Rapid pressure-less and spark plasma sintering of (Ba0.85Ca0.15Zr0.1T0.9)O3 lead-free piezoelectric ceramics

This work shows for the first time the possibility to sinter BCZT powder compacts by rapid heating rates within one hour of sintering, while achieving good piezoelectric properties. The sintering was performed by rapid (heating rates 100 and 200 °C/min) pressure-less sintering (PLS) at 1550 °C/5-60 min and by SPS sintering (100 °C/min, 1450 °C/5?60 min and 1500 °C/15?45 min). The rapid PLS samples reached a relative density up to 94 % and grain sizes of 17–36 μm acquiring d₃₃ up to 414 pC/N. Although the SPS samples reached full density at 1450 °C, their piezoelectric properties worsened due to smaller grains (10?15 μm) as well as formation of cracks at dwell times > 30 min. At elevated SPS temperature of 1500 °C/30 min, the d₃₃ increased to 360 pC/N sustaining full density. Even higher increase in d₃₃ (424 pC/N) of SPS samples was achieved by post-rapid PLS at 1550 °C/60 min resulting from further expansion in grain size.     

Direct ink writing of macroporous lead-free piezoelectric Ba0.85Ca0.15Zr0.1Ti0.9O3

Direct ink writing (DIW) has become a widespread additive manufacturing technique for material engineering, but its application in lead-free Ba_0.85Ca_0.15Zr_0.1Ti_0.9O₃ piezoelectric ceramics from aqueous systems has not been reported so far to our knowledge. The main obstacle is the high extent of hydrolysis reactions undergone by the starting powders when dispersed in water, hindering the attainment of stable water-based colloidal suspensions. This paper reports on the preparation of stable aqueous inks from a deagglomerated and surface-treated powder synthesized by solid-state reaction and on DIW of macroporous lead-free piezoelectrics. Based on zeta potential and rheological measurements, the optimal amounts of processing additives (dispersant, binder, and coagulating agent) were selected to transform the initial fluid suspension to a viscoelastic paste with sufficient stiffness and stability for the printing process. Dielectric and piezoelectric properties of samples sintered under different temperatures were also investigated.     

Band gap narrowing and magnetic properties of transition-metal-doped Ba0.85Ca0.15Ti0.9Zr0.1O3 lead-free ceramics

Transition metal (TM = Mn, Fe, Co, and Ni)-doped Ba_0.85Ca_0.15Ti_0.9Zr_0.1O₃ (BCZT) lead-free ceramics with excellent optical and magnetic properties are synthesized via a solid-state reaction method. The effects of TM elements on the sintering, structure, optical, and magnetic properties of BCZT ceramics are investigated in detail. Structural phase transition from the coexistence of rhombohedral and tetragonal phases to a single rhombohedral phase is observed owing to grain refinement. A narrow band gap of 1.68 eV is achieved in the Co-doped BCZT. The optical absorption of TM-doped BCZT is enhanced, which is ascribed to the molecular orbital rearrangement caused by lattice distortion. Moreover the magnetic behaviors of TM-doped BCZT are observed. The Fe-doped BCZT presents the most evident ferromagnetism, resulting from the exchange coupling interaction between the Fe³⁺ ions and oxygen vacancies. These results provide additional insight into the use of TM-doped BCZT lead-free ferroelectric ceramics for various applications.     

Fabrication and properties of (Ba0.85Ca0.15)(Ti0.9Zr0.1)O3 ceramics and their multilayer piezoelectric actuators

The lead‐free ceramics with nominal composition (Ba_0.85Ca_0.15)(Ti_0.9Zr_0.1)O₃ (BCTZ) were prepared by a conventional solid‐state reaction combined with a liquid precursor mixing method. Structural, dielectric, piezoelectric, and ferroelectric properties of the ceramics were systematically investigated. Excellent electrical properties of T_c ~ 101°C, tanδ ~ (0.003–0.05), k_p ~ 0.46, d₃₃ ~ 560 pC/N, P_s ~17 μC/cm² and a large strain of 0.43% were reproducibly obtained for the BCTZ ceramics. In addition, BCTZ‐based monolithic multilayer piezoelectric actuators were successfully fabricated by alternately laminating the claimed piezoelectric ceramics and internal‐binder. The actuators show large displacements under low driven voltage. These results highlight that the BCTZ ceramics are excellent candidate for multilayer piezoelectric devices.     

