Pradeep Sharma Department of Mechanical Engineering (Joint) Department of Physics

1. Electromechanical Coupling in Hard Materials: Energy Scavenging and Storage Pradeep Sharma Department of Mechanical Engineering (Joint) Department of Physics University of Houston

2. Overview What is piezoelectricity? What is flexoelectricity? Nanoscale effects…. Introduction Possibility of piezoelectric materials without piezoelectric materials ! Enhanced piezoelectricity in nanostructures…. Materials design Size-effects Indentation experiments and theory Energy harvesting and storage Enhancements at the nanoscale, the origins of the dead-layer effect in nanocapacitors New international collaboration models

3. What is piezoelectricity? Coupling between electrical and mechanical behavior of a material

4. Applications • Consumer items like lighters…shoes….tennis rackets… • Powering soldiers…. harvesting energy from pedestrians….sonars • Atomic force microscopy; precise control over mechanical motion • Robotic arms and artificial muscles

5. Force + - + + - + - + - - + - C C + + Polarization = 0 + + - - Absence of piezoelectricity---centrosymmetric crystals* Force Deformed State Undeformed State Center of positive and negative charges coincide in the undeformed state. Plus, the centroid is a center of symmetry. *This cartoon is at odds with the modern theory of polarization based on the Berry-phase concept. Nevertheless, it is used here for ease of illustration

6. + . . C C Working definition of piezoelectricity A A uniform strain causes polarization and vice-versa A - - - + + + + + + + P P - - - - - - - + + B + B Odd order tensor cannot be sustained by centrosymmetric crystal—hence piezoelectricity is restricted to non- centrosymmetric crystals

7. Beyond uniform strain and polarization----flexoelectricity In principle, flexoelectric coefficients are non-zero for all dielectrics (although may be negligibly small in some cases)—experimentally verified for many materials!

8. Graphene, BaTiO3 and others (non-ferroelectric state) Dumitrica et. al., 2002 Cross and co-workers: The magnitude of the flexoelectric coefficient is of the order of 10-6 C/m which is much larger than the generally accepted lower bound of (10-9 – 10-11 C/m). Cross L. Eric, Journal of Materials Science, 41, 53-63, 2006

9. a Apparent piezoelectric behavior at nanoscale without using piezoelectric materials Uniform Stress Direction of Strain Gradient *Cross and co-workers; N. Sharma, R. Maranganti and P. Sharma, J. Mech. Phy. Solids, 2007

10. Apparent piezoelectric behavior at nanoscale without using piezoelectric materials • High elastic and dielectric contrast • Small size • Non-centrosymmetric shape • Optimum volume fraction

11. Coaxing Graphene to be piezoelectric 1 Ensure that the defective structure is dielectric through electronic structure calculations 2 3

12. Coaxing Graphene to be piezoelectric Circular holes 0.398 C/m2 Roughly 50 % of ZnO and 110 % of Boron Nitride Nanotubes • Thinnest piezoelectric material---energy harvesting for stretchable electronics, nearly invisible sensors, artificial muscles • Bio-compatible membranes for artificial ears

13. Average polarization Volume fraction 0 1

14. Hole Size = 3nm σxx σxx Theoretical calculations for BTO %

15. C A A B B C A A A B Manufacturable Superlattices

16. Intrinsically piezoelectric materials • Experiments indicate that flexoelectric coefficients can be almost 1000 - 10,000 time larger in ferroelectrics compared to ordinary dielectrics • This suggests the possibility of an additive effect • Conversely, possible to design structures that eliminate existing piezoelectricity or tailor it as needed • Need further physical insights from both theory and atomistics….complications---anisotropy, potentials

17. Theoretical and atomistic analysis of a paradigmatical nanostructure: cantilever beam

18. Sharma group----University of Houston, Tahir Cagin---Texas A&M, student from Tunisia Atomistic Study of BaTiO3 in cubic and tetragonal phase • Conventional (core-shell) potentials are inadequate…..use fixed charges, cannot re-adjust to match changing electrostatic environment… • We employed a quantum mechanically derived polarizable force field for BaTiO3 (--currently development is in progress for SrTiO3). • Core has a Gaussian distributed fixed charge while the shell has Gaussian distributed variable charge dynamically updated by self-consistent charge equilibration method • Shell charges can move w.r.t core, transfer to shells of other atoms; accurate description of polarization • Non-bonded terms (Pauli repulsion, Van der Waals forces) are accounted for via 3-term Morse potential • Inputs obtained entirely from first principles calculations and validated against experimental data • Well tested…… • Drawback: custom code; non-parallelized; while much faster than first principles, system size is restricted to roughly 1000 atoms (self-consistent charge equilibration is quite expensive)

