OOF Extensions and Applications to Multifunctional Materials and Devices:

An Overview

R. Edwin García

Ed Fuller

Andy Roosen

Steve Langer

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

Lithium concentration(normalized)

Initial Stages of Battery Discharge

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

Late Stages of Battery Discharge

200 MPa

-200 MPa

hydrostatic stresses

50 µm

Galvanostatic Discharge Stresses

cathode microstructure

0.9

1.1

lithium concentration

2

3

4

5

6

graphite LiMn2O4LiCoO2

1

50 µm

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

7

8

Advanced Rechargeable Batteries

graphite LiMn2O4

0 V

4.3 V

depleted after 250s I=80 A/m2

7

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

Energy Materials

Actuator Materials

Outlinerechargeablebatteries

light emitting devices

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)

Crystallography of GaN Pyramids

{1̄01}

{{1̄00}

{

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

Strain Energy Density

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

Polycrystalline PZT Film

2 µm

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).

Electromechanical Helmholtz free energy0

The Piezoelectric Solid

Simulation of Polycrystalline PZT Films

50 µm

PZT microstructure courtesy of Samsung

Di = εijEj + diklσkl

Piezoelectric Force Microscopy of Ferroelectric Films

++

++

+ +

silicon substrate

PZT film

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

Credits

Ferroelectric Materials

Bryan Huey UConn

John E. Blendell Purdue University

W. Craig Carter MIT

Rechargeable Batteries Yet-Ming Chiang, W. Craig Carter MIT

InGaN Light Emmiting Devices Parijat Deb, Tim Sands Purdue University

Electrochemical Actuators Yet-Ming Chiang, Yukinori Koyama MIT