OOF Extensions and Applications to Multifunctional Materials and Devices:
An Overview
R. Edwin García
Energy Materials
Current Research Actuator Materials
Outlinerechargeablebatteries
light emitting devices
piezoelectrics and electrostrictors
ferroelectrics
Rechargeable Lithium-Ion Batteries
250µm 52µm 174µmC. A. Vincent and B. Scrosati “Modern Batteries: An Introduction to Electrochemical Power Sources.” 2nd Ed. Butterworth-Heinemann, 1997.
Yet-Ming Chiang, W. Craig Carter
ohmic load
electromigrationterms
+∇ · (L∇φ)
+∇ · (L∇c)
diffusion term
∂c∂t
= ∇ · (DLi∇c)
ohmic term
0 = ∇ · (ρ∇φ)
surface reaction kinetics
!J · n̂ = Jo
(e
αaFηRT − e−
αcFηRT
)
∇ · σ = 0
elastic fields
σi j = Ci jkl (εkl−βkl(c− co))
graphite LiMn2O4
Model Validation: Comparison with Experiment
Experimental Data: Christopher Marc Doyle “Design and Simulation of Lithium Rechargeable Batteries.” PhD thesis, Department of Chemical Engineering. University of California at Berkeley, 1995
Late Stages of Voltage Distribution of Battery Discharge
1C: 2.0 mA/cm2
Full BatteryMicrostructure
Voltage Distribution(Volts)
Cathode
Cathode
50 µm
Anode
4.2 V
0.0 V
Mass Flux
200 MPa
-200 MPa
hydrostatic stresses
50 µm
Galvanostatic Discharge Stresses
cathode microstructure
0.9
1.1
lithium concentration
1 10 100
10
100
Summary Ragone Plot of Mixed Rocking Chair Batteries
6
43
5
1,21
2
3
5 6
Specific Energy (W h/kg)
Spec
ific
Pow
er (W
/kg)
graphite
LiMn2O4
LiCoO2
4
1 10 100
10
100
7 8
78
1 10 100
10
100
Summary Ragone Plot of Rocking Chair Batteries
6
43
5
1,21
2
3
5 6
Specific Energy (W h/kg)
Spec
ific
Pow
er (W
/kg)
graphite
LiMn2O4
LiCoO2
4
Electrochemical oof OOF2
Electrochemical Couplings
Mass Diffusion EquationCharge Continuity Equation
Heat Diffusion Equation
GMRES SolverTime-Stepper Methods
Multimeshing Techniques
Line (Interfacial) Elements
Heat Diffusion Equation
Multiple Solvers and PreconditionersGeneralized Time-Stepper Methods
Electrochemical Couplings
Mass Diffusion EquationCharge Continuity Equation
Multimeshing Techniques (in progress)
Line (Interfacial) Elements
Stress Engineering of Light Emitting Devices
Solorzano et al. "Near-red emission from site-controlled pyramidal InGaN quantum dots" Applied Physics Letters 87, 163121 (2005)
(Parijat Deb, Tim Sands)
elas
tic e
nerg
y de
nsity
(J/m
3 )
Distance (m)
0 J/m3
108 J/m3
25 nm
In0.2Ga0.8N GaN
[0001]
Elastic Energy Density Dstribution
Embedded Quantum Well Heterostructure
0J/m3
108 J/m3
0
20000000
40000000
60000000
80000000
100000000
03.19681818181813e-106.3936363636364e-109.590454545454539e-101.27872727272726e-091.59840909090909e-091.9180909090909e-092.23777272727272e-092.55745454545454e-092.87713636363636e-093.19681818181817e-093.5165e-093.83618181818181e-094.15586363636363e-094.47554545454545e-094.79522727272727e-095.11490909090908e-095.43459090909091e-095.75427272727272e-096.07395454545454e-096.39363636363636e-096.71331818181818e-097.033e-097.35268181818182e-097.67236363636363e-097.99204545454544e-098.311727272727271e-098.631409090909079e-098.95109090909091e-099.27077272727273e-099.59045454545454e-099.910136363636351e-091.02298181818181e-081.05495e-081.08691818181818e-081.11888636363636e-081.15085454545454e-081.18282272727272e-081.24675909090909e-081.27872727272727e-081.31069545454545e-081.34266363636363e-081.37463181818181e-081.4066e-081.43856818181818e-081.47053636363636e-081.50