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PhasePhase--field modeling of microstructure evolution field modeling of microstructure evolution in multiin multi--component alloyscomponent alloys
NeleNele MoelansMoelansDepartment of Metallurgy and Materials Engineering (MTM)Department of Metallurgy and Materials Engineering (MTM)
K.U.LeuvenK.U.Leuven, , BelgiumBelgium
Liesbeth Liesbeth VanherpeVanherpe, Jeroen , Jeroen HeulensHeulens, Bert , Bert RodiersRodiers
COST MP0602 COST MP0602 –– IndustrialIndustrialSeminarSeminar on on ThermodynamicsThermodynamics, , Bratislava, April 6, 2010Bratislava, April 6, 2010
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2COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
Outline
•• Introduction: Introduction: modelingmodeling of microstructure of microstructure evolutionevolution
•• PrinciplesPrinciples of phase of phase fieldfield modelingmodeling
•• Application Application examplesexamples•• AnisotropicAnisotropic grain grain growthgrowth•• PrecipitatesPrecipitates on grain on grain boundariesboundaries•• LeadLead--free solder jointsfree solder joints•• SolidificationSolidification
•• SummarySummary
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3COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
Role of microstructures in materialsscience
Low-C steel: wt% C < 0.022Ferrite + smallcarbides
250 Pm
50 Pm
Steel: wt% C = 0.4, slow coolingrate
Ferrite + cementite
Chemical Chemical compositioncomposition+ +
TemperatureTemperature, , pressurepressure, , coolingcooling raterate, , deformationdeformation, , ……
MicrostructureMicrostructure
ShapeShape, , sizesize and and orientationorientation of the of the grainsgrains, , mutualmutual distribution of the distribution of the phasesphases
MaterialMaterial propertiesproperties
Strength, deformability, hardness, toughness, fatigue…
50 Pm
Steel: wt% C = 0.4, fast coolingrate
Ferrite needles+ perlite
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4COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
Microstructure evolution in multi-component alloys
•• ConnectedConnected grain structuresgrain structures
•• ComplexComplex morphologiesmorphologies
•• Concurrent Concurrent processesprocesses•• Solidification Solidification -- grain grain growthgrowth --
Ostwald Ostwald ripeningripening –– diffusion diffusion --phase phase growthgrowth
•• MaterialsMaterials’’ propertiesproperties are are largelylargelyrelatedrelated to microstructureto microstructure
•• MaterialMaterial developmentdevelopment•• ReliabilityReliability
Low C-steel, ferritic grain structure
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5COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
Microstructure evolution in multi-component alloys
•• High High complexitycomplexity•• AnisotropyAnisotropy, , segregationsegregation, , solutesolute drag, seconddrag, second--phase phase precipitatesprecipitates, ,
pipe diffusion, pipe diffusion, mutualmutual distribution of phases, distribution of phases, ……
•• ManyMany materialmaterial propertiesproperties: Crystal structure, Gibbs : Crystal structure, Gibbs energyenergy, , diffusion coefficient of diffusion coefficient of differentdifferent phases? Structure, phases? Structure, energyenergy, , mobilitymobility of grain of grain boundariesboundaries? ?
