pyroelectric energy conversion: optimization...

538 ieee transactions on ultrasonics ferroelectrics and frequency control vol 55 no 3 march 2008

Pyroelectric Energy Conversion Optimization Principles

Gael Sebald Elie Lefeuvre and Daniel Guyomar

AbstractmdashIn the framework of microgenerators we present in this paper the key points for energy harvestshying from temperature using ferroelectric materials Thershymoelectric devices profit from temperature spatial gradishyents whereas ferroelectric materials require temporal flucshytuation of temperature thus leading to different applicashytions targets Ferroelectric materials may harvest perfectly the available thermal energy whatever the materials propershyties (limited by Carnot conversion efficiency) whereas thershymoelectric materialrsquos efficiency is limited by materials propshyerties (ZT figure of merit) However it is shown that the necessary electric fields for Carnot cycles are far beyond the breakdown limit of bulk ferroelectric materials Thin films may be an excellent solution for rising up to ultra-high elecshytric fields and outstanding efficiency

Different thermodynamic cycles are presented in the paper principles advantages and drawbacks Using the Carnot cycle the harvested energy would be independent of materials properties However using more realistic cyshycles the energy conversion effectiveness remains dependent on the materials properties as discussed in the paper A particular coupling factor is defined to quantify and check the effectiveness of pyroelectric energy harvesting It is deshyfined similarly to an electromechanical coupling factor as k2 = p290(33cE

) where p 90 are pyroelectric coshy33 cE

efficient maximum working temperature dielectric permitshytivity and specific heat respectively The importance of the electrothermal coupling factor is shown and discussed as an energy harvesting figure of merit It gives the effectiveness of all techniques of energy harvesting (except the Carnot cycle) It is finally shown that we could reach very high efficiency using h111i075Pb(Mg13Nb23)-025PbTiO3 sinshygle crystals and synchronized switch harvesting on inductor (almost 50 of Carnot efficiency) Finally practical impleshymentation key points of pyroelectric energy harvesting are presented showing that the different thermodynamic cyshycles are feasible and potentially effective even compared to thermoelectric devices

I Introduction

Constant advances in electronics push past boundshyaries of integration and functional density toward

completely autonomous microchips embedding their own energy source In this field research continues to develop higher energy-density batteries but the amount of energy available is finite and remains relatively weak limiting the

Manuscript received June 6 2007 accepted November 26 2007 This work was supported by the Agence Nationale pour la Recherche from the French government under grant ANR-06-JCJC-0137

The authors are with INSA-Lyon Laboratoire de Genie Electrique et de Ferroelectricite Villeurbanne France (e-mail gaelsebaldinsashylyonfr)

Digital Object Identifier 101109TUFFC2008680

systemrsquos lifespan which is paramount in portable elecshytronics Extended life is also particularly advantageous in systems with limited accessibility such as biomedical imshyplants structure-embedded microsensors or safety monshyitoring devices in harsh environments and contaminated areas The ultimate long-lasting solution should therefore be independent of the limited energy available in batteries by recycling ambient energies and continually replenishing the energy consumed by the system Some possible amshybient energy sources are thermal energy light energy or mechanical energy Harvesting energy from such renewable sources has stimulated important research efforts over the past years Several devices from millimeter scale down to microscale have been presented with average powers in the 10 microW to 10 mW range [1]

Work on vibration-powered piezoelectric electrical genshyerators has led to new energy conversion techniques such as synchronized switching harvesting (SSH) techniques based on nonlinear processing of the piezoelectric voltshyage [2]ndash[7] As a result the mechanical-to-electrical energy conversion capability of active materials is significantly inshycreased typically by factors of 4 to 15 depending on the considered technique From the efficiency point of view it has been shown that SSH techniques may be implemented with electronic circuits consuming less than 5 of the enshyergy produced by the piezoelectric element This novel apshyproach is very promising for improving the effectiveness and power density of piezoelectric microgenerators But it can also be theoretically extended to most other energy conversion processes (for example strainstress variation temperature variation and other processes)

Thermoelectric modules are the main way for energy harvesting from temperature It is now possible to find commercial thermoelectric generators from microW to kW electric output energy These are based on temperature gradients leading to heat flow through the thermoelectric generator and a small percentage of the heat flow is conshyverted to electric energy Materials properties are the key parameter for improving both the output power (increase of the thermal heat flow thus making it difficult to keep the temperature gradient) and the efficiency (improving the Seebeck coefficient and figure of merit) However the possibility of harvesting thermal energy is limited in the case of microgenerators because the temperature differenshytials across a chip are typically low

Pyroelectric materials may be used for thermal energy to electric energy conversion The pyroelectric effect was discovered before the piezoelectric effect and is mainly used for pyroelectric infrared temperature detectors Contrary

c0885ndash3010$2500 copy 2008 IEEE

539 sebald et al pyroelectric energy conversion optimization principles

to thermoelectric generators pyroelectric materials do not need a temperature gradient (spatial gradient) but temposhyral temperature changes This opens different applications fields where temperature gradients are not possible and where temperature is not static Small-scale microgenerashytors with dimensions smaller than the temperature spatial fluctuation length may with difficulty be subjected to temshyperature gradients Natural temperature time variations occur due to convection process and this thermal energy is difficult to transform in a stable temperature gradient On the other hand it is possible to transform a tempershyature gradient into a temperature variable in time using a caloric fluid pumping between hot and cold reservoirs The pumping unit may require much less energy than the total produced energy (depending on the scale of the deshyvice) and may produce temperature variations of 1 to 20C at 2 Hz for example To optimize energy harvesting from temperature the first step should be the optimization of energy conversion Then the problems of electric loading (modifying the cycles shape) should be addressed

The aim of this paper is to present methods for optimizshying energy conversion from temperature variations using pyroelectric materials and to describe the most important parameters in materials choice and device design The first part is devoted to thermodynamic cycles that could be used for energy conversion and the second part deals with a pyroelectric materials survey Finally the practical apshyplication problems of thermodynamic cycles are discussed in the last part of the article

II Thermodynamic Cycles

When talking about energy harvesting from heat one should first consider classical thermodynamic cycles We aim to answer here several questions

bull What cycles could be imagined to harvest energy from heat

bull What is their efficiency (defined as electric work dishyvided by the heat transferred from a hot reservoir to a cold reservoir)

bull What are the important parameters of the pyroelectric materials for optimizing the efficiency

bull Are those cycles realistic

For a given temperature variation it is possible to conshysider it as a static problem involving two temperature reservoirs which is a common interpretation in thermoshydynamics We need first to establish the equations of pyshyroelectric materials [8]

dD = εθ (1) 33dE + pdθ

dΓ = pdE + cE dθ

(2) θ

where D E θ and Γ are electric displacement electric field temperature and entropy respectively The coeffishycients are defined as

TABLE I Coefficients Used in the Simulations

Coefficient Unit Value

εθ Fmiddotmminus1 lowast 33 1000ε0

p Cmiddotmminus2middotKminus1 10minus3

cE Jmiddotmminus3middotKminus1 25 times 10minus6

θh K 301 θc K 300

lowastFor Carnot cycle εθ 33 = 100ε0 for the sake of clarity on the figure (to

obtain larger difference between adiabatic and isothermal dielectric permittivity)

dD dD dΓ dU

εθ 33 = p = = cE = (3)

dE dθ dE dθθ E

In the following part we present four different energy harshyvesting cycles For each cycle we give PE cycle (polarshyization vs electric field) and Γθ cycle (entropy vs temshyperature) In the two cycles the area of the cycle is the converted energy It is the same area in PE cycle and in Γθ cycle In the PE cycle the cycle is clockwise meaning a negative energy (ie energy given to the outer medium) In the Γθ cycle the cycle counter-clockwise meaning a positive energy (ie energy given by the outer medium to the material) The coefficients defined in (3) are assumed to be constant for the electric field and temperature ranges considered here Coefficients used in simulations are given in Table I

A Carnot Cycle

The Carnot cycle is defined as two adiabatic and two isothermal curves on the (PE) cycle (see Fig 1) It is conshysidered as the optimal energy harvesting cycle whose effishyciency is

θcηCarnot = 1 minus (4)

