With the advent of modern power electronics, embedded circuits and non-conventional energy harvesting, the need for high performance capacitors is bound to become indispensible. The current state-of-art employs ferroelectric ceramics and linear dielectrics for solid state capacitance. However, lead-free ferroelectric ceramics propose to offer significant improvement in the field of electrical energy storage owing to their high discharge efficiency and energy storage density. In this regards, the authors have investigated the effects of compressive stress as a means of improving the energy storage density of lead-free ferroelectric ceramics. The energy storage density of 0.91(Bi0.5Na0.5)TiO3-0.07BaTiO3-0.02(K0.5Na0.5)NbO3 ferroelectric bulk ceramic was analyzed as a function of varying levels of compressive stress and operational temperature .It was observed that a peak energy density of 387 mJ.cm-3 was obtained at 100 MPa applied stress (25oC). While a maximum energy density of 568 mJ.cm-3 was obtained for the same stress at 80oC. These values are indicative of a significant, 25% and 84%, improvement in the value of stored energy compared to an unloaded material. Additionally, material's discharge efficiency has also been discussed as a function of operational parameters. The observed phenomenon has been explained on the basis of field induced structural transition and competitive domain switching theory.
I. INTRODUCTION
With the advent of modern power electronics,1–4 smart grids5 and growing inclination towards non-conventional energy sources, the need for high performance capacitors is bound to become indispensible. Capacitors find a wide array of applications in almost all modern electrical equipment. They are employed for filtering and smoothening of ripples in signal transfer;6–8 energy storage and rapid discharge (high power) for intermittent or pulsed power application9–11 and as snubber12 and bus capacitors13 for protection of electronic equipment. Regardless of function, an ideal capacitor is expected to possess a few basic requirements. The most primitive necessity being the capacitor should possess high power density, high energy density, good discharge efficiency and low dielectric losses associated with its practical applications.14–16 Additionally, the capacitor is also expected to retain its properties at extreme operating conditions and the performance should not deteriorate with repeated use.
Capacitors for energy storage applications are generally fabricated from subclasses of dielectric materials. Mainly the materials used for fabrication of electrical capacitors consist of linear dielectrics,17 ferroelectrics,18,19 relaxor ferroelectrics20,21 and anti-ferroelectrics.22,23 Linear dielectrics are characterized by their low dielectric permittivity (εr ≪ 100) and high electric breakdown strength.24 This enables them to store large energy density (≈ 10 J.cm−3)18 and have been for long an ideal choice for energy storage. Contrastingly, ferroelectric materials have large dielectric constants associated with them but suffer from poor breakdown strengths and hence, can only store a fractional value of this energy.15 However, with recent advances in the materials chemistry and fabrication techniques, energy densities close to those of linear dielectrics (5 J.cm−3)15 have been reported. However, ferroelectric materials are prone to high dielectric losses which can be attributed to their wide hysteresis loops. Thus, ferroelectric ceramics waste a lot of energy in the form of hysteresis losses and have poor discharging efficiency. In this regards, relaxor ferroelectrics perform comparatively better due to their thin hysteresis loops and are slowly gaining popularity as preferred material of choice for ceramic capacitors. However, the number of pervoskite systems capable of displaying relaxor behavior is very limited and most of them are lead based, for example Lanthanum doped Lead Zirconate Titanate (PLZT) and solid solution of Lead Manganese Niobate Titanate (PMN-PT). Since lead is a known carcinogenic pollutant and poses a serious threat to human health and environment, steps are being taken to slowly phase out lead based compositions altogether. In the light of this information, lead-free anti-ferroelectric and relaxor ferroelectric ceramics offer to become a potential candidate for future capacitor applications. 0.91(Bi0.5Na0.5)TiO3-0.07BaTiO3-0.02(K0.5Na0.5)NbO3 (BNT-BT-KNN) is one such composition. Initial studies based on ferroelectric hysteresis loops suggest BNT-BT-KNN to be anti-ferroelectric in nature. However, recent reports reveal it to be a relaxor ferroelectric.25–28 Even though the nature of ferroelectric response in BNT-BT-KNN is yet debatable, the energy storage characteristics are essentially derived from P-E hysteresis analysis. Since the P-E analysis of BNT-BT-KNN exhibits a pinched loop native to anti-ferroelectric compositions, an assumption based on anti-ferroelectric characteristics is expected to provide accurate description.
