Development of A Practical Development of A Practical Phase Field ToolPhase Field Tool

Kaisheng Wu, Shuanglin Chen, Fan Zhang and Y.A.Chang

CompuTherm LLC, Madison, WI

Ximiao Pan and Yunzhi Wang

The Ohio State University, Columbus, OH

NIST Diffusion Workshop, May 12, 2008

PanROMEPanROME

11

Interdiffusion MicrostructuresInterdiffusion MicrostructuresNi-Al-Cr

F-220.5 μm

Disk alloy (courtesy of M.F. Henry)

2μm

IN718 (S. Azadian et al.)

22

Models/SoftwareModels/Software

1D Diffusion

DICTRA

Mean-Field Precipitation

PrecipiCalc

PanPrecipitation (PanSTAR)

TC-PRISMA

Phase Field – Most Feasible for Morphology Considerations

MICRESS

PanROME

33

Multi-component, multi-phase, multi-variant and polycrystallineVery complex microstructural features:

high volume fraction of precipitatesnon-spherical shape and strong spatial correlationelastic interactions among precipitates

Interdiffusion induces both microstructure and phase instabilities.Effect of concentration gradient on nucleation, growth and coarsening.Roles of defects and coherency/thermal stress on interdiffusion and phase transformation.

Multi-component, multi-phase, multi-variant and polycrystallineVery complex microstructural features:

high volume fraction of precipitatesnon-spherical shape and strong spatial correlationelastic interactions among precipitates

Interdiffusion induces both microstructure and phase instabilities.Effect of concentration gradient on nucleation, growth and coarsening.Roles of defects and coherency/thermal stress on interdiffusion and phase transformation.Robustness and computational efficiency of models.

Modeling ChallengesModeling Challenges

Robustness and computational efficiency of models.

44

Phase Field ApproachPhase Field Approach

55

Phase Field ModelsPhase Field Models

Wheeler-Boettinger-McFadden(WBM)Phys. Review A, 45(10), 7424(1992)

MICRESSSteinbach et al., Physica D, 94, 135(1996)

Landau-Type PolynomialL.Q.Chen and Y. Wang, JOM, 48, 13-18(1996)

Kim-Kim-Suzuki(KKS)Phys. Review E, 60(6), 7186(1999)

66

KimKim--KimKim--Suzuki(KKS) ModelSuzuki(KKS) Model

Local Free Energy Density

77

KimKim--KimKim--Suzuki(KKS) ModelSuzuki(KKS) Model

ConcentrationFr

ee E

nerg

y D

ensi

ty

Mass Conservation

Equal Diffusion Potential

88

Advantage of KKS ModelAdvantage of KKS Model

Concentration

Free

Ene

rgy

Den

sity

Adjustable Interfacial Energy

Con

cent

ratio

n

x

Practical Length Scale

99

Software ArchitectureSoftware Architecture

Kinetic Kinetic DatabaseDatabase

PanEnginePanEngine

Thermodynamic Thermodynamic DatabaseDatabase

PanRomePanRome

Nucleation Driving ForceNucleation Driving Force

Diffusion PotentialsDiffusion Potentials

MobilitiesMobilitiesProcessing Processing ConditionsConditions

Nucleation Nucleation Model*Model*

KKS KKS ModelModel

*C.Shen, Ph.D. Thesis, The Ohio State University, 2004;

Y.H. Wen et al., Acta Mater., 51, 1123(2003)

1010

Ni DatabasesNi Databases

Ni Ni

Al Al

HfHf

CrCr

C C B B

FeFe

CoCo

Ir Ir MoMoN N Nb Nb

Pt Pt Re Re

Ru Ru

Si Si

Ta Ta

Ti Ti

Zr Zr W W W

Ni

AlC

Co

Cr

Fe

HfMoNb

Re

Ta

Ti

Pt

Thermodynamic Kinetic*

* Partly from C. E. Campbell, W. J. Boettinger, U. R. Kattner, Acta Mater. 50, 2002, 775-792.

1111

CoarseningCoarsening

Ni-Al-Cr-Pt

γ+γ′

1200οC 500hrs

1212

NucleationNucleation

1313

β+γβ+γ//γγ Diffusion CoupleDiffusion CoupleNi-Al-Cr

1414

β+γβ+γ//γγ Diffusion CoupleDiffusion Couple

Landau-Type Polynomial

Kim-Kim-Suzuki Model200μm

Exp. Observation* 100 hrs at 1200oC

*J.A.Nesbitt and R.W.Heckel, Metall. Trans. A, 18A(11)2087(1987)

1515

SoftwareSoftware

Coded in C++ & provided as a Windows dllScript file for user inputsImageMagick for microstructure imagesPandat GUI under development

1616

Computational EfficiencyComputational Efficiency

A special algorithm/data structure is designed to improve the efficiencyBenchmark:

Computer : Intel Core2 Duo CPU 3.0GHz, 3G MemorySystem: Ni-Al-Cr, β+γ/γ diffusion couple,

1024×256 grid points, 300hrs annealing time at 1200oC

Simulation Time : 24 hrs

1717

SummarySummary

A phase field program for interdiffusion microstructuresIntroduction of Kim-Kim-Suzuki model to

relax the restriction of the length scaleExamples demonstrating feasibilitiesComputational efficiency

1818

Future WorkFuture Work

Non-isothermal conditions Multiphase systemsMore than 4 componentsDifferent alloy systems

More Validations

1919

Future WorkFuture Work

Interfacial energy anisotropyElastic strain energy effect

More Functionalities

2 μm1 μm

2020

Future WorkFuture Work

CVD ProcessingOxidation ( Integrated with COSP)

Wei

ght

Chan

ge, m

g/cm

2

Number of 1-hr Cycles

-5

-10

-15

-20

0

5

10

15

20

0 200 400 600 800 1000 1200 1400 1600 1800

Number of 1-hr Cycles

Wei

ght C

hang

e, m

g/cm

2

Experimentally Determined Weight ChangeWeight Change Simulated by ModelExperimentally Determined Al LossAl Loss Calculated by Model

0 200 400 600 800 1000 1200 1400 1600 1800-20

-10

0

10

20

More Boundary Conditions

Oxidation behavior of a γ+β

alloy