Transcript Deforming films of active materials: new concepts for

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
Richard Jun Cui, Grad student, UMN
Jianwei Dong, Grad student, UMN
Wayne Falk, Grad student, UMN
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
Ni
Mn
Ni2MnGa
N
S
September 6, 2002
Cornell University, Ithaca, NY
…based on
“bulk” theory:
o.k.?
Why martensitic materials?
Work output per volume per cycle of various actuator systems, Krulevitch et al.
Actuator Type
NiTi shape memory
Work/volume (J/m3)
2.5  107
Basic formula
se
6.0  106
Solid liquid phase change 4.7  106
(1/3)(Dv/v) k
Thermo-pneumatic
1.2  106
Fd/V
Thermal expansion
4.6  105
(1/2)(Ef+Es)(Da DT)
Electromagnetic
4.0  105
F d / V, F = -Ms A / 2m
2.8  104
Fd/V
1.6  103
T/ V
Electrostatic
1.8  105
3.4  103
F d / A gap, F = eV2A/2d2
Fd/V
Piezoelectric
7.0  102
1.2  105
1.8  102
T/ V
(d33 E)2 Ef /2
(d33 E)2 Ef /2
Muscle
Microbubble
1.8  104
3.4  102
F d / Vb
September 6, 2002
se
Comments
one time: s = 500MPa, e = 5%
thousands of cycles: s = 300MPa
k = bulk modulus = 2.2 GPa,
8% volume change
F = 20N, d = 50 mm, V = 4mm  4mm  50 mm
Ni on Si (ideal); s = substrate,
f = film, DT = 200 C
variable reluctance (ideal); V = gap
volume, Ms = 1 V sec/m2
variable reluctance (ideal); F = 0.28
mN, V = 100 mm  100 mm  250 mm
external field; T = torque = 0.185 mN m,
V = 400 mm  40 mm  7 mm
F = 100 volts, d = gap = 0.5 mm
comb drive, F = 0.2 mN (@60V)
V = 2 mm  20 mm  3000 mm, d = 2 mm
integrated force array; 120 volts
PZT; Ef = 60GPa, d33 = 500, E = 40KV/cm
ZnO; Ef = 160GPa, d33 = 12, E = 40KV/cm
s = 350 KPa, e = 10%
F = 0.9 mN, d = 71 mm
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)
September 6, 2002
SO(3)
SO(3)
SO(3)
Cornell University, Ithaca, NY
Energy wells
Minimizers...
3 x 3 matrices
U2
RU2
U1
I
Cu69
Al27.5
Ni3.5
a = 1.0619
 = 0.9178
 = 1.0230
Ni30.5
Ti49.5
Cu20.0
a = 1.0000
 = 0.9579
 = 1.0583
September 6, 2002
Cornell University, Ithaca, NY
Energy wells for various materials
Cu68 Zn15 Al17
U1, U2 , … , U12 =
a = 1.087,  = 0.9093,  = 1.010,
d = 0.0250
(Chakravorty and Wayman)
Ni50 Ti50
U1, U2 , … , U12 =
a = 1.0243,  = 0.9563, d = 0.058,
e = 0.0427)
(Knowles and Smith)
September 6, 2002
  0 0