θh

where θc and θh are cold and hot temperatures respecshytively

The demonstration of that result is very interesting to understand the underlying limitations of such cycle In the first adiabatic increase of the electric field (path A-B)

dθ p= minus dE (5)

θ cE θh p

ln = minus EM (6) θc cE

where EM is the maximum amplitude of the applied elecshytric field

In practical applications this means that one should know the maximum temperature variation to know what the necessary electric field is In the isothermal decrease of the electric field (path B-C)

dΓ = pdE and dQ = θdS (7)

Qh = minuspEM θh


Fig 1 Thermodynamic cycles for Carnot cycle (a) PE cycle and (b) Γθ cycle

where Qh is the heat taken from the hot reservoir The two following steps are very similar and are not detailed here

The resulting energy conversion ratio gives

θh minus θcWe = (θh minus θc)δΓ = minuspEM (8)

θh

The resulting conversion ratio was already given in (4) It is very interesting to notice that this conversion ratio does not depend on material properties The only restrictionmdashand main drawbackmdashis that one should know first the temperature variation before starting any cyshycle Furthermore (6) links electric field amplitude to the temperatures ratio Using realistic coefficients values (see for example [9]ndash[11] p = 600 times 10minus6 Cmiddotmminus2Kminus1 and cE = 25 times 106 Jmiddotmminus3middotKminus1 for a 075Pb[Mg13Nb23]O3shy025PbTiO3 ceramic) and for a temperature difference of 1C around room temperature we need an electric field of 14 kVmiddotmmminus1 which is far beyond the electric breakdown of bulk ceramics The maximum temperature variation inshyduced in ferroelectric materials when applying an electric

field is limited to 2 K for bulk ceramics [12]ndash[18] and could reach 5ndash12 K for thin films [19] [20] A too-large temshyperature variation will result in a degraded Carnot cycle because it is impossible to get enough electrocaloric effect Moreover it is hardly realistic to force the electric field at a given value without paying a lot of wasted energy (see Section IV) As a consequence the Carnot cycle is not feasible at all in practical applications

B SECE Cycle

SECE stands for synchronized electric charge extracshytion We use that acronym because of numerous papers concerning the nonlinear switching of the piezoelectric voltage for energy harvesting from vibrations and damping [3] [6] [7]

From the thermodynamics point of view this technique is one of the most natural cycles It consists of extracting the electric charge stored on the active material when the maximum temperature is reached ie when the stored electric energy is maximum and doing it again when the temperature is minimum (Fig 2) This energy extracted may be then transferred to an electrical energy storage cell such as a capacitor or to an electrochemical battery for future needs using for example the circuit described in [3] or the power converter detailed in Section IV

The theoretical description of this cycle is as follows Along the path (C-D) the temperature is decreased reshysulting in a decrease of the open-circuit electric field

Em = minus ε

p θ (θc minus θh) (9) 33

where Em is the minimum electric field on the sample During that temperature variation

2

dQ = cE dθ minus pθdθ (10)

εθ 33

2

Qc1 = cE (θc minus θh) minus 2p

εθ (θc 2 minus θh

2 ) (11) 33

where Qc1 is the heat given to the cold source during the cooling

Then the electric field is decreased to 0 in isothermal condition (by connecting the sample to a resistance for example path D-E) Due to electrocaloric activity in fershyroelectric materials heat is transferred from the sample to the cold source

Qc2 = minuspEmθc (12)

As a result using (9) total heat Qc transferred to the cold source is

2p)2Qc = cE (θc minus θh) + (θh minus θc (13)

2εθ 33

The two other segments of the cycle are very similar Total heat transferred to the hot source is

2pQh = cE (θh minus θc) +

2εθ (θh minus θc)2 (14) 33


Fig 2 Thermodynamic cycles for SECE cycle (a) PE cycle and (b) Γθ cycle

The total electric work is found assuming that the inshyternal energy does not change at the end of one cycle

Qh + Qc = minusWE (15) 2p

WE = minus εθ (θh minus θc)2 (16) 33

where WE is the electric energy Finally the conversion ratio gives

|WE | k2

ηSECE = = ηCarnot (17) Qh 1 + 05k2ηCarnot

with

p2θhk2 =

εθ (18) 33cE

Variable k2 is a dimensionless number giving the elecshytrothermal coupling factor (at temperature θh) similar to the electromechanical coupling factor (coupled coefficient

divided by the product of noncoupled ones) For weakly coupled case ie k2 laquo 1 (most common case as shown in Section III)

ηSECE = k2ηCarnot (19)

For a perfect coupled material (k2 = 1) we obtain a conshyversion ratio that tends to the Carnotrsquos one provided that this latter is much smaller than unity

The advantages of such energy harvesting technique are

bull No control of the voltage bull No special attention to be paid to the temperature

variation do not need to know the temperature in advance

bull Possible whatever the material (only pyroelectric acshytivity is important whatever the electrocaloric activshyity)

The main drawback is the poor conversion ratio compared to Carnot cycles In fact the k2 for common materials (PZT ceramics) is around 2 times 10minus3 and may reach 47 times 10minus2 for some single crystals (see Section III for details about materials)

C SSDI Cycle

SSDI stands for synchronized switch damping on inducshytor This technique was developed prior to the SSH techshyniques for dissipating the mechanical energy of vibrating structures with piezoelectric inserts to damp the structural resonance modes [2] Synchronized switch means that the voltage of the ferroelectric material is switched on an inshyductor at every maximum or minimum of the temperature so that the electric field polarity is quasi-instantaneously reversed (Fig 3) From a thermodynamics point of view the only difference with SECE is that the electric field is not reduced to 0 but nearly to its opposite value The use of resonant circuit including an inductor is in fine an ingeshynious way to perform that operation at minimized energy cost (due to the inductor imperfections a small amount of energy is lost during the electric field polarity reversal process)

Let us start the cycle explanation from point A The temperature is increased in open-circuit condition Due to pyroelectric activity a positive electric field appears on the ferroelectric material Reaching the maximum tempershyature the electric field is inversed from EM0 to minusEm0 with a lossy inversion ratio

Em0

EM0 = β (20)

where β is the inversion quality β = 1 is a perfect invershysion and β = 0 is the SECE case

Then the temperature is decreased to its minimum The absolute value of the electric field is increased and then the inversion process is repeated This cycle is repeated indefinitely The maximum value of the electric field is thus increased for every cycle and would tend to an inshyfinite value for a perfect inversion process It is assumed


Fig 3 Thermodynamic cycles for SSDI cycle (a) PE cycle and (b) Γθ cycle

that the second principle of thermodynamics guarantees an irreversible process due to losses during inversion The cycle area will increase until the electric field gain due to temperature variation equals exactly losses

EM minus Em = minus ε

p θ (θh minus θc) (21) 33

Calculation of heat transferred to hot and cold sources is very similar to the SECE example During temperature increase (path E-F)

2pQh1 = cE (θh minus θc) minus

2εθ (θh 2 minus θ2) (22) c

33

During isothermal voltage inversion (path F-C)

Qh1 = pθh(minusEm minus EM ) (23)

Using (20) and (21)

2p(θh

2 minus θ2Qh = cE (θh minus θc) minus )c2εθ 33

p2 1 + β +

εθ (θh 2 minus θhθc) (24)

1 minus β33

Similarly for the heat transferred to the cold source (path C-D and D-E)

2

Qc = cE (θc minus θh) minus 2p


2 ) 33

p2 1 + β + (θ2 minus θhθc) (25) cεθ 1 minus β33

Using (15)

p2 1 + β WE = minus

εθ (θh minus θc)2 (26) 1 minus β33

Electric energy is very similar to the SECE example The term (1 + β)(1 minus β) shows the energy conversion magnishyfication using the SSDI energy conversion cycle

Finally the conversion ratio is

k2 1 + β ηSSDI = ηCarnot2β ηCarnot 1 minus β

1 + k2 + (27) 1 minus β 2

For weakly coupled materials (k2 laquo 1) we obtain

= k2 1 + β ηSSDI ηCarnot (28)

1 minus β

It is noticeable that the SSDI process may be seen as a coushypling magnification because the apparent coupling factor compared to SECE becomes

= k2 1 + β k2 (29) app 1 minus β

This latter coupling may become much larger than 1 Inshydeed for excellent inversion ((1 + β)(1 minus β) raquo 1) the expression may be simplified

k2

ηSSDI = app ηCarnot (30)

