive GUI
2013
Version 2.0
• Non-Isothermal
Conditions
• Multi-Modal PSD
Analysis
• Interfacial Energy
Model
2016
Thermo-Calc 2016a
• Multiple Nucleation
Types
• Considering wetting
angle
• Integration into
Thermo-Calc
• ....
Precipitation Module (TC-PRISMA)
AA6005: Al - 0.55wt% Mg - 0.82wt% Si - 0.016wt% Cu
AA6061: Al - 0.93wt% Mg - 0.61wt% Si - 0.28wt% Cu
= 0.115 J/m2
TCAL3 and MOBAL3 Databases
530˚C
30 min 185, 175˚C
80, 8 hr
AA6xxx
Myhr et al, Acta Mater. 49(2001)65-75. Bardel et al, Acta Mater. 62(2014)129-140
(Al)
Al3Sc
SSSS → Clusters → GP Zones → β’’ → β’, U1, U2, B’ → β
AA6xxx
AA6005: Al - 0.55wt% Mg - 0.82wt% Si - 0.016wt% Cu
Precipitation of β’’ from (Al) matrix
AA6xxx
AA6061: Al - 0.93wt% Mg - 0.61wt% Si - 0.28wt% Cu
Precipitation of β’’ from (Al) matrix
Example 4 – Heat Treatment
gg’ Microstructure in U720 Li
Continuous cooling at 0.0167 K/s
R. Radis et al., Acta Materialia, 57(2009)5739-5747
R&D
Ni-8Al-8Cr and Ni-10Al-10Cr
R&D – Influence from composition
Exp
Continuous cooling from 1150 to 380 °C with a cooling rate of 14 °C/min.
R&D – Influence from composition
Exp
= 0.023 J/m2
Ni-8Al-8Cr have larger misfit between g and g compared to Ni-10Al-10Cr.
This will give an elastic energy contribution which has not been considered in the simulation.
R&D – Influence from composition
Vertical Section Ni-xAl-xCr Thermodynamic driving force
R&D – Influence from composition
Nucleation rate Thermodynamic driving force
R&D – Influence from composition
Computational tools / Products
Software
o Thermodynamics - Thermo-Calc
o Diffusion kinetics - DICTRA
o Precipitation kinetics - TC-PRISMA
o Software Development Kits – SDKs
Databases
o Thermodynamic
Alloys, e.g. Al-, Cu-, Fe-, Mg-, Ni-, Si-, Ti-based
HEA’s, Solders, Cemented Carbides,…
Oxides, slags and ionic solutions
Molten salts
Compounds
Aqueous solutions
o Kinetic
Alloys, e.g. Al-, Cu-, Fe-, Mg-, Ni-, Si-, Ti-based alloys
Software Development Kits
Thermo-Calc
Application
Inte
rfac
e
A prescribed set of subroutines, functions or classes by which a programmer writing an application program can make requests to Thermo-Calc.
The trend is towards more and more advanced applications and in particular integration of thermodynamic calculation result for modelling of microstructure evolution and property prediction, aiming at designing products, the materials comprising them and their associated processing.
Example 5 – R&D
Phase-field modelling
• Output:
– Detailed morphology
– Concentration fields
– Stress fields
– Plastic strain fields (dislocation density fields)
– ...
• Need or can use input from
– Multicomponent thermodynamics
– Multicomponent diffusion analysis
– Interfacial energy and mobility
– Elastic coefficients and stresses
– Stress-free transformation strain tensor (eigen strains)
– Plastic relaxation
– Fluid flow (Navier Stokes)
– ....
2D phase-field simulation of sigma-phase formation in duplex Stainless steel (SAF 2507)
Fe-25Cr-7Ni-4Mo with continuous cooling from 1273K to 950K
Malik et al. KTH (2015) Full CALPHAD Thermodynamics DICTRA Mobilities
BCC
BCC
FCC
FCC
FCC
FCC
BCC
Sigma
Spinodal decomposition – Fe-45%Cr
T=748K, time=1 Week
Calculation cell is 20x20x20 nm
Composition dependent gradient energy
Barkar et al. KTH (2016 )
Full CALPHAD Thermodynamic & Mobility coupling
Generating insights on materials and processing operations
Thank You!