Multiscale modeling in design ofnovel engineering materials

Modelowanie wieloskalowe w projektowaniu nowoczesnychmateriałów inżynierskich

Dr. Tomasz WejrzanowskiWarsaw University of TechnologyFaculty of Materials Science and Engineering

Dr inż. Romuald DoboszDr inż. Maciej SpychalskiDr inż. Marek MuzykMgr inż. Jakub SkibińskiMgr inż. Mateusz GrybczukJakub Szabelewski

1. Introduction2. Methods3. Design of materials properties4. Design of materials fabrication processes5. Summary

Outline

MATERIALS DESIGN DIVISION

1 mm

30m

Complexity of materials structure

atomic structure

(nano, microstructure)

Features:

phase composition,bonding energy,lattice size, density,electron density

structural elements:volume fraction,surface and numberper unit volume, size,shape, orientation

MATERIALS DESIGN DIVISION

Complexity of materials structure

Size, shape, surfaceroghness

• gradient(FGM)

• layers(films)

anisotropic:microstructure

isotropic

spacialarrangement ofstructuralelements

MATERIALS DESIGN DIVISION

Complexity of materials structure

microstructure

Grain size gradient

Porosity gradient

Composition gradient

MATERIALS DESIGN DIVISIONComplexity of materials structure

macrostructure

Bulk

Films

engineeringmaterials

MATERIALS DESIGN DIVISION

Dimensionality based classification:

• 0D – Point defects– vacancy– Foreign atom

• 1D – Linear defects– dislocation– triple junction (triple point)

• 2D – Surface defects– grain boundary– phase boundary

• 3D – Volume defects– pore– particle– inclusion

Defects in materials

MATERIALS DESIGN DIVISION

• Population of defects described by stochasticvariables

05

101520

2530

36 48 60 72 84 96 108 120 132 144

d2 [nm]

frac

tion

[ %

]

mean diameter = 55 nmstandard deviation of diameter = 37 nm

coefficient of deviation = 0,67………………………..………………………..

MATERIALS DESIGN DIVISION

Properties of materials

Properties dependent on atomicstructure

Properties dependent onmicrostructure

electrochemical potential Corrosion resistance

Melting point

Specific heat

Thermoelectrical potential Resistivity of semiconductors

magnetization coersivity

Young modulusDensity

StrengthDuctility

colour transparency

Quantitative structure description

VV

SV

d3

CV(d3) shape factors Voronoi tesselation

HardnessReactivityFlow stressFracture strengthAnisotropyConductivity

Time and length scale

Methods

Mutiscale modelling

Continuum level

Mesoscale

Atomistic scale

Macroscopic Strain –Stress relations Grain size, shape efect

Mesoscale MonteCarlo

FEM

Strain localization Internal stresses

Molecular Dynamics

Ab initio

Rotation of grains Grains sliding Dislocation creation and motion

Elastic constants Point defects

Atomic-scale MonteCarlo

Cellular Automaton

MATERIALS DESIGN DIVISIONDesign of materials structures at variousscales

Step 1. Definition of the sizedistribution of spheres

20 40 60 80 100 120 140 160

fraction[%]

size

spheres

Step 2. Packing of spheres

Design of materialsmicrostructures

Numerical design of the properties of materials

• Mechanical properties of nanometals – multiscale approach• Thermal stability – multiscale approach• Melting point• Corrosion ressistance

Nanometals

Composites

• Thermal conductivity of Cu,Ag – graphene composites

Foams•Permability•Mechanical properties•Heat dissipation

Numerical design of the materials processes

• Multipass hot-rolling of steel plates• GaN and Graphene epitaxial growth• SiC PVT growth

Application to nanomaterials

Acta Materialia 54 (2006) 297–303S.C. Tjong, H. Chen / Materials Science andEngineering R 45 (2004) 1–88