Lead-free Ba0.85Ca0.15Zr0.1Ti0.9O3 ferroelectric ceramics with refined microstructure and high strain under electric field by mechanosynthesis

Lead-free ferroelectric Ba_0.85Ca_0.15Zr_0.1Ti_0.9O₃ stands out among environmentally friendly alternatives to commercial Pb(Zr,Ti)O₃ piezoceramics for its large piezoelectric coefficients, and it is especially suitable for applications in which thermal depoling is not an issue like bio-implanted devices. However, ceramic processing by conventional means consistently results in exaggerated grain growth, which compromises reliability and has prevented its transfer to industry. We report here the application of high-energy milling for the mechanosynthesis of nanocrystalline Ba_0.85Ca_0.15Zr_0.1Ti_0.9O₃ powders with enhanced reactivity, and to the control of grain growth during ceramic processing to obtain materials with tailored microstructures and decreasing grain sizes down to the sub-10 µm range. Characterization of the electrical and electromechanical properties was accomplished and uncovered triggering of a new mechanism for very large strain under electric field in fine-grained ceramics. Process optimization by precursor selection and preliminary up-scaling studies are also presented.     

Large piezoelectric coefficient with enhanced thermal stability in Nb5+-doped Ba0.85Ca0.15Zr0.1Ti0.9O3 ceramics

Chemical doping is an indispensable tool to tailor the properties of the commercial piezoelectric materials. However, a high piezoelectric coefficient with enhanced thermal stability is rarely achieved by one dopant in some high-performance ferroelectrics, e.g., the recently discovered eco-friendly (Ba_0.85Ca_0.15)(Zr_0.1Ti_0.9)O₃ (BCZT) ceramics. In order to optimize the piezoelectric property in BCZT system by a simple way, we investigated the doping effect of Fe³⁺, Nb⁵⁺ and Bi³⁺ cations in BCZT ceramics respectively. The results indicate that only Nb⁵⁺-doped BCZT ceramics display a combination of large piezoelectric coefficient and enhanced thermal stability, compared with others. Moreover, the established phase diagrams and in-situ transmission electron microscope (TEM) observations reveal that such optimized piezoelectric properties after Nb⁵⁺ doping originates from (i) the low polarization anisotropy near the ambient tetragonal (T)-orthorhombic (O) phase transition and (ii) the easy domain wall motion of persistent miniaturized ferroelectric domains upon heating.     

Y2O3 doped Ba0.9Ca0.1Ti0.9Sn0.1O3 ceramics with improved piezoelectric properties

Lead-free Ba_0.90Ca_0.10Ti_0.90Sn_0.10O₃-xY₂O₃ (BCTSY, x = 0–0.09) ceramics were prepared by traditional solid-state sintering method. All the BCTSY samples showed pure perovskite structures without detectable impurity. Orthorhombic/tetragonal phase coexisted in the sample of x = 0.03 to 0.07. Remarkable enhancement of the electric properties were achieved at x = 0.03 with d₃₃ of 650 pC/N, K_p of 59.6%, and the remnant polarization P_r of 10.2 μC/cm². The strengthened temperature stability of piezoelectricity is beneficial to the application of the piezoceramics.     

Structure,electrical properties and reaction mechanism of (Ba0.85Ca0.15)(Zr0.1Ti0.9)O3 ceramics synthesized by the molten salt method

Lead-free (Ba_0.85Ca_0.15)(Zr_0.1Ti_0.9)O₃ (BCZT) ceramics with excellent electrical properties were successfully synthesized by a molten salt method (MSS). The submicron BCZT powders with pure perovskite phase were obtained by adjusting the KCl-NaCl content that was used as the eutectic salt. The effects of salt content and reaction temperature on the structure and properties of the BCZT materials were systematically investigated. Comparing with BCZT ceramics prepared by solid state method (SS), the reaction temperature of BCZT ceramics synthesized by MSS decreased approximately 200 °C. Moreover, BCZT ceramics sintered at 1360 °C with 50% eutectic salt showed the most outstanding electrical properties, which are as follows: d₃₃ = 604 pC/N, k_p = 57%, P_s = 17.11 µC/cm², P_r = 9.98 µC/cm², ε_m = 15872, ε_r = 2654 and tan δ = 0.013. In addition, this work revealed a possible reaction course processes and mechanism about MSS. The results provide a new design to optimize the performance of BCZT lead-free piezoelectric ceramics.     

