Effects of Heat‐Treatment Temperature on the Properties of (1–x)(Na0.5Bi0.5)TiO3–xBiAlO3 Lead‐Free Piezoelectric Thin Films

Lead‐free sodium bismuth titanate–aluminate bismuth [0.97(Na_0.5Bi_0.5)TiO₃–0.03BiAlO₃] solid‐solution films deposited on (100) Pt/TiO₂/SiO₂/Si substrates by a sol–gel process were pyrolyzed and annealed at different temperatures. The film annealed at 725°C with a pyrolysis temperature of 410°C exhibited the optimal electrical properties and excellent piezoelectric properties, with a remanent polarization 2P_r of 38 μC/cm² and a leakage current density of 10^?7–10^?6 A/cm² (E < 200 kV/cm). The values of the dielectric constant and dissipation factor at 100 kHz were 422 and 0.039, respectively. The piezoelectric coefficient of the film after poling at 168 kV/cm was found to be 57 pm/V, making the BNT‐BA films a viable lead‐free alternative to the lead‐based materials in such as biosensors and ultrasonic transducers.     

Sintering Behavior,Properties, and Applications of Co‐Fired Piezoelectric/Low Temperature Co‐Fired Ceramic (PZT‐SKN/LTCC) Multilayer Ceramics

Materials and processing conditions have been developed allowing co‐firing of fluxed PZT‐SKN materials with commercial low temperature co‐fired ceramic (LTCC) tapes. Previously, Pb(Zr_0.53, Ti_0.47)O₃–Sr(K_0.25, Nb_0.75)O₃ (PZT‐SKN) ceramics fluxed with 1 wt% LiBiO₂ and 1 wt% CuO addition were shown to sinter to high density at 900°C for 1 h, with a large d₃₃ piezoelectric coefficient of ~415 pm/V. Currently, the master sintering curve (MSC) approach has been used to study the densification behaviors of fluxed PZT‐SKN and LTCC tapes. Different sintering mechanisms for fluxed PZT‐SKN ceramics and LTCC materials are confirmed by analyzing the apparent activation energy (Q_a). Using knowledge gained from MSC results, an optimized sintering profile was developed. Multilayer PZT‐SKN/HL2000 (HeraLock^? Tape, Heraeus) stacks co‐fired at 900°C for 0.5 h maintain large piezoelectric coefficient (high field d₃₃ > 340 pm/V). EDS analysis reveal limited interdiffusion of Pb from PZT‐SKN layers in LTCC and the appearance of Al, Ca, and Si in the PZT‐SKN near the PZT‐SKN/LTCC interface. Further, elemental interdiffusion was not detected at the center of piezoelectric layer in PZT‐SKN/LTCC multilayer ceramics and no subsequent reduction in piezoelectric coefficient d₃₃ was observed. Finally, a piezoelectric microbalance with mass sensitivity of 150 kHz/mg was fabricated using the materials and methods developed.     

Low temperature sintering of PZT powders coated with Pb5Ge3O11 by sol–Gel method

Low temperature sintering of PZT powders was investigated using Pb₅Ge₃O₁₁(PGO) as a sintering aid. PZT powders with 150 nm particle size were coated with PGO which was prepared from precursor solutions of Ge(OiPr)₄ and Pb(NO₃)₂ by sol–gel method. 1 wt% PGO-added PZT powders were densified at 750°C for 2 h to sintered bodies with the relative density of approximately 95%. An addition of PGO improved the sinterability of PZT powders with a reduction of sintering temperature by about 300°C. Dielectric and piezoelectric properties of PGO-added PZT ceramics sintered at ≦950°C were superior to those without PGO additives. However, a higher sintering temperature above 1000°C deteriorated the dielectric and piezoelectric properties of PGO-added PZT ceramics. This may be attributed to the change of microstructure involving the formation of solid solution between PZT and PGO. The 1 wt% PGO-added PZT bodies sintered at 750°C exhibited an electromechanical coupling factor, Kp, of about 56%.     

