FIELD OF THE INVENTION This invention relates to methods and apparatus for piezo-pyroelectric energy conversion, and more particularly to such methods and apparatus which utilize the direct conversion of thermal energy to electrical energy using an electrocaloric effect in pyroelectric materials by the use of one or more capacitors having temperature dependent pyroelectric properties, the capacitors being in thermal communication with metal contacts for increasing the converted portion of the heat flow propagating from the hot to cold heat sink and a means for resonating the capacitor at the operating frequency.

BACKGROUND OF THE INVENTION The present invention was developed to fill a need for a device which efficiently converts thermal energy to electrical energy with power densities large enough for practical applications.

Current pyroelectric power converters include stacked capacitors having temperature dependent capacitance and the use of reeds which serve as thermal switches and are caused to vibrate by the flow of vapor carrying heat between stages, thereby pulsing the heat at the proper frequency and phase through the stacked capacitors. Another known device exploits a somewhat different concept in an energy conversion system in which a first material within the region between the electrodes of a capacitor is replaced, following charging of the capacitor, by a second material having a lower dielectric constant than the first material. The capacitor is then discharged and the first material is restored to the region between the capacitor electrodes for subsequent recharging.

Another approach uses a material with a dielectric constant different from that of a vacuum which is inserted between capacitor electrodes. In this case, mechanical work is performed against an electric field and the device is essentially the same as an electromagnetic motor. This approach is different from using pyroelectric materials and electrocaloric effect, because it uses capacitance change at a constant charge. In the case of pyroelectric action, the charge is changing according to the temperature

change. If the relative dielectric constant is also changing with temperature, it is a side effect.

A further approach uses electrocaloric effect for pyroelectric conversion of heat into electricity. However, this approach has a large time constant because the pyroelectric material is mechanically moved from the hot to cold zone. With respect to devices deriving electrical energy by thermally cycling capacitors with temperature dependent properties, the small efficiencies and low power densities have apparently precluded their use in any practical application for the production of electrical energy.

There remains a need to provide a more satisfactory solution to converting thermal energy to electrical energy, and alternatively, electrical energy to refrigeration.

SUMMARY OF THE INVENTION

The present invention seeks to resolve a number of the problems which have been experienced in the background art, as identified above. More specifically, the apparatus and method of this invention constitute an important advance in the art of pyroelectric power conversion, as evidenced by the following objects and advantages realized by the invention over the background art.

One object of the present invention is to combine pyroelectric and piezoelectric effects.

A further object of the present invention is to enhance operating efficiency by resonating high frequency oscillations from a piezoelectric effect.

Additionally, it is an object of the present invention to enhance the pyroelectric effect while decreasing the thermal inertia of the system by placing a metal contact in thermal communication with a pyroelectric material during piezoelectric oscillations. A metal next to the pyroelectric material brings down dramatically the time constant of heat replenishment, which enhances the harvesting of the charge created.

Yet another object of the present invention is to increase performance by matching the thermal inertia of the device with the piezoelectric oscillations.

Additional objects and advantages of the invention will be apparent from the description which follows, or may be learned by the practice of the invention.

Briefly summarized, the foregoing objects are achieved by an apparatus which comprises one or more piezo-pyroelectric material plates with thermally conductive metal electrodes which resonate at high frequency and are in thermal communication with hot and cold heat sinks to create a thermal gradient and thus heat flow along the metal electrodes and across the pyroelectric material. The piezoelectric resonance causes small alternating temperature rises and drops due to pyroelectric action. By removing the pyroelectric charge of one sign with an external electrical circuit. asymmetric heat flow is created from the metal electrodes to the piezo-pyroelectric material. This asymmetric heat flow is converted into electrical energy. The resonance brings down the dissipation losses in the piezo-pyroelectric material. This type of converter can be utilized with most materials showing both pyroelectric and piezoelectric properties at varying efficiencies.

BRIEF DESCRIPTION OF DRAWINGS In order to more fully understand the manner in which the above-recited advantages and objects of the invention are obtained, a more particular description of the invention will be rendered by reference to specific embodiments thereof which are illustrated in the appended drawings. Understanding that these drawings depict only typical embodiments of the invention and are therefore not to be considered limiting of its scope, the presently preferred embodiments and the presently understood best mode of the invention will be described with additional detail through use of the accompanying drawings in which: FIG. 1 is a cross-section view of a pyroelectric converter incorporating teachings of the present invention without the electronics portion.

FIG. 2 is a voltage versus time plot for an electrical circuit powering the present invention.

FIG. 3 is a voltage versus time plot for an electrical circuit powering the present invention.

FIG. 4 is a voltage versus time plot for an electrical circuit powering the present invention.

FIG. 5 shows the dissipation factor vs. voltage for a particular piezoceramic material. FIG. 6 shows the dissipation power vs. voltage for a particular piezoceramic material.

FIG. 7a and 7b show heat sinks which serve to support a stack of pyroelectric materials.

FIG. 8a through 8e are various pyroelectric plate and heat sink configurations. FIG. 9 is a stack of pyroelectric materials with grooves for holding a liquid metal thermal contact.

FIG. 10a and FIG. 10b are stacks of pyroelectric materials having an internal compressing frame for creating a piezoelectric effect.

FIG. 1 la is a pyroelectric material stack having an integrated compressing frame.

FIG. 1 lb is a top view of FIG 1 la.

FIG. 12a through 12c are pyroelectric converters having an integrated heat sink and compressing frame.

FIG. 13 is a graph of the resonant frequency f ₀ . FIG. 14 is a chart of frequency for various oscillation modes of a particular pyroelectric material.

FIG. 15 is a cross-section view of a converter utilizing a PST-based pyroelectric material.

FIG. 16 is one embodiment of an electrical circuit for extracting electrical energy from a pyroelectric converter.

FIG. 17 is a cross-section view of an acoustically coupled PST-based pyroelectric converter.

FIG. 18 is another embodiment of an electrical circuit for extracting electrical energy from a pyroelectric converter. FIG. 19 is another embodiment of an electrical circuit for extracting electrical energy from a pyroelectric converter.

FIG. 20 is a graph of recalculated dependence of extracting circuit resistance on voltage.

FIG. 21 is a graph of the conversion power density dependence for LiTa0 ₃ material on the driving electric field strength. FIG. 22 is a graph of the conversion power density dependence for PZST material.

FIG. 23 is a cross-section view of another embodiment of a pyroelectric converter.

FIG. 24 is a cross-section view of another embodiment of a pyroelectric converter.

FIG. 25 is a cross-section view of another embodiment of a pyroelectric converter.

FIG. 26 illustrates the converting mode of the device shown in FIG. 1.

FIG. 27 illustrates the converting mode of the device shown in FIG. 1 with equal initial temperatures at the hot and cold heat sinks.

FIG. 28 is a block diagram of a frequency adjusting system.

DETAILED DESCRIPTION OF THE INVENTION

The present invention embodies a piezo-pyroelectric converter 10 and is directed to a method and apparatus for conversion of energy generally illustrated in

Figure 1. The present invention utilizes one or more piezo-pyroelectric materials 12 with thermally conductive metal electrodes 14, which resonate at a high frequency and are in thermal communication with a hot heat sink 16 and a cold heat sink 18 to create a thermal gradient and heat flow along the metal electrodes and the piezo- pyroelectric material 12. The hot heat sink 16 and cold heat sink 18 are defined as two thermally conductive materials. Converter 10 operates as a thermal energy to electrical energy converter when the initial temperature differential of the hot and cold heat sinks is greater than zero and a voltage is applied. The converter 10 operates as a heat pump/refrigerator when the initial temperature of the hot and cold heat sinks are equal and a voltage is applied.

The piezoelectric resonance causes small alternating temperature rises and drops across the pyroelectric due to pyroelectric action. By removing the pyroelectric charge of one sign with an external electrical circuit for charge removal, such as a resistive load with a threshold voltage switch or thyristor based switch, asymmetric heat flow is created from the metal electrodes 14 to the piezo-pyroelectric material 12.

