Electrostrictive Coefficient Research Articles

Temperature-insensitive piezoelectric properties of lead-free BiFeO3–BaTiO3 ceramics with high Curie temperature

Temperature-insensitive high piezoelectric strain and low strain hysteresis (Hs) with high Curie temperature (TC) are desirable for piezoelectric actuator applications. The excellent room-temperature piezoelectric performance (d33 = 309 pC/N and d33∗ = 458 pm/V) with very high TC = 482 °C have achieved in 0.67Bi1.03FeO3-0.33Ba1-xLaxTiO3 ceramics. Furthermore, a small variation in the piezoelectric strain (ΔST = 13%) in the temperature range of 25 °C–125 °C with low strain hysteresis (Hs = 12%) and a large average electrostrictive coefficient (Q33 = 0.03 m2/C4) leads to a high figure of merit for piezoelectric actuators. The structural origin of the high piezoelectric performance is related to the crystal structure morphotropic phase boundary and maximum crystal structure lattice distortion (90° ̶ αR = 0.12° and cT/aT = 1.008). While the physical origin is mainly attributed to the soft ferroelectric effect by La3+ as donor doping on Ba2+-site that significantly reduces the coercive field and makes it easy to switch ferroelectric polarization under the applied electric field. We believe that this breakthrough in lead-free ceramics opens a new development window for temperature-insensitive piezoelectric properties for the high-temperature commercial applications.

Large electrostrictive effect and strong photoluminescence properties in Sm2O3-modified lead-free potassium sodium niobate-based piezoelectric ceramics

In this work, the phase transition behavior and electrostrictive and photoluminescence properties of Sm2O3-modified 0.965(K0.48Na0.52)(Nb0.95Sb0.05)–0.035Bi0.5(Na0.82K0.18)0.5HfO3 (KNNS–0.035BNKH) ceramics were investigated. Results showed that the phase structure of the Sm2O3-modified ceramics evolved from coexisting orthogonal and tetragonal ferroelectric phases to a relaxor pseudocubic phase along with the strong destruction of the long-range ferroelectric order. Domain switching in Sm-modified ceramics with a relaxor pseudocubic phase became difficult, evident from the PFM images. Consequently, large electrostrictive effect with an electrostrictive coefficient of 0.022 m4/C2 was obtained in 1.0 mol% Sm-modified samples. With regard to long-term stability, the materials exhibited temperature-independent (20–100 °C) and fatigue−free (up to 105 cycles) behavior, which guarantees their application in various devices. The KNNS–0.035BNKH–xSm ceramics have the advantages of photoluminescence performance with bright orange emission under 407 nm visible light excitation. Overall, KNNS−0.035BNKH−xSm ceramics have broad application prospects in multifunction devices due to their large electrostrictive effect, excellent photoluminescence performance, and long-term stability.

Improve piezoelectricity in BaTiO3-based ceramics with large electrostriction coefficient

A new solid solution of (1 − x)Ba0.86Sr0.14TiO3 − xBa0.86Sr0.14HfO3 (abbreviated as BST − xBSH, 0.00 ≤ x ≤ 0.10) was prepared to search for a high-performance lead-free piezoelectric ceramics. Through the chemical of Hf tailoring, the enhanced electrical property (e.g., d33 ~ 650 pC/N, er ~ 4455, tanδ ~ 0.024, strain ~ 0.151%, and d33* ~ 502 pm/V) and large electrostriction coefficient (Q33 = 0.0528 m4/C2) are obtained in the ceramics with x = 0.06. The relationship between piezoelectric performance and electrostrictive coefficient is studied in detail. It’s worth noting that the variation of Q33 is highly matched with d33 because the electrostrictive effect plays a vital role in the piezoelectricity of ferroelectric materials. Therefore, it is very promising to increase the piezoelectricity by modifying electrostriction coefficient in lead-free materials for electromechanical actuator applications.