1 + k2 app

Thus as for SECE example the conversion ratio may tend to Carnotrsquos one for excellent coupling factor (k2 rarr 1) and for excellent inversion quality (β rarr 1)

As noted in the beginning of this section the SSDI techshynique was not designed for energy harvesting but for meshychanical vibration damping The so-called SSHI technique [6] was derived from SSDI for the purpose of energy harshyvesting Energy conversion cycle of SSHI is relatively near to that of SSDI However understanding of its analysis requires a description of the associated electronic circuit behavior So for clarity of this paper we have chosen to detail the SSHI cycles in Section III


Fig 4 Thermodynamic cycles for resistive cycle (a) PE cycle and (b) Γθ cycle

D Resistive Cycle

When wondering how to consume the electricity conshyverted from heat energy one could think ldquojust connect a resistor to the active material electrodesrdquo This is indeed the simplest way to perform energy conversion cycles on ferroelectric materials (which is known as ldquoStandard ACrdquo in some references [5] [6]) For the sake of presenting a comprehensive argument we study here the correspondshying cycles (Fig 4)

Lefeuvre et al [6] gave detailed calculations for elecshytromechanical conversion using a single resistive load The development presented below is an adaptation to elecshytrothermal conversion

The starting equations become

D = εθ 33 E + pθ (31)

Q = pθ E + cE θ (32)

where dotted variables are time derivatives

Fig 5 Efficiency of the conversion for different techniques as a funcshytion of the coupling factor squared Dashed line is for Carnot cycle solid line is for SSDI with different inversion factors β and dashedshydotted line is for pure resistive load

The external boundary condition is

E = minusρD (33)

where ρ is the resistive load connected to the piezoelectric material

When the temperature variation is sinusoidal there exshyists an optimal load depending on the frequency

1 ρOPT = (34)

ωεθ 33

where ω is the pulsation of the temperature variation Electrical energy dissipated per cycle is

π p2

WE = (θh minus θc)2 (35) 4 εθ

33

If we neglect the electrocaloric coupling

Qh = cE (θh minus θc) (36)

And finally

ηResistive = π

4 k2ηCarnot (37)

E Discussion of Cycles

We show here four different cycles with different effishyciencies and different principles Table II summarizes the results Fig 5 illustrates the efficiency for all techniques as a function of the coupling factor squared It is clear that SSDI is much more efficient than the others (except Carnot) and increases the overall efficiency to 50 of that of Carnot for an inversion quality of 08 and a coupling factor squared of only 10 whereas it is limited to 5 for other techniques


TABLE II Comparison Between Four Different Cycles for Energy Harvesting

Cycle Efficiency η Maximum electric field EM Difficulty to implement Necessary information

Carnot

SECE

ηref = 1 minus θc

θh

η = k2

1 + 05k2ηref ηref

EM = minus cE

p ln(

θh

θc

)

EM = minus p

εθ 33

(θh minus θc)

High voltage amplifier and difficulty to really harvest energy

Simple and efficient electronic circuit

Full temperature profile known in advance

No prerequisite info

SSDI ηSSHI = k2

1 + k2 (

2β

1 minus β +

ηref

2

) 1 + β

1 minus β ηref EM = minus p

εθ 33(1 minus β)

(θh minus θc) Simple and efficient electronic circuit


Resistive ηResistive = π

4 k2ηref EM = minus p

2 radic

2εθ 33

(θh minus θc) Very simple circuitry Frequency information

Fig 6 Efficiency of the conversion as a function of temperature varishyation ∆θ = θh minus θc with θc = 300 K Dashed line is for Carnot cycle and solid line is for SECE cycle with different coupling factors

Fig 6 shows the efficiency of conversion as a function of temperature difference between hot and cold reservoirs Compared to thermoelectric energy harvesting (using Seeshybeck effect) where efficiency is limited by materials propshyerties efficiency for pyroelectric materials may tend to Carnotrsquos one Thermoelectric conversion efficiency may be expressed as [21] [22]

radic θh minus θc ZT + 1 minus 1

η = middot radic (38) θh ZT + 1 + θhθc

For the best thermoelectric materials the figure of merit ZT reaches 1 around room temperature with Bi2Te3 mashyterials for example [23] As a result the best efficiency reaches 17 of Carnot efficiency (considering low tempershyature differences to maximize efficiency) To get 50 of Carnot efficiency one should find a material having a figshyure of merit of 9 which is ten times higher than the best known thermoelectric materials and we have not considshyered here the large temperature differences case which reshy

sults in degrading the efficiency Consequently the Carnot cycle is most interesting for energy harvesting but full temperature profile information is necessary before any temperature variation occurs

This process is indeed possible for a controlled tempershyature variation (as for fuel engines) One could imagine a controlled gas heater inducing temperature variations and pyroelectric energy harvesting Another limitation is the necessary electric field to be applied to the pyroelectric material As described in Section III (for example 1C temperature variation) using realistic materials propershyties the electric field should be in the 14 kVmiddotmm to 1middotKminus1

range When not broken with electric arcs most bulk ferroshyelectric materials are highly nonlinear either for dynamics nonlinearities or for static nonlinearities [24]ndash[27]

For noncontrolled temperature variationsmdashie imagine a temperature perturbation in the vicinity of a pyroelecshytric material such as going outside by minus20C or opening a doormdashimplementing the Carnot cycle is not possible except if one can predict the future temperatures values In such cases the resistive case is not realistic (a temshyperature variation is rarely a sinus) since the resistor is adapted on the frequency of excitation On the contrary SECE SSDI and SSHI could be used With a sinusoidal excitation the voltage of the ferroelectric element should be reversed (SSDI and SSHI) or short-circuited (SECE) at every maximum or minimum of the voltage signal Calshyculations given in sections B and C are suitable for any periodic temperature signal with constant maximum amshyplitude (even if this differs from sinus) When this differs from sinus the necessary choice is this when should the switch occur To solve this problem a probabilistic apshyproach [28] and similar techniques adapted to random sigshynals are necessary to maximize energy harvesting

III Pyroelectric Materials

We aim in this part of the article to present a survey on existing materials What are the important parameshy


Fig 7 Coupling factor squared as a function of voltage response for different materials

ters For standard pyroelectric materials different figures of merit exist The two following ones are dedicated to pyroelectric sensors and are defined as [29]

Current responsivity figure of merit

Fi = p

(39) cE

Voltage responsivity figure of merit

Fv = p

(40) εθ 33cE

In Section II we showed the great importance of anshyother parameter for energy harvestingmdashthe electrothermal coupling factor defined in (18) This parameter may be also named energy figure of merit FE

For every material presented in Table III we give two different figures of merit at room temperature (unless othshyerwise specified) The first one is the electrothermal coushypling factor The electric field sensitivity to temperature variation is also given (= minuspεθ

33) Indeed for a given temshyperature variation the obtained voltage that appears on the ferroelectric material is important Voltages that are too high result in inherent losses of the electronic circuitry of the harvesting devices It is also difficult to harvest enshyergy in the case of very small pyroelectric voltages effishyciently because of the voltage drop of semiconductors One may object that whatever the electric field sensitivity we can adjust the thickness of ferroelectric material to keep the voltage in a given useful range of variation However bulk ceramics below 80 microm are nearly impossible to hanshydle Then the technology of thick and thin films may be used to lower thickness but ferroelectric properties usually decrease quickly [30] [31] Inversely a thick ferroelectric material may generate high voltages for a given tempershyature variation but its high thermal mass opposes quick temperature variations Fig 7 shows the electrothermal coupling factor as a function of voltage response to a temshyperature variation Among all materials a few exhibit a coupling factor squared above 1 Simple harvesting deshyvices such as SECE require a large coupling factor to enshysure an effective energy harvesting To perform the Carnot

cycle with a pyroelectric material one should apply an electric field proportional to cE p (see Table II for deshytails) Assuming that all the materials have very similar heat capacity minimizing the electric field is the same as maximizing the pyroelectric coefficient From that point of view it is highly unrealistic to think about Carnot cycles using polymers Composites could be interesting because they exhibit a very high breakdown electric field while keeping a quite high pyroelectric coefficient Bulk materishyals exhibit a very high pyroelectric coefficient but usually break above 4ndash6 kVmiddotmmminus1 Additional data on electric breakdown resistance of materials is required to get more precise information about the feasibility of Carnot cycles