Charge removal leads to a voltage difference and asymmetric temperatures in the positive and negative cycles which is converted into electricity. Resonating the material 12 at its acoustical resonance frequency allows the dissipation losses in the material 12 to be lowered. This type of converter can be utilized with materials showing both pyroelectric and piezoelectric properties at varying efficiencies.

1. Principle of Operation

The invention operates on an electrocaloric effect, resulting in a change of pyroelectric temperature caused by a change in the electric field (see, Born, M. "On the Quantum Theory of Pyroelectricity" Reviews of Modern Physics, Volume 17,

Nos. 2 and 3, (April-July, 1945), pp. 245-251).

The change in element volume of crystal energy is governed by the equation dU = TdS + EdP (see Lang, S.B. Sourcebook of Pyroelectricity, N.Y., Gordon and Breach, Science Publishers, Inc., 1974, pp. 1-10, the contents of which are specifically incorporated herein), where T is the temperature, S is the entropy, E is the electric field, and P is the pressure. From here: d(U-EP ₎ = TdS - PdE, ^or

(—)S - - (— _Λ E The electrocaloric coefficient follows the equation: dε ds ^'

_q = _ = - EL. where _p - Ξ I is the pyroelectric constant, p is the density, C dE pc ' dT is the specific heat capacitance, and T is the absolute temperature. From these relationships, the change in temperature is: Δr = k — TΈ - p 0)

PC This equation defines the sample temperature change when the electric field E is changed. The additional "pyroelectric quality coefficient" k is introduced in comparison to the electromechanical coefficient for piezoelectric with values from 0.1

to 0.9 and describes dissipation losses in the material. For a Pb (Zr, Sn, Ti)0 ₃ system (PZST—lead zirconate stannate titanate), the pyroelectric quality coefficient is approximately 0.1 (see, Turtle, B.A. and Payne, D.A. "The Effects of Microstructure on the Electrocaloric Properties of Pb(Zr,Sn.Ti)0 ₃ Ceramics" Ferroelectrics, Vol. 37 (1981) pp. 603-606). Tuttle also indicates maximum values of AT = 2.6° K for

PZST.

Whereas pyroelectric and piezoelectric properties are defined by site displacement in a crystalline lattice, it is reasonable to assume that these effects will be similar down to a single atomic layer of about four angstroms for most crystalline pyroelectric materials. Organic pyroelectrics which do not have crystalline structure will be addressed hereafter. If AC voltage is applied to a capacitor comprising a planar geometry pyroelectric with metal electrodes on both sides, its temperature will change in a sine form relative to the initial temperature according to equation (1), with the AC frequency. Pyroelectrics are known for their low thermal conductivity of about 1-20 W/(m- K). If a metal, having a high thermal conductivity of about 50-450

W/(m- K), is on the surface of the pyroelectric, heat will flow from the metal to the pyroelectric during the cold cycle and from the pyroelectric to the metal during the hot cycle. If energy, defined by equations (6.1) and (6.2) set forth hereafter, is extracted during the cycle, the heat flow will be asymmetric and allow conversion of thermal energy to electric energy.

The limiting factor may be the thermal inertia of the system. The temperature change rate can be estimated from a non-stationary thermal conductivity equation. In a planar geometry, a one dimensional approach is sufficient, as follows:

where q _x is the heat flow along the x - axis, C is the heat capacity, and p is the density of the pyroelectric material. Here q _x = -λ dT/dx, where λ is the thermal conductivity. From symmetry considerations on the plate median, q and dT/dx = O, since two equal heat flows from the two metal electrodes compensate for each other. This implies that the heat flow is changing from a certain value on the plate surface to zero

on the median. It is assumed that λ _mcla] »λ _pyroelectπc , and rate limitations come from the pyroelectric material.

In the present invention, _ L equals AT in equation ( 1 ), divided by the lattice dx parameter, giving the gradient value of 3 x IO ⁸ K/m for ΔT = 0.1 °K and PZT-5A (lead

zirconate-titanate) as a pyroelectric. Even for the worst case scenario, when the heat flow changes linearly from a maximum value on the surface to zero on the plate median, the temperature change rate is approximately 10 ⁵ - IO ⁷ K/s with a time constant = AT — — - 10 ^* -10 ■ Therefore, the thermal inertia is not a

* dτ limiting factor for frequencies up to a megahertz. From the same considerations,

pyroelectrics with good thermal conductivities of about 10-20 W/nvK, such as, LiTaO ₃ , have a time constant of about 3 x IO ^"8 s. For these materials, the specific converter power may be improved, in principle, by incorporating higher frequencies. By comparison, at a temperature difference of 100K along the Y - axis, the time constant for a 1 cm long PZT-5A plate τ _y , equals 0.5 s. The conversion condition is: W _x x _λ > W _y τ _y , where W _% is the heat flow due to pyroelectric conversion and W _y is the heat flow through the metal electrode due to the temperature gradient.

Attention is now drawn to Figure 1 where the pyroelectric material 12 acts as a capacitor in thermal contact between hot heat sink 16 and cold heat sink 18 in a manner wherein the thermal gradient is along its plane indicated by arrows 20. If the heat flow from metal electrodes 14 to pyroelectric material 12 is replenished by thermal gradient 20 from hot heat sink 16 to cold heat sink 18 at the rate defined by the conversion power, the conversion efficiency will be defined by coefficient k multiplied by the ideal Carnot cycle efficiency. The k values can be as high as 0.78 for piezo-pyroelectric material PZT-5A. Heat flowing (designated by arrows 22) directly from hot heat sink 16 to cold heat sink 18 through piezo-pyroelectric material 12 is lost. Also, losses in the electrical circuit bring down the overall efficiency of the converter 10. A different condition exists with organic pyroelectrics not having a crystalline structure. The pyroelectric effect in these materials is probably due to temperature

induced molecular tilt (see, Colbrook, R. et al., "Pyroelectric Organo-Metallic Langmuir-Blodgett Films" Ferroelectrics, Vol. 92 (1989), p. 381-386). If this is the case, the rate is defined by the specific molecular oscillation frequency, which is about 10 ^s - IO ⁹ Hz. This condition is also accompanied by lower values of dielectric constant (electric capacitance), thereby allowing higher operating frequencies.

Although the pyroelectric properties of organic compounds are poor in comparison to ceramics, an efficient converter is feasible because of the higher possible operating frequencies.

The driving AC frequency of the converter 10 is defined by an external electrical circuit discussed hereafter. The losses associated with this drive may be high, depending on the dielectric losses tangent (typically 0.001 - 0.1), the material mechanical quality constant Q (10 - 10 ⁵ ), and the design of converter 10. If the converter 10 is in acoustic resonance at the driving frequency, all of the losses can be diminished by a factor of 100 or more. Hence, the driving frequency must be close to the main harmonic of the stack resonance ω ₀ , according to Figure 13. For organic pyroelectrics, the driving frequency should be close to the higher resonance harmonics n- ω ₀ of the converter 10.

Assuming that the driving voltage from the external electrical circuit is a sine wave, the voltage is as follows: V(t) ~ V sin (ωt) ■ The following illustrates the pyroelectric action of a Li Ta 0 ₃ single crystal plate having an area of lxl cm ² and a thickness of 100 microns. This material has a pyroelectric constant of 230 μC/(Km ² ), a relative dielectric constant of about 50, a thermal conductivity of about 20W/(mK), a density of about 4.6 x 10 ³ kg/πr\ and a heat capacitance of about 500 J/(kg K). Assuming that k = 0.5 in equation (1 ), the operating AC voltage amplitude is V ₀ = 50 V, and the operating temperature is 700 °K.

The capacitance of the capacitor is: where ε is the relative dielectric d constant, ε ₀ is the dielectric constant of vacuum (8.854 x 10 ^"12 F/m), σ is the plate

area, and d is the plate thickness. In this instance, the plate capacitance is

4.16 x 10 '° F.

