phase-field modeling of technical alloy systems problems...

Phase-Field Modeling of Technical Alloy Systems

Problems and Solutions

B. Böttger

ACCESS e.V., RWTH Aachen University, Germany

Thermo-Calc User Meeting, Sept 8-9 2011, Aachen

Outline

1. Introduction

2. Pragmatic Multi-Phase-Field Model

3. Coupling to Thermodynamic Data: Quasi-Equilibrium

4. Specific Problems and Solutions

a) Stoichiometric Phases

b) Composition Sets

c) Charged Species

5. Conclusion

Fe C Si Mn P S Al Cr Cu Mo N Ti Ni

Bal. 0,225 0,078 1,66 0,012 0,0015 1,526 0,021 0,019 0,0053 0,0024 0,0038 0,021

Goal: Simulation of microstructure formation during phase transformations in technical alloys

Introduction: Phase-Field Simulation of Complex Technical Microstructures

complex alloys

complex morphologies

complex thermodynamics

complex processes

„pragmatic‟ phase-field approach

carbon steel

equiaxed microstructure

Al piston alloy

die casting

Challenges:

What is a „pragmatic‟ phase-field approach?

Introduction: Pragmatic Phase-Field Approach

multiphase-field model which allows simulation on µm scale

online-coupling to off-the-shelf thermodynamic and diffusion databases

advanced thermal coupling to external process conditions

robust multi-purpose code (no dedicated solutions)

pragmatic simulation strategy (calibration, simplifications)

MICRESS®: MICRostructure Evolution Simulation Software

Outline

1. Introduction





b) Composition Sets

c) Charged Species

5. Conclusion

■ Diffuse interface, described by the phase-field parameter f:

■ The order parameter f = f (x,t) corresponds to a density function for the phase state.

■ h is the interface thickness (numerical parameter)

Phase-Field Model

h

The Multiphase-Field Model

Vector order parameter N1f

what is pragmatic?

bulk thermodynamic data are used only for the chemical free energy fc

f is a function of c, not of c!

coupling to arbitrary thermodynamic databases possible!

fffffh

cf),,,(K

)n,n(

,

ff

f

f : interfacial growth operator

cfff

ff

cf

: pair interaction energies

: chemical free energy

h = interface thickness

= interfacial mobility (anisotropic)

= interfacial energy (anisotropic)

G = driving force

ffh

ff

h

fffff

GJ

n**

n

2

222

2

•Steinbach et al; Physica D 1996

•Tiaden et al. Physica D 1998

•Steinbach, Pezzolla; Physica D 1999

•Eiken, Böttger, Steinbach; Phys. Rev. E 2006

Multiphase-field equation:

dual interface terms

“double_obstacle”

higher interface terms

“multi_obstacle”

chemical

driving force

Multiphase-Field Model: Phase-Field Equation

Outline

1. Introduction





b) Composition Sets

c) Charged Species

5. Conclusion

Phase-Field and Thermodynamics: Quasi-Equilibrium

G

, and are calculated iteratively including the mass balance:kckc

kkk ccc ff

kk

k

k

kkk

dc

df

dc

df~,cc~ffG

minimization of the chemical free energy at constant phase fractions f gives:

f ffc

kckc c

f

ff

ck

G

phase-field simulation: f are additional conditions!

Phase-Field and Thermodynamics: Multiphase Quasi-Equilibrium

Multiphase-field method: additional phases are included into the iteration process:

consistent quasi-equilibria for all phase pairs

iteration for N phases:

,...dc

df

dc

df

dc

df~,cc~ffGkkk

kkkk

k

k

i

kii cc f

G

G

ck ck ck

Phase Phase Phase

ck

f

Use of Thermodynamic Data in MICRESS®

multicomponent diffusion solver

M I C R E S S ®

nucleation model

temperature solver

multiphase-field solver

time loop

Thermo-Calc

CALPHAD database f )GwK()t,x(

?TT critund

f cD)t,x(c

Outline

1. Introduction





b) Composition Sets

c) Charged Species

5. Conclusion

G α β


stoichiometric phases are automatically detected by MICRESS®

G α β

phases with small solubility range should also be treated as “stoichiometric”

a) composition cannot be used as a condition!

use arbitrary activity for calculation of H or D

problems in several places:

c) phase-field equation: possible violation of physical composition range 0< cα <1!

restriction of phase-field increment

restriction of time step

)c()c()c(,ccc kkkkkk 111 ffff

b) quasi-equilibrium: use condition for other phase

quasi-equilibrium calculation starting from ckα

2-phases.:

only one phase can be stoichiometric for each element

ff /)cc(c kkk

Example1: Alloy KS1295 (Al-Si-Fe-Ni-Cu-Mg-Zn), Comparison to Quantitative Metallography