The best materials are (1-x)Pb(Mg13Nb23)-xPbTiO3

(PMN-PT) single crystals with a coupling factor as high as 47 Moreover voltage response is quite high Howshyever those materials are expensive and fragile Single crysshytals are grown by Bridgman technique [43]ndash[46] It should thus be difficult to really think of industrial use unless performance is the main priority It should be noted that the PVDF exhibits a coupling factor as high as bulk ceshyramics but with a voltage response much larger (six times greater than PZT) This material seems to be very intershyesting since it is low cost not fragile and stable under large electric field or temperature variations Another exshycellent material is the PZTPVDF-HFP composite with very high coupling factor This kind of material is easy to use because of its flexibility but suffers large dependence on temperature Moreover the value given here is only for 70C and it decreases quickly when changing the temshyperature Most probably the future of pyroelectric energy harvesting is related to composites investigations

IV Energy Harvesting Devices

Orders of magnitude of the powers consumed by various CMOS electronic devices that could be powered by miniashyture energy harvesting devices are presented in Fig 8 As explained in previous sections implementation of Carnot SECE SSH or SSDI cycles require controlling the pyroshyelectric voltage with the temperature variations Practishycal solutions for voltage control in the cases of SSH and SECE techniques are presented in [2]ndash[7] The following subsections concern the effective energy harvesting comshypared to optimized energy conversion presented in Secshytion II Indeed except the pure resistive case where the resistance connected to the active material electrodes may be considered as the simulation of an electric load the conshyverted energymdashthat is to say the useful or usable energymdash actually differs from harvested energy as shown below

A ldquoIdealrdquo Power Interface

Implementation of energy harvesters using the preshysented energy conversion cycles requires power interfaces for achieving the desired energy exchanges between the active material and the electrical energy storage cell Reshyversible voltage amplifiers could be used for this purpose


TABLE III Pyroelectric Properties for Different Class of Materials

lowast

Coefficient p εθ cE (times106) minuspεθ k2 33 33(times103)

Unit microCmiddotmminus2middotKminus1 ε0 Jmiddotmminus3middotKminus1 Vmiddotmminus1middotKminus1 Ref Note

PZN-PT and PMN-PT single crystals

111 PMN-025PT 1790 961 25 210 479 [932] 110 PMN-025PT 1187 2500 25 54 081 [9] 001 PMN-025PT 603 3000 25 23 017 [9] 001 PMN-033PT 568 5820 25 11 008 [33] 011 PMN-033PT 883 2940 25 34 038 [33] 111 PMN-033PT 979 650 25 170 212 [33] 001 PMN-028PT 550 5750 25 11 008 [33] 011 PMN-028PT 926 2680 25 39 046 [33] 111 PMN-028PT 1071 660 25 183 250 [33] 001 PZN-008PT 520 3820 25 15 010 [33] 011 PZN-008PT 744 1280 25 66 062 [33] 111 PZN-008PT 800 950 25 95 096 [33]

Bulk ceramics

PZT 533 1116 25 54 037 [34] PMN-025PT ceramic 746 2100 25 40 038 [9] (BaSrCa)O3 4000 16000 25 28 144 [35] 22C plusmn 2C PLZT 055347 360 854 25 48 022 [36] PLZT 85347 97 238 25 46 006 [36] PLZT 145347 19 296 25 7 0002 [36]

Thin films

(PZT)PZT composite 180 1200 25 17 0039 [37] PbCaTiO3 220 253 25 98 028 [38] PZT 700 nm 211 372 25 64 017 [39] PMZT 700 nm 352 255 25 156 070 [39]

Polymers and composites

PVDF 33 9 18 314 014 [40] PZTP(VDF-TrFE) 50 331 692 2 54 0028 [34] PZTPVCD-HFP 5050 vol 450 85 2 598 428 [41] 70C plusmn 2C PZT03PU07 vol 90 23 2 442 063 [42]

Fig 8 Powers consumed by CMOS electronic devices

lowastValues given here may not be accurate due to the lack of precisions in references (temperatures of measurement of pyroelecshytric coefficient especially) Moreover the heat capacitance is most of the time estimated using similar materials However the range of variation of CE being quite small and its influence is weak

but a critical parameter for these power interfaces is their efficiency The working principle of so-called ldquolinear voltshyage amplifiersrdquo used in audio applications limits their effishyciency to 50 in theory and to lower values in practice Anshyother possibility is to use switching mode power converters Contrary to linear amplifiers switching mode amplifiers may theoretically reach an efficiency of nearly 100 Inshydeed by principle they are exclusively made up with elecshytronic switches (ON state = very small resistance OFF state = quasi-infinite resistance) associated with quasishylossless passive elements such as inductors transformers and capacitors The circuit presented on Fig 9 could be the ldquoidealrdquo voltage amplifier for controlling the energy harvestshying voltage cycles because it may deliver a perfectly conshytrolled ac voltage and may have very weak energy losses This H-bridge switching mode power converter is a wellshyknown structure used for controlling the power exchanges between ac and dc electrical sources [49] The four elecshytronic switches are controlled through a pulse width modshyulator (PWM) that turns ON and OFF the switches at high frequency (much higher than the temperature variashy


Fig 9 Circuit diagram of the energy harvesting device including the H-bridge switching mode power interface

tion frequency) with variable duty cycle The duty cycle D is the key parameter for controlling the average ac voltage (Vac) respectively to the dc voltage Vdc (0 le D le 1)

(Vac) = Vdc(2D minus 1) (41)

The PWM may be also disabled In this case all the switches are simultaneously opened leaving the electrodes of the active material on an open circuit This particular state is necessary for instance in some stages of SECE or SSDI cycles The inductor L connected between the acshytive material and the electronic circuit forms a low-pass filter with the ferroelectric material capacitor C Thus the voltage V across the active material electrodes can be considered as perfectly smoothed as long as the switching radic frequency of the PWM remains much higher than 2π LC In other words if this condition is verified the voltage ripshyple due to switching across the active material is negligible and thus

V = Vdc(2D minus 1) (42)

Theoretical waveforms in the cases of SECE and SSDI are presented on Fig 10(a) and (b) respectively In pracshytice energy losses due to imperfections of the real composhynents affect the efficiency For instance high power (1 kW to 100 kW) high voltage (500 V to 5 kV) industrial switchshying mode amplifiers have typical efficiencies between 85 and 95 Low power (1 mW to 10 W) low voltage (1 V to 20 V) switching mode amplifiers commonly used in wearshyable electronic devices also have high efficiencies typically between 70 and 90 However it is important to menshytion here that the considered energy harvesting devices are in the microwatt range but with relatively high voltages (50 V to 1 kV) so the characteristics of the required power amplifier are out of usual application domains and require a specific design Such switching mode interfaces have been successfully demonstrated in the cases of vibrationshypowered piezoelectric and electrostatic energy harvesting devices Their efficiency is typically above 80 for output power levels in the 50 microW to 1 mW range and with meshychanical frequencies between 10 Hz and 100 Hz [50] One of the critical points in this ultra low power domain is the OFF state resistance of the electronic switches which are

made up with bipolar or MOSFET transistors Indeed the OFF stage resistance of such transistors is typically below 100 MΩ so the leakage currents of the switches may reach several microamperes and they may dissipate most of the power produced by the pyroelectric material This point becomes even more critical as the frequency of the temshyperature cycle is low As a conclusion although not develshyoped yet it is highly feasible to think about high-efficiency amplifiers for effective regenerative thermodynamic cycles on ferroelectric materials

B Case of SSHI

Section II explored theoretical developments for SECE and SSDI cycles in the case of pure energy conversion without effective energy harvesting It was shown that the SECE cycle is a special case of SSDI cycle where β = 0 For the sake of presenting a comprehensive argument we will develop here the SSHI case

