Controlling the polarization of ferroelectrics to obtain additional energy
V. I. ZUBTSOV
Department of Construction Industry
Polotsk State University
Novopolotsk, BELARUS
Abstract: - A small-size installation created using ferropiezoelectric ceramics for generating additional electric
power is considered. The use of an electrochemical generator in the plant improves the efficiency of power
generation by controlling the polarization of ferropiezoelectric ceramics and applying innovation. At
consumption of 1 joule of electricity (due to mechanical energy), 2...4 joules of electricity are generated at the
output. The technology of energy increase is realized in two stages: at the first stage the degree of polarization
of the ferroelectric element is increased, and at the second stage the electric power supplied to the load is
increased. The efficiency of the electrical installation is about 55...60% and depends on the modification of
ceramics and electrical circuitry.
Keywords: - Reorientation, segnetoelectrics, solid solutions, domains, charging, polarization, energy, batteries,
electric transport
Received: July 18, 2022. Revised: October 13, 2023. Accepted: November 11, 2023. Published: December 11, 2023.
1 Introduction
Studies of two-component systems of
piezoceramic materials based on lead zirconate
titanate (CTS) have led to the development of two-,
three-, four-, and five-component systems [1].
Such high-performance materials possess
segmentoelectric properties and elevated Curie
temperatures (Tc). Four-component systems of
complex lead-containing piezoceramic materials are
widely used in industry, which have significantly
higher electrophysical and mechanical
characteristics (Fig. 1) compared to the two-
component CTC system. However, despite the
significantly improved characteristics, these
multicomponent materials (segnet ceramics) are
unfortunately still not used for additional energy
generation. They are used (as well as previously
developed CTS systems) in energy conversion
devices: piezotransformers, piezosensors,
piezofilters, piezomodulators, etc.
Probably, the existing idea about inexpediency of
using CTS systems for obtaining additional energy
due to their low electrophysical and mechanical
characteristics is automatically (subconsciously)
"transferred" to these more efficient materials.
2 Factors determining the control of
polarization in obtaining additional
energy
One of the main features of materials with piezo
effect is a rigid temperature interval in which their
piezoactive properties are manifested. The upper
point of this interval is the Curie temperature Tk.
Segnetoelectric perovskites exhibit polymorphism
depending on temperature, that is, their cube-shaped
cell is distorted in various ways. Basically 3 forms
or phases are used: tetragonal (T), rhombic and
rhombohedral (Re), Figure 2. The boundaries
between these temperatures are called phase
transitions [2, 3]. These boundaries are "blurred" for
many physical characteristics. As established [1],
for four-component systems of solid solutions, the
"blurring" in concentration transitions between
tetragonal and rhombohedral phases is 2-5% of the
change in titanium concentration along a certain
section with promising material properties for it.
This "blur" is denoted as the morphological region
(MO). The reorientation polarization Pr (the number
of domain reorientations remaining after removal of
the electric field at preliminary polarization of the
segnetoelectric) is important when selecting a
segnetoelectric [1], just as Kp is the mechanical
activity. The excess energy is achieved by
controlling the polarization of the segnetoelectric,
International Journal of Chemical Engineering and Materials
DOI: 10.37394/232031.2023.2.13
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E-ISSN: 2945-0519
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which is determined by the choice of operating
temperature range and frequency range and
basically boils down to the following:
-choice of segnetoelectric material and circuitry for
its inclusion in an electrical circuit;
-Selection of the frequency range and operating
temperature range.
Figure 1 shows the Kp, Pr, d31, g31 and Ԑ/Ԑ0
curves. The figure shows that for the temperature
interval corresponding to the rhombohedral
segmented phase, the values of Kp, Рr , d31, g31, and
Ԑ/Ԑ0 are practically stable. Pr, d31, Kp, and g31
significantly decrease in the transition to the
tetragonal phase.
Ԑ/Ԑ0 is minimal, which corresponds to an increase in
Kp , and increases during the transition to the
tetragonal phase. It follows from the graphs that the
maximum electromechanical activity of the Kp and
the piezoelectric coefficient d31 depend on the
residual polarization Pr and the relative permittivity
ε/ε0 .
These parameters of the crystals of the same name
are in dependence, (1).
Кр= 2
·Q12 ·Pr , (1)
where Q12 is the coefficient of electrostriction, σ
and
are Poisson's and pliability coefficients,
respectively,
-dielectric permittivity.