Enhanced electric field induced strain in electrostrictive polyurethane composites fibers with polyaniline (emeraldine salt) spider-web network

During the last decade, electrostrictive polymers have stood out especially in electromechanical applications because of their high-strain performance. The electrostrictive ability of a polymers is indicated by its electrostrictive coefficient (M) that depends on dielectric constant and Young's modulus. The dielectric constant of a polymer can be increased with fillers to create promising candidate materials for actuators and energy harvesting, because of interfacial polarization at matrix-filler interfaces. Therefore, a large specific interfacial surface is of importance. In this study, fibers were fabricated by electrospinning Polyurethane/Polyaniline (PU/PANI) composites with 0.5, 1, 1.5, or 2 wt% PANI loadings in the spinner. Then, morphology and chemical structure of the obtained fibers were investigated by SEM and FTIR, respectively. The electrical properties, mechanical properties, and electrostrictive properties were also evaluated. The results show that the average spun fiber diameter, its distribution, and occurrence of spider-web conformations depend strongly on the PANI content. Moreover, the dielectric constant increased with PANI loading and was inversely proportional to Young's modulus. The electrostrictive coefficient increased with PANI content and was for the spun fibers about 6 fold that of composite films, which was partly attributed to the spider-web conformations of the fibers.

Superior Electrostrictive Effect in Relaxor Potassium Sodium Niobate Based Ferroelectrics.

Electromechanical actuators with toxic lead-based electrostrictive materials dominate the market of high-precision electronics devices, so one of urgent aims becomes how to explore the new generation of ecofriendly electrostrictive materials with superior electrostriction behaviors. Herein, a strategy of modifying the active space for the B-site in lead-free relaxor ferroelectrics arouses the potential capacity of electrostriction, including K0.5Na0.5NbO3 (KNN). Through co-doping of Bi3+ and Ni2+, typical relaxor ferroelectrics (1 - x)K0.5Na0.5NbO3-xBiNi2/3Nb1/3O3 (KNN-xBNN, 0.03 ≤ x ≤ 0.07) are constructed because of the incorporation of dopants ions on the A- or B-site promotes structural disorder. Importantly, a limited active space for the B-site is obtained owing to the contracted oxygen-octahedron with smaller A-site dopants induced by lattice distortion. Benefiting from the design strategy, a remarkable enhancement of electrostrictive coefficient Q33 of ∼0.0456 m4/C2 is achieved, which is higher than those of KNN-based materials and also twice as large as those of lead based materials. The Q33 also exhibits a relatively good electric field and is temperature-independent. A giant Q33 of 0.0512 m4/C2 is gained at a high frequency of 100 Hz, meeting the requirement of some commercial actuators for fuel injectors. Such a strategy may help us design high-performance electrostrictive materials.

Enhanced Electromechanical Response in Sm and Nd Co-doped Ceria

Highly oxygen defective cerium oxide, e.g., Gd-doped ceria, is a sustainable non-classical electrostrictor with electromechanical properties that are superior to lead-based piezoelectric metal oxides. Here, we report electrostriction in co-doped ceria (Sm, Nd) with a nominally low short-range vacancy-dopant association energy. Such a strategy results in a higher electrostrictive strain coefficient (M33), up to 10−17 (m/V)2 at lower-frequencies, and unexpected electromechanical strain saturation and relaxation effects. These outcomes support the hypothesis that electrostriction is strongly influenced by the local environment of oxygen vacancy and by the ionic migration blocking factors built-in the microstructure.

Negative Piezoelectric-Based Electric-Field-Actuated Mode-Switchable Multilayer Ferroelectric FBARs for Selective Control of Harmonic Resonances Without Degrading Keff².

Mode-switchable ferroelectric thin-film bulk acoustic resonators (FBARs) are presented. Such resonators operate based on a dynamic nonuniform effective piezoelectricity in composite multilayer ferroelectrics with large electrostriction coefficients, like barium strontium titanate (BST). Harmonic resonance modes ( nfo ) of a multilayer ferroelectric bulk acoustic wave (BAW) resonator can be selectively excited with an electromechanical coupling coefficient ( Keff2 ) equal to the fundament mode, which is contrary to the trend Keff2 ∝ 1/n2 exhibited by conventional piezoelectric BAW resonators. Such a device can selectively be set to resonate at its different resonance harmonics by generating a pattern of nonuniform piezoelectric coefficient proportional to the stress field of each mode with an application of a proper set of dc control voltages applied across the ferroelectric layers. Such a resonator allows for the design of a new class of band-switching filters. As an experimental validation, a mode-switchable FBAR and a band-switching ladder-type filter based on a bilayer ferroelectric BST structure are designed and fabricated for the first time. The bilayer BST FBARs not only can be switched ON or OFF but also by choosing different bias configurations, two resonance modes at 2 and 3.6 GHz can be selectively excited having Keff2 of 8% and 7%, respectively.