The SSHI energy conversion cycle may be performed with the ldquoidealrdquo switching mode power interface previshyously presented However understanding of this technique is simpler considering the circuit that was first proposed [2] the pyroelectric element is connected to a switched inshyductor in parallel to the ac side of a rectifier bridge the dc side of the rectifier being connected to an energy storage cell as shown in Fig 11(a) Typical waveforms are shown in Fig 11(b) After reaching a minimum temperature θc the switch S1 is turned ON An oscillating discharge of the pyroelectric capacitor C occurs then through the inductor radic L The switch is turned OFF after a time π LC correshysponding to half a period of the electrical oscillations so that the pyroelectric voltage polarity is reversed A small amount of energy is dissipated in the inductor during this operation so the reversed voltage absolute value is reduced by a factor β compared to its value just before the switch is turned ON (0 le β lt 1) Then the temperature inshycreases resulting in an increase of the open circuit voltage When reaching voltage Vdc the rectifier bridge conductshying and the current flowing out the pyroelectric element directly supply the energy storage cell until the temperashyture reaches its maximum value θh We will consider here that when the diode bridge conducts the total electric charge flowing out the pyroelectric element exactly equals the charge flowing through the energy storage cell In such case we have

Q = CV + pΦθ (43)

where Q V θ C Φ are electric charge voltage temperashyture capacitance of the pyroelectric element and the surshyface of its electrodes respectively Note that it is easier to formulate the problem using voltage and electric charge variables instead of electric induction and electric field variables when the circuit used for achieving the energy conversion cycles is included in the analysis When temshyperature reaches value θcond the rectifier bridge starts to conduct Considering that the ON stage duration of the


Fig 10 Typical waveforms of (a) SECE and (b) SSDI with the H-bridge switching mode power interface

Fig 11 (a) Circuit diagram of SSHI circuit and (b) typical waveforms

switch S1 is much smaller than the temperature cycle peshyriod and this temperature θcond is given by

pΦ(θCond minus θc) = C(Vdc minus β middot Vdc) (44)

Then we calculate the electric charge generated by the pyroelement between time tcond and T2

∆Q = pΦ(θh minus θcond) (45)

The energy received by the storage cell between time tcond

and T2 is given by

∆W = ∆Q middot Vdc (46)

Symmetry of the cycle and combination of (44) with (45) and (46) lead to the expression of the energy harvested per cycle

Wcycle = 2Vdc(pΦ(θh minus θc) minus CVdc(1 minus β)) (47)

According to (47) there is an optimal value of voltage Vdc

that maximizes the harvested energy

pΦ(θh minus θc)(Vdc)opt = (48) 2C(1 minus β)

Thus maximum energy harvested per temperature cycle is given by

(pΦ(θh minus θc))2

WMAX = (49) 2C(1 minus β)

And the maximum harvested energy per cycle and per volume unit of active material is given by

p2(θh minus θc)2

WMAX(J middot m minus3) = 2εθ (50)

33(1 minus β)

To illustrate the order of magnitude of power energy and optimal dc voltage consider a 2C temperature variation at 1 Hz (θM = 1C) with an inversion ratio β of 08 and a pyroelectric element of 1 nF ((111)PMN-PT single crystal


TABLE IV Energy Densities for 300 to 310 K Cyclic Temperature

Variations and Number of Cycles Per Hour for Producing

30 microWCM3

Energy Cycles per hour density for producing

Material (Jcm3) 30 microWcm3

111 PMN-025PT Single crystal 0149 0725 PMN-025PT Ceramic 00118 912 PbCaTiO3 Thin film 000855 126 PVDF 000540 200

area of 1 cm2 and thickness of 850 microm) Those parameters give (Vdc)OPT = 890 V harvested power of 032 mW and harvested energy per cycle of 032 mJ In addition the reshysults presented above show that optimizing energy convershysion in no-load cases is the same as optimizing the energy harvesting especially in terms of materials properties and inversion ratio

Finally the question that comes when speaking about pyroelectric energy harvesting is the performance comparshyison with thermoelectric effect Conditions for energy conshyversion are not the same because energy harvesting using pyroelectric effect requires temperature variations in time whereas thermoelectric effect needs temperature variations in space (temperature gradients) The proposed comparshyison is done considering temperature variations between 300 K and 310 K at frequency F for thermoelectric energy conversion and pyroelectric energy conversion in the case of 300 K and 310 K for the cold and hot sources respecshytively Typical energy density of miniature thermoelectric modules in this case of operation is near 30 microWcm3 power density As a comparison Table IV gives the number of temperatures cycles per hour needed to get 30 microWcm3

power density with pyroelectric effect in the case of SSHI cycles (β = 06) for several materials

V Conclusion

Energy harvesting from heat is possible using pyroshyelectric materials and may be of great interest compared to thermoelectric conversion Pyroelectric energy harvestshying requires temporal temperature variationsmdashwe may say time gradients of temperaturesmdashwhereas thermoelectric energy harvesting requires spatial gradients of temperashytures Usual wasted heat more likely creates spatial gradishyents rather than time gradients However the conversion ratio (defined as the ratio of net harvested energy divided by the heat taken from the hot reservoir) could be much larger for pyroelectric energy harvesting In theory it could reach the conversion ratio of the Carnot cycle whatever the materials properties However the conversion ratio of thermoelectric conversion is highly limited by the materishyals properties

We showed four different pyroelectric energy harvestshying cycles having different effectiveness and advantages

The simplest devices would require a very high elecshytrothermal coupling factor (k2 = p2θ0(ε33

θ cE )) and we focused the investigation on pyroelectric materials comparing that coupling factor We found that using 075Pb(Mg13Nb23)O3-025PbTiO3 single crystals orishyented (111) and SSHI with an inversion factor of 08 it should be possible to reach a conversion of more than 50 of the Carnot cycle ratio (14 of the Carnot cycle for efshyfective energy harvesting) Some important problems were pointed out that can interfere with the technical impleshymentation of such cycles such as the frequency problems and efficiency optimization Nevertheless we can expect to get very high harvested energies using realistic materials compared to standard thermoelectric devices

Finally ferroelectric materials are both pyroelectric and piezoelectric When designing an electrothermal energy harvester it should be possible to get high sensitivity to vibrations (when bonding a ferroelectric material on a host structure) However the solution will be two-fold The freshyquencies may be very different between vibration and temshyperature vibration In such cases electronics may easily be adapted and optimized to address only one frequency range On the other hand frequencies may be close to each other In such cases the resulting voltage on the active elshyement will be the sum of both contributions A smart conshytroller is then necessary to optimize the energy conversion similar to the situation illustrated by the random signals case in electromechanical energy harvesting [18]

References

[1] S Roundy E S Leland J Baker E Carleton E Reilly E Lai B Otis J M Rabaey P K Wright and V Sundararashyjan ldquoImproving power output for vibration-based energy scavshyengersrdquo IEEE Pervasive Computing no 1 pp 28ndash36 2005

[2] D Guyomar A Badel E Lefeuvre and C Richard ldquoTowards energy harvesting using active materials and conversion improveshyment by nonlinear processingrdquo IEEE Trans Ultrason Ferroshyelect Freq Contr vol 52 no 4 pp 584ndash595 2005

[3] E Lefeuvre A Badel C Richard and D Guyomar ldquoPiezoshyelectric energy harvesting device optimization by synchronous electric charge extractionrdquo J Intell Mater Syst Struct vol 16 no 10 pp 865ndash876 2005

[4] A Badel E Lefeuvre C Richard and D Guyomar ldquoEffishyciency enhancement of a piezoelectric energy harvesting device in pulsed operation by synchronous charge inversionrdquo J Intell Mater Syst Struct vol 16 no 10 pp 889ndash901 2005

[5] A Badel D Guyomar E Lefeuvre and C Richard ldquoPiezoelecshytric energy harvesting using a synchronized switch techniquerdquo J Intell Mater Syst Struct vol 17 no 8-9 pp 831ndash839 2006

[6] E Lefeuvre A Badel C Richard and D Guyomar ldquoA comparshyison between several vibration-powered piezoelectric generators for standalone systemsrdquo Sens Actuators A vol 126 no 2 pp 405ndash416 2006

[7] A Badel A Benayad E Lefeuvre L Lebrun C Richard and D Guyomar ldquoSingle crystals and nonlinear process for outshystanding vibration powered electrical generatorsrdquo IEEE Trans Ultrason Ferroelect Freq Contr vol 53 no 4 pp 673ndash684 2006

[8] J Grindlay An Introduction to the Phenomenological Theory of Ferroelectricity Oxford Pergamon Press 1970