Anti-ferroelectric ceramics in their innate state are characterized by the presence of anti-parallel dipolar alignment.29–31 This arrangement of polar moment in the material creates a complete absence of any observable ferroelectric, piezoelectric and pyroelectric properties. However, under the application of a high intensity electric field, the dipoles are rotated to align in the direction of the applied external field.32,33 This is followed by a first order reversible anti-ferroelectric → ferroelectric phase transformation. Thus, at high fields, the anti-ferroelectric material behaves as a ferroelectric material. Since the phase transition is reversible, the ferroelectric phase is reverted back to its original anti-ferroelectric form when the magnitude of applied electric field is reduced below a certain critical value. The low hysteresis losses coupled with the reversible phase transformation have been associated with high power and energy density in anti-ferroelectric materials.22,23 Furthermore, the loss of ferroelectric characteristics at low electric field is also rooted to be responsible for fast discharge rate and high discharge efficiency in anti-ferroelectric materials. Thus, anti-ferroelectric compositions have the potential to become high performing contenders in the field of commercial capacitor applications.
It has been observed that phase transition in BNT-BT-KNN is accompanied by a structural transformation of the material's crystal lattice akin to that observed for anti-ferroelectric materials.29 This structural change generates volumetric expansion in the material in both longitudinal and transverse directions. Thus, it is expected that the phase transition will be sensitive to the compressive stresses applied to the material, which will oppose dimensional variations.22 This knowledge can be effectively utilized to shift the transformation to higher values of electric field and thereby increase the energy density associated with this composition. In this regards, the authors propose to utilize directional confinement to improve the associated parameters of BNT-BT-KNN ceramics for electrical energy storage purposes. It was observed that significant improvement in energy storage density can be obtained upon application of suitable mechanical confinement to the ceramic samples. The phenomenon has been explained on the basis of competing nature of domain motion upon exposure to high intensity electrical and mechanical stimulus. According to the best of our knowledge no such attempt has been made till date.
II. MATERIALS AND METHODS
A. Material
(Bi0.5Na0.5)TiO3-BaTiO3 (BNT-BT) is a lead-free binary solid solution of BNT and BT compositions.34,35 It is a well-known lead-free ferroelectric material and has been extensively documented in the literature, of recent.36–43 BNT-BT's morphotropic phase boundary extends from 5 to 7 mol.% BT.35 The material possesses good pyroelectric coefficients and has been reported to display giant piezoelectric strain characteristics after the addition of small quantity of (K0.5Na0.5)NbO3 (KNN).36,38,42 The original BNT-BT composition is largely ferroelectric at room temperature and displays a rhombohedral structure.36 However, the addition of small quantities of orthorhombic KNN seems to disrupt the long range ferroelectric order and induces altered characteristic in the material system.27,28,36 Tan et al. reported that addition of KNN in increasing quantities was also responsible for reduced depolarization temperature and increasing non-ferroelectric characteristics of the original BNT-BT composition.44 It was observed that 0.91(Bi0.5Na0.5)TiO3-0.07BaTiO3-0.02(K0.5Na0.5)NbO3 possess largely pseudo-cubic structure in contrast to 0.94(Bi0.5Na0.5)TiO3-0.05BaTiO3-0.01(K0.5Na0.5)NbO3 which was characterized by a rhombohedral R3c symmetry and displays largely ferroelectric behavior.44 The significant change was observed for only 1 mol.% change in the amount of KNN. For the purpose of our study we have used 0.91(Bi0.5Na0.5)TiO3-0.07BaTiO3-0.02(K0.5Na0.5)NbO3 (BNT-BT-KNN) composition as it displays largely non-ferroelectric characteristics accompanied by large recoverable strains.
Tan et al. originally fabricated the ceramic through conventional solid state fabrication technique.44 Sintering of the pressed pellets was carried out at 1150oC for 3 hours in a covered alumina crucible.44 The polished pellets were electroded using Ag paste and fired to obtain uniform contact of the sample and the electrode. The polarization versus electric field (P-E) hysteresis loops were measured at different combinations of stress and temperature using a modified Sawyer-Tower circuit and have been plotted in Figure 1.44 The temperature was varied in three stages (of 25oC, 80oC and 140oC) in conjunction with uniaxial compressive stresses of 0, 100 and 250 MPa. These P-E loops have been utilized to estimate the energy storage density and discharge efficiency of the BNT-BT-KNN bulk ceramic samples.