Magneticproperties

Special properties of nanomaterials

MicrocrystallineNanocrystalline

SV= 104-105 m2/m3 SV= 107-108 m2/m3 = 0.1 m2/mm3

Grain boundaries in polycrystalline materialsSpecific surface of grain boundaries

Grain boundaries in polycrystalline materials

Grain boundaries – models

Type of grain boundaries: a) low-angle, b) high-angle, c) twin

Grain boundaries – types

1. Random GB2. Special GB

Grain boundaries – distribution of GB misorientation

10 20 30 40 50 60012345678

fraction [%]

misorientation angle [deg]10 20 30 40 50 600

12345678

fraction [%]

misorientation angel [deg]

Cu after cold rolling

O.V. Mishin, G. Gottstein, V.Y. Gertsman, Distributions of orientations and misorientations in hot-rolled copper, MaterialsCharacterization 38, 1, 39, 1997.

Cu after cold rolling and long annealing

Grain boundaries in polycrystalline materialsStructure of grain boundaries

Mechanical properties of nanometals

σ

ε

dk

0

1nm

Data available

1. GB Young modulus2. GB shear modulus3. GB shear stress

Data is missing !!!

Twistangle

Youngmodulus

[GPa]0 92

12.55 7222.62 7636.87 81

Young modulus of twist grain boundaries in Al

• 120-312 atoms in supercell

• Strain range from -3% up to 3%

•VASP code, GGA-PBE pseudpotential

Young’s modulus of grain boundary

Effect of:

Structure-Tilt, twist angle- GB surface- Size

External conditions-Strain rate-Temperature

Shear stress, shear modulus

shear stress

shear modulus

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 0.05 0.1 0.15

nap

ręże

nie

ścin

ając

e [G

Pa]

odkształcenie

10

40

Shea

r str

ess [

GPa]

Shear strain

Low-angle GBHigh-angle (general) GB

Atomic scale

MolecularDynamics

64 nm

Shear stress, shear modulusGB structure effect

Tilt and Twist angle

0

1

2

3

4

5

6

7

0 10 20 30 40 50 60 70 80 90

shea

r stre

ss [G

Pa]

misorientation angle

Misorientation angle vs shear stress

TILT 100

0102030405060708090

0 10 20 30 40 50 60 70 80 90

shea

r mod

ulus

[GP

a]

misorientation angle

Misorientation angle vs shear modulus

TILT 100

TWIST100

Shear stress, shear modulusGB structure effect

100

Shear stress, shear modulusTemperature effect

Variation coefficient

Cv = SD/EE - mean value

SD - standard deviation

Cv = 0.07 Cv = 0.20 Cv = 0.41

Macroscopic yield stress

Cv = 0.07

Cv = 0.20

Cv = 0.410

100

200

300

400

500

600

700

800

900

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Re 0

2

₫-0.5

Cv = 0.07

Cv = 0.20

Cv = 0.41

32 nm

~100 MPa

Macroscopic yield stress

Thermal stability

Monte Carlo model

MesoscaleMolecular dynamics with EAM

Atomic scale

Grain boundary motion -> Grain Growth

Grain boundary energy vs grains misorientation

0

0,4

0,8

1,2

0 30 60 90

[deg]

J

)]2ln[sin(1)2sin()( max AJJ

(disslocation based model *)

* W.T. Read, W. Shockley, Phys. Rev. 78 (1950) 275.

Grain growth mechanisms

Grains coalescence

[2] A.J. Haslam, S.R. Phillpot, D. Wolf, D. Moldovan, H. Gleiter, Mechanisms of grain growth in nanocrystalline fcc metals by molecular-dynamicssimulation, Materials Science and Engineering A, 318, 1-2, 293, 2001

[1] D. Moldovan, D. Wolf a, S.R. Phillpot, A.J. Haslam, Role of grain rotation during grain growth in a columnar microstructure by mesoscalesimulation, Acta Materialia 50, 3397–3414, 2002

Pd, ~15 nm, 1400K [2]Rotation of grains [1]

n

O BDDAp

max0

1 exp11

Grain growth mechanisms

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0 20 40 60 80 100 120 140 160 180

ener

gy [J

/m2 ]

misorientation angle

Results

2

1arccos 332211 mmm

Misorientation angle ->energy

G. Zhu, W. Mao, Y. Yu, Calculation of Misorientation distributionbetween Recrystallized Grains and Deformed Matrix, Scriptamater. 42, 37, 2000.