•• Evolution Evolution connectedconnected grain structure ?grain structure ?–– MesoscaleMesoscale simulationssimulations
•• ImportanceImportance•• MaterialMaterial developmentdevelopment: : heatheat treatmenttreatment, , alloyingalloying•• ReliabilityReliability
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6COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
Phase-field modelling
•• ComplexComplex shapesshapes•• MultiMulti--grain, multigrain, multi--phase structuresphase structures•• ThermodynamicThermodynamic drivingdriving forcesforces
•• MultiMulti--componentcomponent•• Transport Transport equationsequations
•• Mass and Mass and heatheat diffusion/convectiondiffusion/convection
•• ImplementationImplementation for for realisticrealistic lengthlength scalesscales•• ParameterParameter choicechoice
...chem int elast magnF F F F F= + + + +
StrengthStrength
DifficultiesDifficulties
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Principles of phase field modeling
•• Diffuse interface concept Diffuse interface concept •• Phase Phase fieldfield variables variables •• ThermodynamicThermodynamic free free energyenergy functionalfunctional•• Evolution Evolution equationsequations•• ParameterParameter assessmentassessment•• NumericalNumerical implementationimplementation
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8COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
Diffuse-interface description
•• Sharp interfaceSharp interface
•• DiscontinuousDiscontinuous variationvariation in in propertiesproperties•• RequiresRequires trackingtracking of the interfacesof the interfaces•• SimplifiedSimplified graingrain morphologiesmorphologies
•• Diffuse interfaceDiffuse interface
•• ContinuousContinuous variationvariation in in propertiesproperties•• Interfaces Interfaces implicitlyimplicitly givengiven byby locallocal
variationsvariations in in phasephase--fieldfield variablesvariables•• Complex Complex graingrain morphologiesmorphologies
••Diffuse interface Diffuse interface approachapproach ((van der Waals, van der Waals, CahnCahn--HilliardHilliard (1958), (1958), GinzburgGinzburg--LandauLandau (1950))(1950))
••MicrostructureMicrostructure evolutionevolution startedstarted ±± 20 20 yearsyears agoago
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9COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
Representation of microstructures
•• PhasePhase--fieldfield variables: variables: continuouscontinuous functionsfunctions in in spacespace and timeand time
•• LocalLocal compositioncomposition
•• LocalLocal structurestructure and and orientationorientation
BinaryBinary alloyalloy AA--BB
••PhasePhase DD: : KK = 0= 0
••PhasePhase EE: : KK = 1= 1AntiphaseAntiphase boundaryboundary
( , ), ( , )B Bx r t c r tG G
( , )r tηG
( , )r tφG
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10COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
Thermodynamics and kinetics
•• Free Free energyenergy functionalfunctional
•• EvolutionEvolution of field variablesof field variables•• NonNon--conservedconserved field variables (field variables ( Interface Interface movementmovement))
•• ConservedConserved compositioncomposition fieldsfields (( MassMass diffusiondiffusion))
2 20
1 1
( , , ) ( ) ( )2 2
p C
bulk surface i k k ik iV
F F F f x T x dVκ εη η
= =
= + = + ∇ + ∇∑ ∑∫
1 1( ,..., , ,..., )( , )( ( , ))
( , )C pk
k
F x xr tL r t
t r t
η ηη ξη
∂∂ = − +∂ ∂
G
G
G
1 1( ,..., , ,..., )1 ( , )( ( , ))
( , )C pi
m i
F x xx r tM r t
V t x r t
η ηξ
∂∂ = ∇ ⋅∇ +∂ ∂
G
JG JG G
G
Homogeneous free energy
(chemical, elastic, …)
Gradient free energy
( diffuse interfaces)
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11COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
Homogeneous free energy functional
•• AntiAnti--phasephase boundaryboundary
Boundary energy:
Boundary width:
Boundary velocity:
0 max( )fκ∝ ∆
0 max( )fκ∝
∆
Lκ∝
4 2
0 0 max4( )4 2
f fη η
= ∆ −
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12COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
Homogeneous free energy
