Richard D. James University of Minnesota james@umn

September 6, 2002 Cornell University, Ithaca, NY

Deforming films of active materials: new concepts for producing motion at small scales (using applied fields)

Richard D. JamesUniversity of [email protected]

Chris Palmstrom, UMNKaushik Bhattacharya, CaltechRobert Tickle, Postdoc, UMNRichard Jun Cui, Grad student, UMNJianwei Dong, Grad student, UMNWayne Falk, Grad student, UMN

COLLABORATIONS, POSTDOCS, STUDENTS


Questions

How does one produce motion at small scales?

What concepts are suggested by theory?


Plan of talk Microscale: films of active materials

– Why martensitic materials?– Theory: interfaces, microactuator concepts– Bulk vs. film– MBE growth of Ni2MnGa

Macroscale: ferromagnetic shape memory materials– Martensite + ferromagnetism– Energy wells and interfaces– Bulk measurements: strain vs. field

Nanoscale: Bacteriophage T-4


Martensitic phase transformation

Ga

MnNi

N

S

Ni2MnGa


Why martensitic materials?Work output per volume per cycle of various actuator systems, Krulevitch et al.

Actuator Type Work/volume (J/m3) Basic formula Comments

NiTi shape memory 2.5 107 one time: = 500MPa, = 5%

6.0 106 thousands of cycles: = 300MPa

Solid liquid phase change 4.7 106 (1/3)(v/v) k k = bulk modulus = 2.2 GPa, 8% volume changeThermo-pneumatic 1.2 106 F / V F = 20N, = 50 m, V = 4mm 4mm 50 m

Thermal expansion 4.6 105 (1/2)(Ef+Es)(T) Ni on Si (ideal); s = substrate, f = film, T = 200 CElectromagnetic 4.0 105 F / V, F = -Ms A / 2 variable reluctance (ideal); V = gap volume, Ms = 1 V sec/m2 2.8 104 F / V variable reluctance (ideal); F = 0.28 mN, V = 100 m 100 m 250 m 1.6 103 T/ V external field; T = torque = 0.185 mN m,

V = 400 m 40 m 7 mElectrostatic 1.8 105 F / A gap, F = V2A/22 F = 100 volts, = gap = 0.5 m 3.4 103 F / V comb drive, F = 0.2 mN (@60V) V = 2 m 20 m 3000 m, = 2 m 7.0 102 T/ V integrated force array; 120 voltsPiezoelectric 1.2 105 (d33 E)2 Ef /2 PZT; Ef = 60GPa, d33 = 500, E = 40KV/cm 1.8 102 (d33 E)2 Ef /2 ZnO; Ef = 160GPa, d33 = 12, E = 40KV/cm

Muscle 1.8 104 = 350 KPa, = 10%Microbubble 3.4 102 F / Vb F = 0.9 N, = 71 m

…based on“bulk” theory: o.k.?


Martensitic films

What theory?

vs.

This talk: single crystal films


Bulk theory of martensite

is frame indifferent:

is minimized on “energy wells”:

SO(3)

SO(3)

SO(3)

SO(3) SO(3)

SO(3)


Energy wells

U1 U2

RU2

I

3 x 3 matrices

Minimizers...

Ni30.5

Ti49.5

Cu20.0

= 1.0000 = 0.9579 = 1.0583

Cu69

Al27.5

Ni3.5

= 1.0619 = 0.9178 = 1.0230


Energy wells for various materials

0

0

00

0

0

00

0

0

00

0

0

00

0

00

0

0

00

0

0

00

0

0

00

0

00

0

0

00

0

0

00

0

0

00

0

0

U1, U2 , … , U12 =

Cu68 Zn15 Al17

Ni50 Ti50

= 1.087, = 0.9093, = 1.010,

= 0.0250

(Chakravorty and Wayman)

= 1.0243, = 0.9563, = 0.058,

= 0.0427)

(Knowles and Smith)

structure of these matrices: Ball/James

U1, U2 , … , U12 =


Passage to the thin film limit using -convergence

h

1

x

x.