Microstructure,Ferroelectric, Piezoelectric,and Ferromagnetic Properties of Sc‐Modified BiFeO3–BaTiO3 Multiferroic Ceramics with MnO2 Addition

0.725BiFe_1?xSc_xO₃–0.275BaTiO₃ + y mol% MnO₂ multiferroic ceramics were fabricated by a conventional ceramic technique and the effects of Sc doping and sintering temperature on microstructure, multiferroic, and piezoelectric properties of the ceramics were studied. The ceramics can be well sintered at the wide low sintering temperature range 930°C–990°C and possess a pure perovskite structure. The ceramics with x/y = 0.01–0.02/1.0 sintered at 960°C possess high resistivity (~2 × 10⁹ Ω·cm), strong ferroelectricity (P_r = 19.1–20.4 μm/cm²), good piezoelectric properties (d₃₃ = 127–128 pC/N, k_p = 36.6%–36.9%), and very high Curie temperature (618°C–636°C). The increase in sintering temperature improves the densification, electric insulation, ferroelectric, and piezoelectric properties of the ceramics. A small amount of Sc doping (x ≤ 0.04) and the increase in the sintering temperature significantly enhance the ferromagnetic properties of the ceramics. Improved ferromagnetism with remnant magnetization M_r of 0.059 and 0.10 emu/g and coercive field H_c of 2.51 and 2.76 kOe are obtained in the ceramics with x/y = 0.04/1.0 (sintered at 960°C) and 0.02/1.0 (sintered at 1050°C), respectively. Because of the high T_C (636°C), the ceramic with x/y = 0.02/1.0 shows good temperature stability of piezoelectric properties. Our results also show that the addition of MnO₂ is essential to obtain the ceramics with good electrical properties and electric insulation.     

High electrocaloric effect in hot‐pressed Pb0.85La0.1(Zr0.65Ti0.35)O3 ceramics with a wide operating temperature range

The temperature stability of the electrocaloric effect (ECE) in relaxor ferroelectric Pb_0.85La_0.1(Zr_0.65Ti_0.35)O₃ (PLZT) prepared by the hot‐press sintering method has been investigated. Compared to the PLZTs prepared via the conventional sintering process, the hot‐pressed PLZTs exhibit larger ECE and superior temperature stability. The hot‐pressed sample with an appropriate content of excess PbO presents a high ΔT of 2.4°C and ΔS of 2.3 J kg^?1·K^?1, both of which are 30% greater than those of the conventionally sintered samples measured at 100 kV·cm^?1. More importantly, the hot‐pressed specimens display great stable electrical properties, including the dielectric breakdown strength and electrical resistivity in the temperature range from 0°C to 100°C, whose ECE instability, especially, is only one‐half that of the samples prepared by the conventional solid‐state method. In addition, the ECE and its stability of the hot‐pressed sample can be further enhanced by increasing the operating electric field to a relatively high level of 200 kV·cm^?1. This work demonstrates hot‐press sintering is an effective method to fabricate ferroelectric ceramics with high ECE as well as desirable temperature stability.     

Liquid-phase sintering of Pb(Zr,Ti)O3 using PbO–WO3 additive

The objective of this work was to lower the sintering temperature of lead zirconate titanate (PZT) without reducing the piezoelectric performance. PZT was sintered using PbO–WO₃ additive of eutectic composition, which assists the densification process by liquid-phase formation. Sintering was carried out from 1075 to 1125 °C between 1 and 4 h. Density, dielectric properties and piezoelectric properties were measured. Microstructure and fracture mechanism have been studied by SEM. At the mildest sintering conditions, the additive has a positive effect on dielectric and piezoelectric properties. The liquid-phase sintering leads to a denser material without additional grain growth. PZT with PbO–WO₃ additive is mechanically weaker than pure PZT. The liquid phase leads to weaker grain boundaries and the material cracks in intergranular fracture, whereas pure PZT has a mixture of intergranular and transgranular fracture, and PZT sintered conventionally at 1260 °C has transgranular fracture.     

Piezoelectric Properties of Ink‐Jet–Printed Lead Zirconate Titanate Thick Films Confirmed by Piezoresponse Force Microscopy

An ink consisting of Pb(Zr_0.53Ti_0.47)O₃ (PZT) particles with a median size of 170 nm and a narrow size distribution, in a dispersion of water and glycerol, and with a low viscosity and surface tension, was used for the fabrication of thick films by piezoelectric ink‐jet printing. This study reports the printing conditions, the subsequent thermal treatment of the as‐deposited layers, and the properties of the sintered PZT thick film. The film, sintered at 1100°C, had a locally dense microstructure and consisted of grains that are a few 100 nm across, as revealed by scanning electron microscopy. A local piezoelectric response of 15 pm/V was measured in the ink‐jet–printed PZT thick film by piezoresponse force microscopy.     

