Impedance Spectra Research Articles

Understanding how junction resistances impact the conduction mechanism in nano-networks

Networks of nanowires, nanotubes, and nanosheets are important for many applications in printed electronics. However, the network conductivity and mobility are usually limited by the resistance between the particles, often referred to as the junction resistance. Minimising the junction resistance has proven to be challenging, partly because it is difficult to measure. Here, we develop a simple model for electrical conduction in networks of 1D or 2D nanomaterials that allows us to extract junction and nanoparticle resistances from particle-size-dependent DC network resistivity data. We find junction resistances in porous networks to scale with nanoparticle resistivity and vary from 5 Ω for silver nanosheets to 24 GΩ for WS2 nanosheets. Moreover, our model allows junction and nanoparticle resistances to be obtained simultaneously from AC impedance spectra of semiconducting nanosheet networks. Through our model, we use the impedance data to directly link the high mobility of aligned networks of electrochemically exfoliated MoS2 nanosheets (≈ 7 cm2 V−1 s−1) to low junction resistances of ∼2.3 MΩ. Temperature-dependent impedance measurements also allow us to comprehensively investigate transport mechanisms within the network and quantitatively differentiate intra-nanosheet phonon-limited bandlike transport from inter-nanosheet hopping.

Are Selenides the Same as Sulfides? Structure, Spectroscopy, and Properties of Narrow-Gap Rare-Earth Semiconductors RE2Sn(S1-xSex)5 (RE = La, Ce; x = 0-0.8).

The ternary rare-earth sulfides RE2SnS5 (RE = La-Nd) and the partial solid solutions RE2Sn(S1-xSex)5 (RE = La, Ce; x = 0-0.8) were prepared in the form of polycrystalline samples by reaction of the elements at 900 °C and as single crystals in the presence of KBr flux. They adopt the La2SnS5-type structure (orthorhombic, space group Pbam, Z = 2) consisting of chains of edge-sharing SnCh6 octahedra separated by RE atoms. Although the cell parameters evolve smoothly in RE2Sn(S1-xSex)5, detailed structural analysis by single-crystal X-ray diffraction revealed a pronounced preference for the Se atoms to occupy two out of the three chalcogen sites, which offers a rationalization for why the all-selenide end-members RE2SnSe5 do not form. Solid-state 119Sn NMR spectra confirmed the nonrandom distribution of SnS6-nSen local environments, which could be resolved into individual resonances. The Raman spectra of RE2SnS5 compounds show an intense peak at 307-320 cm-1 assigned to a symmetric A1g mode, which is dominated by Sn-S bonds; the Raman peak intensities varied with Se substitution in La2Sn(S1-xSex)5. Optical diffuse reflectance spectra, band structure calculations, and electrochemical impedance spectra indicated that these compounds are narrow band gap semiconductors; the optical band gaps are insensitive to RE substitution in RE2SnS5 (0.7 eV) but they gradually decrease with greater Se substitution in RE2Sn(S1-xSex)5 (0.7-0.4 eV).

Beneficial effect of 4% Ta addition on the corrosion mitigation of Ti–12% Zr alloy after different immersion times in 3.5% NaCl solutions

Abstract The recent study reports the fabrication and corrosion behavior of two Ti alloys, 88% Ti–12% Zr and 84% Ti–12% Zr–4% Ta, in 3.5% NaCl electrolyte. These alloys were manufactured using powder metallurgy, where the powders were mixed, ball milled, and sintered. The corrosion behavior of these alloys was examined using various electrochemical and spectroscopic tests. Cyclic polarization experiments indicated that adding 4% Ta reduces corrosion of the TiZr alloy by suppressing anodic dissolution, resulting in a lower corrosion rate. The Nyquist and Bode impedance spectra for the tested alloys revealed that the presence of 4% Ta within TiZr alloy highly decreases the corrosion by increasing the impedance of the interface, the maximum degree of phase angle, and polarization resistance. The chronoamperometric current measured at −0.10 V (Ag/AgCl) proved that the presence of 4% Ta powerfully alleviates both uniform and pitting corrosion for TiZr alloy by lowering the obtained absolute currents. The surface investigation using scanning electron microscopy confirmed the homogeneity of the surfaces. The elemental analysis performed on the surface using energy dispersive spectroscopy revealed that the surface of TiZr alloy forms a top film including different oxides such as TiO2 and ZrO2, and for TiZrTa alloy, the surface has TiO2 + ZrO2 plus TaO2. Experiments demonstrated that Ta has the ability to increase the corrosion passivation of TiZr alloy.

Demystifying the Distribution of Relaxation Times: A Simulation-Based Investigation into the Limits and Possibilities of Interpretation for Lithium-Ion Batteries

Abstract Interpreting impedance spectra of electrochemical systems using the distribution of relaxation times analysis remains an incompletely solved task. This study carefully examines various challenges related to the interpretation of resulting distributions of relaxation times using a closed-form lumped Doyle-Fuller-Newman model. First, the physical and phenomenological interpretation of peaks in the distribution of relaxation times are analyzed through a global sensitivity analysis. Second, the assignment of processes to specific ranges of time constants is investigated. Third, the use of half cells for the characterization of full cells is examined, and the clear limitations associated with the use of lithium metal counter electrodes are pointed out. Furthermore, the study provides first insights into the effects of distributed processes such as charge transfer, double-layer effects, and solid-state diffusion. Several prevailing interpretations in the literature are challenged and new insights and guidelines for interpreting distributions of relaxation times are offered.

Temperature-dependent characterization of full tensor properties of [111]c poled Mn-doped 28PIN-43PMN-29PT single crystals

The temperature-dependent characterization of full tensor properties of single-domain relaxor-based single crystals (SCs) is important for understanding the influence of temperature on the properties of their multidomain SCs. However, no relevant results have been published because characterization is difficult to achieve using the traditional electric resonance method. In this Letter, the temperature-dependent elastic and piezoelectric properties of single-domain [111]c poled Mn-doped 28Pb(In1/2Nb1/2)O3-43Pb(Mg1/3Nb2/3)O3-29PbTiO3 SCs were investigated in the range of 20–80 °C by resonant ultrasound spectroscopy (RUS) using a rectangular parallelepiped sample. The temperature-dependent dielectric constants were calculated from the measured capacitances of the sample. The results are self-consistent because they were obtained from the same sample. The elastic constants obtained using the ultrasonic pulse-echo method agree closely with those obtained using RUS. Moreover, the experimental results of electric impedance spectrum agree closely with those simulated using the material constants characterized herein, indicating that the characterization is reliable.

Amplitude-Frequency Effect of Mixed Electric Field on Impedance Spectrum Parameters of Biological Tissue

This work analyzes the electric impedance spectra of liver samples. Nyquist diagrams of experimental samples of different sizes were constructed. Optimal model equivalent electrical circuits of the systems studied were obtained and processed, and the parameters of their components were calculated. Changes in parameters and the tangent of the loss angle were shown. A conclusion was made about the interdependence of the electric field strength and the occurrence of stress, caused by using certain frequencies, on the size of the sample.

Impedance spectra of soft ionics

Impedance spectroscopy is widely adopted for probing the charge and charge mobility of soft ion-conducting media, such as synthetic membranes and biological tissue. The spectra exhibit a variety of distinctive signatures, but the physical basis of these is not well understood, e.g. models have not previously accounted for viscoelasticity, hydrodynamics or microstructural heterogeneity. This study explores a physically grounded continuum model that captures how these factors shape conductivity spectra. Nonlinear thermodynamics and linearised dynamics of a viscous electrolyte and compressible, elastic polymer network are coupled under the forcing of an oscillatory electric field. The model is solved in a one-dimensional spatially periodic unit cell, reporting conductivity and dielectric permittivity spectra, including Nyquist representations. Whereas rigid microstructures exhibit ion-diffusion-controlled relaxation, which manifests as a low-frequency dielectric ‘constant’, hydrodynamic and elastic forces contribute to a strongly diverging dielectric permittivity at low frequencies for heterogeneous anionic microstructures. The model also captures distinctive characteristics of experimentally reported impedance spectra for films bearing alternating layers of cationic and anionic charge, again highlighting the role of coupled hydrodynamic, elastic and electrical forces. Sufficiently thin and highly charged bilayers exhibit a notably low high-frequency conductivity. This is explained by strong low-frequency electrostatic polarisation and counter-ion release. The one-dimensional solutions computed herein provide a foundation for much more challenging computations in two and three dimensions.

Aging behavior difference between aqueous coatings and solvent coatings in sulfuric acid environment

Purpose This paper aims to compare the aging behavior of water-based coatings and solvent-based coatings in sulfuric acid environments and to discuss the related mechanism. Design/methodology/approach A sulfuric acid solution with a concentration of 5 Wt.% was selected for immersion test at 23°C. The failure behavior of the coating was studied by combining the transformation rules of the macroscopic morphology and basic properties with the results of electrochemical impedance spectrum analysis. Findings The results showed that the surface smoothness of the water-based coating was lower than that of the solvent-based coating. The glossiness, thickness and hardness of the water-based coating exhibited more significant changes. The electrochemical test also indicated that the water-based coating was infiltrated by a large number of corrosive media, which may have induced corrosion under the coating. In contrast, the solvent-based coating showed good shielding properties, but the adhesion was seriously affected by the corrosive medium. Originality/value This work clarified the difference of failure behavior and mechanism between water-based coatings and solvent-based coatings in acidic environment and provided a theoretical basis for the selection and mechanism research of anticorrosive coatings.

Realizing Outstanding Energy Storage Performance in KBT-Based Lead-Free Ceramics via Suppressing Space Charge Accumulation.

The great potential of K1/2Bi1/2TiO3 (KBT) for dielectric energy storage ceramics is impeded by its low dielectric breakdown strength, thereby limiting its utilization of high polarization. This study develops a novel composition, 0.83KBT-0.095Na1/2Bi1/2ZrO3-0.075 Bi0.85Nd0.15FeO3 (KNBNTF) ceramics, demonstrating outstanding energy storage performance under high electric fields up to 425kVcm-1: a remarkable recoverable energy density of 7.03Jcm-3, and a high efficiency of 86.0%. The analysis reveals that the superior dielectric breakdown resistance arises from effective mitigation of space charge accumulation at the interface, influenced by differential dielectric and conductance behaviors between grains and grain boundaries. Electric impedance spectra confirm the significant suppression of space charge accumulation in KNBNTF, attributable to the co-introduction of Na1/2Bi1/2ZrO3 and Bi0.85Nd0.15FeO3. Phase-field simulations reveal the emergence of a trans-granular breakdown mode in KNBNTF resulting from the mitigated interfacial polarization, impeding breakdown propagation and increasing dielectric breakdown resistance. Furthermore, KNBNTF exhibits a complex local polarization and enhances the relaxor features, facilitating high field-induced polarization and establishing favorable conditions for exceptional energy storage performance. Therefore, the proposed strategy is a promising design pathway for tailoring dielectric ceramics in energy storage applications.

Efficient manufacture of high-performance electroplated diamond wires utilizing Cr-coated diamond micro-powder

The slicing of silicon ingots using electroplated diamond wires is a fundamental process in the creation of semiconductor devices such as chips and photovoltaic cells. Composite electroplating, a process that uses nickel (Ni) plating to fix diamond particles onto a steel wire, is a critical step in the manufacturing of these diamond wires. In this work, chromium (Cr)-coated diamond was used to achieve rapid and high-quality composite electroplating, thereby aiding the production of high-performance diamond wire saws. The Cr-coated diamond micro-powder was prepared utilizing vacuum slow evaporation technology at a temperature of 850 °C. This resulted in a uniform and firm Cr coating that was firmly bonded to the diamond surface via Cr3C2. Subsequent electrochemical tests were conducted in the composite electroplating bath. Linear scanning voltammetric curves revealed that the Cr-coated diamond was capable of inducing a more positive shift in the overpotential of Ni deposition, thus enhancing the reaction beyond that of uncoated diamond micro-powder. Additionally, the electrochemical impedance spectra indicated a decrease in charge transfer resistance during composite electroplating, attributable to the conductivity of the Cr-coated diamond. Electroplated diamond wires incorporating Cr-coated diamond demonstrated a greater abrasive density per unit length. SEM results showed that Ni was able to deposit on the Cr-coated diamond surface, resulting in the abrasives being completely covered by the Ni plating. The Cr-coated diamond wire exhibits a stronger resistance to abrasive detachment after cutting, which could increase the diamond-protrusion of the wire. The utilization of Cr-coated diamond micro-powder as an abrasive is anticipated to enhance the manufacturing efficiency of diamond wires and improve product quality, thereby promoting advancements in hard and brittle material processing technology.

Improved UV sensitivity in solution-processed PVDF/ZnO nanocomposites via piezo-phototronic effect

In this article, we report the enhanced UV photo-detection property of solution processed poly(vinyledene fluoride) (PVDF) membranes filled with zinc oxide (ZnO) nanoparticles at varying concentration. Microstructural analysis confirms β-crystalline phase formation. PVDF/ZnO membranes show increased photo-current compared to pristine PVDF, under UV (λ∼365 nm, 8.3 μW/cm2) irradiation, with PVDF/10% ZnO achieving 4.34 μA photo-current and 6 second response time at 10 V bias. Under mechanical stress in form of bending, UV photocurrent of the composite is enhanced significantly as a result of piezo-phototronic effect. Impedance spectra show significant variations under UV, revealing modifications in grain-boundary interfaces with ZnO and UV, and bending affecting electrical response, confirming the piezo-phototronic effect.

Humidity impact on polarization dynamics in polymer electrolyte membrane fuel cells through distribution of relaxation times analysis

The interaction among relative humidity, current density, and internal polarization plays a crucial role in optimizing the performance of polymer electrolyte membrane fuel cells (PEMFCs). However, achieving swift analysis and feedback on the internal humidity status of PEMFCs through on-vehicle impedance spectroscopy measurements remains a significant challenge. Conducting a series of impedance spectra under operating conditions of 30 %, 50 %, and 80 % relative humidity sheds light on the impact of humidity on performance. Correlations between specific distribution of relaxation times (DRT) peaks and internal polarization are established. Through DRT analysis, four polarization dynamics related to proton transfer at the proton exchange membrane interface, proton transport in the cathode catalyst layer, charge transfer, and the oxygen diffusion process are effectively identified based on characteristic frequencies and peaks. The rate-determining step of the polarization varies under idling, rated, and overload conditions, providing valuable insights. This study contributes analytical models and strategic guidance for tailoring relative humidity conditions to mitigate polarization, thereby enabling real-time control and enhancement of PEMFC performance.

Development and characterization of fly ash enriched epoxy coatings for corrosion protection in deep sea water

Fly ash (FA) has recently received increasing attention as inexpensive and readily abundant filler for development of epoxy-based anticorrosive coatings. In the present investigation a series of FA enriched epoxy coatings (FECs) has been developed and investigated for their anticorrosive behaviour under immersion in DSW (pH 8.2) over 48 h. The development of FECs was conducted through enrichment of FA ranging 0 to 80 phr (parts of FA per 100 g of epoxy) into epoxy matrix. The formation of FECs was ascertained through spectral, thermal, electrical and microscopic methods. Electrochemical impedance spectra in coherence with DC polarization measurements reveal enhanced corrosion protection efficiency (83 %) of FECs derived at 40 phr enrichment of FA. Enrichment of FA (phr) ranging 40 to 60 has rendered fair (0.01) to moderate (0.05) resistance (mm/year) to FECs against pitting corrosion in DSW. Whereas, FECs derived at 60 phr of FA has shown promising electrical behaviour, moderate heat resistance (TG onset 200 °C with 94.70 % weight residue) with enhanced limiting oxygen index (38.50 %). FECs developed in the present investigation may find their possible applications as anticorrosive coatings sustainable in DSW over 48 h.

Magnetic exchange interactions and non-Debye relaxation in spin-3/2 frustrated Kagomé magnet Co3V2O8

We report the experimental determination of the magnetic exchange parameter ( J/kB = 2.88 ± 0.02 K) for the Spin-3/2 ferromagnetic (FM) Kagomé lattice system: Co3V2O8 using the temperature dependence of dc-magnetic susceptibility χ(T) data by employing the fundamental Heisenberg linear chain model. Our results are quite consistent with the theoretically reported nearest neighbor dominant FM exchange coupling strength Jex−NN∼ 2.45 K. Five different magnetic phase transitions (6.2–11.2 K) and spin-flip transitions (9.6–7.7 kOe) have been probed using the ∂ ( χT )/ ∂T vs. T, heat capacity (CP -T) and differential isothermal magnetization curves. Among such sequence of transitions, the prominent ones being incommensurate antiferromagnetic (AFM) state at 11.2 K, commensurate AFM state at 8.8 K, and commensurate FM state across 6.2 K. All the successive magnetic phase transitions have been mapped onto a single H-T plane through which one can easily distinguish the above-mentioned different phases. The magnetic contribution of the CP -T near TN (11.2 K) has been analyzed using the power-law expression CM = A|T — TN|−α resulting in the critical exponent α = 0.18 ± 0.01 (0.15 ± 0.003) for T < TN (T > TN ), respectively for the Co3V2O8. It is interesting to note that non-Debye type dipole relaxation is quite prominent in Co3V2O8 and was evident from the Kohlrausch–Williams–Watts analysis of complex modulus and impedance spectra (0 ⩽β⩽ 1). Mott’s variable-range hopping of charge carriers process is evident through the resistivity analysis ( ρac -T −1/4 ) in the temperature range 275 ∘C–350 ∘C. Moreover, the frequency-dependent analysis of σac (ω) follows Jonscher’s power law yielding two distinct activation energies ( Ea∼ 0.37 and 2.29 eV) between the temperature range 39 ∘C–99 ∘C and 240 ∘C–321 ∘C.

Effect of Li2O composition and temperature on the ionic conductivity of lithium-borate-silicate glasses containing gold nanoparticles using electrochemical impedance spectroscopy

This research systematically investigates the conductivity properties of a lithium-borate-silicate glass containing varying amounts of Li2O (30 to 50 mol %) in the presence and absence of a fixed concentration of gold nanoparticles (0.05 M). Three techniques were used to characterize the glass material: Electrochemical Impedance Spectroscopy, X-ray diffraction, and Differential Scanning Calorimetry. Impedance spectra were recorded at temperatures of 100 °C, 140 °C, and 200 °C, and the results were analyzed qualitatively and quantitatively using models based on the equivalent circuit approach. It was observed that below a critical concentration of Li2O, namely 35 mol %, the conductivity behavior exhibits a single relaxation process. However, above the critical concentration, the materials present two relaxation processes associated with changes in morphology. Impedance measurements also evaluate the DC and AC conductivity properties of the glasses. Interestingly, regardless of the morphology, conduction in the glasses appears to be thermally activated, with the conduction mechanism being controlled by polaron hopping in a correlated barrier. There is no evidence suggesting that the gold nanoparticles play a significant role in determining the conduction properties of the glasses, at least within the concentration range studied here.

Facile synthesis of Zn2V2O7/RGO nanocomposite for enhancing the electrochemical performance and evaluating the supercapacitor device

Pyrochlore-structured zinc vanadium oxide with RGO (Zn2V2O7/RGO) composite was synthesized using the simple hydrothermal process for energy storage device fabrication. The structural, vibration spectrum, surface morphology, and elemental of the Zn2V2O7/RGO composite were analyzed using different analytical methods. Then, the electrochemical performance was examined using Zn2V2O7/RGO composite modified electrode with 3-electrode and 2-electrode setup by cyclic voltammetry (CV), galvanostatic charge–discharge (GCD), and electrochemical impedance spectrum (EIS) techniques. Consequently, the Zn2V2O7/RGO composite revealed notable pseudo-capacitive behavior which has been confirmed through CV analysis. The nano size-based Zn2V2O7/RGO composite electrode material obtained notable specific capacitance (Csp) of 1400.51F/g owing to the synergistic promotion of Zinc and vanadium oxides. Furthermore, the ASC device of Zn2V2O7/RGO ||RGO displayed the efficient power density of 1371 kW/kg at the energy density of 8Wh/kg and the device has enhanced cycling performance with 72.8 % capacitance.

Extracting and Interpreting Electrochemical Impedance Spectra (EIS) from Physics-Based Models of Lithium-Ion Batteries

This paper implements a highly efficient algorithm to extract electrochemical impedance spectra (EIS) from physics-based battery models (e.g., a P2D model). The mathematical approach is different from how EIS is practiced experimentally. Experimentally, the voltage (current) is harmonically perturbed over a wide range of frequencies and the amplitude and phase shift of the corresponding current (voltage) is measured. The experimental approach can be implemented in simulation software, but is computationally expensive. The approach here is to determine locally linear state-space models from the full physical model. The four Jacobian matrices that are the basis of the state-space models can be derived by numerical differentiation of the physical model. The EIS is then extracted from the state-space model using computationally efficient matrix-manipulation techniques. The algorithm can evaluate the full EIS at an instant in time during a transient, independent of whether the battery is in a stationary state. The approach is also able to separate the full-cell impedance to evaluate partial EIS, such as for a battery anode alone. Although such partial EIS is difficult to measure experimentally, the partial EIS provides valuable insights in interpreting the full-cell EIS.

Boosting the photocatalytic activity of bismuth vanadate (BiVO4) via optimization of the internal polarization

Photocatalytic performance can be improved by optimizing the morphology and surface texture of the photocatalyst or forming different p-n and/or n-n heterojunctions. Although the heterojunction system enhances photocatalytic property; however, an internal spontaneous polarization electric field may be much more effective due to the separation of electron-hole pairs when the polarization field forces them to move in different directions. The present study demonstrated this insight where the BiVO4 synthesis condition and polarization field forces were controlled via homogeneous precipitation in the presence of polyvinylpyrrolidone (PVP). The as-synthesized BiVO4 photocatalysts' structure and morphology were investigated using XRD, SEM, Raman, DRS, and PL. The result revealed that the increase of PVP concentration reformed the shaping to the truncated bipyramid-like shape and creates a spontaneous internal polarization that enhanced BiVO4 photocatalytic performance. The photocatalytic activity of BiVO4 was evaluated by monitoring the photocurrent enhancement using chronoamperometry, electrochemical impedance spectra and the photodegrading of methylene blue (MB) aqueous solution to harmless compounds in the presence of light. The spontaneous polarization between the different facets of BiVO4 crystal enhances the e−/h+ separation during internal facets homojunction and leads to four times photocurrent enhancement and the MB photocatalytic degradation rate increased from 0.43 to 1.92 min−1.

Characteristics of hydride electrodes using Mg-Ti-Ni-Co-Al-based alloys synthesized by mechanical milling

For Ni-MH batteries, crystalline Mg-based alloys such as MgNi, Mg2Ni, REMg12, and La2Mg17 are regarded as hopeful negative electrode materials. Even though these alloys are inexpensive and have promising discharge capacity, they hardly ever electrochemically absorb or desorb hydrogen at room temperature. In this paper, the MgNi-based Mg50-xTixNi45Al3Co2 (x = 0, 1, 2, 3, 4) alloy electrodes were fabricated. The surface of the as-cast alloys was modified by mechanical Ni coating. The nanocrystalline and amorphous Mg50-xTixNi45Al3Co2 (x = 0, 1, 2, 3, 4) + 50 wt.%Ni alloys for Ni-MH batteries were prepared using mechanical ball milling. The effects of Ti content and ball milling time on the structure and electrochemical hydrogen storage properties of the alloys were investigated. The electrochemical testing reveals that the as-milled alloys can electrochemically absorb and desorb hydrogen well at room temperature. Without any activation, the milled alloys can achieve maximum discharge capacity in the first cycle. With the extension of ball milling time and the increase of Ti content, the cycle stability and discharge capacity of the alloys are significantly enhanced. The electrochemical impedance spectrum, high rate discharge ability, potentiodynamic polarization curve, and potential-step measurement all indicate that the electrochemical kinetics of the prepared alloys initially increase and subsequently decrease with the increase of Ti content, while significantly improve with the prolongation of milling time.

Effects of Fe2+ on dielectric and magnetic properties in rare earth garnet type high entropy oxides

Given the important role played by the valence state of the transition metal in determining material this paper investigates the effect of Fe2+ content on the structure and dielectric properties of garnet-structured high entropy oxides (Y0.2Eu0.2Er0.2Dy0.2Lu0.2)3(Al0.5Fe0.5)5O12 through Fe2+ doping. The results of XPS and Mӧssbauer spectra showed that the Fe2+ content in the tetrahedron increased with Fe2+ doping. With increasing Fe2+ content, the dielectric constants gradually increased, and the maximum dielectric constant reached 2.78×104 at 100 Hz under 30ºC. The analysis of the AC impedance spectrum and electrical conductivity revealed that the difference between the activation energy of grain boundary and grain conductivity resulted in increased dielectric constants of the samples. In addition, the doping of Fe2+ increased the maximum magnetization of the samples. This work provides a new idea for designing giant dielectric materials and magnetic materials with a high entropy strategy.