Yan
Zhang
a,
Mengying
Xie
a,
James
Roscow
a,
Yinxiang
Bao
b,
Kechao
Zhou
b,
Dou
Zhang
*b and
Chris R.
Bowen
*a
aDepartment of Mechanical Engineering, University of Bath, BA2 7AY, UK. E-mail: C.R.Bowen@bath.ac.uk
bState Key Laboratory of Powder Metallurgy, Central South University, 410083, China. E-mail: dzhang@csu.edu.cn
First published on 6th March 2017
This paper demonstrates the significant benefits of exploiting highly aligned porosity in piezoelectric and pyroelectric materials for improved energy harvesting performance. Porous lead zirconate (PZT) ceramics with aligned pore channels and varying fractions of porosity were manufactured in a water-based suspension using freeze-casting. The aligned porous PZT ceramics were characterized in detail for both piezoelectric and pyroelectric properties and their energy harvesting performance figures of merit were assessed parallel and perpendicular to the freezing direction. As a result of the introduction of porosity into the ceramic microstructure, high piezoelectric and pyroelectric harvesting figures of merits were achieved for porous freeze-cast PZT compared to dense PZT due to the reduced permittivity and volume specific heat capacity. Experimental results were compared to parallel and series analytical models with good agreement and the PZT with porosity aligned parallel to the freezing direction exhibited the highest piezoelectric and pyroelectric harvesting response; this was a result of the enhanced interconnectivity of the ferroelectric material along the poling direction and reduced fraction of unpoled material that leads to a higher polarization. A complete thermal energy harvesting system, composed of a parallel-aligned PZT harvester element and an AC/DC converter, was successfully demonstrated by charging a storage capacitor. The maximum energy density generated by the 60 vol% porous parallel-connected PZT when subjected to thermal oscillations was 1653 μJ cm−3, which was 374% higher than that of the dense PZT with an energy density of 446 μJ cm−3. The results are beneficial for the design and manufacture of high performance porous pyroelectric and piezoelectric materials in devices for energy harvesting and sensor applications.
Mechanical waste energy that is generated by a vibrating structure or a moving object is a ubiquitous form of energy that can be harvested from our surroundings.7 The three common mechanisms for the conversion of vibrations into electricity include electromagnetic, electrostatic and piezoelectric techniques.8,9 Piezoelectric materials have significant potential due to their high power density, and adaptability in terms of the variety of macro- and micro-scale fabrication methods.10,11 In addition to mechanical energy, waste heat is a necessary by-product of all thermodynamic cycles implemented in power, refrigeration, and heat pump processes12 and recovering even a fraction of this energy has the potential for an economic and environmental impact. The conversion of heat directly into electricity can be achieved by thermoelectricity13 or pyroelectricity.14 The advantages of pyroelectric materials, compared to thermoelectrics, is that they do not require bulky heat sinks to maintain a temperature gradient, and have the ability to operate with a high thermodynamic efficiency for converting temperature fluctuations into useable electrical power.15 Energy conversion by heating and cooling a pyroelectric material therefore offers a novel way to convert heat into electricity and the approach has attracted interest in application areas such as low-power electronics and battery-less wireless sensors.16 Since all pyroelectric materials are piezoelectric it is of significant interest to utilize piezoelectric and pyroelectric materials for energy harvesting applications with electrical properties that are readily adjustable and tailorable to suit the harvestable energy source and are also sufficiently robust to survive any applied mechanical loads and thermal strains.