Structural and piezoelectric properties of <001> textured PZT‐PZNN piezoelectric ceramics

Rhombohedral 0.69Pb(Zr_0.47Ti_0.53)‐0.31Pb(Zn_0.6Ni_0.4)NbO₃ (PZT‐PZNN) ceramics were textured using 10.0 vol. % BaTiO₃ (BT) platelets along the <001> direction at 950°C with a high Lotgering factor of 95.3%. BT platelets did not react with the PZT‐PZNN ceramics, and the textured PZT‐PZNN ceramic had a tetragonal structure. The PZT‐PZNN ceramics exhibited a strain of 0.174% with a piezoelectric strain constant (d*₃₃) of 580 pC/N at 3.0 kV/mm. The textured PZT‐PZNN ceramic showed an increased strain of 0.276% and d*₃₃ of 920 pC/N at 3.0 kV/mm, which can be explained by the domain rotation. However, the d₃₃ values of the textured specimens are smaller than those of the untextured specimens because of the small remanent polarization and relative dielectric constant of BT platelets. The textured PZT‐PZNN ceramic synthesized in this work can be used for piezoelectric multilayer actuators because of its large strain and low sintering temperature.     

Low‐Temperature Sintering of Bi0.5(Na,K)0.5TiO3 for Multilayer Ceramic Actuators

We investigated the influence of CuO amount (0.5–3.0 mol%), sintering temperature (900°C–1000°C), and sintering time (2–6 h) on the low‐temperature sintering behavior of CuO‐added Bi_0.5(Na_0.78K_0.22)_0.5TiO₃ (BNKT22) ceramics. Normalized strain (S_max/E_max), piezoelectric coefficient (d₃₃), and remanent polarization (P_r) of 1.0 mol% CuO‐added BNKT22 ceramics sintered at 950°C for 4 h was 280 pm/V, 180 pC/N, and 28 μC/cm², respectively. These values are similar to those of pure BNKT22 ceramics sintered at 1150°C. In addition, we investigated the performance of multilayer ceramic actuators made from CuO‐added BNKT22 in acoustic sound speaker devices. A prototype sound speaker device showed similar output sound pressure levels as a Pb(Zr,Ti)O₃‐based device in the frequency range 0.66–20 kHz. This result highlights the feasibility of using low‐cost multilayer ceramic devices made of lead‐free BNKT‐based piezoelectric materials in sound speaker devices.     

Processing and electromechanical properties of lead zirconate titanate thick films by electrophoretic deposition

Electrophoretic deposition (EPD) was used for the fabrication of piezoelectric [lead zirconate titanate (PZT)] thick films on alumina substrates. The EPD was performed in constant current mode from an ethanol based suspension consisting of PZT and PbO particles. The influence of addition of ethyl cellulose (EC) and sintering temperature on the thickness, density, homogeneity and functional response of PZT thick films is studied. Results show that the highest electromechanical performance is obtained for the PZT thick films sintered at 900 or 950°C, with a thickness coupling factor k_t of 50%. The addition of EC influenced the thickness of the PZT thick films but had only minor effect on the porosity content for sintering temperatures over 900°C. Moreover, elastic constants of the thick films based on the suspension with EC were lower, which leads to lower acoustic impedance (15?MRa) while maintaining high (k_t) value. In this last case, a better acoustic matching can be expected with propagation media such as water or biological tissues for ultrasound medical imaging applications.     

Effect of carbon content on electrical,thermal, and mechanical properties of porous SiC ceramics with B4C and C additives

The electrical, thermal, and mechanical properties of porous SiC ceramics with B₄C-C additives were investigated as functions of C content and sintering temperature. The electrical resistivity of porous SiC ceramics decreased with increases in C content and sintering temperature. A minimal electrical resistivity of 4.6 × 10^?2 Ω·cm was obtained in porous SiC ceramics with 1 wt% B₄C and 10 wt% C. The thermal conductivity and flexural strength increased with increasing sintering temperature and showed maxima at 4 wt% C addition when sintered at 2000 °C and 2100 °C. The thermal conductivity and flexural strength of porous SiC ceramics can be tuned independently from the porosity by controlling C content and sintering temperature. Typical electrical resistivity, thermal conductivity, and flexural strength of porous SiC ceramics with 1 wt% B₄C-4 wt% C sintered at 2100 °C were 1.3 × 10^?1 Ω·cm, 76.0 W/(m·K), and 110.3 MPa, respectively.     