Q is the Poisson's ratio and is a reference value. In
calculations of devices using piezo- and
segnetoelectrics, as a rule, σ = 0.24 - 0.4 depending
on the chemical composition.
Figure 1. Composition dependences
/ε0 (1), Pr
(2), g31 (3), Kp (4), and d31 (5) for the system
PbTiO3 - PbZrO3 – PbNb2/3Mg1/3О3 –
PbNb2/3Nі1/3О3 .
Thus, the mechanical activity of Kp is sensitive
to Pr and its maximum is in the rhombohedral
region, which is defined for the crystals of the same
name by a certain temperature interval near MO ,
i.e., the interval of operating temperatures tp. The
MO can be analyzed, for example, by means of
concentration-temperature (C-T) phase diagrams,
Figure 2 [1].
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Figure 2. Phase diagram (C-T) of the system PbTіО3
– PbZrO3 – PbNb2/3Nі1/3О3 – PbK1/2 Mn1/2О3 (dashed
lines). The solid lines correspond to the CTS system
The figure shows the slope of the MO toward the
rhombohedral phase for a four-component system of
the form [1]: PbTіО3 - PbZrO3 – Pb
O3 -
Pb
O3, где α(β) = 1/2,1/3,1/4 depending on
the valence of the cations Bʹ, Bʹʹ, Bʹʹʹ, Bʹʹʹʹ.
The cations that provide segnetoelectric properties
can be the chemical elements Sb, Li, Bi and others
of a certain valence.
The slope is determined by the concentration of
the titanium-containing compound PbТіO3 in a
given solid solution of the four-component system.
And the concentration of PbTiO3 in solution is
correlated with the phase transition temperature.
Thus, for example, 41% of PbТіO3 corresponds
to approximately 1100С of the segnetoelectric.
The composition of the rhombohedral phase near
the MO, as the temperature increases, transitions
through the MO to the tetragonal T phase and then
to the cubic K (paraelectric cubic) phase.
This is explained by the fact that at large (critical)
concentrations of titaniumTi near the MO, its atoms
tend to stably shift . Therefore, the whole system
tends to move to the tetragonal phase through the
MO. As a result, the shape and volume of the cell
change.
It was found [1] that the maximum number of
residual 710 - degree domain reorientations of Pr is
in the rhombohedral phase. The orientation is
determined in the direction perpendicular to the
sample surface It is known that the values of
maximum reorientation polarization PR and residual
PR are part of the spontaneous polarization of the Ps
domains and are determined by the sum of all
domain rotations and the polarization process. As a
result of studies the degrees of domain
reorientations under the action of electric field and
residual, after removal of the field were determined.
It was also found [1] that the fraction of 710 –
degree maximal (and also residual) reorientations in
the rhombohedral phase with respect to Рs is
approximately 86% (Pr ≈ 0.866).
Figure 3(b) shows domains of Ps oriented
spontaneously (less than 20%) and domains of Pr
oriented at approximately 710 angles to the crystal
surface (over 80%).
As mentioned above, the reorientation domains in
the rhombohedral segnetophase are oriented at an
angle of 710. In addition, the piezoelectric moduli in
segnetoelectrics, which characterize changes in
electric polarization under the action of mechanical
loads, reach large values in the phase transition
region (rhombohedral), increasing Kp, Figure 1. 710-
degree domains under the action of mechanical
loads, reducing the angle, reduce the residual
deformation, Figure 3, and strengthen the local
electric field inside the dielectric El, lining up along
it.
Figure 3. Ceramic polarization process.
a - electric field is applied; b - after removal of
electric field; 1 - electrostriction [3] deformation ; 2
- residual deformation; Ps - spontaneous
(spontaneous) polarization [3];
Pr,-, oriented polarization.
Thus, the electric energy of the segnetoelectric
increases W: W =-μd· El ·cos Q [3], where μd is the
dipole moment, Q is an angle equal to
approximately 710, figure 4.
.
Figure 4. To calculate the domain energy possessed
by the dipole moment
q - charges; Ua and Uв - charge potentials, ds -
distance between charges.
The energy of segnetoelectric domains W is
directly related to its polarization P. Whereas,
polarization is equal to the average value of electric
moments of dipoles μd located in one cubic meter of
segnetoelectric and is equal to the surface density of
polarization charges q , i.e., P = q/A, where A is the
surface area of the segnetoelectric.