•• BinaryBinary twotwo--phasephase systemsystem
( ) ( )0 1 (( ) ( , ) ),f h hf c T f c gTβ αφ φ ω φ= + − +
f0β f0α
DD
EE
( , ) m
m
Gf c T
V
ββ =with ( , ) ,m
m
Gf c T
V
αα = (CALPHAD)
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13COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
Homogeneous free energy
•• BinaryBinary twotwo--phasephase systemsystem
( ) ( )0 ( ( ), ) 1 ( , )f h f c T h f gc Tβ αφ φ φω= + − +
f0β f0α
Double well function
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14COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
Homogeneous free energy
•• BinaryBinary twotwo--phasephase systemsystem
( ) ( )0 ( , ) 1 ( , ) ( )h hf f c T f c T gβ α ωφ φφ= + − +
f0β f0α
Interpolation function
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15COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
Effect of elastic stresses and strain
•• CouplingCoupling withwith micromicro--elasticityelasticity theorytheory
•• EffectEffect of transformation and thermal of transformation and thermal strainsstrains, , appliedapplied stress/stress/strainstrain•• MartensiticMartensitic transformation, transformation, precipitateprecipitate growthgrowth
chem int elastF F F F= + +
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16COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
Polycrystalline structures
•• Free Free energyenergy functionalfunctional
•• PolycrystallinePolycrystalline microstructuremicrostructure
•• GrainGrain i of i of matrixmatrix--phasephase
1 2( , ,..., ,..., ) (0,0,...,1,...,0)i pη η η η =
1 2, ,..., ( , ),...,i pr tη η η ηG
Graini
Grain j
1iη =
0jη = 0iη =
1jη =
20 1 2
1
( , ,... ) ( )2
p
surface p kkV
F F f dVκη η η η
=
= = + ∇∑∫
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17COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
Multi-phase and multi-component alloys
•• Phase Phase fieldfield variables:variables:•• GrainsGrains
•• CompositionComposition
•• Free Free energyenergy functionalfunctional
1, ( , ),...,A B Cx x r t x −
G
1 2
1 2
, ,..., ( , ),...,
, ,...i
p
r tα α α
β β
η η ηη η η
G
2 phase 2 phase polycrystallinepolycrystalline structurestructure( , ) ( ) ( )
( )( )
bulk k i i k
m ki
m
f x h f x
G xh
V
ρ ρρ ρ ρ
ρ
ρ ρ
ρ ρρ
η η
η
=
=
∑
∑
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18COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
Parameter assessment
•• Different kinds of input data (Different kinds of input data (calculatedcalculated and/and/oror measuredmeasured))
•• PhasePhase stabilitiesstabilities, , phasephase diagram diagram informationinformation–– CALPHAD CALPHAD ((abab--initioinitio, , experimentsexperiments))
•• InterfacialInterfacial energyenergy and and mobilitymobility–– abab--initioinitio, (MD, MC , (MD, MC abab--initioinitio), ), experimentalexperimental
•• ElasticElastic propertiesproperties, , crystalcrystal structurestructure, , latticelattice parametersparameters–– abab--initioinitio, , experimentalexperimental
•• Atomic Atomic diffusiondiffusion mobilitiesmobilities–– CALPHAD CALPHAD ((MC((MC abab--initioinitio), ), experimentalexperimental))
•• OrientationOrientation and and compositioncomposition dependencedependence•• AnisotropyAnisotropy, , segregationsegregation, , solutesolute dragdrag
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19COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
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20COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
Quantitative aspects
•• NumericalNumerical solutionsolution of of partialpartial differentialdifferential equationsequations
••DiscretizationDiscretization
••BoundingBounding box box algortihmalgortihm••SparseSparse data structuredata structure••Object Object orientedoriented C++C++
(L. (L. VanherpeVanherpe et al., K.U.Leuven)et al., K.U.Leuven)
••DiscretizationDiscretization ((FiniteFinite differencesdifferences, , finitefiniteelementselements, Fourier, Fourier--spectral spectral methodmethod
••Adaptive Adaptive meshingmeshing ((M. M. DorrDorr et al. et al. AMPE, LLNL)AMPE, LLNL)
