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

1
Deforming films of active materials new concepts
for producing motion at small scales (using
applied fields)
Richard D. James University of Minnesota james_at_umn
.edu
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
2
Questions

• How does one produce motion at small scales?
• What concepts are suggested by theory?

3
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

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Martensitic phase transformation
Ni2MnGa
5
Why martensitic materials?
based on bulk theory o.k.?
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
s ? e
one time s 500MPa, e 5
6.0 ? 106

thousands of cycles s 300MPa Solid liquid
phase change 4.7 ? 106
(1/3)(Dv/v) k k bulk modulus
2.2 GPa,

8 volume
change Thermo-pneumatic 1.2 ? 106
F d / V F
20N, d 50 mm, V 4mm ? 4mm ? 50 mm Thermal
expansion 4.6 ? 105
(1/2)(EfEs)(Da DT) Ni on Si (ideal) s
substrate,

f film, DT 200
C Electromagnetic 4.0 ? 105 F d / V, F
-Ms A / 2m variable reluctance (ideal) V
gap

volume, Ms 1 V sec/m2
2.8 ? 104
F d / V variable
reluctance (ideal) F 0.28


mN, V 100 mm ? 100 mm ? 250 mm
1.6 ? 103 T/ V
external field T torque 0.185 mN?
m, V 400 mm ? 40 mm ? 7
mm Electrostatic 1.8 ? 105
F d / A gap, F eV2A/2d2 F 100 volts, d
gap 0.5 mm
3.4 ? 103 F d / V
comb drive, F 0.2 mN (_at_60V)


V 2 mm ? 20 mm ? 3000 mm, d 2 mm
7.0 ? 102 T/ V
integrated force array 120
volts Piezoelectric 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 s ? e
s 350 KPa, e 10 Microbubble
3.4 ? 102
F d / Vb F 0.9 mN, d
71 mm
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Martensitic films
What theory?
vs.
This talk single crystal films
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Bulk theory of martensite
is frame indifferent
is minimized on energy wells
SO(3)
SO(3)
SO(3)
SO(3)
SO(3)
SO(3)
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Energy wells
Minimizers...
Cu69 Al27.5 Ni3.5 ? 1.0619 ? 0.9178 ?
1.0230
Ni30.5 Ti49.5 Cu20.0 ? 1.0000 ? 0.9579 ?
1.0583
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Energy wells for various materials
Cu68 Zn15 Al17
U1, U2 , , U12
? 1.087, ? 0.9093, ? 1.010, ?
0.0250 (Chakravorty and Wayman)
structure of these matrices Ball/James
Ni50 Ti50
U1, U2 , , U12
? 1.0243, ? 0.9563, ? 0.058, ?
0.0427) (Knowles and Smith)
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Passage to the thin film limit using ?-convergence
S
.
h

x
Change variables

x1 x1 x2 x2 x3 (1 / h) x3

S

.


y(x) y(x)
x
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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.

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Derivation of thin film theory using ?-convergence
h b(x ,x )
y(x ,x )
(A Cosserat theory)
1
2
h
S
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Predictions
min y, b
The interfacial energy constant ? is ltlt than a
typical modulus that describes how grows
away from its energy wells put ? 0.
Zero energy deformations
from the structure of the energy wells
compatibility plays a role here
solve for b
One phase (say, austenite, i (x) a)
b(x1, x2)
This is a parameterization of all paper folding
deformations
y(x1, x2)
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Two phases austenite and a single variant of
martensite
The main effect of ? is to smooth interfaces
slightly.
(solve for b so that these states are on the
energy wells)
single variant of martensite
austenite
This is compatible if and only if
15
?
16
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
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Bulk vs. film
In both cases the depth is L
Energy lowered by phase change
Energy of transition layer
L3 L3 h L2 gtgt
h2 L (1 gtgt h/L)
L
L
L
h
h
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Tunnel
e3
e
n
Possible (according to theory) if
and
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Tent
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 Cu68Zn15Al17
(approx. in Cu69Al27.5Ni3.5)
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Tent on CuAlNi foil
(010)
16 ?
(100)
Composition Cu-Al(wgt13.95)-Ni(wgt3.93) 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 ?m Orientation Surfac
e Normal 100 Edge of the Tent 0, 4.331,1
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Martensitic pacman
Example drawn with (100) film and measured
lattice parameters of Ni50Ti50
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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

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Martensitic vs. magnetostrictive materials
martensitic
(giant) magnetostrictive
free energy
free energy
Temperature
strain, magnetization
strain
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Ferromagnetic shape memory materials
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
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Lattice parameters vs. temperature (Fe70Pd30)
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Phases (Fe70Pd30)
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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
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Austenite/martensite interface (Fe70Pd30)
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Strain vs. field Fe3Pd
-1 MPa and 10oC
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Strain vs. field in Ni2MnGa
H
30 times the strain of giant magnetostrictive
materials
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Other ideas...
These are pictured using the measured lattice
parameters and easy axes of Ni2MnGa and (100)
films.
austenite
martensite
(also applicable to PbTiO3)
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Scale effects in thin film actuators

• Euler-Bernoulli theory
• Moment-curvature relation

M
? (s)
h
s
b
film modulus
Can we have the cantilever bending, but with
stored energy proportional to h2 or even h?
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Ni2MnGa cantilever
H(t)
picture drawn with measured lattice parameters of
Ni2MnGa
(Electromagnetic force on the cantilever is zero
it is driven by configurational force)
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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 Grow
relaxed Ga1-xInxAs layers
Ni2MnGa
Ga1-xInxAs
InP or GaAs (001)
Ga1-xInxAs Lattice matched x Austenite 0.42 InP
0.53 Martensite 0.66
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Interlayers for Ni2MnGa growth on GaAs
Ga
Ni
The L21 crystal structure is both NaCl-like and
CsCl-like
Mn
L21 structure
ordered CsCl
As
Sc,Er
Sc1-xErxAs NaCl structure
NiGa CsCl structure
GaAs Zincblende
Sc1-xErxAs and NiGa are good interlayers and
template layers for Ni2MnGa growth on GaAs
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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
112lt111gt
As
Sc,Er
Ga
As
Palmstrom/Dong
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Magnetic Characterization SQUID measurements
Ni2MnGa
GaAs
Moment vs. Temperature
In-plane Hysteresis Loop at 10 K
Cool down without field, then warm in a field of
1000 Oe
Tc 340 K
Ms 450 emu/cm3, Hc 230 Oe
No phase transformation in unreleased films!
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Patterning and processing of free standing films
Ni2MnGa
400 ?m
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Mask for free-standing Ni2MnGa films
100 ?m long bridges and cantilevers with
different aspect ratios
J. Dong
100 ?m
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Magnetic Characterization SQUID Measurements on
Partially Released Ni2MnGa Films
Cool down without field, then warm/cool/warm with
100 Oe field applied in-plane
2 3. Cool/Warm overlapped
After the film is partially released from the
substrate, there is a phase transformation 300
K
1. Initial warm up
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Phase Transformation
Cyclic phase transformation observed in a 900Å
thick Ni2MnGa free standing film using polarized
light
Free standing hip roof
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In more recent films
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Tent
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
(approx. in Cu69Al27.5Ni3.5)
but not satisfied in Ni2MnGa)
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Interpretation

• 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

Hip roof
Martensite variant 1
Martensite variant 2
P-phase
Cooling
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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

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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 3142-6

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

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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
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Bio-Molecular Epitaxy (BME)?