Ultrahigh energy storage density in Ba0.85Ca0.15Zr0.1Ti0.9O3-based lead-free ceramics by introducing a relaxor end-member

Dielectric ceramics with relaxor characteristics are promising candidates to meet the demand for capacitors in next-generation pulse devices. In this work, Ba_0.85Ca_0.15Zr_0.1Ti_0.9O₃ (BCZT)-based lead-free ceramics with an ultrahigh recoverable energy storage density (W_rec) were designed and fabricated by introducing the relaxor end-member of Bi(Zn_2/3Ta_1/3)O₃ (BZT). The addition of BZT disrupted the ferroelectric (FE) long-range order and triggered an FE-to-relaxor FE (RFE) phase, leading to the formation of locally polar nano-regions (PNRs) and significantly inhibiting grain growth. Meanwhile, the presence of PNRs with good thermal stability improved the temperature stability of both the dielectric constant (ε') and W_rec. More importantly, the breakdown electric field strength was significantly improved up to ∼640 kV/cm, resulting in an ultrahigh W_rec of ∼7.11 J/cm³ for the 8%BZT doped BCZT (BCZT-BZT8) ceramic. Furthermore, the BCZT-BZT8 ceramic exhibited excellent charge/discharge performances (C_D ∼ 458.4 A/cm², P_D ∼ 50.4 MW/cm³, W_D ∼ 1.354 J/cm³, t_0.9 ∼ 320 ns) with good thermal stability in the temperature range of 298–373 K. The defect chemistry of the BCZT-BZT8 was explored using electron paramagnetic resonance (EPR) spectroscopy which revealed an EPR signal (g ∼ 1.955), associated with oxygen vacancies. The above findings indicate that the novel composition of BCZT-BZT8 has great prospects in energy storage capacitor applications.     

Electrical fatigue behavior of Ba0.85Ca0.15Zr0.1Ti0.9O3 ceramics under different oxygen concentrations

Fatigue degradation is a significant problem in piezo/ferroelectric materials and their commercial applications. The major causes of electrical fatigue degradation are a domain pinning effect and physical damage such as microcracking. This work reports the fatigue behavior of barium calcium zirconate titanate (Ba_0.85Ca_0.15Zr_0.1Ti_0.9O₃) under regular and low oxygen concentration silicone oil. Impedence analyzer and LCR meter are employed to analyzer the dielectric properties and it also revealed the relationship between activation energy and oxygen vacancy. X-ray diffraction, synchrotron X-ray absorption spectroscopy, and scanning electron microscope techniques were employed to study the local structural changes, defect development, physical damage and microcracking in the ceramics. FEFF-8.4 simulations were used to determine the oxygen vacancy creation. The study reveals the relationship of oxygen vacancy creation, domain wall pinning, microcracking and the fatigue behavior of the ferroelectric ceramic. The work investigated the dielectric and ferroelectric properties of BCZT ceramics intermes of applied electric field.     

Structural,dielectric and ferroelectric properties of lead-free Ba0.85Ca0.15Zr0.10Ti0.90O3 ceramics prepared by Plasma Activated Sintering

Lead-free Ba_0.85Ca_0.15Zr_0.10Ti_0.90O₃ (BCZT) ceramics were prepared by Plasma Activated Sintering (PAS). The influence of PAS sintering temperature on the crystalline phase, microstructure, and, dielectric and ferroelectric properties of BCZT ceramics were studied. The phase structure of BCZT ceramics first changed from rhombohedral phase to the coexistence of rhombohedral and tetragonal phases and then to tetragonal phase as the sintering temperature increased. Microstructural characterization of BCZT ceramics indicated that PAS can obtain a compact microstructure at lower temperatures of 1150–1300 °C compared with that from common pressureless sintering. The BCZT ceramics showed different degrees of diffuseness with increased temperature, and the diffuseness exponents C are all approximately on the order of 10⁵ °C. The dielectric and ferroelectric properties of BCZT ceramics were enhanced with increased sintering temperature. BCZT ceramics sintered at 1250 °C exhibited optimum properties of room-temperature ε_r=2863, ε_m=6650, and 2P_r=25.24 μC/cm², resulting from the relatively higher tetragonal phase content of the MPB between tetragonal and rhombohedral phases together with a compact microstructure.     

