High corrosion and wear resistant electroless Ni–P gradient coatings on aviation aluminum alloy parts

A Ni–P alloy gradient coating consisting of multiple electroless Ni–P layers with various phosphorus contents was prepared on the aviation aluminum alloy. Several characterization and electrochemical techniques were used to characterize the different Ni–P coatings’ morphologies, phase structures, elemental compositions, and corrosion protection. The gradient coating showed good adhesion and high corrosion and wear resistance, enabling the application of aluminum alloy in harsh environments. The results showed that the double zinc immersion was vital in obtaining excellent adhesion (81.2 N). The optimal coating was not peeled and shredded even after bending tests with angles higher than 90°and was not corroded visually after 500 h of neutral salt spray test at 35℃. The high corrosion resistance was attributed to the misaligning of these micro defects in the three different nickel alloy layers and the amorphous structure of the high P content in the outer layer. These findings guide the exploration of functional gradient coatings that meet the high application requirement of aluminum alloy parts in complicated and harsh aviation environments.

Surface Metallization of Glass Fiber(GF)/Polyetheretherketone(PEEK) Composite with Cu Coatings Deposited by Magnetron Sputtering and Electroplating

Surface metallization of glass fiber(GF)/polyetheretherketone(PEEK)[GF/PEEK] is conducted by coating copper using electroplating and magnetron sputtering and the properties are determined by X-ray diffraction(XRD), scanning electron microscopy(SEM), and electron backscatter diffraction(EBSD).The coating bonding strength is assessed by pull-out tests and scribing in accordance with GB/T 9286-1998.The results show that the Cu coating with a thickness of 30 μm deposited on GF/PEEK by magnetron sputtering has lower roughness, finer grain size, higher crystallinity, as well as better macroscopic compressive stress,bonding strength, and electrical conductivity than the Cu coating deposited by electroplating.

Bio-Based Waterborne Poly(Vanillin-Butyl Acrylate)/MXene Coatings for Leather with Desired Warmth Retention and Antibacterial Properties

This study presents a solvent-free,facile synthesis of a bio-based green antibacterial agent and aromatic monomer methacrylated vanillin(MV)using vanillin.The resulting MV not only imparted antibacterial properties to coatings layered on leather,but could also be employed as a green alternative to petroleum-based carcinogen styrene(St).Herein,MV was copolymerized with butyl acrylate(BA)to obtain waterborne bio-based P(MV-BA)miniemulsion via miniemulsion polymerization.Subsequently,MXene nanosheets with excellent photothermal conversion performance and antibacterial properties,were introduced into the P(MV-BA)miniemulsion by ultrasonic dispersion.During the gradual solidification of P(MV-BA)/MXene nanocomposite miniemulsion on the leather surface,MXene gradually migrated to the surface of leather coatings due to the cavitation effect of ultrasonication and amphiphilicity of MXene,which prompted its full exposure to light and bacteria,exerting the maximum photothermal conversion efficiency and significant antibacterial efficacy.In particular,when the dosage of MXene nanosheets was 1.4 wt%,the surface temperature of P(MV-BA)/MXene nanocomposite miniemulsioncoated leather(PML)increased by about 15℃ in an outdoor environment during winter,and the antibacterial rate against Escherichia coli and Staphylococcus aureus was nearly 100%under the simulated sunlight treatment for 30 min.Moreover,the introduction of MXene nanosheets increased the air permeability,water vapor permeability,and thermal stability of these coatings.This study provides a new insight into the preparation of novel,green,and waterborne bio-based nanocomposite coatings for leather,with desired warmth retention and antibacterial properties.It can not only realize zerocarbon heating based on sunlight in winter,reducing the use of fossil fuels and greenhouse gas emissions,but also improve ability to fight off invasion by harmful bacteria,viruses,and other microorganisms.

Developing an atmospheric aging evaluation model of acrylic coatings:A semi-supervised machine learning algorithm

To study the atmospheric aging of acrylic coatings,a two-year aging exposure experiment was conducted in 13 representative climatic environments in China.An atmospheric aging evaluation model of acrylic coatings was developed based on aging data including11 environmental factors from 567 cities.A hybrid method of random forest and Spearman correlation analysis was used to reduce the redundancy and multicollinearity of the data set by dimensionality reduction.A semi-supervised collaborative trained regression model was developed with the environmental factors as input and the low-frequency impedance modulus values of the electrochemical impedance spectra of acrylic coatings in 3.5wt%NaCl solution as output.The model improves accuracy compared to supervised learning algorithms model(support vector machines model).The model provides a new method for the rapid evaluation of the aging performance of acrylic coatings,and may also serve as a reference to evaluate the aging performance of other organic coatings.