Superior electrostrictive coefficient of 6BNT-4SCxBT lead-free relaxor ferroelectrics with Ca2+ substitution

In this study, lead-free 0.6(Bi0.5Na0.5)TiO3-0.4(Sr0.7-xCaxBi0.2)TiO3 ceramics (abbreviated as 6BNT-4SCxBT, x=0, 0.05, 0.10, 0.15 and 0.20 mol) were prepared by a traditional solid-state method. The effects of Ca2+ on phase structure, state transformation, ferroelectric and energy storage properties, and electrostrictive performance of 6BNT-4SCBT-x ceramics were comprehensively investigated. Co-occupied Bi3+, Na+, Sr2+ and Ca2+ ions induced the inhomogeneous distribution of A-site ions and charge, which resulted in polar nano-regions (PNRs) for relaxor ferroelectrics. 6BNT-4SCxBT ceramics present the ergodic relaxor state of polar rhombohedral PNRs and weakly polar tetragonal PNRs at room temperature. When the Ca2+ content was increased, 6BNT-4SC0.01BT ceramics showed the properties of weakly polar tetragonal PNRs (with lowest Tp~71 °C). 6BNT-4SCxBT ceramics exhibit electrostrictive effect Q33 (~0.045 m4/C2) and high energy storage efficiency. Moreover, large Q33 (>0.0421 m4/C2) indicates good electrical field stability. This result is a significant advancement in the area of lead-free electrostrictive materials, which has a great prospect in BNT-based ceramics.

High energy storage efficiency and high electrostrictive coefficients in BNT–BS–xBT ferroelectric ceramics

(1 − x)[0.9(Bi0.5Na0.5)TiO3–0.1BiScO3]–xBaTiO3 (BNT–BS–xBT) ceramics are prepared by the traditional solid-state sintering. The structure, morphology, ferroelectricity, strain, energy storage, dielectricity, and impedance of the BNT–BS–xBT ceramics are investigated. XRD shows that all ceramics have pseudo-cubic structures. The results also show that BT can refine the grain size of the ceramics and reduce the corresponding density. At x = 0.20, the energy storage performance of the ceramics is optimum (Wrec = 0.563 J/cm3, η = 63%). At x = 0.10, the electrostriction coefficient (Q33) of the ceramics reaches 2.72325 × 10−2 m4/C2. Dielectric and impedance spectroscopies show that the ceramics are relaxor ferroelectrics and have good insulation properties.

Tailoring the Structure, Energy Storage, Strain, and Dielectric Properties of Bi0.5(Na0.82K0.18)0.5TiO3 Ceramics by (Fe1/4Sc1/4Nb1/2)4+ Multiple Complex Ions

The effects of (Fe1/4Sc1/4Nb1/2)4+ (FSN) multiple complex ions on the structure and electrical properties of Bi0.5(Na0.82K0.18)0.5Ti(1-x)(Fe1/4Sc1/4Nb1/2)xO3 (BNKT-xFSN) ceramics were studied. The FSN complex ions induces the phase transition from ferroelectric state to relaxor state. The coercive field and remanent polarization decrease rapidly with the increase of FSN content. With the increase of the external electric field, the energy storage density of BNKT-xFSN ceramics gradually increases and reaches the maximum value of 0.96 J/cm3 (90 kV/cm) at x=0.09, and the corresponding efficiency is 62%. Meanwhile, the field-induced strain of BNKT-0.07FSN ceramic increases from 0.13% at 50 kV/cm to 0.43% at 80 kV/cm, and the corresponding electrostrictive coefficient Q33 reaches the maximum value of 0.0213 m4/C2. BNKT-xFSN relaxed ceramics with pseudo-cubic structure have large electrostrictive coefficients when TF-R is near room temperature. The local composition inhomogeneity by FSN complex ions at B-sites induces the relaxor characteristics of BNKT-xFSN ceramics.