MICRESS, commercial software MICRESS, commercial software forphaseforphase--fieldfield coupledcoupled withwith CALPHAD CALPHAD
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Examples of applications
•• AnisotropicAnisotropic grain grain growthgrowth•• PrecipitatesPrecipitates on grain on grain boundariesboundaries•• LeadLead--free solder free solder systemssystems•• SolidificationSolidification
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22COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
Columnar films with fiber texture
•• Grain Grain boundaryboundary energyenergy::•• FourfoldFourfold symmetrysymmetry•• Extra Extra cuspcusp atat TT = 37.5= 37.5°°•• ReadRead--shockleyshockley
•• DiscreteDiscrete orientationsorientations
•• Constant Constant mobilitymobility•• InitiallyInitially randomrandom grain orientation grain orientation
and grain and grain boundaryboundary type type distributionsdistributions
White: θ = 1.5Gray: θ = 3Red: θ = 37,5Black: θ > 3, θ � 37.5
1 2 60, ,..., ( , ),..., 1.5i r tη η η η θ⇒ ∆ = °G
2D simulation2D simulation
<0 0 1>
In collaboration In collaboration withwith F. F. SpaepenSpaepen, , School of Engineering School of Engineering and and AppliedApplied Sciences, Sciences, HarvardHarvard UniversityUniversity
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23COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
3D simulations for wires with fibertexture
6ϑ < °
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24COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
Microstructure analysis: films
•• MisorientationMisorientation distribution distribution functionfunction (MDF)(MDF)
•• Evolution Evolution meanmean grain areagrain area
,(0)
1effh
nkt
tA kt
= → ∞+
→
1 ’/ff
efefdA
dk
kt N N
=+
=
0effn
effA tkA− =
•• Evolution Evolution towardstowards steadstead--state state regimeregimeSimple Simple meanmean fieldfield modelsmodels
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Examples of applications
•• AnisotropicAnisotropic grain grain growthgrowth•• PrecipitatesPrecipitates on grain on grain boundariesboundaries•• LeadLead--free solder free solder systemssystems•• SolidificationSolidification
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26COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
Zener pinning
•• MechanismMechanism forfor controllingcontrolling graingrainsizesize
•• E.g. E.g. NbCNbC, , AlNAlN, , TiNTiN,... in ,... in HSLAHSLA--steelssteels
•• NanoNano--graingrain structuresstructures
•• ZenerZener relationrelation forfor limitinglimiting graingrainsizesize
•• InfluenceInfluence ofof•• ShapeShape of the of the particleparticle•• InterfacialInterfacial propertiesproperties of of particlesparticles•• InitialInitial distributiondistribution•• EvolutionEvolution particlesparticles
lim 1b
V
RK
fr=
20 Pm
Fe-0.09 to 0.53 w% C-0.02 w% P withCe2O3 inclusions(PhD. M. Guo)
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27COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
Simulation results: Al thin films
•• ThinThin films films withwith CuAlCuAl22 -- precipitatesprecipitatesFilm preparation
33, 0.12, 21ar f l= = =
lim
0.5
11.28
a
Rfr
=
(exp from H.P. Longworth and C.V. Thompson)
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28COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
Simulation results: effect of particleshape and coarsening
•• EllipsoidEllipsoid particlesparticles •• EvolvingEvolving particlesparticles
lim 11 a V
baKa
R rs r f
=+ ffVV=0.12, L=10M=0.12, L=10M
3, 0.05Vfε = =
L. Vanherpe, K.U. Leuven
3.7, 1, 3.1K b a= = =
ModifiedZener relation
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29COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
Jerky motion during recrystallization in Al-Mn alloy
•• InIn--situ EBSD observation of situ EBSD observation of recrystallizationrecrystallization in AA3103 in AA3103 atat 400 400 °°CC
•• CamScanCamScan X500 Crystal Probe X500 Crystal Probe FEGSEMFEGSEM
•• JerkyJerky grain grain boundaryboundary motionmotion•• StoppingStopping time: 15time: 15--25 s25 s•• PinningPinning by secondby second--phase phase
