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Deforming films of active materials: new concepts for producing motion at small scales ( using applied fields ). Richard D. James University of Minnesota [email protected]. COLLABORATIONS, POSTDOCS, STUDENTS. Chris Palmstrom, UMN Kaushik Bhattacharya, Caltech Robert Tickle, Postdoc, UMN - PowerPoint PPT Presentation
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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
September 6, 2002 Cornell University, Ithaca, NY
Questions
How does one produce motion at small scales?
What concepts are suggested by theory?
September 6, 2002 Cornell University, Ithaca, NY
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
September 6, 2002 Cornell University, Ithaca, NY
Martensitic phase transformation
Ga
MnNi
N
S
Ni2MnGa
September 6, 2002 Cornell University, Ithaca, NY
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.?
September 6, 2002 Cornell University, Ithaca, NY
Martensitic films
What theory?
vs.
This talk: single crystal films
September 6, 2002 Cornell University, Ithaca, NY
Bulk theory of martensite
is frame indifferent:
is minimized on “energy wells”:
SO(3)
SO(3)
SO(3)
SO(3) SO(3)
SO(3)
September 6, 2002 Cornell University, Ithaca, NY
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
September 6, 2002 Cornell University, Ithaca, NY
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 =
September 6, 2002 Cornell University, Ithaca, NY
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
September 6, 2002 Cornell University, Ithaca, NY
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.
September 6, 2002 Cornell University, Ithaca, NY
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)
September 6, 2002 Cornell University, Ithaca, NY
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)
September 6, 2002 Cornell University, Ithaca, NY
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.
September 6, 2002 Cornell University, Ithaca, NY
?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)
September 6, 2002 Cornell University, Ithaca, NY
…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
September 6, 2002 Cornell University, Ithaca, NY
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
September 6, 2002 Cornell University, Ithaca, NY
“Tunnel”
e3
e
n
Possible (according to theory) if
and
September 6, 2002 Cornell University, Ithaca, NY
“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)
September 6, 2002 Cornell University, Ithaca, NY
“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
September 6, 2002 Cornell University, Ithaca, NY
Martensitic pacman
Example drawn with (100) film and measured lattice parametersof Ni50Ti50
September 6, 2002 Cornell University, Ithaca, NY
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
September 6, 2002 Cornell University, Ithaca, NY
Martensitic vs. magnetostrictive materials
Temperature
martensitic (giant) magnetostrictive
strain strain, magnetization
free energy free energy
September 6, 2002 Cornell University, Ithaca, NY
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
September 6, 2002 Cornell University, Ithaca, NY
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)
September 6, 2002 Cornell University, Ithaca, NY
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
September 6, 2002 Cornell University, Ithaca, NY
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
September 6, 2002 Cornell University, Ithaca, NY
Austenite/martensite interface (Fe70Pd30)
September 6, 2002 Cornell University, Ithaca, NY
Strain vs. field: Fe3Pd
-1 MPa and 10oC
September 6, 2002 Cornell University, Ithaca, NY
Strain vs. field in Ni2MnGa
H(010)
(100)
30 times the strain of giant magnetostrictive materials
September 6, 2002 Cornell University, Ithaca, NY
Other ideas... These are pictured using the measured lattice parametersand easy axes of Ni2MnGa and (100) films.
austenite
martensite
(also applicableto PbTiO3)
September 6, 2002 Cornell University, Ithaca, NY
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
September 6, 2002 Cornell University, Ithaca, NY
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)
September 6, 2002 Cornell University, Ithaca, NY
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
September 6, 2002 Cornell University, Ithaca, NY
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
September 6, 2002 Cornell University, Ithaca, NY
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
September 6, 2002 Cornell University, Ithaca, NY
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)
September 6, 2002 Cornell University, Ithaca, NY
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
September 6, 2002 Cornell University, Ithaca, NY
100 m long bridges and cantilevers with different aspect ratios
100 m
Mask for free-standing Ni2MnGa films
J. Dong
September 6, 2002 Cornell University, Ithaca, NY
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
September 6, 2002 Cornell University, Ithaca, NY
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”
September 6, 2002 Cornell University, Ithaca, NY
In more recent films…
September 6, 2002 Cornell University, Ithaca, NY
“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)
September 6, 2002 Cornell University, Ithaca, NY
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
September 6, 2002 Cornell University, Ithaca, NY
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
September 6, 2002 Cornell University, Ithaca, NY
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
September 6, 2002 Cornell University, Ithaca, NY
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
September 6, 2002 Cornell University, Ithaca, NY
Bio-Molecular Epitaxy (BME)?