Large electrostrictive effect in Sn-doped NBT–BT lead-free relaxor ceramics

In this work, we design and adjust the composition in [Formula: see text]–[Formula: see text] lead-free relaxor ferroelectrics by doping SnO2 to introduce a relaxor phase and accordingly obtain prominent lead-free electrostrictors. It was found that all the samples exhibited ideal features of relaxor ferroelectrics and the ferroelectric-relaxor phase transition temperature of the ceramics was adjusted to near or below room temperature after doping with a handful of [Formula: see text]. A relatively high electrostrictive coefficient [Formula: see text] of 0.0293 m4/C2 was achieved for the composition with [Formula: see text], which was attributed to the formation of relaxor pseudocubic phase developed by the [Formula: see text] substitution. These results provide some instructive thoughts for the further development of [Formula: see text]-based electrostrictive materials by B-site doping.

Ferroelectric Behavior in Exfoliated 2D Aurivillius Oxide Flakes of Sub‐Unit Cell Thickness

AbstractFerroelectricity in ultrasonically exfoliated flakes of the layered Aurivillius oxide Bi5Ti3Fe0.5Co0.5O15 with a range of thicknesses is studied. These flakes have relatively large areas (linear dimensions many times the film thickness), thus classifying them as 2D materials. It is shown that ferroelectricity can exist in flakes with thicknesses of only 2.4 nm, which equals one‐half of the normal crystal unit cell. Piezoresponse force microscopy (PFM) demonstrates that these very thin flakes exhibit both piezoelectric effects and that the ferroelectric polarization can be reversibly switched. A new model is presented that permits the accurate modeling of the field‐on and field‐off PFM time domain and hysteresis loop responses from a ferroelectric during switching in the presence of charge injection, storage, and decay through a Schottky barrier at the electrode–oxide interface. The extracted values of spontaneous polarization, 0.04(±0.02) C m−2 and electrostrictive coefficient, 2(±0.1) × 10−2 m4 C−2 are in good agreement with other ferroelectric Aurivillius oxides. Coercive field scales with thickness, closely following the semi‐empirical scaling law expected for ferroelectric materials. This constitutes the first evidence for ferroelectricity in a 2D oxide material, and it offers the prospect of new devices that might use the useful properties associated with the switchable ferroelectric spontaneous polarization in a 2D materials format.

Electrically tunable and reversible selective reflection due to the transition between simple cubic and tetragonal blue-phase liquid crystals

ABSTRACT In this paper, we present experimental results on electrically tunable reflected wavelength in the full visible spectral range from 460 nm to 620 nm in one simple cubic blue-phase cell due to the simple-cubic–tetragonal lattice transition, confirmed by Kossel lines. The reflected wavelength is switched less than few hundreds milli-second and it is reversible. From the experimental observations in the reflection spectra and Kossel lines, we can see the following phenomena as increasing the applied field: the lattice-plane realignment in the simple-cubic blue phase (BPII), the transition between BPII and tetragonal blue-phase liquid crystal (BPX), and the lattice deformation of the BPX. Among them, the lattice deformation of the BPX shows larger electrostriction coefficient to shift the wavelength in a wider range, but it takes the longest response time. Because the reflected wavelength in each applied field exhibited extraordinarily sharp photonic bandgaps (less than 20 nm) with high reflectivity, the BP cell here shows a great potential to be a tunable photonic device.

Tailoring electromechanical performance in BiScO3-modified Bi0.5Na0.5TiO3-based lead-free piezoceramics

The strain response of lead-free ternary solid solution (1 − x) (0.94 Bi0.5Na0.5TiO3–0.06BaTiO3)–xBiScO3 (BNT–BT–BS) have been tailored by controlling the phase transition temperature. The effects of BiScO3 on the phase structure, dielectric, ferroelectric, piezoelectric properties, and electric field-induced strain are systematically investigated. A schematic phase diagram has also been established to clarify the relationship between strain behavior and structure evolution. The field-induced strain increases progressively, and a large strain of 0.35% with Smax/Emax = 471 pm/V is achieved at the critical composition x = 0.03, owing to the shift of the ferroelectric-to-relaxor transition temperature TF–R to ambient temperature. Intriguingly, the established correlation between strain response and TF–R demonstrates that the optimization of strain behavior of BNT-based ceramics can be realized though the regulation of TF–R to room temperature. Furthermore, a high and thermally stable electrostrictive coefficient Q33 of 0.018 m4/C2 can also be attained at the composition x = 0.06. In this study, it is believed that the modulation of phase transition temperature is feasible to achieve the large strain response in BNT-based ceramics.