(100)

Good correlationbelow 20 deg.

Grain boundaries – modelling of the energy

T1

T2

T3

T >1 T >T2 3

10-5

10-9

10-13

10-17

10 20 30 40

A [m

/s]

2

[deg.]

Nanocrystalline iron –1000K

Size: 9nm, time: 2ns

Grain boundary mobility vs misorientation and curvature

10° 20° 25°

Atomistic scale - Molecular Dynamics

T. Wejrzanowski, M. Spychalski, R. Pielaszek,K.J. Kurzydlowski, Grain boundary migration innanocrystalline iron, Solid State Phenomena 129,2007, 145-150

Thermal stability

New configuration

3D modelMonte Carlo

0 30 60 90 120 150 1800

1

2

3

4 wartości zmierzone aproksymacja lognorm

częstość [%]

[deg]

0 10 20 300

10

20

30 wartości zmierzone aproksymacja lognorm

częstość [%]

D

0 10 20 300

10

20

30 wartości zmierzone aproksymacja lognorm

częstość [%]

D

Monte CarloGrain size inhomogeneity effect

homogenous

GB misorientation distribution

Grain size distributionCV(D)=0,13

CV(D)=0,62

Non-homogenous

Freq

uenc

y [%

] Freq

uenc

y [%

]Fr

eque

ncy

[%]

Mesoscale - MonteCarloGrain growth in nanometals

Influence of grain sizehomogeneity

0 50 100 150 2000,1

0,2

0,3

0,4

0,5

0,6

0,7 CV(D)0=0,13 CV(D)0=0,41 CV(D)0=0,62 approximation

CV(D)

t

Changes of grain size dispersion

M. Lewandowska, T. Wejrzanowski, K.J. Kurzydlowski, Grain growth in ultrafine grainedaluminium processed by hydrostatic extrusion, Journal of Materials Science, 43, 2008, 7495–7500

Thermal stability

0 50 100 150 20010

15

20

25

30

35 CV(D)0=0,13 CV(D)0=0,41 CV(D)0=0,62 approximation

Dt

)exp(36,0)( BtADCV

Changes of grain size

Experimental verification – time effectconstant temperature

0 1 2 3 40.1

1

10

100

1000

473K 573K

d 2 [m]

t [h]0 1 2 3 4 5

0.4

0.5

0.6

0.7

0.8

0.9

1.0

473K 573K

CV(d2)

t [h]

Kinetics of grain growth inaluminium after Hydroextrusionannealed at definedtemperature and different time

Temporal changes of grainsize dispersion in samplesannealed at differenttemperature

Thermal stability

Boundary condition effectMelting point

Lindemann index - root mean squared (rms) distancefluctuation

T. Wejrzanowski, M. Lewandowska, K. Sikorski, K. J. Kurzydlowski,Effect of grain size on the melting point of confined thinaluminum films, Journal of Applied Physics 116, 164302 (2014)

Time effectMelting point

Grain size (GB surface) effectMelting point Size and pressure effect

Effect of grain boundary energy on intergranular corrosion

H. Miyamoto et al. / Corrosion Science 44 (2002) 1835–1846

Corrosion resistance

Grain boundaries in iron

Tilt

Twist

0

0,2

0,4

0,6

0,8

1

1,2

1,4

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

E GB

[J/m

2 ]

Twist angle [deg]

100

110

112

0

0,2

0,4

0,6

0,8

1

1,2

1,4

0 10 20 30 40 50 60 70 80 90

E GB

[J/m

2 ]

Tilt angle [deg]

