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Richard D. James University of Minnesota james@umn

Deforming films of active materials: new concepts for producing motion at small scales ( using applied fields ). Richard D. James University of Minnesota james@umn.edu. COLLABORATIONS, POSTDOCS, STUDENTS. Chris Palmstrom, UMN Kaushik Bhattacharya, Caltech Robert Tickle, Postdoc, UMN

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Richard D. James University of Minnesota james@umn

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  1. Deforming films ofactive materials: new concepts for producing motion at small scales (using applied fields) Richard D. James University of Minnesota james@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 Cornell University, Ithaca, NY

  2. Questions • How does one produce motion at small scales? • What concepts are suggested by theory? Cornell University, Ithaca, NY

  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 Cornell University, Ithaca, NY

  4. Ga Ni Mn N S Martensitic phase transformation Ni2MnGa Cornell University, Ithaca, NY

  5. …based on “bulk” theory: o.k.? Why martensitic materials? Work output per volume per cycle of various actuator systems, Krulevitch et al. Actuator TypeWork/volume (J/m3)Basic formulaComments NiTi shape memory2.5  107seone time:s = 500MPa, e = 5% 6.0  106thousands 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)(Ef+Es)(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 (@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 Muscle1.8  104ses = 350 KPa, e = 10% Microbubble 3.4  102 F d / Vb F = 0.9 mN, d = 71 mm Cornell University, Ithaca, NY

  6. Martensitic films What theory? vs. This talk: single crystal films Cornell University, Ithaca, NY

  7. Bulk theory of martensite is frame indifferent: is minimized on “energy wells”: SO(3) SO(3) SO(3) SO(3) SO(3) SO(3) Cornell University, Ithaca, NY

  8. U 3 x 3 matrices 1 I U 2 RU 2 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 Cornell University, Ithaca, NY

  9. 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) Cornell University, Ithaca, NY

  10. h  1 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 Cornell University, Ithaca, NY

  11. 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. Cornell University, Ithaca, NY

  12. h x 1 x 3 x 2 1 2 Derivation of thin film theory using -convergence h b(x ,x ) y(x ,x ) (A Cosserat theory) 1 2 h S Cornell University, Ithaca, NY

  13. e3 e2 e1 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 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) Cornell University, Ithaca, NY

  14. min y,b e 3 e 2 (RU e | RU e ) (e | e ) (y, | y, ) = e 1 1 2 1 2 1 1 1 2 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 Cornell University, Ithaca, NY

  15. ? Cornell University, Ithaca, NY

  16. *unless, by changing composition, we tune the lattice parameters to satisfy very special conditions …but, in bulk, we almost* never see austenite against a single variant of martensite 10 m Cornell University, Ithaca, NY

  17. Bulk vs. film In both cases the depth is L Energy lowered by phase change Energy of transition layer L3 L3 h L2 >> h2 L (1 >> h/L) L L L h h Cornell University, Ithaca, NY

  18. “Tunnel” e3 e n Possible (according to theory) if and Cornell University, Ithaca, NY

  19. e3 austenite e2 (y, | y, ) = (e | e ) e1 1 2 1 2 “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) Cornell University, Ithaca, NY

  20. (010) 90 Co 70 Co 10 Co “Tent” on CuAlNi foil 16 (100) Composition: Cu-Al(wgt%13.95)-Ni(wgt%3.93) 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: Surface Normal: [100] Edge of the Tent: [0, 4.331,1] Cornell University, Ithaca, NY

  21. Martensitic pacman Example drawn with (100) film and measured lattice parameters of Ni50Ti50 Cornell University, Ithaca, NY

  22. 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 Cornell University, Ithaca, NY

  23. Martensitic vs. magnetostrictive materials martensitic (giant) magnetostrictive free energy free energy Temperature strain, magnetization strain Cornell University, Ithaca, NY

  24. Three important temperatures: Curie temperature of austenite: Curie temperature of martensite Austenite-martensite transformation temperature: first order second order 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 Cornell University, Ithaca, NY

  25. a (FCT) a0 (FCC) c (FCT) Lattice parameters vs. temperature (Fe70Pd30) Cornell University, Ithaca, NY

  26. Phases (Fe70Pd30) Cornell University, Ithaca, NY

  27. 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 Cornell University, Ithaca, NY

  28. Austenite/martensite interface (Fe70Pd30) Cornell University, Ithaca, NY

  29. Strain vs. field: Fe3Pd -1 MPa and 10oC Cornell University, Ithaca, NY

  30. (010) (100) Strain vs. field in Ni2MnGa H 30 times the strain of giant magnetostrictive materials Cornell University, Ithaca, NY

  31. Other ideas... These are pictured using the measured lattice parameters and easy axes of Ni2MnGa and (100) films. austenite martensite (also applicable to PbTiO3) Cornell University, Ithaca, NY

  32. membrane: h bending (nonlinear Kirchhoff): h3 von Karman: h5  h 3 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? Cornell University, Ithaca, NY

  33. Energy stored is proportional to h (because of the micromagnetic term ) rather than h3 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) Cornell University, Ithaca, NY

  34. 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 Cornell University, Ithaca, NY

  35. 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 GaAs Zincblende NiGa CsCl structure Sc1-xErxAs and NiGa are good interlayers and template layers for Ni2MnGa growth on GaAs Cornell University, Ithaca, NY

  36. Ga Ni Mn Ni2MnGa Sc0.3Er0.7As GaAs 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 {112}<111> As Sc,Er Ga As Cornell University, Ithaca, NY Palmstrom/Dong

  37. 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! Cornell University, Ithaca, NY

  38. Ar/Cl2 Plasma Photoresist GaAs Photolithography of film side RIE of Ni2MnGa film After selective chemical etching After RIE Backside IR alignment and photolithography Free-standing Cantilever Patterning and processing of free standing films Ni2MnGa 400 m Cornell University, Ithaca, NY

  39. Mask for free-standing Ni2MnGa films 100 m long bridges and cantilevers with different aspect ratios J. Dong 100 m Cornell University, Ithaca, NY

  40. Free-standing films 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 Cornell University, Ithaca, NY

  41. (b) 100C (a) RT (c) 120C (d) 150C (e) <150C (f) ~120C (g) 100C (h) 60C Phase Transformation Cyclic phase transformation observed in a 900Å thick Ni2MnGa free standing film using polarized light Free standing “hip roof” Cornell University, Ithaca, NY

  42. In more recent films… Cornell University, Ithaca, NY

  43. e3 austenite e2 (y, | y, ) = (e | e ) e1 1 2 1 2 “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) Cornell University, Ithaca, NY

  44. 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 Cornell University, Ithaca, NY Cooling

  45. 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 Cornell University, Ithaca, NY

  46. 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? Cornell University, Ithaca, NY

  47. 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 Cornell University, Ithaca, NY

  48. Bio-Molecular Epitaxy (BME)? Cornell University, Ithaca, NY

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