[9] D Guyomar G Sebald B Guiffard and L Seveyrat ldquoFershyroelectric electrocaloric conversion in 075(PbMg13Nb23O3)shy025(PbTiO3) ceramicsrdquo J Phys D Appl Phys vol 39 no 20 pp 4491ndash4496 2006


[10] G Sebald L Seveyrat D Guyomar L Lebrun B Guiffard and S Pruvost ldquoElectrocaloric and pyroelectric properties of 075Pb(Mg13Nb23)O3-025PbTiO3 single crystalsrdquo J Appl Phys vol 100 no 12 art no 124112 2006

[11] G Sebald S Pruvost L Seveyrat L Lebrun D Guyomar and B Guiffard ldquoStudy of electrocaloric properties of high dielectric constant ferroelectric ceramics and single crystalsrdquo J Eur Ceshyramic Society vol 27 no 13-15 pp 4021ndash4024 2007

[12] R Radebaugh W N Lawless J D Siegwarth and A J Morshyrow ldquoFeasibility of electrocaloric refrigeration for the 4Kndash15K temperature rangerdquo Cryogenics vol 19 no 4 pp 187ndash208 1979

[13] R Zhang S Peng D Xiao Y Wang B Yang J Zhu P Yu and W Zhang ldquoPreparation and characterization of (1shyx)Pb(Mg13 Nb23)O3-xPbTiO3 electrocaloric ceramicsrdquo Cryst Res Technol vol 33 no 5 pp 827ndash832 1998

[14] L Shaobo and L Yanqiu ldquoResearch on the electrocaloric efshyfect of PMNPT solid solution for ferroelectrics MEMS microshycoolerrdquo Materials Science Engineering B vol 113 no 1 pp 46ndash49 2004

[15] E Birks L Shebanov and A Sternerg ldquoElectrocaloric effect in PLZT ceramicsrdquo Ferroelectrics vol 69 pp 125ndash129 1986

[16] P D Thacher ldquoElectrocaloric effects in some ferroelectric and antiferroelectric Pb(ZrTi)O3 compoundsrdquo J Appl Phys vol 39 no 4 pp 1996ndash2002 1968

[17] L Shebanovs K Borman W N Lawless and A Kalvane ldquoElectrocaloric effect in some perovskite ferroelectric ceramics and multilayer capacitorsrdquo Ferroelectrics vol 273 pp 137ndash142 2002

[18] L Shebanovs and K Borman ldquoOn lead-scandium tantalate solid solutions with high electrocaloric effectsrdquo Ferroelectrics vol 127 pp 143ndash148 1992

[19] A S Mischenko Q Zhang J F Scott R W Whatmore and N D Mathur ldquoGiant electrocaloric effect in thin-film PbZr095 Ti005O3rdquo Science vol 311 no 5765 pp 1270ndash1271 2006

[20] A S Mischenko Q Zhang R W Whatmore J F Scott and N D Mathur ldquoGiant electrocaloric effect in the thin film reshylaxor ferroelectric 09PbMg13Nb23O3-01PbTiO3 near room temperaturerdquo Appl Phys Lett vol 89 no 24 art no 242912 2006

[21] G Min D M Rowe and K Kontostavlakis ldquoThermoelectric figure-of-merit under large temperature differencesrdquo J Phys D Appl Phys vol 37 no 8 pp 1301ndash1304 2004

[22] I B Cadoff and E Miller Thermoelectric Materials and Deshyvices New York Reinhold Publishing Corporation 1960

[23] H Beyer J Nurnus H Bottner A Lambrecht E Wagner and G Bauer ldquoHigh thermoelectric figure of merit ZT in PbTe and Bi2Te3-based superlattices by a reduction of the thermal conductivityrdquo Physica E vol 13 no 2-4 pp 965ndash968 2002

[24] B Ducharne D Guyomar and G Sebald ldquoLow frequency modshyeling of hysteresis behavior and dielectric permittivity in ferroshyelectric ceramics under electric fieldrdquo J Phys D Appl Phys vol 40 no 2 pp 551ndash555 2007

[25] G Sebald E Boucher and D Guyomar ldquoDry-friction based model for hysteresis related behaviors in ferroelectric materishyalsrdquo J Appl Phys vol 96 no 5 pp 2785ndash2791 2004

[26] G Sebald L Lebrun and D Guyomar ldquoModeling of elasshytic nonlinearities in ferroelectric materials including nonlinear losses Application to relaxors single crystalsrdquo IEEE Trans Ulshytrason Ferroelect Freq Contr vol 52 no 4 pp 596ndash603 2005

[27] R C Smith S Seelecke Z Ounaies and J Smith ldquoA free energy model for hysteresis in ferroelectric materialsrdquo J Intell Mater Syst Struct vol 11 no 1 pp 62ndash79 2000

[28] D Guyomar and A Badel ldquoNonlinear semi-passive multimodal vibration damping An efficient probabilistic approachrdquo J Sound Vibration vol 294 no 1-2 pp 249ndash268 2006

[29] R W Whatmore ldquoPyroelectric arrays Ceramics and thin filmsrdquo J Electroceram vol 13 no 1-3 pp 139ndash147 2004

[30] R A Dorey and R W Whatmore ldquoElectroceramic thick film fabrication for MEMSrdquo J Electroceram vol 12 no 1-2 pp 19ndash32 2004

[31] D Damjanovic ldquoFerroelectric dielectric and piezoelectric propshyerties of ferroelectric thin films and ceramicsrdquo Rep Prog Phys vol 61 no 9 pp 1267ndash1324 1998

[32] A Benayad G Sebald L Lebrun B Guiffard S Pruvost D Guyomar and L Beylat ldquoSegregation study and modeling of Ti in Pb[(Mn13Nb23)060 Ti040]O3 single crystal growth by Bridgman methodrdquo Mater Res Bull vol 41 no 6 pp 1069ndash 1076 2006

[33] G Sebald L Lebrun and D Guyomar ldquoStability of morshyphotropic PMN-PT single crystalsrdquo IEEE Trans Ultrason Ferroelect Freq Contr vol 51 no 11 pp 1491ndash1498 2004

[34] G Sebald L Lebrun B Guiffard and D Guyomar ldquoMorshyphotropic PMN-PT system investigated through comparison beshytween ceramic and crystalrdquo J Eur Ceram Soc vol 25 no 12 pp 2509ndash2513 2005

[35] K Zawilski C Custodio R Demattei S G Lee R Monteiro H Odagawa and R Feigelson ldquoSegregation during the vertical Bridgman growth of lead magnesium niobate-lead titanate single crystalsrdquo J Cryst Growth vol 258 no 3 pp 353ndash367 2003

[36] J Han A von Jouanne T Le K Mayaram and T S Fiez ldquoNovel power conditioning circuits for piezoelectric micropower generatorsrdquo in Proc 19th Annu IEEE Appl Power Electron Conf Expo vol 3 2004 pp 1541ndash1546

[37] X Shengwen K D T Ngo T Nishida C Gyo-Bum and A Sharma ldquoConverter and controller for micro-power energy harshyvestingrdquo in Proc 20th Annu IEEE Appl Power Electron Conf Expo vol 1 2005 pp 226ndash230

[38] Y Tang X Zhao X Wan X Feng W Jin and H Luoa ldquoComshyposition dc bias and temperature dependence of pyroelectric properties of 1 1 1-oriented (1-x)Pb(Mg13Nb23)O3-xPbTiO3 crystalsrdquo Mater Sci Eng B vol 119 no 1 pp 71ndash74 2005

[39] M Davis D Damjanovic and N Setter ldquoPyroelecshytric properties of (1-x)Pb(Mg13 Nb23)O3-xPbTiO3 and (1shyx)Pb(Zn13 Nb23)O3-xPbTiO3 single crystals measured using a dynamic methodrdquo J Appl Phys vol 96 no 5 pp 2811ndash 2815 2004

[40] W Y Ng B Ploss H L W Chan F G Shin and C L Choy ldquoPyroelectric properties of PZTP(VDF-TrFE) 0-3 comshypositesrdquo in Proc 12th IEEE Int Symp Applications Ferroshyelectrics vol 2 2000 pp 767ndash770