In order to assess the properties of materials for energy harvesting, a variety of performance figures of merit containing combinations of physical properties have been developed to describe the ability of materials to generate energy for practical applications. For piezoelectric and pyroelectric energy harvesting applications, the following figures of merit have been widely used for the selection and design of materials:17–20
![]() | (1) |
![]() | (2) |
The two figures of merit above indicate that a porous structure whose permittivity is reduced due to the introduction of low permittivity pores would have beneficial consequences for piezo- and pyro-electric energy harvesting applications; however, it should be noted that the benefit is only achieved if the piezoelectric or pyroelectric coefficients are not reduced significantly by the presence of the pores. In general, it has been considered that porous piezoelectric and pyroelectric materials can be considered as a porosity (air)–ceramic matrix composite.21,22 It is well known that the properties of a ferroelectric composite depend on the depolarization factor, the connectivity of the phases and the permittivity ratio the two phases.23
In this work, freeze-casting, also termed ice-templating, was utilized to fabricate porous PZT ceramics with tailored and aligned porosity to produce high performance materials for piezoelectric and pyroelectric energy harvesting applications. The piezoelectric and pyroelectric parameters and figures of merit for the energy harvesting applications of the porous PZT ceramics both parallel and perpendicular to the freezing direction have been investigated in detail. Based on the properties of these highly aligned materials, the porous composites are then utilized in an energy harvester and are shown to generate more energy compared to the dense material. The work demonstrates that tailored porosity can generate improved materials for piezoelectric and pyroelectric energy harvesting devices.
During the freeze-casting process, dense and cellular zones are formed in the samples at the beginning of the freezing cycle, as shown in Fig. 1(A). This region has a total thickness of less than 250 μm (ref. 30) and is removed by cutting the lower 0.5 mm of material via a low-speed precision diamond sectioning saw machine (Buehler, IsoMet LS). The freeze-cast porous samples of the same porosity (Fig. 1(B)) were further cut both parallel (Fig. 1(C)) and perpendicular (Fig. 1(D)) to the freezing direction to assess their properties in different orientations with almost the same volume. The thickness, c, of both types of porous samples was ∼1.0 mm. Samples cut parallel to the freezing direction had a length a = 14.63 ± 0.43 mm and width b = 5 mm. Samples cut perpendicular to the freezing direction had a diameter, ϕ = 9.65 ± 0.14 mm.
The microstructures of the sintered samples, such as their pore structures and the structure of the PZT walls, were characterized using scanning electron microscopy (SEM, JSM-6480LV, JEOL Techniques, Tokyo, Japan). The apparent porosity of the composites was derived from density data obtained by the Archimedes method.31 The compressive strength of the sintered sample (diameter ∼ 9.5 mm and height ∼ 13 mm) was measured with a crosshead speed of 0.2 mm min−1 using an Electronic Universal Testing Machine (KD11-2, Shenzhen KEJALI Technology Co. Ltd, China). An average of five measurements was taken for each sample. The porosity of the porous ceramic was calculated using eqn (3):
![]() | (3) |
Before electrical properties were measured, corona poling was conducted on the sintered dense and porous samples at 120 °C by applying a potential difference of 14 kV to a point source above the sample for 15 min, and samples were then aged for 24 h before testing. The longitudinal piezoelectric strain coefficient (d33) and the transverse piezoelectric strain coefficient (d31) were measured using a Berlincourt Piezometer (PM25, Take Control, UK). Measurements of the relative permittivity (εT33) of the sintered materials were carried out from 1 Hz to 1 MHz at room temperature (∼30 °C) using an impedance analyzer (Solartron 1260, Hampshire, UK). Ferroelectric properties, such as the maximum polarization, remnant polarization and coercive field, were measured using a Radiant RT66B-HVi Ferroelectric Test system on unpoled materials. The specific heat capacity (Cp) of PZT composites with different porosities was measured from 20 to 100 °C by a MicroSC multicell calorimeter from Setaram, with the Calisto program to collect and process the data. The density of the solid PZT, ρ, is 7.6 g cm−3 (according to the data sheet), therefore the volume specific heat, CV, can be defined as:
CV = ρCp | (4) |
The pyroelectric short circuit current (IP) and pyroelectric open circuit voltage (V) were measured using an electrometer (Model 6517B, Keithley Instruments, Cleveland, OH), and the pyroelectric coefficient was determined by the Byer–Roundy method32 and derived from:
![]() | (5) |
To demonstrate the effectiveness of the porous materials a thermal energy harvesting demonstrator was constructed, with a 1 μF charging capacitor used as an electrical storage element when the energy harvester was subjected to cyclic temperature fluctuations at 1.6 °C s−1. The temperature of the sample was continuously monitored using a K-type thermocouple with a response time of 0.5 s. A charging curve of the storage capacitor was measured for the range of materials, resulting in a maximum voltage on the storage capacitor without any electrical load.
