Pradeep Sharma

Department of Mechanical Engineering

(Joint) Department of Physics

University of Houston

Electromechanical Coupling in Hard Materials: Energy Scavenging and

Storage

What is piezoelectricity? What is flexoelectricity? Nanoscale effects….

Introduction

Materials design

Size-effects

Possibility of piezoelectric materials without piezoelectric materials ! Enhanced piezoelectricity in nanostructures….

Indentation experiments and theory

Energy harvesting and storage

Enhancements at the nanoscale, the origins of the dead-layer effect in nanocapacitors

Overview

New international collaboration models

What is piezoelectricity?

Coupling between electrical and mechanical behavior of a material

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

-

--

-

+

++

+

+

Polarization = 0

C

-

--

-

+

++

+

+

Force

C

Undeformed State

Force

Deformed State

Center of positive and negative charges coincide in the undeformed state. Plus, the centroid is a center of symmetry.

Absence of piezoelectricity---centrosymmetric crystals*

*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

A uniform strain causes polarization and vice-versa

i ijk jkP d

Odd order tensor cannot be sustained by centrosymmetric

crystal—hence piezoelectricity is restricted to non-

centrosymmetric crystals

-

-

++

+

.C

-

-

++

+

.C+

--

++

- -

-

+

+

- PP

A

B

A

B

Working definition of piezoelectricity

0,

jki ijk jk ijkl

lfor non piezo materials

P dx

Cl-

Na+

Cl-

Cl-

Cl- -P

Center of negative charge

Cl-

Na+

Cl-

Cl-

Cl- -P

Center of negative charge

Cl-

Na+

Cl-

Cl-

Cl- -

Cl-

Na+

Cl-

Cl-

Cl- -

Na+

Cl-

Cl-

Cl- --P

Center of negative charge

In principle, flexoelectric coefficients are non-zero for all dielectrics (although may be negligibly small in some

cases)—experimentally verified for many materials!

Beyond uniform strain and polarization----flexoelectricity

Cross L. Eric, Journal of Materials Science, 41, 53-63, 2006

10NaCl

6BST

6PMN

6PZT

2.84 10

100 10

5 10

2 10

C

m

C

m

C

m

C

m

9Graphene 1.128 10

C

m

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).

Graphene, BaTiO3 and others (non-ferroelectric state)

Dumitrica et. al., 2002

Direction of Strain Gradient

Apparent piezoelectric behavior at nanoscale without using piezoelectric materials

a~x a

Uniform Stress

*Cross and co-workers; N. Sharma, R. Maranganti and P. Sharma, J. Mech. Phy. Solids, 2007

High elastic and dielectric contrast

Small size

Non-centrosymmetric shape

Optimum volume fraction

Apparent piezoelectric behavior at nanoscale without using piezoelectric materials

Ensure that the defective structure is dielectric through electronic structure calculations

Coaxing Graphene to be piezoelectric

0.398 C/m2

Coaxing Graphene to be piezoelectric

Roughly 50 % of ZnO and 110 % of Boron Nitride Nanotubes

Circular holes

• Thinnest piezoelectric material---energy harvesting for stretchable electronics, nearly invisible sensors, artificial muscles

• Bio-compatible membranes for artificial ears

Volume fraction10

Average polarization

%

Hole Size = 3nm

σxxσxx

Theoretical calculations for BTO

A

B

AAC

A

A

B

B

C

Manufacturable Superlattices

• 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

Intrinsically piezoelectric materials

Theoretical and atomistic analysis of a paradigmatical nanostructure: cantilever

beam

2eff fd d k

h

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)

Sharma group----University of Houston, Tahir Cagin---Texas A&M, student from Tunisia

BaTiO3 both phases: Enhanced “apparent” piezoelectricity..

* M. Majdoub , P. Sharma, T. Cagin, Phy. Rev., 2008 * M. Majdoub , P. Sharma, T. Cagin, Phy. Rev., Erratum, 2009

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

Energy HarvestingJemai, Najar, Chafra---Tunisia, Ounaies---Penn State

Energy HarvestingJemai, Najar, Chafra---Tunisia, Ounaies---Penn State

Energy Harvesting System

Homogenized AFC patch

Simulation of the harvested electrical power

• Investigation of the energy harvester dynamic behavior of the beam with AFC patch: Harvested power, voltage and current.

Speculation: Indentation size effect?

In principle, the flexoelectric size-effect should be observable in indentation experiments.

Sharma group—University of Houston, Sami El-Borgi--Tunisia

Theoretical Results: A regular piezoelectric material

2 01 22 aCaC wP

1 1

2 2/

P as C s a C

w

[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)1 rC E

Theoretical results: Effect of flexoelectricity on indentation

132 2

size effec

Aa

t

Ce Aa

P a

as C

w

We derived analytical solution of the indentation problem incorporating anisotropy,

piezoelectricity and flexoelectricity----the solution fills 14 pages!

Theoretical results: Effect of flexoelectricity on indentation

132

/22

/

size effect

AaCP

s a a e aw

ACa

We derived analytical solution of the indentation problem incorporating anisotropy,

piezoelectricity and flexoelectricity----the solution fills 14 pages!

Load Application (Coil & Magnet)

Support Springs

Displacement Sensor(Capacitance Gauge)

IndenterSample

Motorized Stage

Berkovich indent on BTO surfaceLoad: 8mN; Depth into surface: 200nm

Nanoindentation - Schematic

In parallel, we conducted experiments with varying indentation size…..single crystal BaTiO3

Indentation experiments (collaboration with Ken White)

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

1

2/s a C

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.

1

2/s a C

Nanocapacitors

Energy storage

Nanocapacitors

Cd

V2

V1

V2 - V1

V(x)

+++++

-----

Energy storageMiniaturization of

electronics

Take 2.7 nm SrTiO3 capacitor……

We can expect a capacitance of 1600 fF/m-2

Reality? ----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…..

1 1 1 1

eff i o iC C C C

The dead-layer bottleneck

Stengel and Spaldin, Nature Materials, 2006

The first, “first principles” calculations clarifying the dead-layer mechanism: Stengel and Spaldin (Nature, 2006; Physical Review B,

2005); Rabe (Nature Nanotechnology, 2006)

State of the art--ab initio calculations [Stengel-Spaldin, 2006]

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?

What is the real cause of the dead-layer?

M. S. Majdoub, R. Maranganti, and P. Sharma, Physical Review B, 2009

• 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)

International Joint Collaborative Program

Participants

• Pradeep Sharma (University of Houston, USA)

• Tahir Cagin (Texas A&M University, USA)

• Zoubeida Ounaies (Penn State, USA)

• Sami El-Borgi (EPT, Tunisia)

• Fehmi Najar (EPT, Tunisia)

• Moez Chafra (EPT, Tunisia)

• Bin Zineb Tarak (Universite de Lorraine, France)

• Students: Mohamed Sabri Madoub, Mohamed

Gharbi, Nikhil Sharma, Raouf Mbarki, Swapnil

Chandratre