precipitatesprecipitates–– AlAl66((Fe,MnFe,Mn), ), DD--AlAl1212((Fe,MnFe,Mn))33SiSi
•• AddedAdded to phase to phase fieldfield modelmodel•• Grain Grain boundaryboundary diffusiondiffusion•• DrivingDriving force for force for recrystallizationrecrystallization
20Pm
In collaboration In collaboration withwith A. A. MirouxMiroux, E. , E. AnselminoAnselmino, S. van der , S. van der ZwaagZwaag, T. U. Delft, T. U. Delft
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30COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
Material properties at 723K
DD0,p0,p = D= D0,0,bulkbulk, , QQpp = 0.65Q= 0.65Qbulkbulk
DDpp = = 1.21951.2195··1010--12 12 mm22/s/sPipe diffusion Pipe diffusion highhigh angle angle boundariesboundaries, , precipitateprecipitate//matrixmatrix interfaceinterface
DD0,0,bulkbulk = 10= 10--22 mm22/s, /s, QQbulkbulk = 211 kJ/mol= 211 kJ/molDDbulkbulk = 5.5973= 5.5973··1010--1818 mm22/s/s
Mn diffusion in Mn diffusion in fccfcc AlAl
γγprpr = 0.3 J/m= 0.3 J/m22InterfacialInterfacial energyenergy AlAl66Mn Mn precipitatesprecipitates
AAm m = 6= 6··10101111; x; xmm0 0 = 0.000258= 0.000258
AApp = 6= 6··10101212; x; xpp0 0 = 0.1429= 0.1429
BulkBulk energyenergy densitydensity: : ffρρ = A= Aρρ(x(x--xxρρ00))22
ccMnMn = 0.3 w% (0.1474 = 0.3 w% (0.1474 atat%)%)((PhDPhD thesisthesis LokLok 2005)2005)
ActualActual composition of composition of matrixmatrix((supersaturatedsupersaturated))
ccMn,eqMn,eq = 0.0524 w% (0.02456 = 0.0524 w% (0.02456 atat%)%)((PhDPhD thesisthesis LokLok 2005)2005)
EquilibriumEquilibrium composition of composition of matrixmatrix
MMhh = 2.94= 2.94··1010--1111 mm22s/kgs/kg((MirouxMiroux et et al.,Materal.,Mater. . SciSci. Forum,467. Forum,467--470,393(2004))470,393(2004))
MobilityMobility highhigh angle grain angle grain boundaryboundaryAtAt solutesolute content 0.3w% Mncontent 0.3w% Mn
γγhh = 0.324 J/m= 0.324 J/m22Grain Grain boundaryboundary energyenergy highhigh angleangle
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31COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
Precipitate coarsening and unpinning
•• PPDD < P< PZS ZS ((PPDD §§ PPZSZS))•• PinningPinning: P: PZSZS=3.6=3.6 MPaMPa•• Rex: PRex: PDD=3.1 =3.1 MPaMPa
•• UnpinningUnpinning mainlymainly throughthrough surface surface diffusion diffusion aroundaround precipitatesprecipitates
0.9µm x 0.375µm
2 2x yJ J J= +
6 s
7·10-10
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32COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
Precipitate coarsening and unpinning
•• PPDD <<< P<<< PZSZS
•• PinningPinning: P: PZSZS = 3.6 = 3.6 MPaMPa•• Rex: PRex: PDD = 1.1 = 1.1 MPaMPa
0.9µm x 0.375µm
•• UnpinningUnpinning throughthrough grain grain boundaryboundary diffusiondiffusion
2 2x yJ J J= +
8 s
1.7·10-10
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Examples of applications
•• AnisotropicAnisotropic grain grain growthgrowth•• PrecipitatesPrecipitates on grain on grain boundariesboundaries•• LeadLead--free solder free solder systemssystems•• SolidificationSolidification
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34COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
Coarsening in Sn(-Ag)-Cu solder joints
•• COST MPCOST MP--0602 (0602 (Advanced Solder Materials for High Temperature Advanced Solder Materials for High Temperature ApplicationApplication))
•• IMC formation and IMC formation and growthgrowth –– precipitateprecipitate growthgrowth –– KirkendalKirkendal voidsvoids ––stresses stresses –– grain grain boundaryboundary diffusiondiffusion
–– CALPHAD description CALPHAD description –– Diffusion coefficients, Diffusion coefficients, growthgrowth coefficient for IMCcoefficient for IMC--layerslayers
SEM-image of Sn – 3.8Ag–0.7 Cu alloy afterannealing for 200h at 150°C
x(A
G)
x(SN)
0.0
0.2
0.3
0.5
0.7
0.9
0.0 0.2 0.4 0.6 0.8 1.00 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
x(SN)
x(AG
)
CU
AG
SN
AGS
B_O
RTH
O+C
U6S
N5_
P+B
CT_
A5
CU
3SN
+CU
6SN
5_P
+AG
SB
_OR
THO
CU
3SN
+FC
C_A
1+FC
C_A
1
FCC_
A1+F
CC_A
1
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35COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