The compressive strengths of PZT ceramics with the porosities ranging from 20 to 60 vol% in both the parallel and perpendicular directions to the unidirectional freezing direction have been shown in Fig. S1.† Compared with the conventional porous PZT ceramics with uniformly distributed porosity,27 the PZT with pores perpendicular to the freezing direction exhibited a compressive strength of 320–580% higher than that of the conventional porous PZT for porosities ranging from 20 to 60 vol%, see Fig. S1.† The strength along the freezing direction was ∼200% higher than that of the uniformly distributed porous PZT. This high strength results from the unidirectional lamellar support and the strong bonding originating from the ceramic bridges between the lamellar ceramic walls, as seen in Fig. 2.
Fig. 3 shows a schematic diagram of the poling direction applied to the freeze-cast porous PZT that were cut both parallel (as in Fig. 1(C)) and perpendicular (as in Fig. 1(D)) to the freezing direction. Both types of PZT were explored to examine the influence of the pore orientation on the poling behaviour and electrical properties, as shown in Fig. 3(A) and (C). To model the influence of the composite microstructure, the highly aligned pores can be considered analogous to the classical parallel-connected (Fig. 3(B)) and series-connected (Fig. 3(D)) models used in estimating the piezoelectric and pyroelectric effects of diphasic composites, respectively.34
The increase in Ec with maximum field then slows down substantially at higher applied fields due to saturation (13–16 kV cm−1 for parallel-connected, 18–24 kV cm−1 for series-connected). Saturated and rectangular loops of the parallel-connected and series-connected freeze-cast PZT ceramics were achieved at 16 kV cm−1 and 24 kV cm−1 respectively; higher electric fields than those presented here could not be applied due to dielectric breakdown.
Fig. 4(B) and (D) show the parallel-connected and series-connected porous PZT ceramics with various porosities (20–60 vol%), respectively. All materials exhibited well-developed and almost symmetric hysteresis loops. The Pr of the parallel-connected PZT decreased gradually from 16.5 to 6.4 μC cm−2, and the Ec monotonously increased from 7.7 to 9.1 kV cm−1 as the porosity fraction increased at a maximum electric field of 16 kV cm−1. The Pr of the series-connected PZT decreased from 11.3 to 3.5 μC cm−2, and the Ec increased from 8.9 to 10.3 kV cm−1 with increasing porosity at a maximum field of 24 kV cm−1. Fig. S2† also shows for comparison the dense PZT with a Pr of 35.0 μC cm−2 and coercive field of 8.7 kV cm−1.
For both types of porous PZT, the remnant polarization decreased gradually when the porosity increased from 20 to 30 vol%, followed by a more rapid decrease when the porosity was higher than 40 vol%. Increasing the porosity reduced the remnant polarisation since the porous PZT ceramics have proportionally reduced active material and ferroelectric domains compared with dense PZT, resulting in a lower polarisation. It should be noted that the parallel-connected PZT exhibited a more square P–E loop, higher polarisation and lower coercive field compared to the series-connected PZT for the same porosity, e.g. at 40 vol% Pr is 16.5 μC cm−2 and Ec is 8.25 kV cm−1 for the parallel-connected PZT and is 11.3 μC cm−2 and 9.6 kV cm−1 for the series-connected PZT. This is due to the improved interconnectivity of the PZT material along the polarisation direction for the parallel-connected PZT, see Fig. 3.
