Achieving a superior Na storage performance of Fe-based Prussian blue cathode by coating perylene tetracarboxylic dianhydride amine

Fe-based Prussian blue(Fe-PB)cathode material shows great application potential in sodium(Na)-ion batteries due to its high theoretical capacity,long cycle life,low cost,and simple preparation process.However,the crystalline water and vacancies of Fe-PB lattice,the low electrical conductivity,and the dissolution of metal ions lead to limited capacity and poor cycling stability.In this work,a perylene tetracarboxylic dianhydride amine(PTCDA)coating layer is successfully fabricated on the surface of Fe-PB by a liquid-phase method.The aminated PTCDA(PTCA)coating not only increases the specific surface area and electronic conductivity but also effectively reduces the crystalline water and vacancies,which avoids the erosion of Fe-PB by electrolyte.Consequently,the PTCA layer reduces the charge transfer resistance,enhances the Na-ion diffusion coefficient,and improves the structure stability.The PTCA-coated Fe-PB exhibits superior Na storage performance with a first discharge capacity of 145.2 mAh g^(−1) at 100 mA g^(−1).Long cycling tests exhibit minimal capacity decay of 0.027%per cycle over 1000 cycles at 1 A g^(−1).Therefore,this PTCA coating strategy has shown promising competence in enhancing the electrochemical performance of Fe-PB,which can potentially serve as a universal electrode coating strategy for Na-ion batteries.

Self-assembly of perovskite nanocrystals:From driving forces to applications

Self-assembly of metal halide perovskite nanocrystals(NCs)into superlattices can exhibit unique collective properties,which have significant application values in the display,detector,and solar cell field.This review discusses the driving forces behind the self-assembly process of perovskite NCs,and the commonly used self-assembly methods and different self-assembly structures are detailed.Subsequently,we summarize the collective optoelectronic properties and application areas of perovskite superlattice structures.Finally,we conclude with an outlook on the potential issues and future challenges in developing perovskite NCs.

Efficient energy transfer from self-trapped excitons to Mn^(2+) dopants in CsCdCl_(3):Mn^(2+) perovskite nanocrystals

Mn^(2+)doping has been adopted as an efficient approach to regulating the luminescence properties of halide perovskite nano-crystals(NCs).However,it is still difficult to understand the interplay of Mn^(2+)luminescence and the matrix self-trapped exciton(STE)emission therein.In this study,Mn^(2+)-doped CsCdCl_(3) NCs are prepared by hot injection,in which CsCdCl_(3) is selected because of its unique crystal structure suitable for STE emission.The blue emission at 441 nm of undoped CsCdCl_(3) NCs originates from the defect states in the NCs.Mn^(2+)doping promotes lattice distortion of CsCdCl_(3) and generates bright orange-red light emission at 656 nm.The en-ergy transfer from the STEs of CsCdCl_(3) to the excited levels of the Mn^(2+)ion is confirmed to be a significant factor in achieving efficient luminescence in CsCdCl_(3):Mn^(2+)NCs.This work highlights the crucial role of energy transfer from STEs to Mn^(2+)dopants in Mn^(2+)-doped halide NCs and lays the groundwork for modifying the luminescence of other metal halide perovskite NCs.

Strengthening-softening transition and maximum strength in Schwarz nanocrystals

Recently,a Schwarz crystal structure with curved grain boundaries(GBs)constrained by twin-boundary(TB)networks was discovered in nanocrystalline Cu through experiments and atomistic simulations.Nanocrystalline Cu with nanosized Schwarz crystals exhibited high strength and excellent thermal stability.However,the grainsize effect and associated deformation mechanisms of Schwarz nanocrystals remain unknown.Here,we performed large-scale atomistic simulations to investigate the deformation behaviors and grain-size effect of nanocrystalline Cu with Schwarz crystals.Our simulations showed that similar to regular nanocrystals,Schwarz nanocrystals exhibit a strengthening-softening transition with decreasing grain size.The critical grain size in Schwarz nanocrystals is smaller than that in regular nanocrystals,leading to a maximum strength higher than that of regular nanocrystals.Our simulations revealed that the softening in Schwarz nanocrystals mainly originates from TB migration(or detwinning)and annihilation of GBs,rather than GB-mediated processes(including GB migration,sliding and diffusion)dominating the softening in regular nanocrystals.Quantitative analyses of simulation data further showed that compared with those in regular nanocrystals,the GB-mediated processes in Schwarz nanocrystals are suppressed,which is related to the low volume fraction of amorphous-like GBs and constraints of TB networks.The smaller critical grain size arises from the suppression of GB-mediated processes.

Nonlinear Absorption and Low-threshold Two-photon Pumped Amplified Stimulated Emission from FAPbBr_(3) Nanocrystals

Formamidinium lead bromide(FAPbBr_(3))nanocrystals(NCs)have been considered to be a good optoelectronic material due to their pure green emission,excellent stability and superior carrier transport characteristics.However,two-photon pumped amplified spontaneous emission(ASE)and the corresponding nonlinear optical properties of FAPbBr_(3) NCs are scarcely revealed.Herein,we synthesized colloidal FAPbBr_(3) NCs with different sizes by changing the molar ratio of FABr/PbBr_(2) in the precursor solution,using ligand assisted precipitation(LARP)technology at room temperature.Photoluminescence(PL)and time resolved photoluminescence(TRPL)spectroscopy were measured to characterize their ASE properties.And their nonlinear optical properties were studied through the Zscan technique and the two-photon excited fluorescence method.The stimulated emission properties including oneand two-photon pumped ASE have been realized from FAPbBr_(3) NCs.With large two-photon absorption coefficient(0.27 cm/GW)and high non-linear absorption cross-section(7.52×10^(5) GM),ASE with threshold as low as 9.8μJ/cm^(2) and 487μJ/cm^(2) have been obtained from colloidal FAPbBr_(3) NCs using one-and two-photon excitations.These results indicate that as a new possible green-emitting frequency-upconversion material with low thresholds,FAPbBr_(3) NCs hold great potential in the development of high-performance two-photon pump lasers.

Isolative Synthesis and Characterization of Cellulose and Cellulose Nanocrystals from Typha angustifolia

The application potential of cellulosic materials in natural composites and other fields needs to be explored to develop innovative, sustainable, lightweight, functional biomass materials that are also environmentally friendly. This study investigated Typha angustifolia (Typha sp.) as a potential new raw material for extracting cellulose nanocrystals (CNCs) for application in wastewater treatment composites. Alkaline treatments and bleaching were used to remove cellulose from the stem fibres. The CNCs were then isolated from the recovered cellulose using acid hydrolysis. The study showed a few distinct functional groups (O-H, -C-H, =C-H and C-O, and C-O-C) in the Fourier Transform Infrared (FTIR) spectra. A scanning electron microscope (SEM) revealed the smooth surface of CPC and CNCs, which resulted from removing lignin and hemicellulose from powdered Typha angustifolia. Based on the crystalline index, the powdered Typha angustifolia, CPC, and CNCs were 42.86%, 66.94% and 77.41%. The loss of the amorphous section of the Typha sp. fibre resulted in a decrease in particle size. It may be inferred from the features of a Typha sp. CNC that CNCs may be employed as reinforcement in composites for wastewater treatment.

Shape-Controlled Synthesis of Platinum-Based Nanocrystals and Their Electrocatalytic Applications in Fuel Cells

To achieve environmentally benign energy conversion with the carbon neutrality target via electrochemical reactions, the innovation of electrocatalysts plays a vital role in the enablement of renewable resources. Nowadays, Pt-based nanocrystals(NCs) have been identified as one class of the most promising candidates to efficiently catalyze both the half-reactions in hydrogen-and hydrocarbonbased fuel cells. Here, we thoroughly discuss the key achievement in developing shape-controlled Pt and Pt-based NCs, and their electrochemical applications in fuel cells. We begin with a mechanistic discussion on how the morphology can be precisely controlled in a colloidal system, followed by highlighting the advanced development of shape-controlled Pt, Pt-alloy, Pt-based core@shell NCs, Pt-based nanocages, and Pt-based intermetallic compounds. We then select some case studies on models of typical reactions(oxygen reduction reaction at the cathode and small molecular oxidation reaction at the anode) that are enhanced by the shape-controlled Pt-based nanocatalysts. Finally, we provide an outlook on the potential challenges of shape-controlled nanocatalysts and envision their perspective with suggestions.

Interconnected and high cycling stability polypyrrole supercapacitors using cellulose nanocrystals and commonly used inorganic salts as dopants

Polypyrrole(PPy)is wildly used as electrode material in supercapacitors due to its high conductivity,low cost,ease of handling,and ease of fabrication.However,limited capacitance and poor cycling stability hinder its practical application.After developing carboxylated cellulose nanocrystals(CNC-COO^(-))as immobile dopants for PPy to improve its cycling stability,we investigated the effect of different commonly used salts(KCl,NaCl,KBr,and NaClO_(4))as dopants during electrode fabrication by electropolymerization.The film’s capacitance increased from 160.6 to 183.4 F g^(-1)after adding a combination of KCl and NaClO_(4) into the electrodeposition electrolyte.More importantly,the porous and interconnected PPy/CNC-COO^(-)-Cl-(Cl O_(4)^(-))_0.5 electrode film exhibited an excellent capacitance of 125.0 F g^(-1)(0.78 F cm^(-2))at a high current density of 2.0 Ag^(-1)(20 m A cm^(-2),allowing charging in less than 1 min),increasing almost 204%over PPy/CNC-COO-films.A symmetric PPy/CNC-COO^(-)-Cl-(ClO_(4)^(-))_0.5 supercapacitor retained its full capacitance after 5000 cycles,and displayed a high energy density of 5.2 Wh kg^(-1)at a power density of 25.4 W kg^(-1)(34.5μWh cm^(-2) at 1752.3μW cm^(-2)).These results reveal that the porous structure formed by doping with CNC-COO-and inorganic salts opens up more active reaction areas to store charges in PPy-based films as the stiff and ribbon-like CNC-COO-as permanent dopants improve the strength and stability of PPy-based films.Our demonstration provides a simple and practical way to deposit PPy based supercapacitors with high capacitance,fast charging,and excellent cycling stability.

Efficient CO_(2)Reduction to Formate on CsPbI_(3) Nanocrystals Wrapped with Reduced Graphene Oxide

Transformation of greenhouse gas(CO_(2))into valuable chemicals and fuels is a promising route to address the global issues of climate change and the energy crisis.Metal halide perovskite catalysts have shown their potential in promoting CO_(2)reduction reaction(CO_(2)RR),however,their low phase stability has limited their application perspective.Herein,we present a reduced graphene oxide(rGO)wrapped CsPbI_3 perovskite nanocrystal(NC)CO_(2)RR catalyst(CsPbI_3/rGO),demonstrating enhanced stability in the aqueous electrolyte.The CsPbI_3/rGO catalyst exhibited>92%Faradaic efficiency toward formate production at a CO_(2)RR current density of~12.7 mA cm^(-2).Comprehensive characterizations revealed the superior performance of the CsPbI_3/rGO catalyst originated from the synergistic effects between the CsPbI_3 NCs and rGO,i.e.,rGO stabilized theα-CsPbI_3 phase and tuned the charge distribution,thus lowered the energy barrier for the protonation process and the formation of~*HCOO intermediate,which resulted in high CO_(2)RR selectivity toward formate.This work shows a promising strategy to rationally design robust metal halide perovskites for achieving efficient CO_(2)RR toward valuable fuels.

Ultrasonic cavitation-enabled microfluidic approach toward the continuous synthesis of cesium lead halide perovskite nanocrystals

Ligand assisted reprecipitation(LARP)is a widely used method for cesium lead halide perovskite nanocrystals(NCs)synthesis.Nevertheless,the ultrafast kinetics of LARP,as well as the inefficient transport properties and discontinuity of batch reactors,challenge the particle size control and experimental repeatability.To address these issues,an ultrasonic cavitation-enabled microfluidic approach was developed to achieve the continuous synthesis of cesium lead halide perovskite via LARP.It was found that the mixing between the good solvent and antisolvent in the microchannel was greatly enhanced by intensive ultrasonic cavitation.The mixing time could be reduced to below 10 ms under the irradiation of 35 W ultrasound.By modulating the mixing degree,LARP was proved to be a mixing-sensitive process.The effects of ultrasonic power,ultrasonic treatment time,total flow rate,water additive,and reprecipitation temperature on the synthesis of CsPbBr_(3) NCs were systematically investigated.As compared to CsPbBr_(3) NCs synthesized in the batch reactor,the sample synthesized via the ultrasonic cavitation-enabled microfluidic approach possessed stronger photoluminescence intensity and better repeatability.Moreover,the ultrasonic cavitation-enabled microfluidic approach could also realize the continuous synthesis of cesium lead halide perovskite NCs with different halide compositions to cover a wide visible spectrum(426-661 nm).The ultrasonic cavitation-enabled microfluidic approach paved the way for the large-scale of high-quality cesium lead halide perovskite NCs.

Surface-functionalized cellulose nanocrystals(CNC)and synergisms with surfactant for enhanced oil recovery in low-permeability reservoirs

Nanocellulose,a natural polymeric nanomaterial,has attracted significant attention in enhanced oil recovery(EOR)applications due to its abundance,nanoscale,high oil-water interfacial adsorption ef-ficiency.In this study,surface-functionalized cellulose nanocrystals(SF-CNCs)were prepared via hy-drochloric acid hydrolysis and chemical modification,with adaptable nanosize and considerable dispersion stability in low-permeability reservoirs.The SF-CNCs were structurally characterized by FT-IR,Cryo-TEM,which have a diameter of 5-10 nm and a length of 100-200 nm.The SF-CNC dispersions possessed higher stability and stronger salt-tolerance than those of corresponding CNC dispersions,due to the strong hydrophilicity of the sulfonic acid group.It was synergistically used with a non-ionic surfactant(APG1214)to formulate a combined flooding system(0.1 wt%SF-CNC+0.2 wt%APG1214).The combined flooding system exhibits strong emulsification stability,low oil-water interfacial tension of o.03 mN/m,and the ability to alter the wettability for oil-wetting rocks.Furthermore,the combined system was_able to provide an optimum EOR efficiency of 20.2%in low-permeability cores with 30.13×10^(-3)μm^(2).Notably.it can enlarge the sweep volume and increase the displacement efficiency simultaneously.Overall,the newly formulated nanocellulose/surfactant combined system exhibits a remarkable EoR performance in low-permeability reservoirs.

Development strategies and improved photocatalytic CO_(2) reduction performance of metal halide perovskite nanocrystals

In recent years,photocatalytic CO_(2)reduction reaction(CRR) has attracted much scientific attention to overcome energy and environmental issues by converting CO_(2)into high-value-added chemicals utilizing solar energy.Metal halide perovskite(MHP) nanocrystals(NCs) are recognized as an ideal choice for CRR owing to their outstanding optoelectronic properties.Although great efforts have been devoted to designing more effective photocatalysts to optimize CRR performance,severe charge recombination,instability,and unsatisfactory activity have become major bottlenecks in developing perovskite-based photocatalysts.In this review,we mainly focus on the recent research progress in the areas of relevance.First,a brief insight into reaction mechanisms for CRR and structural features of MHPs are introduced.Second,efficient modification approaches for the improvement of the photocatalytic activity and stability of the perovskite-based catalysts are comprehensively reviewed.Third,the state-of-the-art achievements of perovskite-based photocatalysts for CRR are systematically summarized and discussed,which are focused on the modification approaches,structure design,and the mechanism of the CO_(2)reduction process.Lastly,the current challenges and future research perspectives in the design and application of perovskite materials are highlighted from our point of view to provide helpful insights for seeking breakthroughs in the field of CRR.This review may provide a guide for scientists interested in applying perovskite-based catalysts for solar-to-chemical energy conversion.

Two-photon absorption of FAPbBr_(3) perovskite nanocrystals

Perovskite nanocrystals(NCs) with high two-photon absorption(TPA) cross-section are of great interest due to their potential applications in three-dimensional optical data storage and multiphoton fluorescence microscopy. Among various perovskite materials, FAPbBr_(3) NCs show a better development prospect due to their excellent stability. However, there are few reports on their nonlinear optical properties. In this work, the nonlinear optical behavior of FAPbBr_(3) NCs is studied.The methods of multiphoton absorption photoluminescence saturation and open aperture Z-scan technique were applied to determine the TPA cross-section of FAPbBr_(3)NCs, which was around 2.76 × 10^(-45)cm^(4)·s·photon^(-1) at 800 nm. In addition,temperature-dependent photoluminescence induced by TPA was investigated, and the small longitudinal optical phonon energy and electron–phonon coupling strength was obtained, which confirm the weak Pb–Br interaction. Meanwhile, it is found that the exciton binding energy in FAPbBr_(3) NCs was 69.668 me V, which may be ascribed to the strong hydrogen bond interaction. It is expected that our findings will promote the application of FAPbBr_(3) NCs in optoelectronic devices.

Enabling High-Performance Sodium Battery Anodes by Complete Reduction of Graphene Oxide and Cooperative In-Situ Crystallization of Ultrafine SnO_(2)Nanocrystals

The main bottleneck against industrial utilization of sodium ion batteries(SIBs)is the lack of high-capacity electrodes to rival those of the benchmark lithium ion batteries(LIBs).Here in this work,we have developed an economical method for in situ fabrication of nanocomposites made of crystalline few-layer graphene sheets loaded with ultrafine SnO_(2)nanocrystals,using short exposure of microwave to xerogel of graphene oxide(GO)and tin tetrachloride containing minute catalyzing dispersoids of chemically reduced GO(RGO).The resultant nanocomposites(SnO_(2)@MWG)enabled significantly quickened redox processes as SIB anode,which led to remarkable full anode-specific capacity reaching 538 mAh g^(−1)at 0.05 A g^(−1)(about 1.45 times of the theoretical capacity of graphite for the LIB),in addition to outstanding rate performance over prolonged charge–discharge cycling.Anodes based on the optimized SnO_(2)@MWG delivered stable performance over 2000 cycles even at a high current density of 5 A g^(−1),and capacity retention of over 70.4%was maintained at a high areal loading of 3.4 mg cm^(−2),highly desirable for high energy density SIBs to rival the current benchmark LIBs.

Clean production of Fe-based amorphous soft magnetic alloys via smelting reduction of high-phosphorus iron ore and apatite

Separated preparation of prealloys and amorphous alloys results in severe solidification-remelting and beneficial element removal-readdition contradictions,which markedly increase energy consumption and emissions.This study offered a novel strategy for the direct production of FePC amorphous soft magnetic alloys via smelting reduction of high-phosphorus iron ore(HPIO)and apatite.First,the thermodynamic conditions and equilibrium states of the carbothermal reduction reactions in HPIO were calculated,and the element content in reduced alloys was theoretically determined.The phase and structural evolutions,as well as element migration and enrichment behaviors during the smelting reduction of HPIO and Ca_(3)(PO_(4))_(2),were then experimentally verified.The addition of Ca_(3)(PO_(4))_(2)in HPIO contributes to the enrichment of the P element in reduced alloys and the subsequent development of Fe_(3)P and Fe_(2)P phases.The content of P and C elements in the range of 1.52 wt% -14.63 wt% and 0.62 wt% -2.47 wt%,respectively,can be well tailored by adding 0-50 g Ca_(3)(PO_(4))_(2)and controlling the C/O mole ratio of 0.8-1.1,which is highly consistent with the calculated results.These FePC alloys were then successfully formed into amorphous ribbons and rods.The energy consumption of the proposed strategy was estimated to be 2.00×10^(8) kJ/t,which is reduced by 30% when compared with the conventional production process.These results are critical for the comprehensive utilization of mineral resources and pave the way for the clean production of Fe-based amorphous soft magnetic alloys.

Direct observation of the distribution of impurity in phosphorous/boron co-doped Si nanocrystals

Doping in Si nanocrystals is an interesting topic and directly studying the distribution of dopants in phosphorous/boron co-doping is an important issue facing the scientific community.In this study,atom probe tomography is performed to study the structures and distribution of impurity in phosphorous/boron co-doped Si nanocrystals/SiO_(2) multilayers.Compared with phosphorous singly doped Si nanocrystals,it is interesting to find that the concentration of phosphorous in co-doped samples can be significantly improved.Theoretical simulation suggests that phosphorous-boron pairs are formed in co-doped Si nanocrystals with the lowest formation energy,which also reduces the formation energy of phosphorous in Si nanocrystals.The results indicate that co-doping can promote the entry of phosphorous impurities into the near-surface and inner sites of Si nanocrystals,which provides an interesting way to regulate the electronic and optical properties of Si nanocrystals such as the observed enhancement of conductivity and sub-band light emission.

Enhancement and recovery of photoluminescence and stability by multifunctional etching ligands treatment for perovskite nanocrystals

Perovskite nanocrystals(PNCs)have recently become promising optoelectronic materials due to their excellent photophysical properties.However,the highly dynamic binding state between ligands and the surface of PNCs has severely restricted their luminescent properties and stabilities.In this work,1,3-bisbenzyl-2-oxoimidazolidine-4,5-dicarboxylic acid(cycle acid,CA)is introduced as both an etchant and a ligand upon post-synthetic surface treatment of PNCs.By removing the imperfect octahedrons[Pb X_(6)]^(4-)and passivating the surface defects synergistically,this treatment improves photoluminescence quantum yields from 76%to 95%and enhances the stability of PNCs against polar solvent,moisture,heat,and illumination.Meanwhile,CA can effectively and instantly recover the luminescence emission for aged PNCs.As a result,the CA-Cs Pb Br_(3)PNCs and CA-Cs Pb IxBr_(3-x)PNCs are applied as color-converting layers on a blue LED chip for warm white light-emitting diodes(WLEDs)with a color coordinate of(0.41,0.40).Importantly,the CA-based WLED device exhibits superior stability in operational conditions.

Efficient transfer of metallophosphor excitons via confined polaritons in organic nanocrystals

We investigate the transfer of phosphorescent energy between co-assembled metallophosphors in crystalline nanostructures [Angew. Chem. Int. Ed. 57 7820(2018) and J. Am. Chem. Soc. 140 4269(2018)]. Neither Dexter's nor Forster's mechanism of resonance energy transfer(RET) could account fully for the observed rates, which exceed 85% with significant temperature dependence. But there exists an alternative pathway on RET mediated by intermediate states of resonantly confined exciton–polaritons. Such a mechanism was used to analyze artificial photosynthesis in organic fluorescents [Phys.Rev. Lett. 122 257402(2019)]. For metallophosphors, the confined modes act as extended states lying between the molecular S_(1) and T_(1) states, offering a bridge for the long-lived T_(1) excitons to migrate from donors to acceptors. Population dynamics with parameters taken entirely based on experiments fits the observed lifetimes of phosphorescence across a broad range of doping and temperature.

Ultrasmall NiS_(2)Nanocrystals Embedded in Ordered Macroporous Graphenic Carbon Matrix for Efficiently Pseudocapacitive Sodium Storage

Sodium-ion hybrid capacitor(SIHC)is one of the most promising alternatives for large-scale energy storage due to its high energy and power densities,natural abundance,and low cost.However,overcoming the imbalance between slow Na^(+)reaction kinetics of battery-type anodes and rapid ion adsorption/desorption of capacitive cathodes is a significant challenge.Here,we propose the high-rate-performance NiS_(2)@OMGC anode material composed of monodispersed NiS_(2) nanocrystals(8.8±1.7 nm in size)and N,S-co-doped graphenic carbon(GC).The NiS_(2)@OMGC material has a three-dimensionally ordered macroporous(3DOM)morphology,and numerous NiS_(2) nanocrystals are uniformly embedded in GC,forming a core-shell structure in the local area.Ultrafine NiS_(2) nanocrystals and their nano-microstructure demonstrate high pseudocapacitive Na-storage capability and thus excellent rate performance(355.7 mAh/g at 20.0 A/g).A SIHC device fabricated using NiS_(2)@OMGC and commercial activated carbon(AC)cathode exhibits ultrahigh energy densities(197.4 Wh/kg at 398.8 W/kg)and power densities(43.9 kW/kg at 41.3 Wh/kg),together with a long life span.This outcome exemplifies the rational architecture and composition design of this type of anode material.This strategy can be extended to the design and synthesis of a wide range of high-performance electrode materials for energy storage applications.

Behavior of Medium-frequency Core Loss in Fe-based Nanocrystalline Soft Magnetic Alloys

The dependences of the power loss per cycle on frequency have been investigated in the ranges of 100 Hz<= f<=25000 Hz and 0.1 T< =Bm <=1.0 T for three main original magnetic states in five sorts of Fe-based nanocrystalline soft magnetic alloys. The measured and calculated results showed that the total power loss per cycle clearly exhibited a nonlinear behavior in the range below 3 kHz～5 kHz depending on both the magnetic state and the value of Dm, whereas it showed a quasi-linear behavior above this range. The total loss was decomposed into hysteresis loss, classical eddy current loss and excess loss, the obvious nonlinear behavior has been confirmed to be completely determined by the dependence of the excess loss on frequency. It has been indicated that the change rate of the excess loss per cycle with respect to frequency sharp decreases with increasing frequency in the range below about 3 kHz～5 kHz, wherease the rate of change slowly varies above this range, thus leading to the quasilinear behavior of the total loss per cycle. In this paper, some linear expressions of the total loss per cycle has been given in a wider medium-frequency segment, which can be used for roughly estimating the total loss.