Using equation (1), the temperature drop in one cycle is 0.017 °K (precision is defined by calculations, i.e. δ = IO ^"6 ). The pyroelectric voltage change associated with this temperature change is: V = poATIC , (3), where/? is the pyroelectric coefficient.

Substituting the variables, the equation becomes:

V ) = ^kTp V(t) = V sin(ω (4), εε _o pC where k is the material quality constant, T is the absolute temperature, p is the

pyroelectric coefficient, ε is the relative dielectric constant, ε ₀ is the vacuum dielectric

constant, p is the density, and C is the heat capacity.

In our case V _p is 0.97V, or a 2% change over driving voltage V ₀ , or 4% over the energy in a driving cycle. This situation is illustrated in Figures 2 and 3. The solid sine line is the driving voltage F ₀ and the dashed line V is the sum of the driving voltage V ₀ and the pyroelectric voltage V _p , where V(t) = V„(t) + V _p (t).

With a voltage sensitive electrical circuit, the dashed area 26 illustrated in Figure 2 can be directed to the useful load and compensate for the driving losses. The circuit can be self-sustaining if initiated with an external pulse generator, such as a

Hewlett Packard pulse/function generator model 81 16A or sine wave generator, through piezoelectric action, as long as the integral energy losses are less than 4% per cycle. For LiTaO ₃ single crystal losses are extremely low due to low values of tan δ (IO ⁴ to IO ^"3 ) and high Q _m (10 ⁵ ). In resonance, energy losses are less than 0.01% per cycle, which are negligible. For polycrystalline materials the losses are higher, but in a reasonable region, e.g., 0.5% for PZT-5A, and can be easily compensated for with pyroelectric action. For materials with high pyroelectric coefficients, e.g., PZST, V _p may be comparable with the driving voltage.

Two examples of power managing electronic circuits are: 1 . Amplitude sensitive (Fig. 2).

2. Phase and amplitude sensitive (Fig. 3).

The circuit for the voltages illustrated in Figure 3 allows more power to be extracted from the same converter 10, than for the circuit for the voltages illustrated in Figure 2. The energy stored in the capacitor plate at the driving voltage follows the equation:

W.(t) = — V] sin ² (ωt) .

2 The energy stored in the capacitor plate at the driving voltage plus the pyroelectric

voltage follows the equation: _{w jt) =} _ι _v * _{} +a sin} 2 _{(ω )} .

2 °

The difference between these two energies, corresponding to Figure 3 (phase and amplitude sensitive power harvesting electrical circuit) are as follows:

AW(t) = — °-V ₀ ² (2α+α ² ) sin ² (ωt). ( ⁵ )

For one cycle shown in Figure 3, the converted electrical energy will be: π

(6.1) ^W cy _c le = ^C _o ^{V '} _< ? (2« +tt ² ) sin ² (GH) d(iύt). o

For one cycle shown in Figure 2, the converted electrical energy will be:

2 2 ^W cycle = ^C o ^V o ² K ¹ ^ / "^W ^{dx ~} / ^{d X} 1 ( ⁶ " ² )' arcsιn( ) arcsinf — ) p o p If V ₀ »V _p , the lower integration limit in (6.2) may be replaced for arcsin (1-α).

The specific converting power per square centimeter of the hot heat sink for a stack of plates having a width of one centimeter will be:

W= AW _cyc]e ωN, (7) where ω is the driving frequency and N is the number of plates per centimeter of the stack.

For a LiTaO ₃ plate at ω = IO ⁶ Hz, W equals 0.53 W/cm ² for the switch according to Figure 2 and 3.2 W/cm ² for the switch according to Figure 3. Calculation results are shown in Figure 21. There is a possibility that the energy

stored as the difference between the positive and negative cycles will be stored in the resonant circuit and will be stored by the pyroelectric material. The result is a higher amplitude during the next cycle and an equalization in the difference between switches in favor of higher value (see Figure 4). In Figure 4 the solid sine wave is the driving voltage F ₀ and the dashed line with increasing amplitude is the sum of the driving voltage V„ and the pyroelectric voltage, V _p , where V(t) = V t) + V _p (t). The amplitude increases until the circuit losses compensate for the losses associated with growth, which are proportional to the voltage amplitude. If the extracting voltage starts at a value V _z , (V >V ₀ ), the extracted sectors are illustrated in Figure 4 as the cross-hatched areas 30 under the sine curve. The electric circuit in this case must have a high frequency transformer with one winding forming a resonant circuit with the pyroelectric stack, a second winding for starting the driving voltage from a pulse generator, and a third (extracting) winding in series with a Zener diode having a V, threshold voltage and a full wave rectifier connected to a useful load. Until the voltage in the resonant circuit reaches V _z , this circuit is not extracting energy.

For PZST material and the same driving voltage, the converting power W corresponds to an unmanageable thousands of watts per square centimeter. Therefore, the driving voltage must be much lower (see Figure 22). The figure of merit for a converter pyroelectric material as in 6.1 and 6.2 depends on , which in itself is a figure of merit in pyroelectric infrared sensors. If α «1 , which is true for most

pyroelectrics, the material figure of merit is: _F <P (8), where p is the

^{1 "} PC pyroelectric coefficient, p is the density, and C is the thermal capacity. In this case,

the material figure of merit does not depend on the dielectric constant. If α »2 (i.e.

for PZST), the figure of merit is: _F _ ^cP (9), where ε is the dielectric ερ ² C ² constant.

The calculated power densities for efficient pyroelectrics, such as lead scandium tantalate (PST), or PZST having the same geometry, are in the range of 10 - 100 W/cm ² , which are very attractive for low temperature energy conversion.

For PVDF (Deuterated Polyvidilene Fluoride) at a driving electric field strength of 1 MV/m and ω ₀ equal to 2 x 10 ⁶ Hz at room temperature, the power density is approximately 0.5 W/cm ² .

Previously, it has been assumed that the heat flow from the electrodes 14 to the pyroelectric material 12 is replenished by the thermal gradient from the hot to cold heat sinks. When the power density is increased, dissipation losses tend to heat material 12 due to piezo-pyroelectric cycle, and the temperature of material 12 rises with power increase. This results in a countergradient, working against the hot and cold heat sink temperature difference. Part of the heat dissipates with the heat flow towards the cold heat sink and thus will not effect operation. However, part of the heat remains, thereby reducing the replenishing heat flow. When the temperature gradient across material 12 exceeds the pyroelectric gradient, the converter will not operate. This suggests that pyroelectric material 12 must be in better thermal communication with cold heat sink 18. This can be solved in various ways. The simplest, but not preferred approach, is to introduce additional thermal resistance on the hot heat sink 16, i.e., increasing the thickness of electric insulator 19 on the hot heat sink 16 side so that it is thicker than electric insulator 19 thickness on the cold heat sink 18 side. A more preferred embodiment is shown in Figure 23. The design is similar to that shown in Figure 1, with the addition of material 78 which has a lower thermal conductivity than pyroelectric material 12, including but not limited to pressed fiberglass or mica. Another embodiment is shown in Figure 24. This design requires more complex technology, since both pyroelectric material 12 and electrodes 14 are made in a wedge form or other geometrical configuration where the electrode cross-section is the widest adjacent the cold heat sink. Because metal electrodes 14 are thicker near cold heat sink 18, the thermal communication is greater in this region. Acoustic resonance in this case is also much more complex between surfaces 80 and 82.

