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