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The local electric field in a segnetoelectric
induced by charges generated under the action of
mechanical loads can be significant and exceed the
external electric field.
The increase in the local electric field El is also
promoted by another piezoelectric modulus g31,
figure 1. The maximum g31 is shifted to the
rhombohedral region and characterizes the tension
El arising under the action of mechanical stresses T,
in accordance with the dependence E≈ -g·T [3].
Thus, by varying the concentration of the
titanium-containing compound PbTіО3 in the system
of solid solutions of multicomponent
segnetoelectrics, it is possible to control the tp of
devices based on them and to reach the maximum
value of Kp.
Assume that a ferroelectric ceramic plate serves
as an electromechanical transducer and creates
compression oscillations along its length, Figure 5.
To create a mathematical model it is necessary to
develop the equation of motion of the transducer, to
select the equations of the piezoelectric effect, and
to make basic assumptions. The basic assumptions
are as follows:
- all mechanical stresses, except those in the
direction of the transducer, are zero;
- the amplitude of alternating mechanical stresses
and strains does not exceed the maximum limiting
values;
-the change in the reactive component of the
transducer impedance at operating frequencies has a
capacitive character.
Let us determine the frequency constants of the
transducer by solving the differential equations of
piezoelectric oscillations for the assumptions
defined above.
To create a mathematical model it is necessary to
develop the equation of motion of the transducer, to
select the equations of the piezoelectric effect, and
to make basic assumptions. The basic assumptions
are as follows:
- all mechanical stresses, except those in the
direction of the transducer, are zero;
- the amplitude of alternating mechanical stresses
and strains does not exceed the maximum limiting
values;
-the change in the reactive component of the
transducer impedance at operating frequencies has a
capacitive character.
Let us determine the frequency constants of the
transducer by solving the differential equations of
piezoelectric oscillations for the assumptions
defined above
Figure 5. Diagram of the electromechanical
transducer in interaction with ECG.
The equation of motion of the transducer is:
2
2
2
2
t
1
x
,
(2)
where is amplitude of oscillation (displacement);
- speed of elastic wave propagation
in the plate;
- modulus of elasticity of ferropiezoelectric
ceramics;
-ferropiezoelectric ceramics density;
l, a and b - length, width and thickness of the plate,
respectively;
t- time.
This is a well- studied partial differential equation
of second order.
The equation of motion of the transducer is solved
by variable separation method:
)t(T)x(X)t,x(
,
2
2
2
22
2
n
t
T
)t(T
11
x
x
)x(X
1
(3)
The solutions are the following, respectively:
where
(m = 1,2,3 ...). (4)
The resonance and antiresonance oscillation
frequencies of the ferro-piezoelectric plate are
determined for a fixed transducer. The boundary
conditions are written as follows:
0)()0(),( tTXtx
,
0)()l(),( tTXtx
, (5)
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where l is the length of the plate. Omitting the
intermediate calculations given in [4, 5], we give
the expressions for fr and fa, (6).
(6)
Thus, resonant and antiresonant frequencies can
be approximated, which is important for calculating
power plant specifications.
If an alternating electric voltage is applied to a
segmented dielectric, the polarization does not
follow the electric field, which leads to dielectric
losses. When a mechanical load is applied, the
deformation is established with a delay. That is,
these processes correspond to a phase shift. All
materials are subject to relaxation processes to a
greater or lesser degree. Relaxation processes in
ferroelectrics appear due to mechanical and
dielectric losses. The peculiarities of
ferropiezoelectrics of ferroelectrics operating in the
dynamic mode is the presence of both types of
losses. At low frequencies, the angles of dielectric
and mechanical losses in it make a total loss angle δ,
defined through Кс [3-7], see equation (7).
Therefore, the polarization is considered as a
complex number: =-
, where is
relative dielectric constant;
- imaginary part of the
complex number, loss coefficient (
= tgδ·; tgδ -
loss characteristic: δ - phase shift angle.
The frequency characteristics,
and δ
depending on the normalized frequency ω/ω0 are as
shown in figure 6.