100

110

112

Surface and misorientation(room temperature, atmospheric pressure)

0

0,5

1

1,5

2

2,5

0 200 400 600 800 1000 1200

Ener

gy [J

/m2 ]

T [K]

ESF EGB

-4

-3,6

-3,2

-2,8

-2,4

-2

0 200 400 600 800 1000 1200

Ekoh

[J/

m2 ]

T [K]

Temperature behaviour of 210 Fe GB

ESF – free surface energyEGB – grian boundary energyEkoh – cohesion energy

GB energy vs misorientationCorrosion resistance

Grain boundary energy in Al

Tilt angle

GB

Ene

rgy

Angle Cu Fe Mg Mn

12.55 0.1596 0.1211 -0.0418 0.1234

22.62 -0.3510 0.1206 -0.0397 0.1330

36.87 -0.1700 0.1817 -0.0629 -0.1794

Positions of the atoms inaluminium calculated for aflat grain boundary

0.400.450.500.550.600.650.70

0 10 20 30 40Rotation angle (degree)

Ener

gy (J

/m^2

)

Segragation energy of impurities ingrain boundary in Al

Fields of interest:

• Grain boundary energy

• Structure of grain boundary

• Segregation energy of impurities

• Cohesion of grain boundary

Grain boundaries in alluminium alloys Atomic scale – ab initioCorrosion resistance

Grain boundaries revealed in 2014aluminium alloys: the coloured linesindicate the grain boundaries of mis-orientation angle from different range

Experimental evidencesCorrosion resistance

Distribution function of the grainboundaries misorientation angle(a) and propensity of grainboundaries to grain boundarycorrosion (b)

Experimental evidencesCorrosion resistance

MATERIALS DESIGN DIVISIONGraphene Composites- Electronics cooling

• Limiting factor• Densly packed integrated circuits• More computational power

• Specific shape of electronic devices – flat, thin – heat flowis limited by small area of cooling elements and at thesame time heat must travel long way to be dissipated

Moore A.L., Shi L., Emerging challenges and materials for thermal management ofelectronics. Materials Today. 2014, 17(4), 163-74.

http://www.computerworlduk.com/

Graphene – metal composite for energy dissipation fromlocalized heat sources

Single layer Graphene+ Cu grapheneinterfaces6A thickness

Cu layer – variablethickness

Dimensions and properties rescaled because of FEM and computer numberrepresentation limitations

{100}

Periodic Boundary conditionsAtom count: 114240Box dimensions: 62x72x303 ÅTime: ~150 ps

Atomic scale

1 20E+001E+082E+083E+084E+085E+086E+087E+08

AgCu

graphene layers count

hc =

[W/(m

2̂K)]

MATERIALS DESIGN DIVISION

Results TC across layersFEM and analytical calculations results

Wzory analityczneLienhard J., IV, Lienhard J., V., A heat transfer textbook. Cambridge, Massachusetts: Philogiston Press, 2012.Chapter 2.3

MATERIALS DESIGN DIVISIONResults – TC along layersFEM and analytical calculations

results

Lienhard J., IV, Lienhard J., V., A heat transfer textbook. Cambridge, Massachusetts: Philogiston Press,2012. Chapter 2.3

MATERIALS DESIGN DIVISION

Heat sink

Cuthickness[A]

λ alonglayers [Wm-

2K-1]

λ acrosslayers [Wm-

2K-1]Heat rate[W/s]

1,00E+00 400 400 117,461,00E+06 400 392 117,441,00E+05 400,28 335,76 117,341,00E+04 402,76 137,3 116,929,90E+02 427 19,87 117,19,40E+01 676 2,08 121,76

MATERIALS DESIGN DIVISIONDesign of foamstructures

Porosity

Coefficient of pore volume

variation

Surface to volume ratio

Permeability

Young’s Modulus

Poisson ratio

Thermal conductivity

MATERIALS DESIGN DIVISIONStructural parameters ofthe designed structures

Commercial aluminafoam filter

(10 pores per inch)