.

S

S

Change variables:

x1 = x1

x2 = x2

x3 = (1 / h) x3

~

~

~

~

y(x) = y(x)~ ~

h


Estimate the energy of the minimizer using a series of test functions

Let y(h) W1,2 be a minimizer. Compare the energy of y(h)(x) with any test function satisfying

BC and having bounded energy as h 0. Get some weak convergence:

Use the weak limits as test functions. Strengthen the convergence above ( to ). Learn

more and more about the form of the minimizer y(h). Pass to the limit: find the limiting energy of y(h). Use the prototypical test function and establish the limiting

variational principle.


Derivation of thin film theory using -convergence

h

x 1

x 3

x 2

hS

h b(x ,x )1 2

y(x ,x )1 2

(A Cosserat theory)


Predictions: min y, b

The interfacial energy constant is << than a typical modulus that describes how grows away from its energy wells: put = 0.

Zero energy deformations

One phase (say, austenite, i (x) = a)

e3

e1

e2

compatibility plays a role here

solve for b

from the structure of the energy wells

This is a parameterizationof all “paper folding” deformations y(x1, x2)

b(x1, x2)


Two phases: austenite and a single variant of martensite

min y, b

e

e 1

3

e 2

1(e | e ) 2

1(RU e | RU e )

2 1 11(y, | y, ) = 2

This is compatible if and only if

austenite single variant of martensite

(solve for bso that thesestates are on the energy wells)

The main effect of is to smooth interfaces slightly.


?Exact interfaces between austenite and variant 1 ofmartensite in Ni50Ti50

Film normal

100010001

1101-1010110-101101-1

111-1111-1111-1

Austenite/martensiteinterface?

yesyesyes

noyesyesyesyesyes

noyesyesyes

Interface lines

(0, -0.9639, 0.2664) & (0, 0.3841, 0.9233)(-0.9639, 0, 0.2664) & (0.3841, 0, 0.9233)(-0.9728, 0.2317, 0) & (0.2317, -0.9728, 0)

(0.1892, 0.1892, 0.9636) & (0.6080, 0.6080, -0.5105)(-0.3339, 0.8815, 0.3339) & (0.5018, 0.7046, -0.5018)(0.1351, -0.9816, 0.1351) & (0.6840, -0.2538, 0.6840)(0.8815, -0.3339, 0.3339) & (0.7046, 0.5018, -0.5018)(-0.9816, 0.1351, 0.1351) & (-0.2538, 0.6840, 0.6840)

(0.3505, 0.8139, -0.4634) & (0.5952, -0.1864, 0.7816)(0.8139, 0.3505, -0.4634) & (-0.1864, 0.5952, 0.7816)(-0.3238, 0.8110, 0.4872) & (0.8110, -0.3238, 0.4872)

In-plane principalstretches

(0.9358, 1.0473) (0.9358, 1.0473) (1.0840, 0.9663)

(1.1066, 0.9320) (0.9464, 1.0286) (1.1005, 0.9574) (0.9464, 1.0286) (1.1005, 0.9574)

(1.1001, 0.9424) (1.1001, 0.9424) (1.0582, 0.9663)


…but, in bulk, we almost* never see austenite against a single variant of martensite

*unless, by changing composition, we tune the lattice parameters to satisfy very special conditions

10 m


Bulk vs. film

In both casesthe depth is L

L

L

Energy lowered by phase change

Lh

Energy of transition layer

L3 L3

h L2 >> h2 L (1 >> h/L) h


“Tunnel”

e3

e

n

Possible (according to theory) if

and


“Tent”

1(y, | y, ) = 2

variants of martensite, (RiUie1 | RiUie2), i = 1, …, n

e3

e1

e2

1(e | e ) 2austenite

Possible if

and

e3 is an n-fold (n = 3, 4, 6) axis of symmetry of austenite

Quite restrictive but satisfied for (100) films in:

Ni30.5Ti49.5Cu20.0 Cu68Zn15Al17 (approx. in Cu69Al27.5Ni3.5)


“Tent” on CuAlNi foil

10 Co

70 Co

90 Co

Composition:Cu-Al(wgt%13.95)-Ni(wgt%3.93)

DSC Measurement: ( ±2 Co)Ms: 20 Af: 10Mf: 10 Af: 50

Size of the Tent: (inch)0.400 x 0.400 x 0.188

Film Thickness: 40 m

Orientation:Surface Normal: [100]Edge of the Tent: [0, 4.331,1]

(100)

(010)

16


Martensitic pacman

Example drawn with (100) film and measured lattice parametersof Ni50Ti50


Martensitic vs. magnetostrictive materials

Temperature

martensitic (giant) magnetostrictive

strain strain, magnetization

free energy free energy


Ferromagnetic shape memory materials

Three important temperatures:Curie temperature of austenite: Curie temperature of martensiteAustenite-martensite transformation temperature: first order

second order

T

Two ways to field-induce a shape change:

1) Field-induce the austenite-martensite transformation

2) Rearrange variants of martensite below transformation temperature. picture below drawn with measured

lattice parameters of Ni2MnGa

H


Lattice parameters vs. temperature (Fe70Pd30)

Lattice Parameter as Function of Temperature

3.5000

3.6000

3.7000

3.8000

3.9000

-40 -30 -20 -10 0 10 20 30 40 50 60 70

Temperature (C)

Lattic

e P

ara

mete

r a o

r c (

A)

Averagea0 FCC 3.7524a FCT 3.8375c FCT 3.5938a/a0 1.0224c/a0 0.9535

a (FCT)

c (FCT)

a0 (FCC)


Phases (Fe70Pd30)

-60

-40

-20

0

20

40

60

80

100

0.28 0.285 0.29 0.295 0.3 0.305 0.31

Composition at.%Pd

Tra

nsfo

rmat

ion

Tem

pera

ture

C

FCT

FCC

BCT


Microstructure (Fe70Pd30)

Visual observations at various temperatures:

Heat Treatment: 900 C x 120 min, ice water quench

FCC Austenite 25 oC

Austenite & FCT Martensite 10 oC FCT Martensite -10 oC FCT & BCT Martensite -60 oC


Austenite/martensite interface (Fe70Pd30)


Strain vs. field: Fe3Pd

-1 MPa and 10oC


Strain vs. field in Ni2MnGa

H(010)

(100)

30 times the strain of giant magnetostrictive materials


Other ideas... These are pictured using the measured lattice parametersand easy axes of Ni2MnGa and (100) films.

austenite

martensite

(also applicableto PbTiO3)


Scale effects in thin film actuators

Euler-Bernoulli theory

Moment-curvature relation

s (s)

M

h b

“film” modulus

h 3

Can we have the cantilever bending, but with stored energy proportional to h2 or even h?

membrane: hbending (nonlinear Kirchhoff): h3

von Karman: h5


Ni2MnGa cantilever

H(t) Energy stored is proportional to h (because of the micromagnetic term ) rather than h3 dxhm

picture drawn with measured lattice parameters of Ni2MnGa

(Electromagnetic force on the cantilever is zero; it is driven by configurational force)


Stabilization of Ni2MnGa austenite and martensite phases through epitaxy.