*

* Mg2Si + Al5Cu2Mg8Si

** Al3Ni

**

databases: TTAL5, MOBAL1

collaboration with

Kolbenschmidt/Germany and University of Manchester

Outline

1. Introduction





b) Composition Sets

c) Charged Species

5. Conclusion

LIQUID FCC_A1

#1: FCC

#3: Nb(C,N)#2: Ti(N,C)

G

composition

Composition Sets

calculation of quasi-equilibrium (parallel tangents in Gibbs energy diagram) gives several solutions!

for numerical reasons, composition can switch between different phases!

in phase-field simulation, switching is not allowed because phase identity is linked to objects or grid points

in MICRESS®, user-defined concentration limits can be used, as Calphad does not give support

in many databases (e.g. TTNI7), identical thermodynamic descriptions are used for several phases!

the composition sets are only distinguished by the start values for numerical iteration

δ

Laves

TiN

NbC

(Ni,Cr)3B2

fcc

h

Nb

Example 2: Equiaxed Solidification Microstructure of IN718

h

Laves

TiN

NbC

(Ni,Cr)3B2

fcc

δ

Ti

Example 3: Columnar Ni-Base Microstructure before and after Diffusion Heat Treatment

after:before :

beforeafter

beforeafter

TiTi

Outline

1. Introduction





b) Composition Sets

c) Charged Species

5. Conclusion

Charged Species

b) use composition of uncharged species, example: CaO, SiO2, Al2O3

may not be possible for all phases…

a) treatment as stoichiometric phase (even if not true!)

composition is not used as condition

but: only possible if no interaction to other stoichiometric phases are needed!

additional electroneutrality condition: Example Slag: Ca2+, Si4+, Al3+, O2-

element composition as condition would not work!

c) if elements with more than one oxidation state are present in phase

extra degree of freedom compensates electroneutrality condition!

How can it work?

Examples: - O2 diffusion through Co1-δO membrane

- ionic liquid in system Ag-Cu-O

v

Example 4: O2 diffusion through Co1-δO membrane

<

membrane is moving in oxygen pressure gradient

morphological instability?

Co(1-δ)O Membrane½ O2+2 Co2+

2 Co3++ O2- O2-+2 Co3+ ½ O2+2 Co2+

1

2Op 1

2Op

O2(g)O2(g) VA

Co3+

Example 4: O2 diffusion through Co1-δO membrane

M. Martin, Materials Science Reports 7 (1991) 1-86.

Can be treated in MICRESS as a ternary system ABC:

construction of a linearized phase diagram using experimental concentration of vacancies:

mA/mB = cV/cO2 = const

gas phase is considered as a dissolution of A(O2) in C(vacuum)

membrane: A(O2- = 0.5at%), B(Co) and C(VA)

Example 4: O2 diffusion through Co1-δO membrane: MICRESS results

gas CoO gas

A=0.01 A=0.5 A=0.1

B=0 B=0.4995 B=0

x(B)

Example 4: O2 diffusion through Co1-δO membrane: Experimental results

Membrane is moving towards higher chemical potential of O2:



Formation of morphological instability:



Finally break-through towards the oxygen-rich side:


Example 4: Ag-Cu-O system, Ag8Cu Brazing with Contact to Air

Al2O3 brazed

with Ag8Cu at: 970 °C 1150°C

Al2O3

Ag

CuO

(Cu,Al)O

Al2O3

Ag

CuO

What happens during solidification?

Which is the role of Cu for wetting?

Phase Diagram of Ag-Cu-O

Reference: Assal, J.; Hallstedt, B.; Gauckler, L.J., J. Phase Equilib., 19, 351-360, 1998

Species: Cu2+, Cu+, Ag+, O2-, VA

MICRESS® Simulation: First Results and Comparison to DSC Experiment

ionic liquid #1 (cAg = 0.98)

ionic liquid #2 (cAg = 0.36)

CuO

O2 gas (0.21 atm)

fcc (Ag)

“virtual DSC“

L2L1+CuO

L1CuO+Ag

Outline

1. Introduction





b) Composition Sets

c) Charged Species

5. Conclusion

Conclusion

■ MICRESS® is a software for simulation of technical alloys as it uses a pragmatic phase-field model and

robust coupling to arbitrary Calphad databases

■ Specific solutions for topics like stoichiometric phases or composition sets are needed

■ Simulation of charged species is possible under certain conditions, as shown for the system Ag-Cu-O

Thank you for

your attention!

phase-field modeling of technical alloy systems problems...

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