[41] D S Kang M S Han S G Lee and S H Song ldquoDielectric and pyroelectric properties of barium strontium calcium titanate ceramicsrdquo J Eur Ceram Soc vol 23 no 3 pp 515ndash158 2003

[42] A Pelaiz Barranco F Calderon Pinar and O Perez Martinez ldquoPLZT ferroelectric ceramics on the morphotropic boundary phase Study as possible pyroelectric sensorsrdquo Phys Stat Sol (a) vol 186 no 3 pp 479ndash485 2001

[43] M K Cheung K W Kwok H L W Chan and C L Choy ldquoDielectric and pyroelectric properties of lead zirconate titanate composite filmsrdquo Integrated Ferroelectrics vol 54 no 1 pp 713ndash719 2003

[44] E Yamaka H Watanabe H Kimura H Kanaya and H Ohkuma ldquoStructural ferroelectric and pyroelectric of highly cshyaxis oriented Pb1-xCaxTiO3 thin film grown by radio-frequency magnetron sputteringrdquo J Vacuum Sci Technol A Vacuum Surfaces Films vol 6 pp 2921ndash2928 1988

[45] Q Zhang and R W Whatmore ldquoImproved ferroelectric and pyroelectric properties in Mn-doped lead zirconate titanate thin filmsrdquo J Appl Phys vol 94 no 8 pp 5228ndash5233 2003

[46] S B Lang and S Muensit ldquoReview of some lesser-known applishycations of piezoelectric and pyroelectric polymersrdquo Appl Phys A Mater Sci Proc vol 85 no 2 pp 125ndash134 2006

[47] L F Malmonge J A Malmonge and W K Sakamoto ldquoStudy of pyroelectric activity of PZTPVCD-HFP compositerdquo Mateshyrials Research vol 6 no 4 pp 469ndash473 2003

[48] K S Lam Y W Wong L S Tai Y M Poon and F G Shin ldquoDielectric and pyroelectric properties of lead zirshyconatepolyurethane compositesrdquo J Appl Phys vol 96 no 7 pp 3896ndash3899 2004

[49] R W Erickson and D Maksimovic Fundamentals of Power Electronics Berlin Science+Business Media Inc 2001

[50] E Lefeuvre D Audigier C Richard and D Guyomar ldquoBuckshyboost converter for sensorless power optimization of piezoelectric energy harvesterrdquo IEEE Trans Power Electron vol 22 no 5 pp 2018ndash2025 2007


Gael Sebald was born in 1978 He graduated from INSA Lyon in Electrical Engineering in 2001 (MS degree) and received a masterrsquos deshygree in acoustics the same year He received a PhD degree in acoustics in 2004 He was then a Japan Society for Promotion of Scishyence Awardee (2004ndash2005) for a post-doctoral position in the Institute of Fluid Science of Tohoku University Sendai Japan where he worked on ferroelectric fibers and vibration control

Gael Sebald is now associate professor at INSA Lyon Lyon France His main research interests are now mateshyrials characterization hysteresis modeling multiphysics coupling in smart materials and energy harvesting on vibration and heat

Elie Lefeuvre was born in France in 1971 He received the BS and MS degrees in elecshytrical engineering respectively from Paris-XI University Paris France in 1994 and from Institut National Polytechnique de Toulouse Toulouse France in 1996 At the same time he was a student at the electrical engineershying department of Ecole Normale Superieure de Cachan Cachan France He prepared his PhD degree at Laval University of Quebec Quebec Canada and at the Institut National

Polytechnique de Toulouse France He received the diploma from both universities in 2001 for his work on power electronics converters topologies In 2002 he got a position of assistant professor at Institut National des Sciences Appliquees (INSA) de Lyon Lyon France and he joined the Laboratoire de Genie Electrique et Ferroelectricite His current research activities include piezoelectric systems energy harvesting vibration control and noise reduction

Daniel Guyomar received a degree in meshychanical engineering a Doctor-engineer deshygree in acoustics from Compiegne University and a PhD degree in physics from Paris VII University Paris France From 1982 to 1983 he worked as a research associate in fluid dyshynamics at the University of Southern Calishyfornia Los Angeles CA He was a National Research Council Awardee (1983ndash1984) deshytached at the Naval Postgraduate School to develop transient wave propagation modeling He was hired in 1984 by Schlumberger to lead

several research projects dealing with ultrasonic imaging then he moved to Thomson Submarine activities in 1987 to manage the research activities in the field of underwater acoustics Pr Daniel Guyomar is presently a full-time University Professor at INSA Lyon (Lyon France) director of the INSA-LGEF laboratory His present research interests are in the field of semi-passive vibration control energy harvesting on vibration and heat ferroelectric modeling elecshytrostrictive polymers and piezoelectric devices


to thermoelectric generators pyroelectric materials do not need a temperature gradient (spatial gradient) but temposhyral temperature changes This opens different applications fields where temperature gradients are not possible and where temperature is not static Small-scale microgenerashytors with dimensions smaller than the temperature spatial fluctuation length may with difficulty be subjected to temshyperature gradients Natural temperature time variations occur due to convection process and this thermal energy is difficult to transform in a stable temperature gradient On the other hand it is possible to transform a tempershyature gradient into a temperature variable in time using a caloric fluid pumping between hot and cold reservoirs The pumping unit may require much less energy than the total produced energy (depending on the scale of the deshyvice) and may produce temperature variations of 1 to 20C at 2 Hz for example To optimize energy harvesting from temperature the first step should be the optimization of energy conversion Then the problems of electric loading (modifying the cycles shape) should be addressed

The aim of this paper is to present methods for optimizshying energy conversion from temperature variations using pyroelectric materials and to describe the most important parameters in materials choice and device design The first part is devoted to thermodynamic cycles that could be used for energy conversion and the second part deals with a pyroelectric materials survey Finally the practical apshyplication problems of thermodynamic cycles are discussed in the last part of the article

II Thermodynamic Cycles

When talking about energy harvesting from heat one should first consider classical thermodynamic cycles We aim to answer here several questions

bull What cycles could be imagined to harvest energy from heat

bull What is their efficiency (defined as electric work dishyvided by the heat transferred from a hot reservoir to a cold reservoir)

bull What are the important parameters of the pyroelectric materials for optimizing the efficiency

bull Are those cycles realistic

For a given temperature variation it is possible to conshysider it as a static problem involving two temperature reservoirs which is a common interpretation in thermoshydynamics We need first to establish the equations of pyshyroelectric materials [8]

dD = εθ (1) 33dE + pdθ

dΓ = pdE + cE dθ

(2) θ

where D E θ and Γ are electric displacement electric field temperature and entropy respectively The coeffishycients are defined as

TABLE I Coefficients Used in the Simulations

Coefficient Unit Value

εθ Fmiddotmminus1 lowast 33 1000ε0

p Cmiddotmminus2middotKminus1 10minus3

cE Jmiddotmminus3middotKminus1 25 times 10minus6

θh K 301 θc K 300

lowastFor Carnot cycle εθ 33 = 100ε0 for the sake of clarity on the figure (to

obtain larger difference between adiabatic and isothermal dielectric permittivity)

dD dD dΓ dU

εθ 33 = p = = cE = (3)

dE dθ dE dθθ E

In the following part we present four different energy harshyvesting cycles For each cycle we give PE cycle (polarshyization vs electric field) and Γθ cycle (entropy vs temshyperature) In the two cycles the area of the cycle is the converted energy It is the same area in PE cycle and in Γθ cycle In the PE cycle the cycle is clockwise meaning a negative energy (ie energy given to the outer medium) In the Γθ cycle the cycle counter-clockwise meaning a positive energy (ie energy given by the outer medium to the material) The coefficients defined in (3) are assumed to be constant for the electric field and temperature ranges considered here Coefficients used in simulations are given in Table I

A Carnot Cycle

The Carnot cycle is defined as two adiabatic and two isothermal curves on the (PE) cycle (see Fig 1) It is conshysidered as the optimal energy harvesting cycle whose effishyciency is

θcηCarnot = 1 minus (4)

θh

where θc and θh are cold and hot temperatures respecshytively

The demonstration of that result is very interesting to understand the underlying limitations of such cycle In the first adiabatic increase of the electric field (path A-B)

dθ p= minus dE (5)