While the decrease in remnant polarisation with increasing porosity is simply due to the reduction in polarisable material, the increase in coercive field with an increase in porosity is less obvious. The porous ceramics are effectively composites with a high permittivity ceramic phase and a low permittivity pore phase (air). Such a structure strongly influences the distribution of the electric field throughout the material microstructure during the poling process. It has been shown that for porous ferroelectric ceramics, the local electric field in the ceramic phase near the pore is much lower than the applied field. This inhomogeneous field distribution results in the existence of unpoled areas along the poling direction.35 Consequently, the parallel-connected PZT exhibit less unpoled regions and easier domain switching and polarisation compared to the series-connected materials, leading to higher polarisation and lower coercive field.
A Finite Element Modelling approach has been used to investigate the effect of porosity in the freeze-cast microstructure on the electric field distribution in the PZT during the poling process,36 and to account for the increase in coercive field with increasing porosity (see Fig. 3(B) and (D)). Previous work36 has demonstrated the ability of such models to predict the behaviour of porous PZT, although they have focused on uniformly distributed porosity within a ferroelectric material, i.e. systems with 3–0 and 3–3 connectivity. This approach has been adapted in this work to investigate the 2–2 connectivity structures achieved using the freeze-casting process. A three dimensional cubic mesh of 29791 (i.e. 313) elements was split into an idealised 2–2 structure where alternate planes were assigned the properties of either unpoled PZT (εr = 158536) or air (εr = 1). In reality, the freeze-casting process does not produce ideal 2–2 structures due to ceramic links, as seen in Fig. 2(C) and (D), and therefore a further step was incorporated in which randomly selected elements in the pore channels were reassigned the properties of PZT and randomly selected elements in the PZT channels reassigned the properties of air. To create geometries of varying porosity (20, 30, 40 and 50 vol%), the ratio of PZT channel width to pore channel width was varied. To model the electric field distribution in the dense material (96% of theoretical density), 4% of elements were randomly assigned the properties of air with the remaining elements assigned the properties of unpoled PZT. An electric field was applied across the structure parallel to the lamellar channel direction and the local electric field in each element was recorded.
Fig. 5 shows the electric field distribution for dense PZT (4 vol% porosity) and ceramics with increasing porosity levels. A high electric field concentration is observed within the low permittivity pore volume, with regions of low electric field observed in the immediate vicinity of the pore parallel to the direction of the applied field, which in a ferroelectric material may lead to incomplete poling in these regions, as shown in Fig. 5. Meanwhile, a lower field is observed in the ceramic regions, compared to the lower permittivity pore channels. A higher external electric field must therefore be applied to switch domains in the ceramic regions and hence the coercive field increases with increasing porosity, as in Fig. 4(D). This phenomenon can be described by an adaptation of Gauss' law where the electric field, Ef, is related to the relative permittivity by:
![]() | (6) |
![]() | ||
Fig. 5 Model of electric field distribution in porous PZT and for dense (4 vol% porosity) to 50 vol% obtained by the Finite Element Modelling approach. |
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Fig. 7 Relative permittivity of porous freeze-cast PZT ceramics with both experimental and modelling results as a function of the porosity. The dense material is also shown. |
In addition, the parallel-connected porous PZT exhibited a longitudinal piezoelectric coefficient d33 which was 3.0 to 4.7 times higher than that of the series-connected samples, shown in Fig. 6(A), while the d31 was ∼2.5 times higher than that of the series-modelled PZT, shown in Fig. 6(B). These results are consistent with the P–E loops of Fig. 4 with a higher polarization in the parallel-connected PZT due the better interconnectivity of the PZT along the poling direction.