Polarization versus electric field (P-E) hysteresis loops for 0.91(Bi0.5Na0.5)TiO3-0.07BaTiO3-0.02(K0.5Na0.5)NbO3 bulk ceramic as observed for varying intensity of applied compressive stress and temperature.
Polarization versus electric field (P-E) hysteresis loops for 0.91(Bi0.5Na0.5)TiO3-0.07BaTiO3-0.02(K0.5Na0.5)NbO3 bulk ceramic as observed for varying intensity of applied compressive stress and temperature.
B. Methods
The energy storage density of any ferroelectric ceramic can be estimated form its P-E hysteresis loops by using the following expression:45
Here, W presents the electrical energy density stored in the material; E refers to the applied external electric field and Pr and Pmax are the remnant and maximum polarization values respectively. Anti-ferroelectrics, relaxor ferroelectrics and linear dielectric materials possess negligible remnant polarization (Pr = 0). Therefore, for these materials, Eq. (1) can be rewritten with limits varying from 0 to Pmax. However, this expression represents the recoverable energy density, when the integration is done with respect to discharging curve on the P-E hysteresis loops (Figure 2). The total energy required to charge a ferroelectric capacitor is the sum of recoverable (W) energy and dielectric losses (Wloss). The lost or unreleased energy density (Wloss) is the energy equivalent to the inherent hysteresis in the material. This unrecoverable energy is defined as the area enclosed by charging and discharging curve and y axis (numerical integration of closed area of the hysteresis loops). These losses are generally manifested in the material in the form of self-heating or ferroelectric noise. Thus, the total energy (Wtotal) required to charge a capacitor can be represented as:
Considering equations (1) and (2), the storage efficiency η of the material can be calculated as:45
A small value of η is indicative of large losses in the form of hysteresis. It is made apparent form Eq. (3) that energy storage efficiency can be increased if the losses can be reduced. Compressive pre-stresses in the form of mechanical confinement can be used to this effect. Exposure to external mechanical field is expected to interfere with the phase transition. It can be effectively applied for tuning the hysteresis associated with the ferroelectric phase, thereby reducing losses. This is expected to have a direct bearing on the energy storage density and discharge efficiency of the material. Figure 2 has been employed to represent the characteristic P-E behavior of anti-ferroelectric materials (pinched loops) under the application of stress. The ferroelectric response of BNT-BT-KNN has been studied under varying levels of compressive stress and temperature. Equations (1) and (3) have been utilized to estimate the energy storage density and efficiency, respectively. The results thus obtained and their inference is discussed in the following section.
Graphical representation of enhanced electrical energy storage density originating from mechanical confinement, associated with ferroelectric materials. The superscripts 1 and 2 in the figure represent the materials behavior under unstressed and stressed conditions, respectively.
Graphical representation of enhanced electrical energy storage density originating from mechanical confinement, associated with ferroelectric materials. The superscripts 1 and 2 in the figure represent the materials behavior under unstressed and stressed conditions, respectively.
III. RESULTS AND DISCUSSION
Figure 1 displays the P-E hysteresis loops as obtained for BNT-BT-KNN for different value of stress and temperature. Figures 3 and 4 illustrate the peak energy density and material efficiency as a function of compressive stress and applied temperatures. It is observed that a peak energy density of 568 mJ.cm−3 is obtained for an applied uniaxial compressive stress of 100 MPa and a temperature of 80oC. While a peak energy density of 387 mJ.cm−3 was observed for 100 MPa stress at room temperature. These values are significantly larger compared to those obtained for unloaded material at room temperature (309 mJ.cm−3). Thus, an increment of 84% and 25% can be obtained by means of combined loading and mechanical confinement alone, respectively. Additionally, the material's discharge efficiency was also improved considerably owing to thermal and mechanical fields. The unloaded sample registered an efficiency of 37%, which was later improved to a value of 49% for 250 MPa at room temperature and 72% for 100 MPa at 80oC. A peak efficiency of 90.42% was observed for measuring conditions of 140oC and 250 MPa applied stress. However, since exposure to high intensity fields deteriorates energy storage density, the latter value is of little significance. These observations can be explained on the basis of field induced structural change, phase transition energetics and competing domain switching effects, as follows.