Structural,ferroelectric, magnetic and magnetoelectric properties of (1-x) Ba0.85Ca0.15Zr0.1Ti0.9O3 -x La0.67Sr0.33MnO3 lead-free magnetoelectric composites

The influence of an additional La_0.67Sr_0.33MnO₃ (LSMO) magnetic phase on the structural, ferromagnetic, ferroelectric, and magnetoelectric properties of Ba_0.85Ca_0.15Zr_0.1Ti_0.9O₃ (BCZT) ferroelectric phase was studied for composites of (1-x)BCZT -xLSMO (x = 0, 25, 50, 75 and 100%). The ferroelectric BCZT sample showed a perovskite single phase formation with a tetragonal crystal structure of the P4mm space group, and the magnetic phase of LSMO presented a rhombohedral crystal structure of R3c space group as shown by XRD. The composite sample with 25% LSMO exhibited large ferroelectric and piezoelectric properties with remnant, saturation polarization, and coercive electric field P_r ~7.74 μC/cm², P_s ~11.69 μC/cm² and E_C ~12.22 kV/cm with a piezoelectric coefficient d₃₃ ~ 231 pC/N. The magnetic characterization for the composites showed that the sample containing 75% of LSMO revealed the highest remnant, saturation magnetization, and coercive field of M_r ~1.358 emu/g, M_s ~19.17 emu/g, and H_C ~33.19 Oe, respectively. Moreover, it revealed the largest magnetoelectric coupling coefficient α_ME ~2.51 mV/cm.Oe with high coupling quality at a lower applied magnetic field. The results highlight the value of these composites as lead-free room temperature magnetoelectric sensors and actuators.     

Enhancing low-temperature energy harvesting by lead-free ferroelectric Ba(Zr0.1Ti0.9)O3

The energy-harvesting ability of the lead-free ferroelectric Ba(Zr,Ti)O₃ was investigated and greatly enhanced using the Kim novel electrothermodynamic cycle for low-temperature application. Ba(Zr,Ti)O₃ was synthesized with a Zr:Ti ratio of 10:90 (BZT10) by hot-press sintering, which exhibited a mix relaxor-ferroelectric behavior. For power generation using the Kim cycle with low and high temperatures of T_L = 25°C, T_H = 120°C, the most optimized temperature pattern occurred for a heating time of 12.5 s and a cooling time of 22.5 s. Under these conditions, the electric field increased during the novel isodisplacement process, and the displacement variation in the isoelectric step reached the highest value and maximized the BZT10 cycle loop area. Applying these conditions while lowering T_L to 20°C, an energy density N_D = 504 mJ/cm³ was achieved. This value is the highest obtained energy density in a practical test for lead-free ferroelectric bulk material in the BaTiO₃ family.     

Piezo/pyro/photo-catalysis activities in Ba0.85Ca0.15(Ti0.9Zr0.1)1-xFexO3 ceramics

Ba_0.85Ca_0.15(Ti_0.9Zr_0.1)_1-xFe_xO₃ (x = 0, 0.5, and 1%) ceramics were studied for piezocatalysis, photocatalysis, and pyrocatalysis using dye degradation in the simulated wastewater. The effect of electrical poling was also performed and found a significant impact of poling on all three catalytic reactions. Fe decreased the optical bandgap of Ba_0.85Ca_0.15Ti_0.9Zr_0.1O₃ (BCZTO) to the visible region. Bandgap for x = 0, 0.005, and 0.01 was found to be 3.14 eV, 2.75 eV, and 2.61 eV, respectively. Interestingly, visible light photocatalytic activity was observed after Fe inclusion in BCZTO lattice. These compositions have also demonstrated dye degradation under ultrasonication (piezocatalytsis) and during temporal temperature change (pyrocatalysis). Results indicate promising multicatalysis in BCZTO ceramics which can be tuned using Fe substitution.     