Now it is possible to explain ECG operation
principle in more detail. Under mechanical load, as a
result of the clamping of ferroelectric, there is a
sharp decrease in , Figure 6, which leads to
electrical capacity reduction and an increase in Кс,
that is, to a sharp increase in the efficiency of
conversion of mechanical energy into electrical
energy. In a certain frequency range between the
resonance and the antiresonance, where the
deformation will increase sharply to a greater extent
than is due to mechanical load, a sudden absorption
of mechanical energy occurs. This leads to a sharp
increase in the degree of polarization.
Reducing the electrical capacitance of the
ferroelectric ECG leads to an increase in the
electrical voltage UO, see equation (8), and,
therefore, an increase in the electrical power in the
load EU. Phase transitions in ferroelectrics occur
within certain temperature ranges. In this connection,
it should be noted that in ferroelectrics some
piezoelectric moduli, characterizing the change in
the degree of polarization under mechanical loading,
reach very large values during phase transitions,
theoretically passing into infinity. Thus, the effect of
mechanical load in a certain frequency range and the
effect of thermal energy in a certain temperature
range are a sort of a catalyst of chemical reactions in
solid solutions of ferroelectrics and mainly increase
the specific power and specific energy of the ECG.
Figure 6. To the analysis of ECG resonance
parameters.
The absolute dielectric constants,
of the
clamped element in this case are, of course, less
than
of the free one and are linked by equation
of electromechanical coupling:
2
11
2
Кс
s
dT
a
T
a
E
T
a
S
a
(7),
where Кс is electromechanical coupling coefficient,
is elastic compliance while the electric field
strength is Е=0,
is absolute dielectric constants
where the mechanical stress is T=0 and d is
piezoelectric module [3-5].
In the general case, the transformation function
(ECG) is of the form: expression (8).
From equation (7) it is obvious that the value of
Кс has a significant effect on the ratio of dielectric
constant of clamped and free ferroelectrics, i. e
change in the dielectric constant under the action of
mechanical load. For example, in case of Кс = 0.5
(an averaged value), this ratio will be 0.75. Which,
in its turn, is highly important (especially since in
modern ferropiezoelectric ceramics Кс = 0.6...0.7
for output electricvoltage (output power) of the
power plant, see equation (8), as dielectric constant
and electrical capacity are directly proportional.
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UO= Ku
,
(8)
where UO means output electric voltage of ECG,
F is acting mechanical force, CECG is electrical
capacity of ECG, CL is electrical load capacity
(load electrical devices), Ku is coefficient of
electric voltage increase due to the increased
degree of polarization of ferroelectric and dij is
piezoelectric module, induced polarization per unit
of mechanical stress.
3 Applying technology to generate
additional energy
In the future, a large amount of additional
electricity and networks of chargers and charging
stations will be required to charge electric vehicles.
To address this problem, a power supply unit (EU),
Figure 7, was developed for slow, fast, and
accelerated battery charging, which is a battery
charger and charging station using polarization
control of segnetoelectrics.
Polarization control creates a technology to reduce
energy consumption by changing the compressibility
and electroelasticity of segnetoelectrics [3, 7-10]. As
a result, additional energy is released that is 2.5 to 3
times greater (depending on the segnetoelectric
modification and inclusion in electric circuits) than
the energy consumed from an alternating electric
voltage source. This additional electrical energy is
also the result of the second kind of segnetoelectric
transition, migration and dipole polarization.
Figure 7. Functional diagram of the EU for
charging.
The range of an electric car on a single charge is
much less than the consumer needs. Its energy
source (batteries) weighs a lot and is expensive. The
reason is that the energy density of modern batteries
is too low. Although the energy density of batteries
has recently increased, they still weigh a lot, are
large and expensive. The known simple ways to
increase the energy density of batteries have all but
been exhausted. In order for batteries to replace
traditionally used internal combustion engines, their
energy density must be increased by a factor of
about 10. The use of solar and wind energy is still
inefficient. In addition, the national interests of
hydrocarbon-producing countries are a deterrent to
the development of electric vehicles. Thus, the
problem of battery energy needs to be solved.
Toyota's solid-state batteries, which promise to
greatly increase energy density, are still under
development. And it could be a decade or more
before these batteries become mass-produced.