Liquid-phase sintering of PZT ceramics

Lead zirconate titanate (abbreviated as PZT) ceramics are of considerable commercial importance for a host of piezoelectric and pyroelectric applications. Conventionally, many PZT ceramics are sintered at temperatures above 1250°C. Such extreme temperatures are undesirable due to the increased energy consumption, limitation of electrode material and evaporation of volatile components. A liquid-phase sintering aid incorporating Cu₂O and PbO is presented which demonstrates a reduction in the required sintering temperature of these ceramics. This new aid is described with particular reference to a commercial PZT, termed Pz26, used industrially for its optimised piezoelectric properties. Pz26 has a composition near the morphotropic phase boundary and possesses a tetragonal crystalline structure. Typically this material is sintered between 1260 and 1300°C for 1 h to achieve the required densification. With the inclusion of sintering aid, sintered densities comparable to those obtained by conventional sintering are achieved at only 800°C. The optimum weight percentage of sintering aid varies for different ceramic materials, particle sizes, morphology and the desired sintering temperature. However, with standard “mixed-oxide” produced Pz26 powder and with a median particle size in the range 1.6–1.7 μm, a value of 5 wt.% allows sintering at 800°C, according to densification, dielectric and piezoelectric measurements (ϵ=873, tan δ=1.13 %, k_p=43.1%). When finer grained powder is used (d_0.5=1.1 μm), improved properties (ϵ=960, tan δ=1.04%, k_p=51.7%) are obtained for an addition of 3 wt.% sintering aid and a sintering temperature of 850°C.     

Fabrication and Characterization of Anode‐Supported Low‐Temperature SOFC Based on Gd‐Doped Ceria Electrolyte

Large‐size, 9.5 cm × 9.5 cm, Ni‐Gd_0.1Ce_0.9O_1.95 (Ni‐GDC) anode‐supported solid oxide fuel cell (SOFC) has been successfully fabricated with NiO‐GDC anode substrate prepared by tape casting method and thin‐film GDC electrolyte fabricated by screen‐printing method. Influence of the sintering shrinkage behavior of NiO‐GDC anode substrate on the densification of thin GDC electrolyte film and on the flatness of the co‐sintered electrolyte/anode bi‐layer was studied. The increase in the pore‐former content in the anode substrate improved the densification of GDC electrolyte film. Pre‐sintering temperature of the anode substrate was optimized to obtain a homogeneous electrolyte film, significantly reducing the mismatch between the electrolyte and anode substrate and improving the electrolyte quality. Dense GDC electrolyte film and flat electrolyte/anode bi‐layer can be fabricated by adding 10 wt.% of pore‐former into the composite anode and pre‐sintering it at 1,100 °C for 2 h. Composite cathode, La_0.6Sr_0.4Fe_0.8Co_0.2O₃, and GDC (LSCF‐GDC), was screen‐printed on the as‐prepared electrolyte surface and sintered to form a complete single cell. The maximum power density of the single cell reached 497 mW cm^–2 at 600 °C and 953 mW cm^–2 at 650 °C with hydrogen as fuel and air as oxidant.     

The effect of sintering atmospheres on the properties of CSBT-0.15 ferroelectric ceramics

Ca_0.15Sr_1.85Bi₄Ti₅O₁₈ (CSBT-0.15) ferroelectric ceramics were developed by the conventional solid-state reaction method under various sintering atmospheres. The influences of these sintering atmospheres on grain orientation, grain size, oxygen vacancies, ferroelectric properties and leakage mechanisms were systematically investigated. It was found that the samples sintered under N₂ showed higher a-axis orientation and smaller grain sizes than those sintered under O₂ and air. From XPS analysis, it can be observed that the amount of Ti³⁺ in the ceramics sintered under N₂ is relatively high, which indicates a high number of oxygen vacancies in these samples. The samples sintered under N₂, air and O₂ all delivered well-saturated hysteresis loops with a remnant polarization (2Pr) of 13.8?μC/cm², 12.4?μC/cm² and 7.2?μC/cm² and corresponding coercive fields (2Ec) of 100?kV/cm, 86?kV/cm and 80?kV/cm, respectively. At 70?kV/cm, the leakage current densities of the samples sintered under N₂, air and O₂ are 4.2?×?10^?6 A/cm², 1.9?×?10^?6 A/cm² and 1.0?×?10^?6 A/cm², respectively. The leakage conduction mechanism transformed from Ohmic conduction in a relatively low applied electric field range (0–15?kV/cm) to space-charge-limited conduction (SCLC) in higher electric field ranges.     