Another embodiment is shown in Figure 25. Here the pyroelectric materials 12 are wedge-shaped; however, electrodes 14 are planar- shaped. Acoustic resonance occurs between surfaces 84 and 86. Pyroelectric material 12 is now in better thermal communication with cold heat sink 18. Passive wedge 88 comprises a

material having a low thermal conductivity, including but not limited to mica for temperatures up to 1500°C and KAPTON™ for low temperature (T<200°C) applications. Porous materials, though having low thermal conductivity, are not preferred, as the sound attenuation for this class of materials is too high. If no heat source is on the hot side and a driving voltage V ₀ is applied, a refrigerator effect exists because the driving voltage and switching device cause asymmetric heat flow from electrodes 14 to the material 12 which is replenished from the heat sinks resulting in cooling. Figure 26 represents the converting mode of the device shown in Figure 1. Here, T, is the equilibrium temperature distribution along the Y-axis without driving voltage, T ₂ is the equilibrium temperature distribution with driving voltage, with a maximum temperature at the hot heat sink and a minimum at the cold heat sink (L ₀ - plate length). Reference is now made to Figure 27 with equal initial temperatures at the hot and cold heat sinks. T, represents the temperature distribution without driving voltage, and T ₂ represents the temperature distribution with driving voltage. This is so because heat flows are asymmetric and remain as such, resulting in cooling a heat sink with better thermal communication. This process is less efficient than the conversion process since the net process depends on the absolute temperature squared. In other words, beginning at room temperature with a 30K available pyroelectric temperature gradient, the conversion is 1.49 times more efficient than refrigeration with the same device.

For very efficient pyroelectric materials, including but not limited to PZST, PST, and the like, this refrigerator can also work as an environmental heat pump after the initial start from an external power source providing electricity by cooling ambient air or a working fluid.

2. Thermodynamic Considerations

The two main modes of operation for the device include a heat pump/refrigerator, and a thermal to electric energy converter.

In terms of irreversible losses, the difference between these two modes is in external ohmic and transforming losses in the outer electric circuit. Since electric leads for the device can be made sufficiently thick and existing high frequency

transformers have an efficiency of 0.9 - 0.95, ohmic losses in the converter mode may be approximately 10% higher for the same device.

Considering energies involved in terms of a time base equal to one second, the input electrical energy is ω ₀ ^• (C ₀ V ₀ ² ) 12, where ω ₀ is the resonant frequency, C ₀ is the capacitance, V ₀ is the driving voltage amplitude, and (1-k) is dissipated in the form of thermal energy in the pyroelectric material. Referring to Figure 1 with the hot heat sink temperature T ₂ and the cold heat sink temperature T„ heat flow to the device is Q ₀ = (T ₂ - T,) (λ;, S, + λ ₂ S ₂ ), where index 1 in the second bracket corresponds to the thermal conductivity and the cross section area of the metal electrode and index 2 corresponds to the pyroelectric material. According to equation (6.1) set forth previously, the extracted energy equivalent is C ₀ V ₀ ² (2α + α ² )x 0.785 x ω ₀ , where a is defined by equation (4) set forth previously. By definition, the extracted energy cannot be more than the difference between the heat flow through the electrode and the pyroelectric material. The ratio of the extracted energy to the total heat passed through the device, η, defines the efficiency of the converter. Similar to other thermal machines, it appears like an ideal Carnot cycle efficiency (reversible cycle), multiplied by the irreversible losses cycle. If the formulae from the previous paragraph is substituted, the expression for the efficiency is too complex and does not allow for a simple interpretation as in the case of thermoelectric energy conversion. Assuming a best case scenario in all components of the efficiency, the dissipation portion can be as high as 0.8, or η « K(T ₂ - T*)/T ₂ .

In the case of refrigeration and assuming that α « 1 and most of the pyroelectric material stays at the cold heat sink temperature, the refrigeration coefficient ζ is as follows:

, where C is heat capacitance of the pyroelectric material, C ₀ is the electric capacitance, ε is the relative dielectric constant

of vacuum, p is the density, p is the pyroelectric coefficient, V ₀ is the driving voltage amplitude, and ω ₀ is the driving frequency.

3. Materials

Two figures of merit, F. and F ₂ , for material 12 performance of the converter 10 were previously discussed where F, = T j ² /Cp and F ₂ = TJJVZD ² C ² , wherein T _c is the material 12 Curie temperature, p is the pyroelectric coefficient, C is the heat capacity, and p is the density (all variables are in SI units). F ₂ applies particularly to materials with extremely high pyroelectric coefficients, i.e. p > 10 ²

C/m ² -k.

F* can be used for the approximate material 12 evaluation. Two other parameters are present by default in evaluations, dielectric losses ( tan δ) and electromechanical quality parameter Q _m . Both parameters define the efficiency of the converter 10 because the heat dissipated inside the material 12 itself is wasted. The best Q _m values can be found in single crystal materials with values of IO ⁴ - IO ⁶ . For sintered ceramic materials, e.g., PZT, tan δ values are in the region of 0.1 - 10% and decrease with frequency. These losses also depend on the driving voltage. In reality, losses in acoustic resonance may be very low. The losses can be illustrated by monolithic multi-layer actuators, which in many respects resemble the energy converter stacks of the present invention.

Figures 5 and 6 show dissipation losses in monolithic piezoceramic actuators made of PZT-type material. This stack has a resonant frequency of 60 kHz. If the stack had all of the features of a converter such as electrodes of solid metal and no coating, it should self-resonate at a driving voltage of 10 V, provided that a sufficient thermal gradient is applied with a plate thickness less than 70 microns at which the pyroelectric gain becomes larger than the integral losses.

For temperatures below 80°C, deuterated-polyvinylideneflouride (PVDF) is a preferred material because it can be produced economically with thin layers. Another preferred material is lead - zirconium titanate (Pb(Ti ₄₈ Zr ₅₂ )0 ₃ or PZT) based ceramics. Other materials include lead zirconate-stannate-titanate (Pb(Zr ₄₃ Sn ₄₃ Ti , ₄ )O ₃ or PZST ceramics), lead scandium tantalate (PST), LiTa0 ₃ , and

LiNbO ₃ for high temperature applications (see also Lang, S.B. Sourcebook of Pyroelectricity, N.Y., Gordon and Breach, Science Publishers, Inc., 1974, pp. 69-79, the contents of which are specifically incoφorated herein).

Table 1 depicts the characteristics of select pyroelectric materials:

TABLE 1

The preferred materials 12 have high pyroelectric coefficients and F _* >10 ^"9 .

4. Electrodes

The electrodes are electrically and thermally conductive materials, including but not limited to most of the metals and some nitrides and carbides such as C, TiN, ZiN, HfN, TiC, ZrC, WC, or combinations or alloys thereof. Electrodes 14 are subject to high mechanical, electrical and thermal stresses, which increase diffusion of the metal electrode 14 into the material 12 and vice- versa. Hence, at high temperatures, electrodes 14 of typical materials such as Au, Au-Ni, Ag, Sn, Cr, Fe, Co, Pd, Ni, Cu, Al, Mg, Ag-Pd, or combinations and alloys thereof can have only limited applications. Use of heavy metals, including but not limited to Pt and Ir, for electrostrictive stacks improve the situation but may be cost prohibitive. The

condition may be improved by placing diffusion barriers between the material 12 and electrode 14, including but not limited to SiC, SiN (Si0 ₂ is dielectric), or diamond-like electrically conductive coatings such as boron-doped diamond or other p-type diamonds. Other materials include W, Re, Os, Ir, Pt, Ag, Nb, Rh, Ru, Mo, Th, U, or combinations thereof. Some of these metals cannot operate in the air and require inert gas or vacuum as operation media.

Published results for electrostrictive stacks which operate at higher mechanical but lower thermal stresses are 10" - IO ¹² cycles, which corresponds to about three years of continuous operation at a 10 kHz frequency. Life cycles for pyroelectric energy converters should be similar.

The electrode 14 thickness can be defined from thermal conductivity considerations, which are illustrated in Figure 1. Here, T _hot and T _co)d are the temperatures of hot heat sink 16 and cold heat sink 18. Arrows 20, 22, and 24 show the heat flow propagation. The condition to define the thickness is governed by the following equation: / _{w ω ≥} χ T ^h °> -T ^co,d ^ (10), where Δ^ _cyc | _e is defined by cycle _j equations (6.1) or (6.2), ω is the driving frequency, λ is the electrode material thermal

conductivity, L is the plate height, 1 is the plate width (electrode covers the entire plate), and d is the electrode 14 thickness. With a material 12 comprising a LiTa0 ₃ plate from the previous example and silver as an electrode 14 material, the electrode 14 thickness is approximately 1000 angstroms.