Ferroelectric and piezoelectric properties of Ca2+ and Sn4+ substituted BaTiO3 lead-free electroceramics on the emphasis of phase coexistence

The Ba1-xCaxTi1-ySnyO3 (abbreviated as BCxTSy, x = 0.01, y = 0.01; x = 0.03, y = 0.015; x = 0.05, y = 0.02; and x = 0.07, y = 0.025 mol.) electroceramics were synthesized by solid-state reaction method and investigated their structural, dielectric, ferroelectric and piezoelectric properties. Rietveld refinement of X-ray diffraction data for the composition x = 0.03, y = 0.015 reveals the phase co-existence of two non-centrosymmetric orthorhombic (Amm2) (7.71%) + tetragonal (P4mm) (92.29%) lattice symmetries near room temperature which is also evidenced by temperature-dependent Raman and dielectric studies. All compositions reveal the dense microstructure having relative density ~92%–96% and average grain size ~10.7–22.5 μm. The phase diagram based on dielectric study suggests that the composition x = 0.03, y = 0.015 reveals T(R–O) ~ − 60 °C, T(O-T) ~ 19 °C and TC ~ 126 °C with Pr = 11.80 μC/cm2, Ec = 3.5 kV/cm, Pmax = 21.92 μC/cm2, d33* = 505.5 pm/V, d33 = 287 pC/N and electrostrictive coefficient (Q33) = 0.036 m4/C2 properties which could be useful for developing the piezoelectric AC devices. Here, we have achieved the phase-coexistence of two non-centrosymmetric lattice symmetries near room temperature to invoke the reliable ferroelectric and piezoelectric properties and discussed the results with the structure-property-composition relation.

The effect of Sn4+ doping on the electrostrictive property of PLZT (9/65/35) transparent electro-optical ceramics

SnO2-doped PLZT (9/65/35) transparent ceramics have been prepared by the hot press sintering method. The microstructure, dielectric, ferroelectric, and electrostrictive properties of the materials were examined and analyzed. All the samples present typical relaxor ferroelectric characteristics. Owing to the lowering of the long-range order by Sn4+ doping, the Tm peaks decrease gradually with the increasing SnO2 content. Compared with the high field-induced strains, the antiferroelectric-ferroelectric phase transformation in all the PLZST samples can be induced under the electric field. The electrostrictive property of the PLZT (9/65/35) ceramics was obviously improved by the Sn4+ ion doping. In addition, the polarization-related electrostrictive coefficient Q33 increased gradually from 0.024 m4/C2 to 0.027 m4/C2 as the SnO2 content increased from 0.0 wt % to 0.6 wt %.

Large electrostrictive effect and energy storage density in MnCO3 modified Na0.325Bi0.395Sr0.245□0.035TiO3 lead-free ceramics

The Na0.325Bi0.395Sr0.245□0.035TiO3 + x % MnCO3 (NBST-100xMn) lead-free ceramic samples had been fabricated by solid-state reaction method. Microstructure and electrical properties with the addition of MnCO3 had been studied in detail. The NBST-4Mn showed a low hysteresis behavior with the maximum electrostrictive coefficient (Q) of 0.0294 m4/C2 and the recoverable energy storage density (Wrec) of 1.3 J/cm3 at 95 kV/cm. In addition, the electrostrictive effect and energy storage ability presented outstanding temperature stability and fatigue resistance, which indicated a promising lead-free ceramic for high precise actuator.

Effect of Sr2+ on phase structure and properties for 0.6(Na0.5Bi0.5)TiO3-0.4(Bi1-ySry)TiO3 relaxor ferroelectrics

0.6(Na0.5Bi0.5)TiO3-0.4(Bi1-ySry)TiO3 ceramics (abbreviated BNT-BSyT, y = 0.2, 0.3, 0.5, 0.7, and 0.9 mol) were fabricated using a traditional solid-state processing route, and the effects of Sr2+ on phase structure, di- and ferroelectric properties, and electrostrictive properties were systematically investigated. The values of γ for BNT-BSyT ceramics are greater than 1.8, revealing that these materials exhibit relaxor ferroelectric properties derived from the co-occupation of Bi3+, Na+, and Sr2+ in the A-site and inhomogeneous polarization states (i.e., coexistence of rhombohedral and tetragonal states). In addition, Td decreases with increasing Sr2+ content along with a stable and increased tetragonal phase. BNT-BS0.9T ceramic has a slightly large maximum polarization Pmax = 16.15 μC/cm2, a small remanent polarization Pr = 1.6 μC/cm2, and a relatively good energy storage property (density W1 = 0.220 J/cm3 and efficiency η = 72.13%), indicating that Sr2+ substitution helps to promote energy storage characteristics. Moreover, there is a superior electrostrictive coefficient (Q33 = 0.0385 m4/C2) for BNT-BS0.3T ceramic. Therefore, we propose that this lead-free electrostrictor is a good candidate for practical applications.

