Electromechanical Coupling in Hard
Materials: Energy Scavenging and
Storage
Pradeep Sharma
Department of Mechanical Engineering
(Joint) Department of Physics
University of Houston
Overview
Introduction
What is piezoelectricity? What is flexoelectricity?
Nanoscale effects….
Materials design
Possibility of piezoelectric materials without
piezoelectric
materials
!
Enhanced
piezoelectricity in nanostructures….
Size-effects
Energy harvesting
and storage
New international
collaboration models
Indentation experiments and theory
Enhancements at the nanoscale, the origins of
the dead-layer effect in nanocapacitors
What is piezoelectricity?
Coupling between electrical and mechanical behavior of a
material
Applications
• Consumer
items
lighters…shoes….tennis
rackets…
like
• Powering
soldiers….
harvesting
energy
from
pedestrians….sonars
• Atomic
force
microscopy;
precise
control
over
mechanical motion
• Robotic arms
muscles
and
artificial
Absence of piezoelectricity--centrosymmetric crystals*
+
Force
-
+
+
-
C+
-
-
+
-
+
+
Polarization = 0
Undeformed State
C
-
+
+
-
-
+
Force
Deformed 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
Working definition of piezoelectricity
A uniform strain causes polarization and vice-versa
A
-
Pi  dijk  jk
A
-
+
+
+
.
+
C
.
C
-
-
-
-
+
+
+
P
P
B
B
Odd order tensor cannot be sustained by centrosymmetric
crystal—hence piezoelectricity is restricted to noncentrosymmetric crystals
Beyond uniform strain and polarization---flexoelectricity
In principle, flexoelectric
 jk coefficients
are non-zero for
Pi 
d ijk  jk
 ijkl
all dielectrics (although may
xl
be negligibly small in some
0, for non  piezo materials
cases)—experimentally
verified for many materials!
Cl-
Na+
Cl-
P
-
Cl-
Center of
negative
charge
Cl-
Graphene, BaTiO3 and others (nonferroelectric state)
Dumitrica et. al., 2002
C

m
Graphene  1.128 109 
 
Cross and co-workers: The
 NaCl  2.84  1010  
m
magnitude of the flexoelectric
coefficient is of the order of 10-6 BST  100 106  C 
m
C/m which is much larger than
C 
the generally accepted lower
 PMN  5  106  
m
bound of (10-9 – 10-11 C/m).
C
C 
 PZT  2  106  
m
Cross L. Eric, Journal of Materials
Science, 41, 53-63, 2006
Apparent piezoelectric behavior at nanoscale
without using piezoelectric materials
Uniform Stress
  
~
x
a
a
Direction
of Strain
Gradient
*Cross
and co-workers; N. Sharma, R. Maranganti and P. Sharma, J. Mech. Phy. Solids, 2007
Apparent piezoelectric behavior at nanoscale
without using piezoelectric materials
High elastic and dielectric contrast
Small size
Non-centrosymmetric shape
Optimum volume fraction
Coaxing Graphene to be piezoelectric
Ensure that the defective structure is dielectric through
electronic structure calculations
Coaxing Graphene to be piezoelectric
0.0035
0.003
P (C/m2)
0.0025
0.002
0.0015
0.001
Circular
holes
0.398 C/m2
0.0005
0
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
Strain
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
Average polarization
Volume fraction
0
1
Theoretical calculations for BTO
Hole Size = 3nm
σxx
%
σxx
Manufacturable Superlattices
C
A
A
B
B
C
A
A
B
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
Theoretical and atomistic analysis of a
paradigmatical nanostructure: cantilever
beam
d
eff
f
d k 2
h

Atomistic Study of BaTiO3 in cubic and tetragonal phase
Sharma group----University of Houston, Tahir Cagin---Texas
A&M, student from Tunisia
•
•
•
•
•
•
•
•
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)
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 Harvesting
Jemai, Najar, Chafra---Tunisia, Ounaies---Penn State
Energy Harvesting
Jemai, Najar, Chafra---Tunisia, Ounaies---Penn State
Homogenized AFC patch
Energy Harvesting System
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?
Sharma group—University of Houston, Sami El-Borgi--Tunisia
In principle, the flexoelectric size-effect should
be observable in indentation experiments.

Theoretical Results: A regular
piezoelectric material
[Karapetian, Kachanov, Kalinin and co-workers]
Purely mechanical
loading on an anisotropic
piezoelectric material
P
For example, in the isotropic
purely elastic half-space case
(Oliver, Pharr)
2aC1 w


2aC2 0

C1   Er
P 2a
2
s

C1  s / a  C1
w 

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!
2C3
P 2a
s

C1 
w 
a

 e

A
 a


   Aa 

size  effect
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!
2C3
P
2
s/a
/ a  C1 
w

 a2

 e

A
 a


   Aa 

size  effect
Indentation experiments (collaboration
with Ken White)
In parallel, we conducted experiments with
varying indentation size…..single crystal BaTiO3
Load Application
(Coil & Magnet)
Support Springs
Displacement Sensor
(Capacitance Gauge)
Indenter
Sample
Motorized Stage
Nanoindentation - Schematic
Berkovich indent on BTO surface
Load: 8mN; Depth into surface: 200nm
Contact stiffness vs contact radius for
BaTiO3
•
•
•
s/a
2

C1
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
Contact stiffness vs contact radius for
Quartz
•
•
s/a
2

C1
No size-effect is observed
for Quartz!
This
observation
strengthens our argument
that flexoelectricity is the
cause of indentation sizeeffect 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.
Nanocapacitors
Energy storage
Nanocapacitors
Energy storage
Miniaturization of
electronics
C

d
V2
+
+
+
+
+
V(x)
V1
V 2 - V1
The dead-layer bottleneck
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
1
1
1
1
 

Ceff Ci Co Ci
Mechanism?---growth induced defects, incomplete electrode
screening, strain, grain boundaries, poor interface…..
Stengel and Spaldin, Nature Materials, 2006
State of the art--ab initio calculations [StengelSpaldin, 2006]
The first, “first principles” calculations clarifying the dead-layer
mechanism: Stengel and Spaldin (Nature, 2006; Physical Review B,
2005); Rabe (Nature Nanotechnology, 2006)
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
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
ofb)Houston.
a)
•
c)
Four more students are expected to join UH in February/March.
d)
e))
f)
g)
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