Antibacterial HA-coatings on bioresorbable Mg alloy

In this study,a calcium-phosphate coating was formed on a Mg-Mn-Ce alloy by the plasma electrolytic oxidation(PEO).The antibiotic vancomycin,widely used in the treatment of infections caused by Staphylococcus aureus(S.aureus),was impregnated into the coating.Samples with vancomycin showed high bactericidal activity against S.aureus.The mechanical and electrochemical properties of the formed coatings were studied,as well as in vitro cytotoxicity tests and in vivo tests on mature male rats were performed.According to SEM,EDS,XRD and XPS data,coatings had a developed morphology and contained hydroxyapatite,which indicates high biocompatibility.The analysis of roughness of coatings without and with vancomycin did not reveal any differences,confirming the high roughness of the samples.During electrochemical tests,an increase in corrosion resistance by more than two times after the application of PEO coatings was revealed.According to the results of an in vivo study,after 28 days of the implantation of samples with calcium phosphate PEO coating and vancomycin,no signs of inflammation were observed,while an inflammatory reaction developed in the area of implantation of bare alloy,followed by encapsulation.Antibiotic release tests from the coatings show a sharp decrease in the concentration of the released antibiotic on day 7 and then a gradual decrease until day 28.Throughout the experiment,no significant deviations in the condition and behavior of the animals were observed;clinical tests did not reveal a systemic toxic reaction.

Structure and corrosion behavior of FeCoCrNiMo high-entropy alloy coatings prepared by mechanical alloying and plasma spraying

FeCoCrNiMox composite powders were prepared using the mechanical alloying technique and made into high-entropy alloy(HEA)coatings with the face-centered cubic phase using plasma spraying to address the element segregation problem in HEAs and pre-pare uniform HEA coatings.Scanning electron microscopy,transmission electron microscopy,and X-ray diffractometry were employed to characterize these coatings’microstructure and phase composition.The hardness,elastic modulus,and fracture toughness of coatings were tested,and the corrosion resistance was analyzed in simulated seawater.Results show that the hardness of the coating is HV0.1606.15,the modulus of elasticity is 128.42 GPa,and the fracture toughness is 43.98 MPa·m^(1/2).The corrosion potential of the coating in 3.5wt%NaCl solution is-0.49 V,and the corrosion current density is 1.2×10^(−6)A/cm^(2).The electrochemical system comprises three parts:the electrolyte,the adsorption and metallic oxide films produced during immersion,and the FeCoNiCrMo HEA coating.Over in-creasingly long periods,the corrosion reaction rate increases first and then decreases,the corrosion product film comprising metal oxides reaches a dynamic balance between formation and dissolution,and the internal reaction of the coating declines.

HVOF-sprayed HAp/S53P4 BG composite coatings on an AZ31 alloy for potential applications in temporary implants

Bioactive thermal spray coatings produced via high-velocity oxygen fuel spray(HVOF)from hydroxyapatite(HAp)and bioactive glasses(BG)have the potential to be employed on temporary implants due to the ability of both HAp and BG to dissolve and promote osseointegration,considering that both phases have different reaction and dissolution rates under in-vitro conditions.In the present work,75%wt.HAp-25%wt.S53P4 bioactive glass powders were HVOF-sprayed to obtain HAp/S53P4 BG composite coatings on a bioresorbable AZ31 alloy.The study is focused on exploring the effect of the stand-off distance and fuel/oxygen ratio variation as HVOF parameters to obtain stable structural coatings and to establish their effect on the phases and microstructure produced in those coatings.Different characterization techniques,such as scanning electron microscopy,X-ray diffraction,and Fourier transform infrared spectroscopy,were employed to characterize relevant structural and microstructural properties of the composite coatings.The results showed that thermal gradients during coating deposition must be managed to avoid delamination due to the high temperature achieved(max 550℃)and the differences in coefficients of thermal expansion.It was also found that both spraying distance and oxygen/fuel ratio allowed to keep the hydroxyapatite as the main phase in the coatings.In addition,in-vitro electrochemical studies were performed on the obtained HAp/S53P4 BG composite coatings and compared against the uncoated AZ31 alloy.The results showed a significant decrease in hydrogen evolution(at least 98%)when the bioactive coating was applied on the Mg alloy during evaluation in simulated body fluid(SBF).