0 a d 
0 d  


a 0 d 


0  0
d 0  


 0 0 


0 a d 
0 d  


a 0  d 


0  0 
d 0  


  0 0  

 
0  d  0
0 d a  0

 
 0 d  

 
0  0 0
d 0 a    d

 
a d 0 


d  0 
0 0  


a  d

d 
0 0 

 d 0 


d a 0
0 0  


a

d
e

a

e
d



e
e

0

0


d e  a d  e 
 

a e  d a  e 
e     e  e  
e d  a  e d 
 

 e  e  e 
e a   d  e a 
e e   e e 
 

a d  e a d 
d a    e d a 
0 0 

 d 
 d a 
0 d 

 0 
0 a 
  d

d a
0 0 

a  d  e 


d a e 
e e  


a  e  d 


e  e 
d e a 


 e e 


e a d 
e  d a 


0

0


structure of these
matrices: Ball/James
a  d e 


d a e 
e  e  


a e  d 


e   e 
d e a 


 e e 


e a  d 
e d a 


Cornell University, Ithaca, NY
Passage to the thin film limit using convergence
S
.x
h
~
h
Change variables:
~
x1 = x1
x2 = ~x2
x3 = (1 / h) x~ 3
~
y(x) = ~y(x)
September 6, 2002
S
x
.
1
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
x3
x2
x1
h
h b(x 1 ,x 2 )
y(x 1 ,x2 )
(A Cosserat theory)
h
S
September 6, 2002
Cornell University, Ithaca, NY
Predictions:
min
y, b
The interfacial energy constant  is << than a typical modulus that describes how
from its energy wells: put  = 0.
Zero energy deformations
grows away
e3
from the structure of the energy wells
e2
e1
compatibility plays
a role here
solve for b
One phase (say, austenite, i (x) = a)
This is a parameterization
of all “paper folding” deformations
September 6, 2002
b(x1, x2)
y(x1, x2)
Cornell University, Ithaca, NY
Two phases: austenite and a single
variant of martensite
min
y, b
The main effect of  is to smooth interfaces slightly.
e3
(y, 1| y, 2) =
e2
(e 1 | e 2 )
austenite
e1
(RU1 e 1 | RU1e 2 )
single variant of
martensite
(solve for b
so that these
states are on
the energy wells)
This is compatible if and only if
September 6, 2002
Cornell University, Ithaca, NY
?
Exact interfaces between austenite and variant 1 of
martensite in Ni50Ti50
Film normal
Austenite/martensite Interface lines
interface?
100
010
001
yes
yes
yes
(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)
(0.9358, 1.0473)
(0.9358, 1.0473)
(1.0840, 0.9663)
110
1-10
101
10-1
011
01-1
no
yes
yes
yes
yes
yes
(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)
(1.1066, 0.9320)
(0.9464, 1.0286)
(1.1005, 0.9574)
(0.9464, 1.0286)
(1.1005, 0.9574)
111
-111
1-11
11-1
no
yes
yes
yes
(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)
(1.1001, 0.9424)
(1.1001, 0.9424)
(1.0582, 0.9663)
September 6, 2002
In-plane principal
stretches
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 mm
September 6, 2002
Cornell University, Ithaca, NY
Bulk vs. film
In both cases
the depth is L
Energy lowered Energy of
by phase change transition layer
L3
L3
L
L
h L2
(1
September 6, 2002
>>
>>
h2 L
h/L)
h
L
h
Cornell University, Ithaca, NY
“Tunnel”
e3
e
n
Possible (according to theory) if
and
September 6, 2002
Cornell University, Ithaca, NY
“Tent”
e3
e2
e1
(y, 1| y, 2) =
(e 1 | e 2 )
austenite
variants of
martensite,
(RiUie1 | RiUie2),
i = 1, …, n
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
September 6, 2002
Cu68Zn15Al17 (approx. in Cu69Al27.5Ni3.5)
Cornell University, Ithaca, NY
(010)
“Tent” on CuAlNi foil
(100)
16 
Composition:
Cu-Al(wgt%13.95)-Ni(wgt%3.93)
10 Co
70 Co
DSC Measurement: ( ±2 Co)
Ms: 20
Af: 10
Mf: 10
Af: 50
Size of the Tent: (inch)
0.400 x 0.400 x 0.188
Film Thickness: 40 mm
90 Co
September 6, 2002
Orientation:
Surface Normal: [100]
Edge of the Tent: [0, 4.331,1]
Cornell University, Ithaca, NY
Martensitic pacman
Example drawn with (100) film and measured lattice parameters
of 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
martensitic
Temperature
free energy
strain
September 6, 2002
(giant) magnetostrictive
free energy
strain, magnetization
Cornell University, Ithaca, NY
Ferromagnetic shape memory materials
Three important temperatures:
Curie temperature of austenite:
second order
Curie temperature of martensite
Austenite-martensite transformation temperature: first 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
3.9000
Lattice Parameter a or c (A)
a (FCT)
3.8000
a0 (FCC)
3.7000
3.6000
a0 FCC
a
FCT
c
FCT
a/a0
c/a0
c (FCT)
3.5000
-40
-30
-20
-10
0
10
20
30
40
50
Average
3.7524
3.8375
3.5938
1.0224
0.9535
60
70
Temperature (C)
September 6, 2002
Cornell University, Ithaca, NY
Phases (Fe70Pd30)
100
Transformation Temperature C
80
60
FCC
40
20
0
FCT
-20
BCT
-40
-60
0.28
September 6, 2002
0.285
0.29
0.295
0.3
Composition at.%Pd
0.305
0.31
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
September 6, 2002
FCT Martensite -10 oC
FCT & BCT Martensite -60 oC
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 parameters
and easy axes of Ni2MnGa and (100) films.
austenite
martensite
(also applicable
to PbTiO3)
September 6, 2002
Cornell University, Ithaca, NY
Scale effects in thin film actuators

Euler-Bernoulli theory
M
s

 (s)
h
b
“film” modulus
Moment-curvature relation
 h
3
Can we have the cantilever bending, but with
stored energy proportional to h2 or even h?
September 6, 2002
membrane:
h
bending (nonlinear
Kirchhoff): h3
von Karman:
h5
Cornell University, Ithaca, NY
Ni2MnGa cantilever
H(t)
Energy stored is proportional to h
(because of the micromagnetic term
 m  h dx ) rather than h3