The graphs 3(a), (b) and (c) represent the electrical energy storage density of BNT-BT-KNN bulk ceramic as a function of increasing compressive stress and temperature levels.
The graphs 3(a), (b) and (c) represent the electrical energy storage density of BNT-BT-KNN bulk ceramic as a function of increasing compressive stress and temperature levels.
This figure represents the variation of material's (BNT-BT-KNN) discharge efficiency as a function of compressive stress and operating temperature.
This figure represents the variation of material's (BNT-BT-KNN) discharge efficiency as a function of compressive stress and operating temperature.
Field induced structural transformation in ferroelectric ceramics is often accompanied by inception of volumetric changes and accompanying piezoelectric strains. These strains are more pronounced when the material in question is fabricated in the vicinity of its morphotropic phase boundary (MPB). MPB signifies coexistence of two or more phases in a homogeneous solid solution of ferroelectric material.46–48 Since the coexisting phases are separated by only a small difference in their free energies, a first order reversible transformation between the two phases can be achieved by suitable application of external impetus. The manner of which can be explained on the basis of energetic of phase transition.
The Helmholtz free energy densityA, of the ferroelectric materials is given by:49
Here, σ, ε, E, D, T and S denote stress, strain, electric field intensity, electric displacement, temperature, and entropy respectively. From equation (4) it can be deducted that the equilibrium can be shifted in the favor of a preferred state by suitable application of stress, electric field or temperature. Therefore, equation (4) can be rewritten to represent phase change as follows:50
Here, α and β indicate the initial and final phases of material. This effect has been documented to drive phase change in a large number of studies.49,51–56 It may also be inferred from equations (4) and (5) that if dε ≠ 0, externally applied mechanical stress will influence the phase transformation. The nature of effect that compressive stresses will have on structural transition depends on dε. As is the case of BNT-BT-KNN phase change, it is accompanied by volumetric expansion in both lateral and axial directions. Thus, application of compressive stress or mechanical confinement to the material will shift the value of electric field required to drive the transition to a higher magnitude. This effect has been previously observed22 and is verified in this study. Therefore, it can be hypothesized that, provided the applied mechanical stress has no degrading effect on saturation polarization, the value of energy storage density increases with increasing magnitude of stress.
This phenomenon can be explained on the basis of competing nature of mechanical and electrical domain switching modes. In its innate state, a bulk ferroelectric ceramic consists of randomly aligned domains. Thus, the material as a whole displays lack of any spontaneous polarization or ferroelectric activity. However, when the same material is subjected to an electric field of increasing magnitude, domain realignment is initiated. Initially a minor domain wall motion is observed which favors the growth of preferentially aligned domains. However, upon being subjected to higher magnitude of electric field, the domains themselves are rotated in the direction of the applied electric field. This phenomenon is known as ferroelectric domain switching and is generally associated with 180o domain rotation. Conversely, when a poled or activated ferroelectric material is subjected to compressive stress, the domains realign themselves to face away from the direction of stress applied. This has been termed as ferroelastic domain switching. The movement of the domains is such that it minimizes structural energy to accommodate the additional strain being generated in the material. Ferroelastic domain rotations are inherently non-180o in nature and the switching direction has been observed to be dependent on the crystallographic structure of the material.
Thus, when a material is subjected to a combined electro-mechanical loading, the domain alignment is decided by the equilibrium value of the competing fields. It is possible to utilize this phenomenon to create stress induced domain pinning in the ferroelectric material. Since hysteresis is the equivalent energy utilized by the electric field in rotating the dipoles, domain pinning counters this effect directly. With increasing magnitude of applied compressive stress, a growing number of domains are ‘pinned’ to their position. Consequently, the switchable part of polarization gets reduced and this in turn is manifested in the form of reduced hysteresis.