Designed structurewith homogeneous

pore volumedistribution

Porosity [%] 75.01 78.17

Surface to volume ratio[1/mm] 0.77 0.76

Mean pore diameter [mm] 2.56 2.83

Examples of generated foam structures

CV(V) = 0.45 CV(V) = 0.7 CV(V) = 1.2

Poro

sity

~ 9

0%Po

rosi

ty 7

0%

Properties of foam structures

Analysis of material properties of the designed structures

Permeability(pressure drop)

Finite Element MethodFinite VolumeMethod

Lattice Boltzmannmethod

Mechanical properties(Youngs’ Modulus, Poisson

ratio)

Finite Element Method

Thermal conductivity

MATERIALS DESIGN DIVISIONCorrelation of properties withstructural parameters

4,5E-7

5,0E-7

5,5E-7

6,0E-7

6,5E-7

7,0E-7

7,5E-7

8,0E-7

0,4 0,75 1,1 1,45 1,8 2,15

Perm

eabi

lity

[m2 ]

CV(V)

1,00

1,40

1,80

2,20

0,4 0,9 1,4 1,9 2,4

E [G

Pa]

CV(V)

30,00

34,00

38,00

42,00

46,00

50,00

0,4 0,9 1,4 1,9 2,4

λ [W

/mK

]

CV(V)

900

920

940

960

980

1000

1020

1040

1060

1080

1100

0 10 20 30 40 50 60 70

Tem

pera

tura

,°C

Czas, s

Multi-pass hot-rolling of steel plates

PVT reaktor - ITME

Heat and mass transport in PVT reactor

Temperatura wewnątrz reaktora w zależności od układu izolacji

2200222022402260228023002320234023602380

0 20 40 60 80 100pionowa odległość od kryształu zarodka [mm]

T [ºC

]

o wąskim prześwicie

o szerokim prześwicie

mieszana 1/1

mieszana 1/3

z grafitowymi przekładkami

z n. um. grafitowymiprzekładkami

1. Reactor geometry- Thermal insulation- crystal thickness

2. Process conditions- temperature- pressure

SiC PVT growth

Projekt “Opracowanie technologii otrzymywania nowoczesnych materiałów półprzewodnikowych na bazie węglika krzemu” jest współfinansowanyze środków Europejskiego Funduszu Rozwoju Regionalnego w ramach Programu Operacyjnego Innowacyjna Gospodarka

Distribution of temperature

Evolution ofdisslocations

Crystalgrowth rate(15d1 vs.

8d8)

SiC PVT growth

Temperature distributionGrapheneepitaxy

Numerical models

GaN epitaxy

Gas velocity distribution

Density distribution

GaN and Graphene epitaxial growth

Velocity - MOVPE

Temperature - MOVPE

Velocity - CVD

1,4

1,5

1,6

1,7

1,8

1,9

2

2,1

2,2

-3,00-1,001,003,00

GaN

Gro

wth

Rat

e [m

i/h]

X [cm]

6250 (4950/1300)

5550 (4250/1300)

4850 (3550/1300)

4150 (2850/1300)

3450 (2150/1300)

GaN crystal growth rate

GaN and Graphene epitaxial growth

Summary

1. Many materials properties and processes can benowadays modeled at various time and lengthscales

2. Software for atomic scale and continuum scale iswell developed

3. There is still lack of software dedicated to meso-scale applications

Hardware and software

•Materials Studio(Accelrys)•MedeA•VASP•Phonon•Abinit•CPMD•IMD•XMD•LAMMPS•Abaqus•ANSYS•Marc/Mentat•Nastran/Patran•Fluent/Fidap•AMIRA•Atomeye•AVS

Local workstations

• 64-bit cluster (76 AMD-Opteron cores)

• 64-bit cluster (360 AMD-Opteron cores – 90processors)

• 5 x workstations (2xAMD-Opterion Dual Core)

Hardware and software