5.6

5.7

5.8

5.9

6.0

6.1

0 0.2 0.4 0.6 0.8 1

In-p

lane

latt

ice

para

met

er (

Å)

In concentration, x

Austenite

Martensite

InAs

InP

GaAsG

aAs

InA

s

Ga1-x

InxAs

InP or GaAs (001)

Ga1-xInxAs

Ni2MnGa

Adjust substrate lattice parameter to match in-plane (a0) of desired crystal structure

Grow relaxed Ga1-xInxAs layers

Ga1-xInxAsLattice matched xAustenite 0.42InP 0.53Martensite 0.66

Palmstrom/Dong/James


Ga

Mn

Ni

Sc,Er

As

Sc1-xErxAs NaCl structure NiGa CsCl structure

Interlayers for Ni2MnGa growth on GaAs

L21 structure “ordered” CsCl

GaAs Zincblende

The L21 crystal structure is both

NaCl-like and CsCl-like

Sc1-xErxAs and NiGa are good interlayers and template layers for Ni2MnGa growth on GaAs


Ga

Mn

Ni

Sc,Er

As

Ga

As

GaAs

Sc0.3Er0.7As

Ni2MnGa

{112}<111>

Cross-section TEM Study: Ni2MnGa(900 Å) / Sc0.3Er0.7As(17 Å) / GaAs

Spot splitting Pseudomorphic growth of Ni2MnGa films: (a = 5.65 Å, c = 6.18 Å)

Palmstrom/Dong


Cool down without field, then warm in a field of 1000 Oe

Magnetic Characterization: SQUID measurements

GaAsNi2MnGa

No phase transformation in unreleased films!

100

300

500

700

0 50 100 150 200 250 300 350

Mom

ent (

em

u)

Temperature (K)

Moment vs. Temperature In-plane Hysteresis Loop at 10 K

Tc ~ 340 K Ms ~ 450 emu/cm3, Hc ~ 230 Oe

-1000

-500

0

500

1000

-2000 -1000 0 1000 2000M

omen

t ( e

mu)

Field (Oe)


Patterning and processing of free standing films

400 m

GaAs

Ni2MnGaPhotoresist

Photolithography of film side

Ar/Cl2 Plasma

RIE of Ni2MnGa film

After RIEAfter selective chemical etching

Backside IR alignment and photolithography

Free-standing Cantilever


100 m long bridges and cantilevers with different aspect ratios

100 m

Mask for free-standing Ni2MnGa films

J. Dong


0

20

40

60

80

0 50 100 150 200 250 300 350

Mom

ent (

em

u)

Temperature (K)

Magnetic Characterization: SQUID Measurements on Partially Released Ni2MnGa Films

Cool down without field, then warm/cool/warm with 100 Oe field applied in-plane

1. Initial warm up

2 & 3. Cool/Warm

overlapped Free-standing films

After the film is partially released from the substrate, there is a phase transformation ~ 300 K


Phase Transformation Cyclic phase transformation observed in a 900Å thick Ni2MnGa free standing film using polarized light

(a) RT

(b) 100C

(c) 120C

(d) 150C

(e) <150C

(f) ~120C

(g) 100C

(h) 60C

Free standing“hip roof”


In more recent films…


“Tent”

1(y, | y, ) = 2

variants of martensite, (RUe | RUe), i = 1, …, n

e3

e1

e2

1(e | e ) 2austenite

Possible if

and

e3 is an n-fold (n = 3, 4, 6) axis of symmetry of austenite

Quite restrictive but satisfied for (100) filmsNi30.5Ti49.5Cu20.0 Cu68Zn15Al17 (approx. in Cu69Al27.5Ni3.5) …but not satisfied in Ni2MnGa)


Interpretation

Hip roof

P-phase

Martensite variant 1 Martensite variant 2

Compatible, energy minimizing structure Does not require special conditions on lattice parameters Geometry does not appear to agree (?) using the lattice parameters for the thermal martensite, pictured below


A 100nm bioactuator

Bacteriophage T-4 attackinga bacterium: phage at the right

is injecting its DNA

• How can it generate forces sufficient to penetrate the cell wall?• Man made analogs?

Falk and JamesWakefield, Julie (2000) The return of the phage. Smithsonian 31:42-6


Martensitic transformation and thin film interfaces

(Olson and Hartman)

Force generated upon contraction: Falk/James

This transformation strain satisfies theconditions, given above, for “thin film”

interfaces


Bio-Molecular Epitaxy (BME)?

Richard D. James University of Minnesota james@umn

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