If the heat sink area is more critical than the piezo-pyroelectric material 12 cost, it is possible to change the specific power density by varying the specific area of the material 12 (simultaneously increasing the height of the material 12 and electrode 14 thickness). The theoretical limit for PZST with metal/diamond electrodes is around 1000 W/cm ² for 1 x 1 cm ² plates due to thermal conductivity limitations.

5. Design The following example assumes a conversion of energy from a heat source providing a 100K temperature difference, and a stack of 100 (100 μm thickness)

PZT-5A lxlcm ² plates with matching thermal conductivity of electrical contacts (electrodes) between the leaves. Because the thermal conductivity of the contact metal is roughly 100 times greater than it is for PZT, their contribution to the stack thickness is negligible. The thickness of the stack is roughly 1 cm, giving a 1 cm ³ cube. The thermal conductivity of this stack along the plates and electrodes results in a heat flow of 3.4 W/cm ² (34 kW/m ² ). If the voltage at resonance is 3V, a resonant frequency higher than 340 kHz is required, which is near the sound velocity divided by the length frequency (-400 kHz). This is close to the first stack acoustic resonance harmonic. The actual resonant frequency will be affected by the compressing frame and thermal contacts since the resonant frequency of the piezoelectric stack depends on compression. (See, Aoyagi, M. et al., "High Torque Ultrasonic Motor Using Longitudinal and Torsional Vibrations" 1992 IEEE Conference on Applications of Ferroelectrics, pp. 541-544.) This reference indicates a 5% resonant frequency shift with force. Furthermore, the friction between the stack of plates and heat sinks acts like additional mass which shifts the resonant frequency.

In order to drive a non-resonance circuit with a parallel plate connection, the same amount of energy produced would also be spent, therefore, rendering the device useless. With tan δ for PZT=0.005, theoretically 99.5% of the pyroelectric cycle energy may be extracted on a useful load, rendering the device nearly 50% of ideal Carnot cycle efficiency. In reality, there are a variety of losses such as mechanical, thermal and losses in the outer electrical circuit. However, the device may still be near ideal Carnot cycle, with the only serious physical limitation being the electromechanical coefficient of the material 12.

a. Description of the Design Elements

(1) Heat Sinks. The main requirement for the hot heat sink 16 and the cold heat sink 18 is thermal conductivity. The thermal conductivity of a piezo- pyroelectric material 12 is low. For example, the thermal conductivity for PZT pyroelectric is only 1.7 W/(m*K). Basically, all metals or metal alloys will suffice, as long as the recrystallization point (T _z = 0.4 T _m ) is higher than the operating temperatures, the material does not oxidize in air, and the material can be polished and

coated with an insulator material. The heat sinks 16 and 18 may also serve to support the material 12, as illustrated in Figures 7a and 7b.

Heat sinks 16 and 18 may be made of ceramic materials having good thermal conductivity and low electrical conductivity, including but not limited to, A1N, BeO, Si0 ₂ , SiC, MgO, NiO ₂ , TiB ₂ , W ₂ B ₅ , and SiN. In this case, the internal surface must be polished and there is no need for an electric insulator 19 shown in Figure 1. Aluminum nitride is a material with a significantly higher hardness than PZT or any metal, ensuring low friction between the material 12 and heat sinks 16 and 18, and low losses. Another possibility is to coat the material 12 with a thermally conductive dielectric such as non-doped diamond, aluminum, aluminum nitride, aluminum oxide, zirconium oxide, titanium oxide, yttrium oxide, magnesium oxide, beryllium oxide, silicon oxide (glass or quartz), nickel dioxide, scandium oxide, hafnium oxide, lanthanoid oxides, thorium oxide, and uranium oxide. In this case, heat sinks 16 and 18 may be graphite or a metal with thermally conductive graphite lubrication. (2) Electric Insulator. Either heat sinks 16 and 18 or material 12 may be coated with an insulator. The following materials may be used at the indicated maximum operating temperatures: TEFLON (< 150°C), KAPTON (< 250°C), Al ₂ O ₃ or A1N (< 2700°C), MgO, NiO ₂ , SiO ₂ , and BeO. If the material 12 is made by co-firing with painted electrodes, thermal contact surfaces with a dielectric material should preferably be painted and fired simultaneously. The painted surface must then be polished to ensure good thermal contact. Graphite lubrication lowers the requirements for planar surfaces and smoothness since thermal resistivity is essential. It is also beneficial to have an insulator with a high, comparable to metal, thermal conductivity (i.e., A1N), even if it is thin, because more than half of the total thermal flow goes through electrodes 14, which have very good thermal conductivity and thus require low contact losses.

(3) Converter Stack

(a) Pyroelectric material thickness. The material 12 thickness is affected by the allowed voltage, technology and cost. More charge can be extracted per area unit in one cycle as the material 12 thickness is decreased, thereby improving the performance. For PZT-5A the initial depolarization field is

0.5V/micron. For a 3 volt operating voltage it corresponds to 6 microns and 20 microns for reliable operation. For sintered PZT, the preferred thickness is at least about 50 microns, which is close to the limit set by depolarization. Utilizing a thin film deposition method, the material 12 may be made very thin, with the limitation set by metal contacts. Below 300A, material 12 exhibits quantum effects that effect its electrical conductivity. This limits material 12 thickness to 1-3 microns with an operating voltage of a fraction of volts, for example, 0.5 volts for a PZT-5A plate having a thickness of one micrometer.

(b) Material to Electrode Thickness Ratio At the minimal required frequency f _min and when all of the heat flow along electrode contact 14 is converted to electrical energy, the approximation of optimal contact thickness is

defined as: t > t • k , where t and t„ are the thicknesses of electrode 14 λm and material 12 respectively, λm, λo are the thermal conductivities of electrode 14

and material 12 respectively, and k is the electromechanical coupling coefficient

(efficiency) in the compression mode. Precise values for given temperatures are given by equation (10) set forth previously.

Another option for the converter 10 design is to increase the thickness of material 12. In the same planar geometry the effect should be the same, for example, the material 12 thickness increased ten times. This results in a ten-fold decrease in the capacitance, a ten-fold increase in the mass, and a ten-fold increase in the voltage. As a result, the temperature difference and the energy extracted will be the same, but at a higher voltage and higher losses. The difficulty is that the thermal reaction time decreases. Another difficulty is the high voltage of a few hundred volts per millimeter of material 12 thickness, which is detrimental to the switches, transformers, and insulation. Because of these problems, the maximum practical material 12 thickness is limited to about one millimeter.

(c) Pyroelectric material length. Depending on the temperature gradient, pyroelectric material and required power density, the material 12 length between heat sinks 16 and 18 may be varied, with lengths less than

50mm allowing for higher specific heat flow per area unit. For sintered ceramics, lengths below 1-2 mm may not be practical because of contact problems.

(d) Material shape. The shape of the material 1 ?. is preferably in the form of a plate and may vary as illustrated in Figures 8a through 8e. The configurations illustrated in Figures 8b and 8c have higher thermal contact surfaces. The configurations shown in Figure 8d and Figure 8e have holes in the plates for a more compact compression frame design.

Hypothetically, a very high voltage converter may be constructed in geometries different from a stack of plates including, but not limited to one or more rods with central and surface electrodes having an acoustic wave traveling from one end to another , thus allowing low resonant frequencies (see, e.g., piezoelectric materials available from Morgan Matroc - Electro Ceramics Div., Lake Forest, CA).

(e) Thermal Contacts. Dry and liquid thermal contacts may be utilized between material 12 and heat sinks 16 and 18. Dry contacts may be used with or without lubrication. When using contacts without lubrication, the surfaces of material 12 and heat sinks 16 and 18 must be planar and polished. During preparation stages, a small amount of fine abrasive powder may be used between material 12 and heat sinks 16 and 18, which will lead to automatic surface finishing during operation. A combination of graphite with A1 ₂ 0 ₃ , or boron nitride or diamond powder may be used.