In the 2–2 connectivity composite, where the first phase is the active PZT piezoelectric ceramic, and the second phase is the passive pore channel (denoted as ‘pc’, henceforth), the piezoelectric coefficients for the series and parallel connection can be calculated by eqn (S1)–(S4).†34 As can be seen from the SEM micrographs in Fig. 2, there are a number of ceramic bridges between the adjacent lamellar structures; therefore, in practice the aligned pore channel is a mixture of the PZT and air, rather than simply air. If we assume the piezoelectric coefficient and the elastic compliance of air are zero and infinite respectively, then the series and parallel equations can be simplified.
For series connection:
![]() | (7) |
![]() | (8) |
For parallel connection:
![]() | (9) |
d31 = VPZTdPZT31 | (10) |
Fig. 7 shows the relative permittivity of the dense and freeze-cast porous PZT measured at 1 kHz and room temperature. The dielectric loss measured from 0.1 to 100 kHz is also shown in Fig. S3,† with a similar loss for the ceramics across the porosity range. The relative permittivity decreased with increasing porosity in the range of 20–60 vol% due to the reduced volume fraction of the high permittivity material, which is consistent with previously reported data27 under different temperatures from 20 to 400 °C, showing that the dielectric loss of both the porous and dense PZT remained almost constant below the Curie temperature. Moreover, the parallel-connected freeze-cast PZT exhibited 3.7–41.3 times higher relative permittivity than the series-connected PZT on increasing the porosity from 20 to 60 vol%, which is due to the improved interconnection in the parallel-connected freeze-cast PZT ceramic. In addition, it is noted that the relative permittivity of the parallel-connected freeze-cast PZT decreased almost linearly with porosity, while there was a non-linear relationship in series-connected PZT, in particular a gentle decrease can be observed with porosity >40 vol%. Lichtenecker's equation can be used to predict the dielectric function of a two-phase composite,41 given by eqn (11):
εLk = v1εPZTk + v2εpck | (11) |
Porosity (%) | Series-connected | Parallel-connected |
---|---|---|
20 | −0.016 | 0.511 |
30 | −0.037 | 0.611 |
40 | −0.038 | 0.632 |
50 | −0.039 | 0.639 |
60 | −0.043 | 0.692 |
Fig. 8 shows the piezoelectric generator figure of merit, FoMij, calculated using eqn (1) at a constant stress as a function of porosity. For the longitudinal d33 piezoelectric figure of merit, the parallel-connected PZT exhibited a higher value than the series-connected PZT. However, the parallel-connected PZT had a lower transverse d31 piezoelectric figure of merit (FoM31) in the whole porosity range. In the series-connected PZT, both longitudinal FoM33 and transverse FoM31 piezoelectric figures of merit increase with increasing porosity and were higher than those of the dense material. The increase in the figures of merit with porosity in Fig. 8 results from the large decrease in relative permittivity with increasing porosity in Fig. 7. However, in the parallel-connected PZT, the transverse FoM31 figure of merit decreased with increasing porosity and was lower than that of the dense material when the porosity >40 vol%. This is due to the more rapid decrease of the d31 (Fig. 6(B)) compared to the permittivity (Fig. 7) with porosity for this orientation. A further increase in the porosity level beyond 60 vol% can result in a decrease of the piezoelectric figure of merit since d33 falls rapidly at higher porosity;43 in addition it is of no benefit to the mechanical strength, as shown in Fig. S1.†
![]() | ||
Fig. 8 Piezoelectric FoM33 and FoM31 generator figure of merit at a constant stress of porous freeze-cast PZT ceramics as a function of porosity. The dense material is also shown. |
For the series connection:
![]() | (12) |
For the parallel connection:
p = VPZTpPZT | (13) |
Fig. 9(A) shows that the pyroelectric coefficient decreased in both types of freeze-cast PZT ceramics with increasing porosity, and is lower than that of the dense PZT. The parallel-connected PZT had a higher pyroelectric coefficient than the series-connected PZT at the same porosity, e.g. 3.0 μC m−2 K−1 and 4.0 μC m−2 K−1 for the series-connected PZT and parallel-connected PZT, respectively, at the 40 vol% porosity. As seen in Fig. 4, the decreased polarization in the porous samples results in the decreased pyroelectric coefficient (p) due to the relationship between the pyroelectric coefficient and polarization where p = dP/dT, and dP and dT are the change in polarization and temperature respectively. The measured specific heat capacities of the porous PZT were 260, 227, 201, 163, and 140 J kg−1 K−1 at room temperature when the porosity increased from 20 to 60 vol%, as shown in Fig. 9(B). The F′E figures of merit for thermal harvesting (eqn (2)) are shown in Fig. 9(C). Although the pyroelectric coefficient of the parallel-connected PZT decreased by ∼49%, see Fig. 9(A), the corresponding figure of merit F′E = p2/(ε0εT33 × (CE)2) increased by ∼405% when the porosity increased from 20 to 60 vol% due to the combination of the reduced permittivity (Fig. 7) and specific heat capacity (Fig. 9(B)). The same trends were also found in the series-connected PZT with a larger decrease in the pyroelectric coefficient and lower increase in F′E which were ∼76% and ∼151%, respectively. The modelling results demonstrate a good fit with the experimental data.