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.
Palmstrom/Dong/James
Adjust substrate lattice parameter
to match in-plane (a0) of desired
crystal structure
InP or GaAs (001)
Lattice matched
Austenite
InP
Martensite
September 6, 2002
Ga1-xInxAs
x
0.42
0.53
0.66
6.0
Martensite
5.9
InP
Austenite
5.8
5.7
GaAs
5.6
0
0.2
0.4
0.6
In concentration, x
Ga1-x In x As
0.8
1
InAs
Ga1-xInxAs
InAs
GaAs
Ni2MnGa
In-plane lattice parameter (Å)
Grow relaxed Ga1-xInxAs layers
6.1
Cornell University, Ithaca, NY
Interlayers for Ni2MnGa growth on GaAs
Ga
Ni
Mn
The L21 crystal
structure is both
NaCl-like and
CsCl-like
“ordered” CsCl
L21 structure
As
Sc,Er
Sc1-xErxAs NaCl structure
GaAs Zincblende
NiGa CsCl structure
Sc1-xErxAs and NiGa are good interlayers and template layers for Ni2MnGa growth on GaAs
September 6, 2002
Cornell University, Ithaca, NY
Cross-section TEM Study:
Ni2MnGa(900 Å) / Sc0.3Er0.7As(17 Å) / GaAs
Pseudomorphic growth of Ni2MnGa films: (a = 5.65 Å, c = 6.18 Å)
Spot splitting
Ga
Ni
Mn
As
Ni2MnGa
Sc,Er
Sc0.3Er0.7As
GaAs
Ga
As
September 6, 2002
Palmstrom/Dong
Cornell University, Ithaca, NY
Magnetic Characterization: SQUID
Ni MnGa
measurements
GaAs
2
Moment vs. Temperature
In-plane Hysteresis Loop at 10 K
1000
Moment ( memu)
Moment ( memu)
700
500
Cool down without
300 field, then warm in a
field of 1000 Oe
100
0
50
100
150
200
250
Temperature (K)
Tc ~ 340 K
300
350
500
0
-500
-1000
-2000
-1000
0
1000
2000
Field (Oe)
Ms ~ 450 emu/cm3, Hc ~ 230 Oe
No phase transformation in unreleased films!
September 6, 2002
Cornell University, Ithaca, NY
Patterning and processing of free
standing films
Ar/Cl Plasma
2
Photoresist
Ni2MnGa
GaAs
Photolithography of film side
After RIE
Backside IR alignment
and photolithography
Free-standing Cantilever
September 6, 2002
RIE of Ni2MnGa film
After selective
chemical etching
400 mm
Cornell University, Ithaca, NY
Mask for free-standing Ni2MnGa films
100 mm long
bridges and
cantilevers with
different aspect
ratios
100 mm
September 6, 2002
J. Dong
Cornell University, Ithaca, NY
Magnetic Characterization: SQUID Measurements on
Partially Released Ni2MnGa Films
80
Cool down without field,
then warm/cool/warm
with 100 Oe field applied
in-plane
Moment (memu)
60
2 & 3. Cool/Warm
overlapped
Free-standing films
40
After the film is partially
released from the
substrate, there is a
phase transformation
~ 300 K
20
1. Initial warm up
0
0
50
September 6, 2002
100 150 200 250
Temperature (K)
300
350
Cornell University, Ithaca, NY
Phase Transformation
Cyclic phase transformation observed
in a 900Å thick Ni2MnGa free standing
film using polarized light
(a) RT
(h) 60C
(b)
100C
(g)
100C
(c)
120C
(f)
~120C
(d)
150C
(e)
<150C
Free standing
“hip roof”
September 6, 2002
Cornell University, Ithaca, NY
In more recent films…
September 6, 2002
Cornell University, Ithaca, NY
“Tent”
e3
e2
e1
(y, 1| y, 2) =
(e 1 | e 2 )
austenite
variants of
martensite,
(RUe |
RUe),
i = 1, …, n
Possible if
and
e3 is an n-fold (n = 3, 4, 6) axis of symmetry of austenite
Quite restrictive but satisfied for (100) films
Ni30.5Ti49.5Cu20.0
Cu68Zn15Al17
…but
(approx. in Cu69Al27.5Ni3.5)
September 6, 2002
not satisfied in Ni2MnGa)
Cornell University, Ithaca, NY
Interpretation
Hip roof
 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
Martensite variant 1
Martensite variant 2
P-phase
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 attacking
a bacterium: phage at the right
is injecting its DNA
Falk and James
Wakefield, Julie (2000) The return of the phage. Smithsonian 31:42-6
• How can it generate forces sufficient to penetrate the cell wall?
• Man made analogs?
September 6, 2002
Cornell University, Ithaca, NY
Martensitic transformation and thin film
interfaces
This transformation strain satisfies the
conditions, given above, for “thin film”
interfaces
(Olson and Hartman)
Force generated upon
contraction: Falk/James
September 6, 2002
Cornell University, Ithaca, NY
Bio-Molecular Epitaxy (BME)?
September 6, 2002
Cornell University, Ithaca, NY