However, ferroelectric and ferroelastic switching act to counter each other. Thus, if magnitude of one of the fields is increased beyond a certain critical value it will completely override the effect of other. In such a situation, no phase change can be initiated and thus material performance starts to degrade. This behavior has been confirmed in the BNT-BT-KNN samples used for this study. The application of stress up to 100 MPa was able to raise the energy storage density as it causes a reduction in hysteresis without appreciable loss of saturation polarization. However, application of compressive stress exceeding 100 MPa was greeted with a significantly reduced saturation polarization. As a result, the energy storage density decreases in accordance to the values obtained by using equation (1). The storage density as a function of applied compressive stress, electric field and temperature is displayed in Figure 3. In all the three cases, it can be observed that the energy storage density increases only upto a stress application of 100 MPa, after which a sharp decline is observed.
The effect of temperature increment on the material performance has also been investigated in this study. Thermal degradation of performance is often a limiting constraint for ferroelectric ceramic capacitors under practical applications. Increasing the temperature of ferroelectric materials causes dipolar randomness to increase in the material. This is a direct consequence of the enhanced lattice vibrations owing to increased energy content in the material. Thus, increasing temperature is associated with increased losses, as electric field has to do more work to realign the domains in the preferred direction. However, in the present study it was observed that energy density increases with increasing temperature up to 80oC and decreases henceforth. This behavior can be attributed to combined electro-mechanical loading that the material is prone to. Since, there is no appreciable change in the value of saturation polarization, it is hypothesized that presence of compressive stresses helps to contain lattice vibrations. Mechanical confinement must act to reduce the degree of freedom that is normally associated with thermal vibrations. Additionally, due to increased energy content it is possible that, up to a certain temperature, enhanced thermal energy actually ‘lubricates’ the ferroelastic domain wall motion. Thus, a more enhanced pinning effect is obtained which further reduces the hysteresis loss. Nevertheless, increasing the temperature beyond 80oC reduces the energy density of the material. This follows in accordance with prediction obtained from using equation (5). When the applied temperature increases beyond a threshold value, it overrides the effect of the other two fields and causes a drop in saturation polarization. This adversely affects the storage density of material. However, the discharge efficiency shows a continuous increment in correlation to enhanced temperatures (Figure 4). This is because with increasing temperature, the paraelectric behavior increases, for which the discharge efficiency is high. A complete depolarization is not observed even after the application of 140oC and the material still retains its non-linear behavior. This is despite the fact that considered composition of BNT-BT-KNN reportedly has a depolarization temperature of 46oC.57
The predicted value of energy storage density and discharge efficiency indicate towards plausible application of either mechanical or self-confinement of BNT-BT-KNN ceramics for enhanced electrical energy storage. The results also indicate towards possible tuning of material performance through application of compressive stresses as it can be used to both increase and decrease the storage density. Therefore, knowledge of confinement/clamping is of potential applicability for determining the optimum operating parameters of a practical system. Even though the results are indicative of a positive outcome, the effect of additional parameters like stress relaxation, nature of electric potential, frequency of operation and fatigue cannot be ignored. Thus further investigation is warranted in this direction owing to the economic benefits associated with similar outcomes, before this technology can lead to competitive commercial products.
IV. CONCLUSION
This article deals with enhancement of electrical energy storage density in lead-free BNT-BT-KNN ceramics through application of suitable compressive pre-stresses. For the purpose of investigation, 0.91(Bi0.5Na0.5)TiO3-0.07BaTiO3-0.02(K0.5Na0.5)NbO3 polycrystalline non-ferroelectric ceramics were selected. The P-E hysteresis loops at different stress and temperatures were used to estimate the energy storage density and discharge efficiency of the material. It was observed that a peak energy density of 387 mJ.cm−3 was obtained for a 100 MPa stress applied at room temperature. While a maximum energy density of 568 mJ.cm−3 was obtained for the same stress level at 80oC. These values are indicative of a significant, 25% and 84%, improvement in the value of stored energy compared to an unloaded material. The observed phenomenon has been explained on the basis of field induced structural transition and domain switching theory. Additionally, the improvement in material's discharge efficiency and the effect of temperature has also been discussed. This study is aimed at promoting research interest in the field of mechanical confinement of ceramic capacitors for tailoring their performance. As indicated from the results, further research is warranted in this field owing to the vested commercial interest and future application prospects.
ACKNOWLEDGMENTS
One of the authors (Rahul Vaish) acknowledges support from the Indian National Science Academy (INSA), New Delhi, India, through a grant by the Department of Science and Technology (DST), New Delhi, under INSPIRE faculty award-2011 (ENG-01) and INSA Young Scientists Medal-2013.