Additively patterned ferroelectric thin films with vertical sidewalls

The functional properties of electroceramic thin films can be degraded by subtractive patterning techniques used for microelectromechanical (MEMS) applications. This work explores an alternative deposition technique, where lead zirconate titanate (PZT) liquid precursors are printed onto substrates in a desired geometry from stamp wells (rather than stamp protrusions). Printing from wells significantly increased sidewall angles (from ~1 to >35 degrees) relative to printing solutions from stamp protrusions. Arrays of PZT features were printed, characterized, and compared to continuous PZT thin films of similar thickness. Three‐hundred‐nanometer‐thick printed PZT features exhibit a permittivity of 730 and a loss tangent of 0.022. The features showed remanent polarizations of 26 μC/cm², and coercive fields of 95 kV/cm. The piezoelectric response of the features produced an e_31,f of ?5.2 C/m². This technique was also used to print directly atop prepatterned substrates. Optimization of printing parameters yielded patterned films with 90° sidewalls. Lateral feature sizes ranged from hundreds of micrometers down to one micrometer. In addition, several device designs were prepatterned onto silicon on insulator (SOI) wafers (Si/SiO₂/Si with thicknesses of 0.35/1/500 μm). The top patterned silicon was released from the underlying material, and PZT was directly printed and crystallized on the free‐standing structures.     

Electrical properties of lead-free 0.98(Na<Subscript>0.5</Subscript>K<Subscript>0.5</Subscript>)NbO<Subscript>3</Subscript>-0.02Ba(Zr<Subscript>0.52</Subscript>Ti<Subscript>0.48</Subscript>)O<Subscript>3</Subscript> piezoelectric ceramics by optimizing sintering temperature

Lead-free 0.98(Na_0.5K_0.5)NbO₃-0.02Ba(Zr_0.52Ti_0.48)O₃ [0.98NKN-0.02BZT] ceramics were fabricated by the conventional mixed oxide method with sintering temperature at 1,080°C to 1,120°C. The results indicate that the sintering temperature obviously influences the structural and electrical properties of the sample. For the 0.98NKN-0.02BZT ceramics sintered at 1,080°C to 1,120°C, the bulk density increased with increasing sintering temperature and showed a maximum value at a sintering temperature of 1,090°C. The dielectric constant, piezoelectric constant [d ₃₃], electromechanical coupling coefficient [k _p], and remnant polarization [P _r] increased with increasing sintering temperature, which might be related to the increase in the relative density. However, the samples would be deteriorated when they are sintered above the optimum temperature. High piezoelectric properties of d ₃₃ = 217 pC/N, k _p = 41%, dielectric constant = 1,951, and ferroelectric properties of P _r = 10.3 μC/cm² were obtained for the 0.98NKN-0.02BZT ceramics sintered at 1,090°C for 4 h.     

Submicron crystalline buildup and size‐dependent energy harvesting characteristic in PZN–PZT ternary ferroelectrics

Piezoelectric energy harvester converts low‐frequency vibrational energy in the environment into electrical energy, enabling the purpose of self‐supplying power for low‐energy consumption devices. The key to miniaturizing energy harvester is the buildup of the submicron‐grained ceramic with a high transduction coefficient (d×g), which is still a big challenge from a technical point of view. In this work, the popular ternary system of Pb(Zn_1/3Nb_2/3)O₃–Pb(Zr_0.5Ti_0.5)O₃ (PZN–PZT) has been selected as objective compound, and the submicron‐grained ceramics were prepared by a combination of high‐energy ball milling and pressureless sintering technology. The results revealed that nanocrystalline PZN–PZT powders can be synthesized by one step mechanochemical route without the calcination stage. Using these nanopowders as precursors, dense ceramics with different grain size have been prepared through tailoring the sintering temperature. The study of size‐dependent energy harvesting characteristic evidenced an optimum transduction coefficient of 7980×10^?15 m²/N was obtained for 950°C sintered specimen, which has uniform microstructure with mean grain size of 0.33 μm. In the mode of the cantilever‐type energy harvester constructed by this material, the output power at low frequency of 89 Hz was as high as 69 μW at an acceleration of 10 m/s², showing the suitability for piezoelectric generators harvesting environmental vibrational energy.     