Enhancing piezoelectric properties of Ba0.88Ca0.12Zr0.12Ti0.88O3 lead-free ceramics by doping Co ions

The piezoelectric properties of lead-free Ba_0.88Ca_0.12Zr_0.12Ti_0.88O₃ (BCZT) ceramics were greatly optimized by doping Co ions using a CoO powder. The role of Co²⁺ and Co³⁺ in enhancing the piezoelectric properties and the relationship between the content ratio Co³⁺/Co²⁺ and piezoelectric performance were studied. The X-ray diffraction patterns of all samples indicated that crystalline phases were a BCZT-based single perovskite structure regardless of the Co ion content. The phase transition temperature and lattice distortion degree were related to the Co ion content and the content ratio Co³⁺/Co²⁺ because Co²⁺ resulted in higher oxygen vacancy generation, whereas Co³⁺ induced larger lattice shrinkage. The ceramic containing 0.10 wt% of Co ion showed the best piezoelectric and dielectric performance with the highest piezoelectric constant d₃₃ ~ 490 p.m./V at room temperature and the highest Curie temperature T_c of 110 °C, which increased by 29% and 16%, respectively. In this case, the content ratio Co³⁺/Co²⁺ reached the maximum value of 0.86. The high piezoelectric properties and phase stability of BCZT ceramics by doping Co ions make these ceramics promising piezoelectric materials for practical applications.     

Giant room-temperature electrocaloric effect within wide temperature span in Sn-doped Ba0.85Ca0.15Zr0.1Ti0.9O3 lead-free thin films

The electrocaloric (EC) effect cooling technique of environmentally friendly lead-free thin film materials driven by electric fields has recently gained tremendous attention due to the urgent demand for microelectronic and integrated circuit refrigeration devices. However, the widespread use of lead-free materials in EC devices is seriously hindered due to the small electrocaloric temperature change (ΔT) within a narrow operation temperature span (T_span) near room temperature. Here, lead-free Ba_0.85Ca_0.15Zr_0.1Ti_0.9-xSn_xO₃ (BCZT-xSn, 0 ≤ x ≤ 0.03) thin films were prepared on substrates (Pt/Ti/SiO₂/Si) via a sol-gel route. The BCZT-0.02Sn thin film presents an excellent EC effect (ΔT = 32.74 K, ΔS = 37.18 J kg^?1 K^?1) and large EC strength (ΔT/ΔE = 0.033 K cm kV^?1, ΔS/ΔE = 0.037 J cm K^?1 kg^?1 kV^?1) over a wide T_span (～26 K) under 1000 kV cm^?1 near room temperature. The giant ΔT is mainly attributed to the emergence of an intermediate O phase and the formation of a multiphase (R, O and T phases) coexistence structure at room temperature, while the diffuse phase transition behavior is responsible for the wide T_span. Our study provides a new idea for developing environment-friendly EC materials with an excellent room-temperature ΔT over a broad operational temperature region.     

Tuning of electrocaloric performance in (Ba0.85Ca0.15)(Zr0.1Ti0.9)O3 by induced relaxor-like behavior

Induced relaxor-like behavior is reported by addition of a sintering additive to the (Ba_0.85Ca_0.15)(Zr_0.1Ti_0.9)O₃ solid solution. The effect of Bi₂O₃ sinter additive on microstructure is determined. The phase transition behavior is highlighted by dielectric permittivity measurements. The electrocaloric temperature change is directly measured and comparison with literature data is provided on basis of the material related cooling power. Addition of Bi₂O₃ drastically increases the temperature stability and an ultra-wide temperature range of over 100?K is achieved. The findings path a way to tune electrocaloric materials for optimization of properties for solid-state coolers based on the electrocaloric effect.     

Critical role of CuO doping on energy storage performance and electromechanical properties of Ba0.8Sr0.1Ca0.1Ti0.9Zr0.1O3 ceramics

CuO doped Ba_0.8Sr_0.1Ca_0.1Ti_0.95Zr_0.05O₃ (BSCTZ) ceramics were prepared by a modified mechano-chemical activation technique with the aim of improving energy storage properties for ceramic capacitor applications. CuO can effectively improve the microstructural characteristics along with a transformation of BSCTZ from classical ferroelectric to relaxor, which is the prime requirement for obtaining high discharge energy density and energy efficiency. The effect of CuO doping on the microstructural, ferroelectric, dielectric, and piezoelectric properties have been systematically studied. The study reveals that an appropriate amount of CuO doping can significantly enhance the morphological properties along with improvement in material density, which is very beneficial in a material for attaining improved energy storage performance. The BSCTZ sample with 3 mol% CuO doping has shown a highly dense microstructure, high saturation polarization (33.01 μC/cm²), low remnant polarization (6.74 μC/cm²), ultrahigh discharge energy density (1.81 J/cm³) and high energy efficiency (81.9%). The CuO doping in BSCTZ has also led to a slight improvement in breakdown strength and electromechanical properties compared to pure BSCTZ ceramics, which is mainly attributed to excellent density and optimum grain size of the material.     