Frequency-dependent ferro-antiferro phase transition and internal bias field influenced piezoelectric response of donor and acceptor doped bismuth sodium titanate ceramics

The influence of donor (La3+) and acceptor (Sc3+) dopant on structural and electrical properties of lead-free Bi0.5Na0.5TiO3 (BNT) ceramics system was investigated. Both donor and acceptor substitutions induced a structural transformation of pure BNT ceramics from a rhombohedral to a pseudocubic structure. Splitting of the (111)pc peak in pure BNT was considered symmetry identification for a rhombohedral structure. A micrometer level grain size (1.70 μm–2.81 μm), dense microstructure with good ferroelectric and piezoelectric performance (d33=56−45pC/N) was obtained. The 3% La content BNT ceramic shows an improved dielectric property. The Curie temperature increases from 355 °C for pure BNT to 365 °C for donor-doped and 370 °C for acceptor-doped BNT. The donor doping created cationic vacancies; acceptor doping induces oxygen vacancies that stabilized the polarization level. Maximum remnant polarization (Pr) value has been obtained for 3% La-doped (Pr=27μC/cm2) and 5% Sc-doped (Pr=20μC/cm2) BNT system. Bipolar strain increased with the increase in donor dopant concentration resulting in a large electrostrictive coefficient (Q11 ∼ 0.0122%–0.045%) has been obtained. Electric field-induced unipolar strain value was enhanced to its maximum value (Smax = 0.14%) for 3% La content with normalized strain d33∗=209pm/V and Smax = 0.13% for 5% Sc with normalized strain d33∗=155pm/V at an applied electric field of 70 kV/cm and 50 kV/cm, respectively. The enhanced strain was considered to be associated with low internal bias field and maximum polarization level. In terms of capacitive response, 5% Sc holds a maximum current (∼0.017 mA) during polarization switching.

BNT‐based ferroelectric ceramics: Electrical properties modification by Ta2O5 oxide addition

AbstractDue to their superior piezo‐responses (strain S > 0.3%), bismuth sodium titanate (BNT)‐based relaxor ferroelectrics have received much attention. Compared to other chemical elements, tantalum (Ta) doping provides superior electro‐strain for these ferroelectrics, while the effect of Ta2O5 as oxide additive has been rarely reported. Herein, lead‐free piezoceramics of Bi0.5(Na0.72K0.22Li0.06)0.5TiO3‐xTa2O5 (BNKLT‐xTa2O5, x = 0‐0.015) are synthesized. We study the effects of Ta2O5 addition on the crystal structure, piezoelectric responses, dielectric properties, and ferroelectric properties of BNKLT ceramics. All of the ceramics exhibit a typical perovskite structure, and Ta2O5 diffuses into the BNKLT lattice to form a uniform solid solution. The addition of Ta2O5 can make the grains more regular and uniform, while excess Ta2O5 result in finer grains. The undoped BNKLT ceramics show good ferroelectric and piezoelectric properties (remnant polarization Pr = 22.5 μC/cm2 and piezoelectric coefficient d33 = 250 pC/N); however, the addition of Ta2O5 leads to an clear degradation in d33 and Pr. Meanwhile, the addition of an appropriate Ta2O5 amount leads to an increase in the electro‐strain, and the unipolar strain reaches 0.385% under 60 kV/cm for x = 0.003, together with a higher normalized strain (d33*=Smax/Emax) of 633 pm/V (x = 0.003). The enhanced strain behaviors can be attributed to the coexistence of the ferroelectric and relaxor states, and an excellent electrostriction coefficient Q33 (Q33 = S/P2) value of 0.038 m4C−2 is obtained under 60 kV/cm for x = 0.003.