Electrical Properties of a 0.95(Na0.5K0.5)NbO3–0.05CaTiO3 Thin Film Grown on a Pt/Ti/SiO2/Si Substrate

An amorphous phase was formed in a 0.95(Na_0.5K_0.5)NbO₃–0.05CaTiO₃ (NKN‐CT) film grown at 300°C, and a low‐temperature transient Ca₂Nb₂O₇ phase was formed in the film grown at 500°C. In films grown at high temperatures (≥600°C), secondary phases such as K_5.75Nb_10.85O₃₀ and K₄Ti₁₀Nb₂O₂₇ were developed without the formation of a NKN‐CT phase, probably because of Na₂O evaporation. The same secondary phases were formed in the film grown at 300°C and subsequently annealed at 850°C under an air atmosphere. However, a homogeneous NKN‐CT phase was formed in films grown at 300°C and subsequently annealed at 830°C–880°C under the K₂O and Na₂O atmospheres. Moreover, the film annealed at 830°C in particular exhibited good electric and piezoelectric properties, including a high dielectric constant of 747 with a low dissipation factor of 0.93% at 100 kHz, low leakage current density of 2.0 × 10^?7 A/cm² at 0.1 MV/cm, and high P_r and d₃₃ values of 15.4 μC/cm² and 124 pm/V at 100 kV/cm, respectively.     

Ultra-high-temperature piezoelectric responses and ultra-high thermal stability of piezoelectricity in ceramic PbZr0.54Ti0.46O3

To date, most piezoceramics with a high piezoelectric coefficient (d₃₃ > 500 pC/N) and a high Curie temperature (T_C around 400°C) are BiScO₃-PbTiO₃-based (BS-PT-based) systems, containing the rare-earth element Sc, whose high cost hinders mass production. We investigated the effect of Nd-doping on the morphotropic phase boundary and synthesized low-cost Nd-doped PbZr_0.54Ti_0.46O₃ (PZT) piezoceramics, achieving high piezoelectric performance. At room temperature, the piezoelectric coefficient d₃₃ reached 550 pC/N with a T_C = 375°C and this changed by only 3.6% over a broad temperature range (30–260°C). The d₃₃ value reached an ultra-high value of 941 pC/N at 345°C, which is higher than that of a BS-PT-based ceramic (810 pC/N at 350°C). The developed PZT ceramic material has a superior electrostrictive strain of 0.45% at 40 kV/cm, and a room temperature piezoelectric coefficient d₃₃* of 1312 pm/V at 20 kV/cm. Our research provides a new paradigm for designing piezoceramics that can be used over a wide temperature range.     

Optimizing the piezoelectric properties of Ba0·85Ca0·15Zr0·10Ti0·90O3·lead-free ceramics via two-step sintering

The two-step sintering of lead-free Ba₀·₈₅Ca₀·₁₅Zr₀·₁Ti_0·9O₃·(BCZT) ceramics was investigated as a way to enhance its piezoelectric properties. The variations in grain size as a function of the calcination and sintering conditions and its effect on performance is discussed. Results indicate that as the calcination and first-step sintering temperatures increased, grain size became large and was independent of the second sintering step. Large grains were responsible for the enhanced piezoelectric properties by causing lattice distortion, larger domains, and easy motion of domain walls. The BCZT ceramic calcined at 1200 °C and sintered at 1540 °C without holding and then cooled to 1400 °C and held at 1400 °C for 4 h exhibited optimal performance with the highest remnant polarization P_r ∼13.5 μC/cm², the largest piezoelectric constant d₃₃ ∼ 529 pC/N at room temperature, and the highest Curie temperature T_c ∼125 °C. Two-step sintering has been turned out to be an effective method to realize high-performance BCZT ceramics by microstructure optimization.