Liquid lubrication may not be preferred for the following reasons. Due to an acoustic-capillar effect, liquid lubrication will tend to fill every gap between the plates and push the plates apart, thus changing the resonant frequency. At lower temperatures there are many available dielectric liquids, and the stack immersed in liquid will work at its specific frequency. At elevated temperatures liquid metals are an option. When using liquid metals, the plates must be hermetically sealed, i.e., co- fired and insulated. Co-firing technology is standard in multi-layer stack fabrications. This process involves wet ceramics and wet layers of metallized ceramics powder (electrodes) being pressed together at high temperatures (roughly 1000°C) to form a monolithic stack. When utilizing hermetically sealed plates, material 12 or heat

sinks 16 and 18 should have grooves for holding the liquid metal 32 in place (see Figure 9).

(4) Holding plates together. Various methods may be utilized for holding the plates together depending on the piezo-pyroelectric plate material. These methods include, but are not limited to, compression, gluing, sintering, diffusion welding, co-firing, soldering, etc.

A compressing frame is preferred for holding the plates together, even if the plates are co-fired, to assure long life and to improve efficiency. Compression compensates for cracks and voids in the plates and for gaps between the materials comprising the stack, while maintaining the structural integrity of each material. The frame may be either internal or external to the plates, with an internal frame giving a more compact design. The difference between the converter frame and known electrostrictive stack designs (See, Aoyagi, M., IEEE 9th International Conference on the Application ofFerroelectrics, (1992) pp. 541-544, the contents of which are specifically incoφorated herein) is that the thermal conductivity of the converter frame must be small relative to the stack and the frame elements must withstand converter operating temperatures.

Examples of internal frame designs are shown in Figures 10a and 10b. In the design shown in Figure 10a, a stack of plates (material 12) is compressed by means of tightening nut 36 on central rod 34 along which the stack is disposed. Disposed between the stack of plates and nut 36 are compression washers 38 and springs 40. Compressing washers 38 also act as thermal insulators and are made of a material with a low thermal conductivity, including, but not limited to MACOR™ or other ceramics, together with nut 36. Compressing washers 38 may also be made of a metal with a low thermal conductivity (Figure 10b), including but not limited to Ni-Cr alloy, enclosed in a dielectric tube 42. Spring 40 provides for a uniform load over a wide temperature range and is particularly recommended if the electrical circuit does not include electronic correction for resonance. A low thermal conductivity of the frame is essential to minimize the losses due to heat exchange at elevated temperatures (more than 200 - 300°C).

An external compressing frame may be integrated either with one or more materials 12 with either heat sink 16 or 18. Figures 1 la and 1 lb are two examples of a stack integrated frame. In the embodiment shown in Figure I la, the stack of one or more materials 12 are disposed in compressing frame 44 and are compressed by tightening bolt 48, which is threaded through compressing frame 44, against the stack.

Washers 46 are disposed on both ends of the one or more materials 12. Spring 40 is disposed on the end of the stack having bolt 48. Figure 1 lb is a top view of the embodiment shown in Figure 1 la and illustrates thermal contact with heat sinks 16 and 18. The construction materials preferably should have a low thermal conductivity. If the operating temperatures are low enough, i.e., below 200 - 300 °C where radiation heat exchange is small compared to the thermal conductivity of the stack, the frame may be made of, including but not limited to, metal, ceramics and composites.

Figures 12a and 12b illustrate a heat sink integrated frame. Figure 12a illustrates an internal frame, and 12b illustrates an external frame. Another embodiment is shown in Figure 12c, illustrating a simplistic assembly. In the embodiments shown in Figures 12a - 12c, one or more materials 12 are disposed between compressing elements 54 and supporting element 50, which are compressed by tightening compressing element 54, including but not limited to a bolt which is threaded through compressing element 54, against the stack. Dielectric washers 52 are placed on both ends of one or more materials 12. Dielectric washers 52 are needed to evenly distribute compression on one or materials 12. Washers 52 must have mechanical strength and a thermal conductivity of less than about 1 W/mK. The operative temperature range of washer 52 must be higher than the hot heat sink temperatures. For most applications, MACOR™ machinable ceramics are adequate.

Mica-based ceramics, composites, and high temperature ceramics may also be utilized.

6. Resonance The resonant converter stack 10 resembles ceramic resonant filters and resonant activators with a long history of manufacturing and applications. If the stack

is made of a uniform material, resonant conditions in the thickness resonance mode will be as follows: _n λ = E , where L is the stack thickness, λ is the acoustic

2 wave length, and n = 1, 2, 3, . . . . ( harmonic number or overtone). The wavelength is defined as λ = c/f where c is the speed of sound in the material and /is the frequency. Thus, the resonant frequency is:

f - H . . Normally, minimum losses occur at n-l(f, . In our case it is 21 inconsequential, since even at n = 1 , the resonant frequency is very high at about

1 OMHz/mm for PZT-5 A. The actual frequency f ₀ depends on many parameters such as the electrode thickness, the electrode material, the compression frame, the compression force, the environment (gas air liquid), temperature and friction. For frequencies lower than 10 MHz the stack must be sufficiently thick to withstand 1 OMHz/mm. Actuators with about a 100 kHz resonant frequency have a thickness of about 2 cm. As set forth previously, the minimum frequency required for efficient converter operation depends on the pyroelectric material 12. For lead scandium tantalate, the resonant frequency should be roughly 10 ⁶ times less than it is for PZT - 5 A at the same geometry and electric input. However, fabrication of a long stack (when the stack length is more than the height or width) creates other problems such as plate parallelism, sound attenuation, and increasing losses. The resonance width is important because it defines the required stability of the electrical circuit, which may be a problem in the case of changing temperatures and vibrations. The resonance width Δf is defined as the frequency deviation which provides resonance (see Figure 13). Since the capacitance changes with the temperature, it is beneficial to keep cold and hot heat sinks at constant temperatures. Otherwise, the electric circuit must have frequency correction means.

For ceramic filters, - . is normally 1-3%. These values apply even to / simple LC circuits. If it is less than 1% it may require individual circuit tuning for each stack.

To this point, a pure compression mode of the stack has been addressed, which can be affected by an external spring or end mass. This mode is easy to understand and control, however, the reported frequency is apparently higher than 10 kHz (see Figure 14). Figure 14 shows that irrespective of the vibrational mode, frequencies below

10 kHz must be evaluated. Note that even a 10 kHz frequency corresponds to about a 30 year life for a PZT-made stack.

For complex and powerful systems, i.e., W > lkW, working over a wide temperature range, a different approach for a converter system is employed. Though acoustic resonance frequency variation with temperature is not dramatic, it exists and causes a shift. Much more important is the change in relative dielectric constant ε of the pyroelectric, which can easily change by a factor of 2. Consequently, inductance L in the resonant electric circuit must be adjusted correspondingly using variable inductance (transformer with moving core). The frequency may also be adjusted using a variable capacitance device connected in series or in parallel with the capacitor stack. For variable inductance, both the stack acoustic resonance ω ₀ and capacitance C ₀ are calibrated in terms of L = L(x), where x is the core position. A standard satellite tracking system may be used for frequency adjustment, comprising temperature sensors, a programmed amplifier and a step motor. A block diagram of the entire frequency adjusting is shown in Figure 28. A more complicated system may include a computer-controlled measuring system which measures ω ₀ during periods without load and adjusts variable inductance correspondingly. It may also control the driving voltage, the heat source (hot heat sink temperature), etc. Hence, either the hot or cold heat sink temperature is controlled, or the frequency is controlled, or a combination thereof.