Ultrahigh and field-independent energy storage efficiency of (1-x)(Ba0.85Ca0.15)(Zr0.1Ti0.9)O3-xBi(Mg0.5Ti0.5)O3 ceramics

Relaxor ferroelectrics are attracting an increasing interest in the application of pulse power systems due to their excellent energy storage performance. In this paper, the (1-x)(Ba_0·85Ca_0.15)(Zr_0·1Ti_0.9)O₃-xBi(Mg_0·5Ti_0.5)O₃ ((1-x)BCZT-xBMT, x ≤ 0.2) relaxor ceramics are prepared by the solid state method. The influence of BMT on the microstructure, dielectric and energy storage properties of the prepared ceramics is investigated. The XRD results show that the peak intensity of impurities (Bi₂O₃, TiO₂ and Ba₂Bi₄Ti₅O₁₈) is gradually stronger than that of BCZT phase with x increasing. Meanwhile, the grain size of (1-x)BCZT-xBMT ceramics gradually increases on account of the appearance of impurities Bi₂O₃. Influenced by the impurities and BMT, the dielectric constant of prepared ceramics gradually decreases with x increasing. A large W_rec value of 0.65 J/cm³ with an ultrahigh η value of 97.89% is achieved at x = 0.15 due to the high breakdown strength and slim P-E hysteresis loop. Meanwhile, the η is insensitive to the electric field. The ultrahigh η leads to lesser energy loss during the charge and discharge process. It makes the 0.85BCZT-0.15BMT ceramic more attractive in the application of pulse power systems.     

Magnetoelectric coupling studies in lead-free multiferroic (Ba0.85Ca0.15)(Zr0.1Ti0.9)O3−(Ni0.7Zn0.3)Fe2O4 ceramic composites

Lead-free multiferroic 3–0 type particulate composites with a composition (1?x)(Ba_0.85Ca_0.15Zr_0.1Ti_0.9O₃) – x(Ni_0.7Zn_0.3Fe₂O₄) [(1?x)BCZT – xNZFO with 0 ≤ x ≤ 100 at%] were prepared using solid state reaction method. Structural and microstructural analysis using XRD, FESEM and Raman techniques confirmed the phase formation of the ferroelectric (BCZT) and magnetostrictive (NZFO) phases without any detectable presence of impurity phases. Rietveld refinement of the XRD data revealed a tetragonal (P4mm) and a cubic structure (Fd$\stackrel{￣}{3}$m) for the BCZT and NZFO phases, respectively. Elemental compositions of the constituent phases were assessed by EDS and XPS analyses. Electrical, magnetic, and magnetoelectric (ME) measurements were performed. The composites exhibit typical well-saturated magnetic hysteresis (M?H) loops at room temperature, having very low coercive field ($H_C$) values, indicating their soft ferromagnetic behavior. Various parameters extracted from the M?H curves including $H_C$, magneto-crystalline anisotropy, squareness, and magnetization were found to depend on x. Frequency dependence of capacitance and admittance exhibited a resonance behavior corresponding to the radial mode of the electromechanical resonance (EMR). ME coefficients were studied in both longitudinal (${\alpha }_{\text{E}33}$) and transverse (${\alpha }_{\text{E}31}$) modes. The highest coupling coefficients, ${\alpha }_{\text{E}31}$ ～14.5 mV/Oe.cm and ${\alpha }_{\text{E}33}$ ～13 mV/Oe.cm were obtained for composite with 50 at% NZF at off-resonance frequency of 1 kHz. At the EMR frequency of 314 kHz, the ${\alpha }_{\text{E}31}$ value in 0.5BCZT-0.5NZFO composite enhanced enormously to ～5.5 V/Oe.cm. The studies conclude that x = 0.5 is an optimum atomic fraction of NZFO in the particulate composite for maximum ME coupling.