250454545454e-081.53447272727272e-081.56644090909091e-081.59840909090909e-081.63037727272727e-081.66234545454545e-081.69431363636363e-081.72628181818181e-081.75825e-081.79021818181818e-081.82218636363636e-081.85415454545454e-081.88612272727272e-081.9180909090909e-081.95005909090909e-081.98202727272727e-082.01399545454545e-082.04596363636363e-082.07793181818181e-082.1099e-082.14186818181818e-082.17383636363636e-082.20580454545454e-082.23777272727272e-082.2697409090909e-082.30170909090909e-082.33367727272727e-082.36564545454545e-082.39761363636363e-082.42958181818181e-082.46155e-082.49351818181818e-082.52548636363636e-082.55745454545454e-082.58942272727272e-082.6213909090909e-082.65335909090909e-082.68532727272727e-082.71729545454545e-082.74926363636363e-082.78123181818181e-082.8132e-082.84516818181818e-082.87713636363636e-082.90910454545454e-082.94107272727272e-082.9730409090909e-083.00500909090909e-083.03697727272727e-083.06894545454545e-083.10091363636363e-083.13288181818181e-083.16485e-08
Zero strain energy density
5 * 107 J/m3
0 J/m3
GaN
GaN
2 * 107 J/m3
In0.2Ga0.8N
107
0Ener
gy d
ensi
ty (
J/m3 )
0 25distance (nm)
Energy Materials
Actuator Materials
Outlinerechargeablebatteries
light emitting devices
piezoelectrics and electrostrictors
ferroelectrics
105
Maximum Actuation Strain
Max
imum
Act
uatio
n St
ress
(M
Pa)
Shape Memory Effect
Hydraulics
Pneumatic
Human Muscle
Solenoid
Voice Coil Transducer
Magnetic SMA
Magnetostriction
Thermal Expansion (100K)
Thermal Expansion (10K)
Piezo Polymer
Electrostrictors
High Strain PiezoActive Fiber Composite
Low Strain Piezo
1 10 102 103 104
10-2
10-1
100
101
102
103
10-6 10-5 10-4 10-3 10-2 10-1 100 101
J. E. Huber, N. A. Fleck, and M. F. Ashby “The Selection of Mechanical Actuators Based on Performance Indices” Proc. R. Soc. Lond. A, 453, 2185-2205 (1997).
Simulation of Polycrystalline PZT Films
50 µm
PZT microstructure courtesy of Samsung
Di = εijEj + diklσkl
30 µm
x
y
z
110
010001
2 µm diameter probed area
Virtual Piezoelectric Force Microscopy of Ferroelectric Films
110
010001
Pola
riza
tion
(C/m
2 )
Electric Field (V/m)
Electric Field (V/m)
Pola
riza
tion
(C/m
2 )
2 µm
Pola
riza
tion
(C/m
2 )
Electric Field (V/m)
××××
Electric Field (V/m)
Pola
riza
tion
(C/m
2 )
110
010001
2 µm Pola
riza
tion
(C/m
2 )
Electric Field (V/m)××××
distance (µm)
Nor
mal
ized
Hys
tere
sis A
rea Experimental
Numerical
distance (µm)
Nor
mal
ized
Hys
tere
sis A
rea
20 MPa
-30 MPa hydrostatic stress 0 V/m
7 ×105 V/m
built-in electric field
110
01000130 µm
0.24 C/m2
0.27 C/m2
polarization vector magnitude
x
y
zsc
0.25 C/m2
-0.25 C/m2
0
out-of-plane polarization
0.25 C/m2
-0.25 C/m2 out-of-plane polarization
110
01000130 µm
0.24 C/m2
0.27 C/m2
polarization vector magnitude
x
y
z
sc
110
010001
x
y
z×
×××
Pola
riza
tion
(C/m
2 )
Electric Field (V/m)
0 V/m
7 ×105 V/m
built-in electric field
Ferroelectric oof OOF2
Generalized Piezoelectric Couplings
Improved Non-Linear Solvers
Advanced Adaptive Meshing Tools
Coulomb’s Equation
Piezoelectric Couplings
Non-Linear Solvers
Elementary Adaptive Meshing Tools
Runge-Kutta Solvers
Coulomb’s Equation
Ferroelectricity
Predictor-Corrector Method
Energy Materials
Current Research Actuator Materials
Outlinerechargeablebatteries
light emitting devices
piezoelectrics and electrostrictors
ferroelectrics
solid oxide fuel cells
thermoelectric generators