θ cE θh p

ln = minus EM (6) θc cE

where EM is the maximum amplitude of the applied elecshytric field

In practical applications this means that one should know the maximum temperature variation to know what the necessary electric field is In the isothermal decrease of the electric field (path B-C)

dΓ = pdE and dQ = θdS (7)

Qh = minuspEM θh






θh



B SECE Cycle




Em = minus ε



2


εθ 33

2



2 ) (11) 33






2εθ 33










|WE | k2


with

p2θhk2 =

εθ (18) 33cE










C SSDI Cycle



Em0

EM0 = β (20)











33



Using (20) and (21)

2p(θh


p2 1 + β +


1 minus β33


2



2 ) 33


Using (15)






1 + k2 + (27) 1 minus β 2



1 minus β


= k2 1 + β k2 (29) app 1 minus β


k2


1 + k2 app





D Resistive Cycle




D = εθ 33 E + pθ (31)

Q = pθ E + cE θ (32)




E = minusρD (33)



1 ρOPT = (34)

ωεθ 33


π p2


33



And finally

ηResistive = π

4 k2ηCarnot (37)






Carnot

SECE

ηref = 1 minus θc

θh

η = k2

1 + 05k2ηref ηref

EM = minus cE

p ln(

θh

θc

)

EM = minus p

εθ 33

(θh minus θc)





SSDI ηSSHI = k2

1 + k2 (

2β

1 minus β +

ηref

2

) 1 + β


εθ 33(1 minus β)





2 radic

2εθ 33

















Fi = p

(39) cE


Fv = p

(40) εθ 33cE













lowast





Bulk ceramics


Thin films















B Case of SSHI



Q = CV + pΦθ (43)










and T2 is given by











p2(θh minus θc)2


33(1 minus β)





30 microWCM3







V Conclusion






References
































































θh



B SECE Cycle




Em = minus ε



2


εθ 33

2



2 ) (11) 33






2εθ 33










|WE | k2


with

p2θhk2 =

εθ (18) 33cE










C SSDI Cycle



Em0

EM0 = β (20)











33



Using (20) and (21)

2p(θh


p2 1 + β +


1 minus β33


2



2 ) 33


Using (15)






1 + k2 + (27) 1 minus β 2



1 minus β


= k2 1 + β k2 (29) app 1 minus β


k2


1 + k2 app





D Resistive Cycle




D = εθ 33 E + pθ (31)

Q = pθ E + cE θ (32)




E = minusρD (33)



1 ρOPT = (34)

ωεθ 33


π p2


33



And finally

ηResistive = π

4 k2ηCarnot (37)






Carnot

SECE

ηref = 1 minus θc

θh

η = k2

1 + 05k2ηref ηref

EM = minus cE

p ln(

θh

θc

)

EM = minus p

εθ 33

(θh minus θc)





SSDI ηSSHI = k2

1 + k2 (

2β

1 minus β +

ηref

2

) 1 + β


εθ 33(1 minus β)





2 radic

2εθ 33

















Fi = p

(39) cE


Fv = p

(40) εθ 33cE













lowast





Bulk ceramics


Thin films















B Case of SSHI



Q = CV + pΦθ (43)










and T2 is given by











p2(θh minus θc)2


33(1 minus β)





30 microWCM3







V Conclusion






References

































































|WE | k2


with

p2θhk2 =

εθ (18) 33cE










C SSDI Cycle



Em0

EM0 = β (20)











33



Using (20) and (21)

2p(θh


p2 1 + β +


1 minus β33


2



2 ) 33


Using (15)






1 + k2 + (27) 1 minus β 2



1 minus β


= k2 1 + β k2 (29) app 1 minus β


k2


1 + k2 app





D Resistive Cycle




D = εθ 33 E + pθ (31)

Q = pθ E + cE θ (32)




E = minusρD (33)



1 ρOPT = (34)

ωεθ 33


π p2


33



And finally

ηResistive = π

4 k2ηCarnot (37)






Carnot

SECE

ηref = 1 minus θc

θh

η = k2

1 + 05k2ηref ηref

EM = minus cE

p ln(

θh

θc

)

EM = minus p

εθ 33

(θh minus θc)





SSDI ηSSHI = k2

1 + k2 (

2β

1 minus β +

ηref

2

) 1 + β


εθ 33(1 minus β)





2 radic

2εθ 33

















Fi = p

(39) cE


Fv = p

(40) εθ 33cE













lowast





Bulk ceramics


Thin films















B Case of SSHI



Q = CV + pΦθ (43)










and T2 is given by











p2(θh minus θc)2


33(1 minus β)





30 microWCM3







V Conclusion






References



































































33



Using (20) and (21)

2p(θh


p2 1 + β +


1 minus β33


2



2 ) 33


Using (15)






1 + k2 + (27) 1 minus β 2



1 minus β


= k2 1 + β k2 (29) app 1 minus β


k2


1 + k2 app





D Resistive Cycle




D = εθ 33 E + pθ (31)

Q = pθ E + cE θ (32)




E = minusρD (33)



1 ρOPT = (34)

ωεθ 33


π p2


33



And finally

ηResistive = π

4 k2ηCarnot (37)






Carnot

SECE

ηref = 1 minus θc

θh

η = k2

1 + 05k2ηref ηref

EM = minus cE

p ln(

θh

θc

)

EM = minus p

εθ 33

(θh minus θc)





SSDI ηSSHI = k2

1 + k2 (

2β

1 minus β +

ηref

2

) 1 + β


εθ 33(1 minus β)





2 radic

2εθ 33

















Fi = p

(39) cE


Fv = p

(40) εθ 33cE













lowast





Bulk ceramics


Thin films















B Case of SSHI



Q = CV + pΦθ (43)










and T2 is given by











p2(θh minus θc)2


33(1 minus β)





30 microWCM3







V Conclusion






References





























































D Resistive Cycle




D = εθ 33 E + pθ (31)

Q = pθ E + cE θ (32)




E = minusρD (33)



1 ρOPT = (34)

ωεθ 33


π p2


33



And finally

ηResistive = π

4 k2ηCarnot (37)






Carnot

SECE

ηref = 1 minus θc

θh

η = k2

1 + 05k2ηref ηref

EM = minus cE

p ln(

θh

θc

)

EM = minus p

εθ 33

(θh minus θc)





SSDI ηSSHI = k2

1 + k2 (

2β

1 minus β +

ηref

2

) 1 + β


εθ 33(1 minus β)





2 radic

2εθ 33

















Fi = p

(39) cE


Fv = p

(40) εθ 33cE













lowast





Bulk ceramics


Thin films















B Case of SSHI



Q = CV + pΦθ (43)










and T2 is given by











p2(θh minus θc)2


33(1 minus β)





30 microWCM3







V Conclusion






References






























































Carnot

SECE

ηref = 1 minus θc

θh

η = k2

1 + 05k2ηref ηref

EM = minus cE

p ln(

θh

θc

)

EM = minus p

εθ 33

(θh minus θc)





SSDI ηSSHI = k2

1 + k2 (

2β

1 minus β +

ηref

2

) 1 + β


εθ 33(1 minus β)





2 radic

2εθ 33

















Fi = p

(39) cE


Fv = p

(40) εθ 33cE













lowast





Bulk ceramics


Thin films















B Case of SSHI



Q = CV + pΦθ (43)










and T2 is given by











p2(θh minus θc)2


33(1 minus β)





30 microWCM3







V Conclusion






References































































Fi = p

(39) cE


Fv = p

(40) εθ 33cE













lowast





Bulk ceramics


Thin films















B Case of SSHI



Q = CV + pΦθ (43)










and T2 is given by











p2(θh minus θc)2


33(1 minus β)





30 microWCM3







V Conclusion






References





























































lowast





Bulk ceramics


Thin films















B Case of SSHI



Q = CV + pΦθ (43)










and T2 is given by











p2(θh minus θc)2


33(1 minus β)





30 microWCM3







V Conclusion






References



































































B Case of SSHI



Q = CV + pΦθ (43)










and T2 is given by











p2(θh minus θc)2


33(1 minus β)





30 microWCM3







V Conclusion






References



































































and T2 is given by











p2(θh minus θc)2


33(1 minus β)





30 microWCM3







V Conclusion






References






























































30 microWCM3







V Conclusion






References



























































pyroelectric energy conversion: optimization...

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