Cu-Sn system
( ) 25
3 16 2
6 5 15 2
( ) 12 2
10
5 10 m /s
10 m /s
10 m /s
CuSn
Cu SnSn
Cu SnSn
SnSn
D
D
D
D
−
−
−
−
=
= ⋅
=
=
Annealing temperature:
180 °C
Eutectic Composition: Sn-2at%Cu
Cu Sn
20.35 J/mgbσ =
••EquilibriumEquilibrium compositionscompositions •• InterdiffusionInterdiffusion coeffcientscoeffcients
•• InterfacialInterfacial energyenergy
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36COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
Effect of precipitates in Sn-2at%Cu
( ) 12 2
6 5 16 1
25
13
12
2 2
( ) 2
,10 m /s
10 ,
10
10 ,10 m /s
m10 /s
CuSn
Cu SnSn
SnSn
D
D
D
−
−
−
−
−−
=
=
=
•• Initial compositionsInitial compositions
••System size: 0.1System size: 0.1PPmx0.5mx0.5PPm m
•• InterdiffusionInterdiffusioncoefficients:coefficients:
•• InterfacialInterfacial energiesenergies::
•• Initial volume fraction Initial volume fraction precipitatesprecipitates::
•• InterfacialInterfacial reactionsreactions are are diffusion diffusion controlledcontrolled
20.35J/m
0.04Vf =
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37COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
Effect of grain boundary diffusion
( ) 25 25 2
3 15 13 2
6 5 15 13 2
( ) 12 12 2
2 10 ,*2 10 m /s
2 10 ,*2 10 m /s
2 10 ,*2 10 m /s
2 10 ,*2 10 m /s
CuSn
Cu SnSn
Cu SnSn
SnSn
D
D
D
D
− −
− −
− −
− −
= ⋅ ⋅
= ⋅ ⋅
= ⋅ ⋅
= ⋅ ⋅
SnJ ↑G
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38COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
Growth behavior Cu3Sn ?
••
( ) 25 2
3 15 2
6 5 15 2
( ) 12 2
12 2
2 10 m /s
2 10 m /s
2 10 m /s
2 10 m /s
D 2 10 m /s
CuSn
Cu SnSn
Cu SnSn
SnSn
surfSn
D
D
D
D
−
−
−
−
−
= ⋅
= ⋅
= ⋅
= ⋅
= ⋅
Grain structureGrain structure Composition: Composition: xxSnSn
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Examples of applications
•• AnisotropicAnisotropic grain grain growthgrowth•• ZenerZener pinningpinning•• CoarseningCoarsening of of precipitatesprecipitates on grain on grain boundariesboundaries•• LeadLead--free solder free solder systemssystems•• SolidificationSolidification
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40COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
Solidification
J. Heulens, K.U. Leuven4-fold anisotropy in interface mobility
•• EutecticEutectic growthgrowth
•• FacetedFaceted growthgrowth ((strongstrong anisotropyanisotropy))
4-fold anisotropy in interface energy
•• DendriticDendritic growthgrowth
4-fold weak anisotropy in interface energy, Cu-Ni
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41COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
Summary
•• UnderstandingUnderstanding microstructuremicrostructure evolutionevolution is important is important forformaterialmaterial sciencescience, , butbut processesprocesses cancan bebe veryvery complexcomplex•• PhasePhase--fieldfield techniquetechnique + + otherother models and models and experimentalexperimental inputinput
•• PrinciplesPrinciples phasephase--fieldfield modelingmodeling•• Diffuse interface concept, Diffuse interface concept, conservedconserved and and nonnon--conservedconserved field field
variablesvariables•• EvolutionEvolution equationsequations derivedderived fromfrom a free a free energyenergy functionalfunctional•• QuantitativeQuantitative aspectsaspects: Parameter : Parameter choicechoice + + advancedadvanced
implementationimplementation techniquestechniques
•• ApplicationsApplications•• GrainGrain growthgrowth, , recrystallizationrecrystallization, , coarseningcoarsening, , solidificationsolidification, , growthgrowth
intermetallicintermetallic phasesphases, , ……
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42COST MP0602 Industrial Seminar onThermodynamics, Bratislava, April 6, 2010
Thank you for your attention ! Questions ?
•• AcknowledgementsAcknowledgements•• Research Foundation Research Foundation -- FlandersFlanders ((FWOFWO--VlaanderenVlaanderen))•• FlemishFlemish SupercomputingSupercomputing Center (VSC)Center (VSC)
•• More More informationinformation onon http//http//nele.studentenweb.orgnele.studentenweb.org