With this in mind, an innovative small-scale
alternative powertrain (EU) technology has been
developed that uses an electrochemical generator
(ECG) based on ferropiezoelectric ceramics and
provides a simultaneous increase in power density
and specific energy. The unit also includes a
mechanical energy generation unit and an
electromechanical converter Figure 8. The energy
consumption of 1 joule when using mechanical
energy makes it possible to obtain 2.5...4 joules of
electrical energy at the output. The mechanical
energy used is produced by a device of simple
design. The unit also includes a device for obtaining
mechanical energy and electromechanical converter,
Figure 8.
Figure 8. Functional diagram of the EU.
4 Dependence of the EU mass on the
electric power it generates
Theoretical and experimental studies [5-7, 11, 12]
showed that an increase in the electrical power in
the load (PL) by 2 times leads to an increase in the
ECG mass (MECG) by 2√2 times, by 3 times - by 3√3
times and etc. In other words, these changes occur
according to the law of geometric progression. And
electromechanical converter and device, which
From AC
voltage
source
Electroche
mical
generator
Control
unit
Storage
battery
Reconcilia
tion
device
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generates mechanical energy increase this mass by
2,12...2 times.
Thus, the mass of the power plant (without battery
and electric motor) makes 2.12...2.2. MECG.
Figure 9 shows the growth-increase diagram of
the MECG – РL. The above the diagram makes it
possible to calculate the mass of the EU (without the
battery and electric motor) taking РL into account.
You can find a point on the diagram where РL =
1.89 kW and MECG = 0.83 kg, near which РL and
MECG change almost directly in proportion. The
MECG grows slower below this point and faster
above it.
MECG, kg
PL, kW
Figure 9. МECG – РL growth-increase diagram.
Figure 10 shows the character of the electrical
voltage change for ECG at frequencies below
resonance, where the oscillator resistance can be
considered purely capacitive [5].
0.01 0.02 0.05 0.1 0.5 1 2510 20
1.00
0.75
0.5
0.25
0w
U1/U0
RC
Figure 10. Frequency response of ECG.
UO - this is the amplitude value of the voltage that
appeared on the capacitance С at
R
.
1
U
- voltage proportional to the change in
mechanical load F, (8).
The curve in Figure 10 is a part of the
experimental amplitude-frequency response of the
electromechanical transducer made of the
ferroelectric material PZT-19, diameter 10x1 mm
with a mechanical load of 2.5 MPa (see in [4],
Figure 4. 1, curve 2), in the frequency range between
antiresonance and resonance. Depending on the
nature of the electrical load of the EU (reactive or
active), the scheme of connection and consumption
of electrical energy changes [4,5]
5 Conclusion
The proposed alternative innovative technology
for obtaining additional energy compared to solar
and wind technologies has an advantage: it does not
depend on climatic conditions, time of day and has a
high efficiency. The efficiency of conversion of
mechanical energy into electric voltage is increased
by about an order of magnitude due to the
electrophysical characteristics of segnetoelectrics
and physical and technical solutions (technologies).
The papers [4,5] present experimental dependences
of the output electric voltage on the mechanical load
of segmentoelectric elements of different
modification and inclusion scheme.
The increase in energy density occurs in two
stages: at the first stage there is an increase in the
polarization of the segnetoelectric, and at the second
stage there is an increase in the electric power at the
output of the EU power unit [13, 14].
Engineering-physical solutions (innovations)
have been applied in the technology. Technical
details of the innovations are not disclosed yet, as
work is underway to improve the technology. The
main components of EU are protected by copyright
certificates and patents, and their performance has
been confirmed by experimental studies [4,5].
Further research is aimed at studying the
effectiveness of EU application for hydrogen and
hybrid vehicles, as well as for increasing the energy
density of batteries used for electric energy storage.
So, controlling the degree of polarization of
ferroelectrics to produce additional energy is mainly
determined by the following:
- The modification of ferroelectrics and the electrical
connection scheme;
- mechanical loading (design features of the EU);
- interlayer or dipole polarization of ferroelectrics in
the range of operating temperatures, as well as
frequencies in the range of about 1...1.5 (103 - 105)
.
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DOI: 10.37394/232031.2023.2.13
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Volume 2, 2023
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Policy)
The author contributed in the present research, at all
stages from the formulation of the problem to the
final findings and solution.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflict of Interest
The author has no conflict of interest to declare that
is relevant to the content of this article.
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(Attribution 4.0 International, CC BY 4.0)
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DOI: 10.37394/232031.2023.2.13
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E-ISSN: 2945-0519
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Volume 2, 2023