19. BaTiO3 both phases: Enhanced “apparent” piezoelectricity.. * M. Majdoub , P. Sharma, T. Cagin, Phy. Rev., Erratum, 2009 * M. Majdoub , P. Sharma, T. Cagin, Phy. Rev., 2008

20. Energy Harvesting • Piezoelectric nanostructures can dramatically enhance energy harvesting* • For PbTiO3 cantilever beams, our results indicate that the total harvested power peak value can increase by 100% at the nano-size (under short circuit conditions) and nearly a 200% increase may be achieved for specifically tailored cross-section shapes. * M. Majdoub , P. Sharma, T. Cagin, Phy. Rev., 2008

21. Energy Harvesting Jemai, Najar, Chafra---Tunisia, Ounaies---Penn State

22. Energy Harvesting Jemai, Najar, Chafra---Tunisia, Ounaies---Penn State Homogenized AFC patch Energy Harvesting System

23. Simulation of the harvested electrical power Investigation of the energy harvester dynamic behavior of the beam with AFC patch: Harvested power, voltage and current.

24. Speculation: Indentation size effect? Sharma group—University of Houston, Sami El-Borgi--Tunisia In principle, the flexoelectric size-effect should be observable in indentation experiments.

25. Theoretical Results: A regular piezoelectric material [Karapetian, Kachanov, Kalinin and co-workers] Purely mechanical loading on an anisotropic piezoelectric material For example, in the isotropic purely elastic half-space case (Oliver, Pharr)

26. Theoretical results: Effect of flexoelectricity on indentation We derived analytical solution of the indentation problem incorporating anisotropy, piezoelectricity and flexoelectricity----the solution fills 14 pages!

27. Theoretical results: Effect of flexoelectricity on indentation We derived analytical solution of the indentation problem incorporating anisotropy, piezoelectricity and flexoelectricity----the solution fills 14 pages!

28. Indentation experiments (collaboration with Ken White) In parallel, we conducted experiments with varying indentation size…..single crystal BaTiO3 Nanoindentation - Schematic Berkovich indent on BTO surface Load: 8mN; Depth into surface: 200nm

29. Contact stiffness vs contact radius for BaTiO3 • Indentation experiments indicate a large size effect (see the star-data points). For example, compared to the size-independent behavior (red line), around 10 nm, there is a doubling of contact stiffness. • Incorporation of flexoelectricity correctly captures the size-effect • Another possible source of size-effect dislocation activity---role of domains unlikely

30. Contact stiffness vs contact radius for Quartz • No size-effect is observed for Quartz! • This observation strengthens our argument that flexoelectricity is the cause of indentation size-effect since Quartz has very small flexoelectricity constants (in contrast to BaTiO3) while the dislocation nucleation behavior between the two is not expected to be dramatically different.

31. Nanocapacitors Energy storage

32. Nanocapacitors Energy storage Miniaturization of electronics V2 + + + + + - - - - - V(x) V1 V2 - V1

33. The dead-layer bottleneck Take 2.7 nm SrTiO3 capacitor……We can expect a capacitance of 1600 fF/m-2Reality? ----258 fF/m-2 !! The reason is ascribed to the so-called dead-layer effect Mechanism?---growth induced defects, incomplete electrode screening, strain, grain boundaries, poor interface….. Stengel and Spaldin, Nature Materials, 2006

34. State of the art--ab initio calculations [Stengel-Spaldin, 2006] The first, “first principles” calculations clarifying the dead-layer mechanism: Stengel and Spaldin (Nature, 2006; Physical Review B, 2005); Rabe (Nature Nanotechnology, 2006)

35. What is the real cause of the dead-layer? Electric field penetration in real metals triggers a secondary mechanism--flexoelectricity • Even though flexoelectricity will not occur without apriori presence of field penetration; it becomes quite important • Why is this “hair-splitting” important? M. S. Majdoub, R. Maranganti, and P. Sharma, Physical Review B, 2009

36. International Joint Collaborative Program • New graduate degree models: Tunisian M.S. student is co-advised by collaborator from Tunisia and faculty from University of Houston. The student spends 4-8 months in the US and the remainder part of the time Tunisia. • The student defends his/her M.S. thesis in Tunisia. All PI’s jointly publish the results • The student returns to US to pursue PhD • Two students have successfully gone through this and are now pursuing their PhD at University of Houston. • Four more students are expected to join UH in February/March. a) b) c) d) e)) f) g)

37. Participants • Pradeep Sharma (University of Houston, USA) • TahirCagin (Texas A&M University, USA) • ZoubeidaOunaies (Penn State, USA) • Sami El-Borgi (EPT, Tunisia) • FehmiNajar (EPT, Tunisia) • MoezChafra (EPT, Tunisia) • Bin ZinebTarak (Universite de Lorraine, France) • Students: Mohamed SabriMadoub, Mohamed Gharbi, Nikhil Sharma, RaoufMbarki, SwapnilChandratre