7. PST-Based Device

Recent developments on Lead Scandium Tantalate compositions (PST) resulted in a material with extremely high values of pyroelectric coefficient (See, Patel, A. et al. "Ferroelectric Ceramics and Thin Films for Uncooled Thermal

Imaging Arrays" 9th IEEE International Symposium on Applications of

Ferroelectrics, Penn State University, USA August 7-10 (1994) pp. 647-652). Because of its properties (p= 2.5 C/K- cm ² ) this material does not need a resonant stack to overcome inefficiencies. As a result, the limiting factor is the thermal conductivity of the metal electrodes. For a one volt driving voltage at ten kilohertz and a 1 x 1 cm ² plate with a thickness of 1 mm, the converting power is about 30 W.

This system requires copper or silver electrodes with a thickness of about 1 mm for an electrode length of 1cm. The design of the converter in this case, as illustrated in Figure 15, is somewhat different from the stacked pyroelectrics disclosed previously, because a pyroelectric stack and thin electrodes are not required. In this embodiment, the PST material 62, preferably in the form of a plate, is disposed between U-shaped electrodes 64 in thermal contact with hot heat sink 56 and cold heat sink 58. The electrodes 64 are U-shaped to overcome contact thermal resistance through a larger contacting area. Disposed between electrodes 64 and heat sinks 56 and 58 are electric insulators 60. Gap 66, comprising air, gas, vacuum, or a breakdown resistant material such as a dielectric, exist between PST material 62 and electric insulators 60 because electrodes 64 are sufficiently thick to provide mechanical stability on their own. Gap 66 must withstand the voltage potential between electrodes 64. Gap 66 increases the efficiency of the converter by eliminating heat flow from material 62 to heat sinks 56 and 58. Gap 66 is not necessary for the side adjacent to the cold heat sink 58. The energy extracting electrical circuit for PST is similar to that shown in

Figure 16. However, measures should be taken to protect the pulsed or sine wave generator from pyroelectric voltage, which can be as high as a few kilovolts for this material. Therefore, the electric insulation 60 must be capable of withstanding the pyroelectric voltage. One way to avoid high voltage on the output of the generator is to have acoustic coupling. Here, the generator is driving the piezoelectric plate (PZT-

5A) which is electrically insulated from the PST plate, but acoustically coupled to it. Acoustic oscillations of PST produce an oscillating voltage on the plate and pyroelectric action as a result. The corresponding design is shown in Figure 17. In this embodiment, the following elements are disposed in compression between U- shaped electrode 64 and compressing member 74 in the following succession: PST material 62, electrode 68 electric insulator 70, electrode 68, piezoelectric material 72.

and electrode 68 in the form of a plate. Electrode 68 comprises a solid metal or alloy, including but not limited to Ag or Au/Ni, with a thickness of at least about 100 microns.

Electric insulator 70 should withstand high voltages of about lkV and temperatures up to 180°C. Most glass and ceramic insulators are adequate at thicknesses of at least about 100 microns. Plastics such as KAPTON or TEFLON are also adequate.

Electrode 68 is a standard electrode coating on piezoelectric material, which is about 0.25 Ni or Au-Ni. Ag or Ag/Pd alloys are also suitable. The piezoelectric material must be operable up to about 180 °C temperatures. Most of the standard PZT compositions are adequate. The design of figure 17 corresponds to a rugged design providing for high mechanical and electrical strength. A main consideration with this kind of device is that all the air gaps must be wide enough to withstand about 1 kV AC, i.e., a gap of at least about 1cm. The converter must also have cover protection against moisture or be filled with freon to prevent breakdowns.

The elements just described between electrode 64 and compressing member 74 are compressed by compressing system 76, including but not limited to a bolt threaded through compressing member 74 and electrode 64. Electrodes 64 and 68 are connected to an extracting circuit, such as that shown in Figure 16. Dielectric layer 70 is capable of withstanding a kilovolt range voltage from PST and having a low ultrasound attenuation, including, but not limited to, quartz or dense aluminum oxide. Piezoelectric plate 72 is made of any material with a Curie point higher than PST (180°C). Piezoelectric plate electrodes 68 are connected to a sine wave or pulse generator. Compressing member 74 is preferably made of an electric insulator. Bolted to electrode 64 are bolts made of an insulator, such as MACOR™ , or metal which is insulated on the surface. Electrode/thermal conductor 64 is electrically insulated from the heat sinks 56 and 58 by insulators 60, preferably A1N insulators. The extracting circuit is basically the same as in Figure 16, except the Zener diode (actually Schottky diodes stack) must now handle kilovolt range voltage, and the extracting transformer windings are from high voltage to low and not vice-versa as before. The oscillating voltage generator can be powered either from an external

battery or from an extracting circuit, with an external battery used only for start up. Computer controlled starter and converter efficiency optimization, by changing the driving frequency on piezoelectric 8, can be employed if the device power is in the kilowatt range.

8. Electrical Circuit

The devices for removing electrical charge from the capacitor stack are either amplitude sensitive or phase and amplitude sensitive.

Figure 16 shows a resonant circuit formed of pyroelectric Capacitor C and winding No. 1 as an inductance which forms a resonant contour with the pyroelectric stack. Losses in this circuit (resistance of the leads) are reflected by resistance R _r Winding 1 with inductance L is experimentally tuned to the resonant frequency of this stack at room temperature. As the temperature increases on the stack, its capacitance shifts, so the circuit is tuned to the specific temperature range, for example 300-350K. In principle, this condition can be solved by using variable transformers (with a moving core). Winding 2 is positioned across the Zener diode and the rectifier. The Zener is constructed of a number of Schottky diodes in series. Each diode (MBR 340) gives a drop of about 0.3 V with a limiting frequency of 100 MHz. The rectifier is made of the same Schottky diodes. Rectified current is used on the load R,. Winding 3 is used to start converter operation by a function generator (Hewlett Packard Model

81 16A) with a current amplifier (emitter repeater). An emitter repeater was utilized on the basis of NTE-56 transistors; however, any standard current amplifier that can handle MHz-type frequency will be sufficient. The stack operating voltage is adjusted by changing the number of diodes in a Zener diode. Another device comprises a switch comprising an inductance forming a resonant contour with a capacitor and a transformer having first, second, and third windings, the first winding being connected with a Zener diode and in parallel with the resonant contour, the second winding being connected to a full wave rectifier, and the third winding being connected to a generator. The resonant frequency is defined by the acoustic resonance of the stack and is dependant upon parameters such as thickness, material, compression, temperature and

friction. The resonance frequency ω ₀ of the external circuit, is governed by the following equation: ω = (11).

With a stack 1 cm long consisting of 70 micron thick PZT-5A plates connected in parallel, the capacitance is equal to 3 μF, giving inductance L from eq. 1 1 as 9.4 x IO ^"8 H. This inductance was achieved with an air filled coil having a diameter of about two millimeters and five turns. At resonance, the reactive impedance is compensated for and only ohmic resistance exists. Ohmic losses for sine wave AC look like 0.5 x V _σ ² x R _r At 10 V it corresponds to 50 R _τ watts. This stack according to equation (6) gives 0.1 W at a 200K temperature gradient. Hence, the wire resistance must be less than 2 x 10 ³ ohms. With a 3 mm ² diameter copper wire and a winding plus contacts length of 10 cm, the resistance is about 0.5 x IO ^"4 ohms and ohmic losses are 25% of the converter output. The electrodes on the plates provide about 60% of the additional ohmic losses, thus limiting the overall efficiency to about 15% of the possible output. Another roughly 5% of the losses come from the stack itself, leaving only about 10% of 0.1 W. The thickness of the electrodes are preferably thicker than the ones used, because most of the heat flow will pass through without conversion, thereby further decreasing the converter efficiency.

The solution for PZT-5A is to make the nickel electrodes about 0.5 to 1.0 micron thick, but not to allow the metal to touch the heat sinks on both sides, thus limiting the heat flow through the pyroelectric stack. Materials with high (p» IO ^"2 -

10 ^"3 C/K- m ² ) pyroelectric coefficients, do not have these problems, as the output is sufficient to compensate for any ohmic losses.