In addition to potential energy harvesting applications, there are other important pyroelectric detection figures of merit to describe the performance of a material as a pyroelectric sensor.44 These include the current responsivity, FI = p/CE, voltage responsivity, FV = p/(CEε33Tε0) and signal to noise figure of merit, FD = p/(CE(ε33Tε0tan
δ)0.5), where CE is the heat capacity. The current responsivity, FI, remains constant with increasing porosity for the parallel connected material since the decrease in pyroelectric coefficient is similar to the decrease in heat capacity, see Fig. 10(A). For the series connected material there is a decrease in FI, due to the low pyroelectric coefficient in this direction (Fig. 9(A)). The voltage responsivity, FV in Fig. 10(B), increases with increasing porosity in both directions due to the decrease in heat capacity and permittivity. The FV is larger for the series connected materials due to the lower permittivity, see Fig. 7. Finally, FD increases with increasing porosity, Fig. 10(C), in both directions due to the reduced specific heat and permittivity; changes in loss are relatively small. Interestingly, while the series connection is advantageous for the FV and FD detection figures of merit, the parallel connection is highest for the F′E harvesting figure of merit, see Fig. 9(C); this is due to its p2 dependency (see eqn (2)) and higher pyroelectric coefficient in this direction (Fig. 9(A)).
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Fig. 10 (A) Figures of merit for the pyroelectric detectors. (A) Current responsivity FI, (B) voltage responsivity FV and (C) FD. |
The measured forward voltage drop of the rectifier circuit was 2V and during the charging process, the energy is CV2/2, where C and V are the capacitance and the voltage of the capacitor, respectively. It can be clearly seen that on increasing the level of aligned porosity from 20 vol% to 60 vol%, the parallel-connected porous PZT produced an increasing peak voltage from 8.3 to 15.2 V after 3600 s (Fig. 11(C)) with a corresponding increase of energy from 34 μJ to 116 μJ (Fig. 11(D)) and energy density from 490 to 1653 μJ cm−3 (inset in Fig. 11(D)). The dense PZT had the lowest voltage of 7.8 V, energy (31 μJ) and energy density (446 μJ cm−3). Both the voltage and the energy density increased with an increase of the porosity level, which is entirely consistent with the improvement in the pyroelectric figure of merit shown in Fig. 10(B). A maximum voltage of 15.2 V was obtained in the storage capacitor utilising parallel-connected PZT with the highest porosity of 60 vol% which demonstrated the fastest charging speed to obtain a stable voltage level of the capacitor, and the corresponding maximum energy and energy density (1653 μJ cm−3) were 374% higher than those of the dense PZT (446 μJ cm−3).
Footnote |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/c7ta00967d |
This journal is © The Royal Society of Chemistry 2017 |