Multiscale Simulation of Microstructure Evolution during Preparation and Service Processes of Physical Vapor Deposited c-TiAlN Coatings

Physical Vapor Deposited(PVD)TiAlN coatings are extensively utilized as protective layers for cutting tools,renowned for their excellent comprehensive performance.To optimize quality control of TiAlN coatings for cutting tools,a multi-scale simulation approach is proposed that encompasses the microstructure evolution of coatings considering the entire preparation and service lifecycle of PVD TiAlN coatings.This scheme employs phase-field simulation to capture the essential microstructure of the PVD-prepared TiAlN coatings.Moreover,cutting simulation is used to determine the service temperature experienced during cutting processes at varying rates.Cahn-Hilliard modeling is finally utilized to consume the microstructure and service condition data to acquaint the microstructure evolution of TiAlN coatings throughout the cutting processes.This methodology effectively establishes a correlation between service temperature and its impact on the microstructure evolution of TiAlN coatings.It is expected that the present multi-scale numerical simulation approach will provide innovative strategies for assisting property design and lifespan prediction of TiAlN coatings.

Design multifunctional Mg–Zr coatings regulating Mg alloy bioabsorption

Magnesium(Mg)alloys are widely used for temporary bone implants due to their favorable biodegradability,cytocompatibility,hemocompatibility,and close mechanical properties to bone.However,rapid degradation and inadequate strength limit their applicability.To overcome this,the direct current magnetron sputtering technique is employed for surface coating in Mg-based alloys using various zirconium(Zr)content.This approach presents a promising strategy for simultaneously improving corrosion resistance,maintaining biocompatibility,and enhancing strength without compromising osseointegration.By leveraging Mg’s inherent biodegradability,it has the potential to minimize the need for secondary surgeries,thereby reducing costs and resources.This paper is a systematic study aimed at understanding the corrosion mechanisms of Mg–Zr coatings,denoted Mg-xZr(x=0–5 at.%).Zr-doped coatings exhibited columnar growth leading to denser and refined structures with increasing Zr content.XRD analysis confirmed the presence of the Mg(00.2)basal plane,shifting towards higher angles(1.15°)with 5 at.%Zr doping due to lattice parameter changes(i.e.,decrease and increase of“c”and“a”lattice parameters,respectively).Mg–Zr coatings exhibited“liquidphilic”behavior,while Young’s modulus retained a steady value around 80 GPa across all samples.However,the hardness has significantly improved across all samples’coating,reaching the highest value of(2.2±0.3)GPa for 5 at.%Zr.Electrochemical testing in simulated body fluid(SBF)at 37℃ revealed a significant enhancement in corrosion resistance for Mg–Zr coatings containing 1.0–3.4 at.%Zr.Compared with the 5 at.%Zr coating which exhibited a corrosion rate of 32 mm/year,these coatings displayed lower corrosion rates,ranging from 1 to 12 mm/year.This synergistic enhancement in mechanical properties and corrosion resistance,achieved with 2.0–3.4 at.%Zr,suggests potential ability for reducing stress shielding and controlled degradation performance,and consequently,promising functional biodegradable materials for temporary bone implants.

Improvement strategy on thermophysical properties of A_(2)B_(2)O_(7)-type rare earth zirconates for thermal barrier coatings applications:A review

The A_(2)B_(2)O_(7)-type rare earth zirconate compounds have been considered as promising candidates for thermal barrier coating(TBC) materials because of their low sintering rate,improved phase stability,and reduced thermal conductivity in contrast with the currently used yttria-partially stabilized zirconia (YSZ) in high operating temperature environments.This review summarizes the recent progress on rare earth zirconates for TBCs that insulate high-temperature gas from hot-section components in gas turbines.Based on the first principles,molecular dynamics,and new data-driven calculation approaches,doping and high-entropy strategies have now been adopted in advanced TBC materials design.In this paper,the solid-state heat transfer mechanism of TBCs is explained from two aspects,including heat conduction over the full operating temperature range and thermal radiation at medium and high temperature.This paper also provides new insights into design considerations of adaptive TBC materials,and the challenges and potential breakthroughs are further highlighted for extreme environmental applications.Strategies for improving thermophysical performance are proposed in two approaches:defect engineering and material compositing.

Comparative review of corrosion-resistant coatings on metal bipolar plates of proton exchange membrane fuel cells

In the realm of proton exchange membrane fuel cells(PEMFCs),the bipolar plates(BPs)are indispensable and serve pivotal roles in distributing reactant gases,collecting current,facilitating product water removal,and cooling the stack.Metal BPs,characterized by outstanding manufacturability,cost-effectiveness,higher power density,and mechanical strength,are emerging as viable alternatives to traditional graphite BPs.The foremost challenge for metal BPs lies in enhancing their corrosion resistance and conductivity under acidic conditions,necessitating the application of various coatings on their surfaces to ensure superior performance.This review summarizes and compares recent advancements in the research of eight distinct types of coatings for BPs in PEMFCs,including noble metal,carbide,ni-tride,and amorphous carbon(a-C)/metal compound composite coatings.The various challenges encountered in the manufacturing and fu-ture application of these coatings are also delineated.

Effect of Ta_(2)O_(5)nanoparticles on bioactivity,composition,structure,in vitro and in vivo behavior of PEO coatings on Mg-alloy

The present study investigates the physical and chemical characteristics,behavior in vitro and in vivo,and biocompatibility of coatings containing Ta_(2)O_(5),which are obtained by plasma electrolytic oxidation(PEO)on MA8 magnesium alloy.The obtained coatings demonstrate in vivo biocompatibility and in vitro bioactivity.Compared to the base PEO coating,the layers containing Ta_(2)O_(5)facilitate the development of apatite in simulated body fluid,suggesting that the inclusion of nanoparticles improves bioactivity of the coatings.It was found that incorporation of Ta_(2)O_(5)nanoparticles increases roughness and porosity of the formed layers by increasing particle concentration in electrolytes for the PEO process contributing to sufficient soft tissue ingrowth in vivo.Based on in vivo studies,these coatings also provide favorable tissue response and minimal inflammatory reaction in comparison with the bare magnesium alloy due to protection of living tissues from deleterious corrosion events of magnesium implant such as local alkalization and intense hydrogen evolution.The results obtained in the present study concluded biocompatibility,tissue integration of the PEO coatings containing Ta_(2)O_(5)nanoparticles making them a promising protective layer for biodegradable magnesium implants.

Optical facet coatings for high-performance LWIR quantum cascade lasers atλ∼8.5μm

We report on the performance improvement of long-wave infrared quantum cascade lasers(LWIR QCLs)by studying and optimizing the anti-reflection(AR)optical facet coating.Compared to the Al2O3 AR coat⁃ing,the Y_(2)O_(3)AR coating exhibits higher catastrophic optical mirror damage(COMD)level,and the optical facet coatings of both material systems have no beam steering effect.A 3-mm-long,9.5-μm-wide buried-heterostruc⁃ture(BH)LWIR QCL ofλ~8.5μm with Y_(2)O_(3)metallic high-reflection(HR)and AR of~0.2%reflectivity coating demonstrates a maximum pulsed peak power of 2.19 W at 298 K,which is 149%higher than that of the uncoated device.For continuous-wave(CW)operation,by optimizing the reflectivity of the Y_(2)O_(3)AR coating,the maximum output power reaches 0.73 W,which is 91%higher than that of the uncoated device.

Process and performance of DAAF microspheres prepared by continuous integration from synthesis to spherical coating based on microfluidic system

In order to improve the energy output consistency of 3, 3’-diamino-4, 4’-azoxyfurazan(DAAF) in the new insensitive booster and the safety and efficiency in the preparation process, a continuous preparation system of DAAF from synthesis to spherical coating was designed and established in this paper, which combined ultrasonic micromixing reaction with microdroplet globular template. In the rapid micromixing stage, the microfluidic mixing technology with ultrasonic was used to synergistically strengthen the uniform and rapid mass transfer mixing reaction between raw materials to ensure the uniformity of DAAF particle nucleation-growth, and to prepare high-quality DAAF crystals with uniform structure and morphology and concentrated particle size distribution. In the microdroplet globular template stage, the microfluidic droplet technology was used to form a droplet globular template with uniform size under the shear action of the continuous phase of the dispersed phase solution containing DAAF particles and binder. The size of the droplet template was controlled by adjusting the flow rate ratio between the continuous phase and the dispersed phase. In the droplet globular template, with the diffusion of the solvent in the dispersed phase droplets, the binder precipitates to coat the DAAF into a ball, forming a DAAF microsphere with high sphericity, narrow particle size distribution and good monodispersity. The problem of discontinuity and DAAF particle suspension in the process was solved, and the coating theory under this process was studied. DAAF was coated with different binder formulations of fluororubber(F2604), nitrocellulose(NC) and NC/glycidyl azide polymer(GAP), and the process verification and evaluation of the system were carried out. The balling effects of large, medium and small droplet templates under different binder formulations were studied. The scanning electron microscope(SEM) results show that the three droplet templates under the three binder formulations exhibit good balling effect and narrow particle size distribution. The DAAF microspheres were characterized by powder X-ray diffraction(XRD), differential scanning calorimetry(DSC), thermo-gravimetric(TG) and sensitivity analyzer. The results showed that the crystal structure of DAAF did not change during the process, and the prepared DAAF microspheres had lower decomposition temperature and lower mechanical sensitivity than raw DAAF. The results of detonation parameters show that the coating of DAAF by using the above three binder formulations will not greatly reduce the energy output of DAAF, and has comparable detonation performance to raw DAAF. This study proves an efficient and safe continuous system from synthesis to spherical coating modification of explosives, which provides a new way for the continuous, safe and efficient preparation of spherical explosives.

Degradation and biocompatibility of one-step electrodeposited magnesium thioctic acid/magnesium hydroxide hybrid coatings on ZE21B alloys for cardiovascular stents

Constructing a functional hybrid coating appears to be a promising strategy for addressing the poor corrosion resistance and insufficient endothelialization of Mg-based stents.Nevertheless,the steps for preparing composite coatings are usually complicated and time-consuming.Herein,a novel composite coating,composed of bioactive magnesium thioctic acid(MTA)layer formed by deposition and corrosion-resistant magnesium hydroxide(Mg(OH)_(2))layer grown in situ,is simply fabricated on ZE21B alloys via one-step electrodeposition.Scanning electron microscopy(SEM)shows that the electrodeposited coating has a compact and uniform structure.And the high adhesion of the MTA/Mg(OH)_(2)hybrid coating is also confirmed by the micro-scratch test.Electrochemical test,scanning kelvin probe(SKP),and hydrogen evolution measurement indicate that the hybrid coating effectively reduces the degradation rate of Mg substrates.Haemocompatibility experiment and cell culture trial detect that the composite coating is of fine biocompatibility.Finally,the preparation mechanism of MTA/Mg(OH)_(2)hybrid coatings is discussed and proposed.This coating shows a great potential application for cardiovascular stents.

Study on the effective elastic performance of composites containing decagonal symmetric two-dimensional quasicrystal coatings

On account of the Mori-Tanaka approach,the effective elastic performance of composites containing decagonal symmetric two-dimensional(2D)quasicrystal(QC)coatings is studied.Explicit expressions for the effective elastic constants of rare-earth QC reinforced magnesium-based composites are provided.Detailed discussion is presented on the effects of the volume fraction of the inclusions,the aspect ratio of the inclusions,the coating thickness,and the coating material parameters on the effective elastic constants of the composites.The results indicate that considering the coating increases the effective elastic constants of the composites to some extent.

Effect of chromium on hot corrosion behavior of arc-sprayed NiCr coatings

In this article,NiCr coatings with chromium content of 13%,27%and 41%were prepared by arc spraying.They were exposed in molten salts(NaCl-Na_(2)SO_(4))at 800℃for 200 hours.The effect of chromium content on the hot corrosion behavior of the coatings was in-vestigated.X-ray diffraction(XRD)and scanning electron microscope with energy dispersion spectrum(SEM-EDS)were used to analyze the phase compositions,morphologies and chemical compositions of the coatings.The results show that NiCr13 coating exhibited the worst hot corrosion resistance due to the low chromium content,which resulted in NiO being the major reaction product.It should be noted that the hot corrosion resistance of NiCr27 coating was better than that of NiCr41 coating.The basic fluxing of Cr_(2)O_(3) lowered its protection during the hot corrosion process and led to the formation of porous Cr_(2)O_(3) on the NiCr41 coating.The molten salts accelerated the oxidation reac-tion resulting in thicker and porous oxide scales formed on the surfaces of coatings.

Self-repairing Al_(2)O_(3)-TiO_(2)coatings fabricated through plasma electrolytic oxidation with various cathodic pulse parameters

The influence of cathodic pulse parameters was evaluated on plasma electrolytic oxidation(PEO)coatings grown on 7075 aluminum alloy in a silicate-based electrolyte containing potassium titanyl oxalate(PTO)using pulsed bipolar waveforms with various cathodic duty cycles and cathodic current densities.The coatings were characterized by SEM,EDS,and XRD.EIS was applied to investigate the electrochemical properties.It was observed that the increase of cathodic duty cycle and cathodic current density from 20%and 6 A/dm^(2) to 40%and 12 A/dm^(2) enhances the growth rate of the inner layer from 0.22 to 0.75μm/min.Adding PTO into the bath showed a fortifying effect on influence of the cathodic pulse and the mentioned change of cathodic pulse parameters,resulting in an increase of the inner layer growth rate from 0.25 to 1.10μm/min.Based on EDS analysis,Si and Ti were incorporated dominantly in the upper parts of the coatings.XRD technique merely detectedγ-Al_(2)O_(3),and there were no detectable peaks related to Ti and Si compounds.However,the EIS results confirmed that the incorporation of Ti^(4+)into alumina changed the electronic properties of the coating.The coatings obtained from the bath containing PTO using the bipolar waveforms with a cathodic duty cycle of 40%and current density values higher than 6 A/dm^(2) showed highly appropriate electrochemical behavior during 240 d of immersion due to an efficient repairing mechanism.Regarding the effects of studied parameters on the coating properties,the roles of cathodic pulse parameters and PTO in the PEO process were highlighted.

Effects of plasma spraying process on microstructure and mechanical properties of Cr_(2)AlC/410 composite coatings

To investigate the influences of Cr_(2)AlC mass fraction and supersonic plasma spraying process on the microstructure and mechanical properties of Cr_(2)AlC reinforced 410 stainless steel composite coatings,the coatings containing different mass fractions of Cr_(2)AlC were prepared and investigated.The composite coating exhibited low porosity and high adhesion strength.The addition of Cr_(2)AlC significantly enhanced the hardness of the composite coatings through particle strengthening.However,when the mass fraction of Cr_(2)AlC was 20%,the aggregation of Cr_(2)AlC resulted in a strong decrease in the coating preparation efficiency,as well as a decline in adhesion strength.In the supersonic plasma spraying process,the Ar flow rate mainly influenced the flight velocity of the particles,while the H_(2) flow rate and the current mainly affected the temperature of the plasma torch.Consequently,all of them influenced the melting degree of particles and the quality of the coating.The lowest porosity and the highest hardness and adhesion strength could be obtained when the Ar flow rate is 125 L/min,the H_(2) flow rate is 25 L/min,and the current is 385 A.

Calculation of high-speed abrasion forces for ceramic coatings based on the Hertzian contact model

Aero engine seal coatings can effectively improve the air tightness of aircraft engines and increase fuel efficiency.However,due to the frictional forces between the blades and the coating,the coating often flakes off,resulting in damage to the blades and causing eco-nomic losses.Therefore,it is necessary to analyze the friction between the blades and the coating.In this paper,three ceramic-based high-temperature seal coatings with different polyphenylene ester contents and a pure Yttria-stabilised zirconia coating were prepared by atmo-spheric plasma spraying(APS).The hardness and modulus of elasticity of the coated surfaces were obtained by hardness and modulus of elasticity tests,and the coatings were subjected to high-speed touch abrasion tests.The Hertzian contact model was used to calculate the maximum normal contact load on the coating during the process.The test values were compared with the theoretical values and it was found that the calculated values were always greater than the test values.In order to make the Hertzian contact model more accurate in calculating the touching and abrasion forces,the contact coefficients in the Hertzian contact model were optimized.Substituting the optimized coeffi-cients into the Hertzian contact model,the results show that the calculated results after optimizing the coefficients are much closer to the test values,with deviations from the test values ranging from 1%to 38%.