The Zener diode gives a threshold voltage of 10V, plus another 0.5 V comes from diodes in the rectifier. When the driving voltage with a 10V amplitude from a pulse generator with the same resonant frequency is applied to winding 3, a resonance in the contour is obtained. However, nothing happens in winding 2, since its impedance is close to infinity. As the amplitude of the generator pulse is increased, the condition illustrated in Figure 4 occurs. When the pulse amplitude reaches the threshold voltage, the Zener diode starts to conduct current and DC current flows

through the load R _L . The generator may be switched off, since the losses will be automatically compensated for by pyroelectric action.

At high frequencies (ω ₀ > 1 MHz) and high capacitance (C ₀ > lμF) of the stack, the transformer inductance required to form a resonant circuit is less than one microhenry. If the transformer is of a conventional type with coiled windings, it is difficult to retain high efficiency since a core cannot be utilized to keep a magnetic flux inside the transformer. In this case, the circuit shown in Figure 19 is preferred. It does not have extracting winding 2, but operates in the same manner as the circuit in Figure 16. The difference is that the limiting factor is now the operating frequency of the diodes which can be as high as 100 MHz for Schottky diodes. The Zener diodes may be Schottky diodes connected in series, 0.3 - 0.7 V per diode, for example, 30 diodes for ₇ = 10V.

The circuit shown in Figure 18 was designed with the assumption that the pyroelectric component of the voltage was large enough to be used as is, i.e., for PZST it is two times larger than the driving voltage, or a few volts. If this assumption is incorrect as in the case of PZT-5A material, it must have an additional high frequency transformer. However, unlike T, this one does not have to be a low inductance transformer and can be very efficient (See Figure 19). For PZT-5A, the windings ratio in T ₂ must be IO ² - IO ³ . Figure 19 represents a resonant stack with an equivalent capacitance of 4 microfarads. The Zener diode is formed of 20 Schottky diodes (Motorola MBR 340). connected in series having a voltage rate of change 10000 V/microsecond. The recalculated dependence of resistance on voltage for this stack 1^ = R^V) is shown in Figure 20 (Ohm vs. VJ. The resistance at 5 volts is effectively infinity and at ten volts is zero. High frequency (1 MHz rated) power transformer T ₂ has a primary winding resistance of R ₀ - 10 ohms. The rectifier bridge has a maximum operating frequency of 40 MHz and the load resistance is ten ohms. Low resistance winding 1 of a transformer T, forms a resonant contour with the stack C. The resonant frequency of the stack is 500 kHz. Resonance is initiated by winding 3 from the function generator. When resonant voltage V ₀ is lower than 5 volts, current does not flow through transformer T ₂ because the Zener diode Z blocks it. When current

begins to flow, it flows through the resistance R _B + R _z and the extracted power is:

( sin(ωt) - V f . _t . . . _t . , . ₌ __ £__ . Integrating this equation by time gives an average

R +R extracted power of about .05W at V ₀ = 10 V. Estimated component ratings circuit losses are 8% and can be lower with a more efficient transformer T ₂ . With a pyroelectric power gain of 0.8W and stack internal losses of about 0.1 W, a reasonably efficient extracting circuit exists.

The circuits illustrated in Figures 18 and 19 are assembled on the same principle as that shown in Figure 16. The Zener diode and rectifier may be constructed not only of MBR 340 Schottky diodes, but of any commercial diodes handling high frequency and currents of up to at least about 1000 A at low losses and at any required voltage. For example, 100 diodes can sustain 1 OkV.

The switch may take the form of many circuits. It may comprise a resonant contour formed of the pyroelectric capacitor and inductance L, where the contour is driven by a pulse/sine generator. If the generator has a high output impedance (1 > 1 kΩ), it may be connected directly across the resonant contour. In one embodiment, inductance L is the first winding of a high frequency transformer (of at least the resonant frequency of the capacitor) and a second winding is connected to the generator. Another embodiment comprises a resonant contour formed of a pyroelectric capacitor and inductance L, where the contour is driven by a pulse/sine generator, inductance L is the first winding of a high frequency transformer (of at least the resonant frequency of the capacitor) and a second winding is connected to the generator, and the contour is connected in parallel to an extracting circuit which comprises a Zener diode and a first winding of a high frequency transformer (of at least the resonant frequency of the capacitor), and a second winding of the transformer is connected to a useful load through a rectifier. Part of the useful load may also feed the generator. Also, the generator may be powered by a start-up battery having a timer which is part of the useful load.

A more sophisticated extraction circuit, comprising a thyristor current interrupter is described in U.S. Patent No. 5,288,336, entitled THERMOELECTRIC ENERGY CONVERSION, and issued to John S. Strachan and Harold Aspden. In

principle, a thyristor interrupter allows a circuit without a start-up battery, when the initial temperature change will provide for interrupter operation due to pyroelectric voltage build-up.

9. Applications

Since energy conversion is the basis of modern civilization, an efficient energy converter has numerous applications, such as existing utility power plants, solar power plants, residential electricity supplies, residential/solar electricity supply, automotive, maritime, solar/maritime, environmental heat pump, refrigeration (cooling, air conditioning, etc.), propulsion and aerospace.

Power plants have a tremendous amount of waste heat with a potential of 300°C and lower. Converting the waste heat at 30-50% of Carnot efficiency will give an additional 15-25% overall plant efficiency with equivalent savings on fuel.

The proliferation of low-cost converters will lower the capital costs of solar concentrator power plants with a higher efficiency than current steam/electricity cycles. Lower operating temperatures will also lower maintenance costs.

Residential electric supplies based on direct heat to electrical energy conversion is ideal for remote areas, where it is difficult or inconvenient to install power lines. The heat source may either be in the form of fossil fuel or solar concentrators. Solar concentrators can also be in the form of solar heated water pools, utilizing day/night temperature differences. A few hundred cubic meters of water with a hundred square meters of surface and cover could provide the electricity supply for a house in areas with a temperature differential of about 10°C.

A pyroelectric converter in combination with a conventional engine driving an electric generator and an electric motor would substantially increase mileage.

Direct energy conversion has tremendous application in electric cars. Three main approaches are possible. One approach involves using inexpensive materials with operating temperatures up to about 150 to 300°C as overall efficiency boosters. A car with an electric drive has a conventional engine coupled with an electric generator having a converter array as an intermediate radiator.

Another approach utilizes high temperature converters with operation temperatures of about 1000°C. This type of car will have fewer moving parts, higher combustion temperatures, and lower emissions. Currently, high-efficiency furnaces have a thermal efficiency of about 90-95%, which is much higher than internal combustion efficiencies. In combustion engines with about 50% Carnot efficient converters, the mileage would improve roughly two to three times over existing automobiles with similar characteristics.

Automotive applications are also applicable to maritime applications. In addition, solar concentrators may be used in a sail-type fashion. A combination of light and inexpensive plastic Fresnel lenses with pyroelectric converters may be incoφorated into modern rigid wing-type sails, providing for the use of wind and sun energy to propel a boat with about 100-200 W/m ² of the sail solar component.

Since the converter can utilize very small temperature gradients in a self- sustaining mode, a temperature gradient between the heat sinks will be created with asymmetric heat exchange on the surface (e.g., one heat sink can be thermally insulated). Also, the system will run until something malfunctions, cooling the environment and producing electricity. The power densities will be low, as a reasonable developed gradient can be only a few degrees. However, the energy consumption in its normal sense is zero. This device must have additional features, such as a guaranteed electric load in order to not disrupt operation. This will bring a useful power density down further. Notwithstanding, the possible benefits far outweigh the technical hurdles.

In summary, the method and apparatus disclosed herein is a significant improvement from the present state of the art of pyroelectric energy conversion. The invention may be embodied in other specific forms without departing from its spirit or essential characteristics. The described embodiments are to be considered in all respects only as illustrative and not restrictive. The scope of the invention is, therefore, indicated by the appended claims rather than by the foregoing description. All changes which come within the meaning and range of equivalency of the claims are to be embraced within their scope.

What is claimed is: