Short-range ordering(SRO)is one of the most important structural features of high entropy alloys(HEAs).However,the chemical and structural analyses of SROs are very difficult due to their small size,complexed composit...Short-range ordering(SRO)is one of the most important structural features of high entropy alloys(HEAs).However,the chemical and structural analyses of SROs are very difficult due to their small size,complexed compositions,and varied locations.Transmission electron microscopy(TEM)as well as its aberration correction techniques are powerful for characterizing SROs in these compositionally complex alloys.In this short communication,we summarized recent progresses regarding characterization of SROs using TEM in the field of HEAs.By using advanced TEM techniques,not only the existence of SROs was confirmed,but also the effect of SROs on the deformation mechanism was clarified.Moreover,the perspective related to application of TEM techniques in HEAs are also discussed.展开更多
The high entropy alloys(HEAs)are the newly developed high-performance materials that have gained significant importance in defence,nuclear and aerospace sector due to their superior mechanical properties,heat resistan...The high entropy alloys(HEAs)are the newly developed high-performance materials that have gained significant importance in defence,nuclear and aerospace sector due to their superior mechanical properties,heat resistance,high temperature strength and corrosion resistance.These alloys are manufactured by the equal mixing or larger proportions of five or more alloying elements.HEAs exhibit superior mechanical performance compared to traditional engineering alloys because of the extensive alloying composition and higher entropy of mixing.Solid state welding(SSW)techniques such as friction stir welding(FSW),rotary friction welding(RFW),diffusion bonding(DB)and explosive welding(EW)have been efficiently deployed for improving the microstructural integrity and mechanical properties of welded HEA joints.The HEA interlayers revealed greater potential in supressing the formation of deleterious intermetallic phases and maximizing the mechanical properties of HEAs joints.The similar and dissimilar joining of HEAs has been manifested to be viable for HEA systems which further expands their industrial applications.Thus,the main objective of this review paper is to present a critical review of current state of research,challenges and opportunities and main directions in SSW of HEAs mainly CoCrFeNiMn and Al_xCoCrFeNi alloys.The state of the art of problems,progress and future outlook in SSW of HEAs are critically reviewed by considering the formation of phases,microstructural evolution and mechanical properties of HEAs joints.展开更多
W-based WTaVCr refractory high entropy alloys (RHEA) may be novel and promising candidate materials for plasma facing components in the first wall and diverter in fusion reactors. This alloy has been developed by a po...W-based WTaVCr refractory high entropy alloys (RHEA) may be novel and promising candidate materials for plasma facing components in the first wall and diverter in fusion reactors. This alloy has been developed by a powder metallurgy process combining mechanical alloying and spark plasma sintering (SPS). The SPSed samples contained two phases, in which the matrix is RHEA with a body-centered cubic structure, while the oxide phase was most likely Ta2VO6through a combined analysis of X-ray diffraction (XRD),energy-dispersive spectroscopy (EDS), and selected area electron diffraction (SAED). The higher oxygen affinity of Ta and V may explain the preferential formation of their oxide phases based on thermodynamic calculations. Electron backscatter diffraction (EBSD) revealed an average grain size of 6.2μm. WTaVCr RHEA showed a peak compressive strength of 2997 MPa at room temperature and much higher micro-and nano-hardness than W and other W-based RHEAs in the literature. Their high Rockwell hardness can be retained to at least 1000°C.展开更多
High entropy alloys usually show good weldability.The weldability problems of high entropy alloys are segregation,cracks,and hardening or softening of weld,etc.When an Al_(x)CoCrFeNi alloy is welded,Al and Ni will seg...High entropy alloys usually show good weldability.The weldability problems of high entropy alloys are segregation,cracks,and hardening or softening of weld,etc.When an Al_(x)CoCrFeNi alloy is welded,Al and Ni will segregate to the interdendritic region in the weld,but the degree of segregation is less than that of the base metal.When an Al_(x)CoCrCu_(x)FeNi alloy or a CoCrCu_(x)FeNi alloy is welded,Cu tends to segregate to the interdendritic region in the weld.Increasing the cooling rate of the welding process,such as with laser welding,is conducive to reducing the segregation in the weld.The segregation in the weld and the heat affected zone,especially the segregation of Cu,will lead to the generation of hot cracks.Hot cracking is the main form of cracking in high entropy alloys joints.Welding will lead to changes in the hardness of the weld.The main factors affecting the hardness change are the grain sizes and the precipitations.With laser welding,if the base metal is cold rolled,the hardness of the weld will decrease.If the base metal is hot rolled and annealed or cast,the hardness of the weld will increase.With TIG welding,the hardness of the weld is usually lower than that of the base metal,unless the grain of the base metal is particularly coarse before welding.With friction stir welding,recrystallization and grain refinement occur in the stir zone,and the hardness of the stir zone will be significantly improved no matter the original base metal is cold rolled or cast.展开更多
FeNiCrCoSi_(x) and FeNiCrCoTi_(x)(x=0,0.3,0.6,and 0.9 wt.%)high entropy alloys(HEAs)were prepared via the powder metallurgy technique.A homogenous distribution of the elements in all alloys due to the formation of a s...FeNiCrCoSi_(x) and FeNiCrCoTi_(x)(x=0,0.3,0.6,and 0.9 wt.%)high entropy alloys(HEAs)were prepared via the powder metallurgy technique.A homogenous distribution of the elements in all alloys due to the formation of a solid solution phase is observed.The density and hardness of the prepared HEAs are improved by Si and Ti additions,compared to FeNiCrCo HEA.The wear rate of the prepared alloys was studied at different loads and the results indicate that the alloys that contain 0.3 wt.%Si and 0.9 wt.%Ti have the lowest wear rates.X-ray diffraction,SEM,and EDX were used to understand the phases,grain sizes,and microstructures in different investigated HEAs.The effects of Si and Ti content on the corrosion behavior and surface morphologies of sintered FeNiCrCoSi_(x) and FeNiCrCoTi_(x) HEAs were studied by immersion in H_(2)SO_(4),HNO_(3),and HCl solutions.Uniform corrosion and localized pitting are observed in different sizes in the corrosive media used.Because of the smaller pit size and the reduced pit density,the FeNiCrCoSi_(0.3) HEA has an excellent microstructure.展开更多
High entropy alloys(HEAs)possess good mechanical properties and a wide range of industrial applications.In this paper,phase formation prediction theory,microstructure,properties and preparation methods of light-weight...High entropy alloys(HEAs)possess good mechanical properties and a wide range of industrial applications.In this paper,phase formation prediction theory,microstructure,properties and preparation methods of light-weight HEAs(LWHEAs)were reviewed.The problems and challenges faced by LWHEAs development were analyzed.The results showed that many aspects are still weak and require investigation for future advanced alloys,such as clarification of the role of entropy in phase formation and properties of HEAs,improved definition and different generations division of HEAs,close-packed hexagonal(HCP)phase structure prediction and corresponding alloy design and fabrication.Finally,some suggestions were presented in this paper including in-depth research on formation mechanism of multi-component alloy phase and strengthening of large-scale HEA preparation methods via technology compounding and 3D printing technology.Also,there is a need for more research on the in-situ preparation of HEA coatings and films,as well as developing LWHEAs with superior strength and elevated temperature resistance or ultra-low temperature resistance to meet the requirements of future engineering applications.展开更多
High entropy alloys(HEAs)with multi-component solid solution microstructures have the potential for large-scale industrial applications due to their excellent mechanical and functional properties.However,the mechanica...High entropy alloys(HEAs)with multi-component solid solution microstructures have the potential for large-scale industrial applications due to their excellent mechanical and functional properties.However,the mechanical properties of HEAs limit the selection of processing technologies.Additive manufacturing technology possesses strong processing adaptability,making itthe best candidate method to overcome this issue.This comprehensive review examines the current state of selective laser melting(SLM)of HEAs.Introducing SLM to HEAs processing is motivated by its high quality for dimensional accuracy,geometric complexity,surface roughness,and microstructure.This review focuses on analyzing the current developments and challenges in SLM of HEAs,including defects,microstructures,and properties,as well as strengthing prediction models of fabricated HEAs.This review also offers directions for future studies to address existing challenges and promote technological advancement.展开更多
Effects of Ti addition on the microstructures and mechanical properties of AICrFeNiMo0.5 Tix (x = 0, 0.25, 0.4, 0.5, 0.6, 0.75) high entropy alloys (HEAs) are investigated. All these HEAs of various Ti contents po...Effects of Ti addition on the microstructures and mechanical properties of AICrFeNiMo0.5 Tix (x = 0, 0.25, 0.4, 0.5, 0.6, 0.75) high entropy alloys (HEAs) are investigated. All these HEAs of various Ti contents possess dual BCC structures, indicating that Ti addition does not induce the formation of any new phase in these alloys. As Ti addition x varies from 0 to 0.75, the Vickers hardness (HV) of the alloy system increases from 623.7HV to 766.2HV, whereas the compressive yield stress firstly increases and then decreases with increasing x above 0.5. Meanwhile, the compressive ductility of the alloy system decreases with Ti addition. The AlCrFeNiMo0.5 Ti0.6 and AlCrFeNiMo0.5Ti0.75 HEAs become brittle and fracture with very limited plasticity. In the AlCrFeNiMo0.5Tix HEAs, the AlCrFeNiMoo.5 HEA possesses the highest compressive fracture strength of 4027 MPa and the largest compressive plastic strain of 27.9%, while the AlCrFeNiMo0.5 Ti0.5 HEA has the highest compressive yield strength of 2229 MPa and a compressive plastic strain of 10.1%. The combination of high strength and large plasticity of the AICrFeNiMoo.sTix (x = 0, 0.25, 0.4, 0.5) HEAs demonstrates that this alloy system is very promising for engineering applications.展开更多
Refractory high entropy alloys have superior mechanical properties at high temperatures, and the oxidation behavior of these alloys is very important. The present work investigated the high temperature oxidation behav...Refractory high entropy alloys have superior mechanical properties at high temperatures, and the oxidation behavior of these alloys is very important. The present work investigated the high temperature oxidation behavior of three alloys with compositions of TiNbTa0.5Zr, TiNbTa0.5ZrAl and TiNbTa0.5ZrAlMo0.5, and the effects of alloying elements were discussed. Results indicated that the oxidation rates of the TiNbTa0.5Zr and TiNbTa0.5ZrAl alloys are controlled by diffusion, and obey the exponential rule. However, the oxidation rate of the TiNbTa0.5ZrAlMo0.5 alloy is controlled by interface reaction, and obeys the linear rule. The addition of Al leads to a better oxidation resistance by forming a protective oxide scale. However, the protection of Al-rich scale is weakened by the addition of Mo. Extensive pores and cracks occur in the oxide scale of the TiNbTa0.5ZrAlMo0.5 alloy, resulting in a significant decrease in oxidation resistance.展开更多
To study the effects of La on the microstructure and mechanical properties of refractory high entropy alloys,NbMoTiVSi0.2 alloys with different La contents were prepared.Phase constitution,microstructure evolution,com...To study the effects of La on the microstructure and mechanical properties of refractory high entropy alloys,NbMoTiVSi0.2 alloys with different La contents were prepared.Phase constitution,microstructure evolution,compressive properties and related mechanisms were systematically studied.Results show that the alloys with La addition are composed of BCC solid solution,eutectic structure,MSi2 disilicide phase and La-containing precipitates.Eutectic structure and most of La precipitates are formed at the grain boundaries.Disilicide phase is formed in the grains.La can change the grain morphologies from dendritic structure to near-equiaxed structure,and the average grain size decreases from 180 to 20μm with the increase of La content from 0 to 0.5 at.%.Compressive testing shows that the ultimate strength and the yield strength increase with the increase of La content,which is resulted from the grain boundary strengthening.However,they cannot be greatly improved because of the formation of MSi2 disilicide phase with low strength.The ductility decreases with the increase of La content,which is due to the La precipitates and brittle MSi2 disilicide phase.展开更多
Owing to superior comprehensive performance than conventional superalloys at high temperature,refractory high entropy alloy(RHEA)is becoming a promising candidate for the next generation high-temperature material.Here...Owing to superior comprehensive performance than conventional superalloys at high temperature,refractory high entropy alloy(RHEA)is becoming a promising candidate for the next generation high-temperature material.Herein,contemporary aspects of corresponding development of RHEAs are reviewed to discuss various factors affecting the organization structure and service performance.It mainly covers alloying system and strengthening mechanism,the preparation method,plastic deformation and the related mechanism,as well as microstructure control by heat treatment.Firstly,the alloy systems and strengthening mechanism are introduced.This is followed by different preparation methods and the comparison of strengths and shortcomings based on different RHEAs.Then,hot deformation behavior and plastic deformation under different loadings are analyzed.Based on this,the influence of heat treatment on microstructures prior to and after the deformation is further summarized.Finally,some important research areas to be carried out in future are pointed out.This review will give a deep understanding of the effects of different factors on the service performance and provide scientific guide in designing RHEAs with improved performance.展开更多
High entropy alloys(HEAs)attract remarkable attention due to the excellent mechanical performance.However,the origins of their high strength and toughness compared with those of the traditional alloys are still hardly...High entropy alloys(HEAs)attract remarkable attention due to the excellent mechanical performance.However,the origins of their high strength and toughness compared with those of the traditional alloys are still hardly revealed.Here,using a microstructure-based constitutive model and molecular dynamics(MD)simulation,we investigate the unique mechanical behavior and microstructure evolution of FeCoCrNiCu HEAs during the indentation.Due to the interaction between the dislocation and solution,the high dislocation density in FeCoCrNiCu leads to strong work hardening.Plentiful slip systems are stimulated,leading to the good plasticity of FeCoCrNiCu.The plastic deformation of FeCoCrNiCu is basically affected by the motion of dislocation loops.The prismatic dislocation loops inside FeCoCrNiCu are formed by the dislocations with the Burgers vectors of a/6[112]and a/6[112],which interact with each other,and then emit along the<111>slip direction.In addition,the mechanical properties of FeCoCrNiCu HEA can be predicted by constructing the microstructure-based constitutive model,which is identified according to the evolution of the dislocation density and the stress-strain curve.Strong dislocation strengthening and remarkable lattice distortion strengthening occur in the deformation process of FeCoCrNiCu,and improve the strength.Therefore,the origins of high strength and high toughness in FeCoCrNiCu HEAs come from lattice distortion strengthening and the more activable slip systems compared with Cu.These results accelerate the discovery of HEAs with excellent mechanical properties,and provide a valuable reference for the industrial application of HEAs.展开更多
Here, the composition of TaMoNbZrTiAl refractory high entropy alloy (RHEA) is optimized by increasing Ti content to improve its mechanical property especially the ductility, through comparing two RHEAs with different ...Here, the composition of TaMoNbZrTiAl refractory high entropy alloy (RHEA) is optimized by increasing Ti content to improve its mechanical property especially the ductility, through comparing two RHEAs with different Ti content. The RHEAs contain two body-centered-cubic (BCC) phases. The BCC phase in the dendritic region is rich in Ta, Mo and Nb, and the BCC phase in the interdendritic region is enriched in Zr, Ti and Al. The as-cast RHEA with a higher Ti content remains dendritic microstructures, and Ti is mainly enriched in the interdendritic region. After annealing treatment at 1300 ℃ for 48 h, the dendritic microstructures change into equiaxed-grain morphology, accompanied by needle-like micron precipitates at grain boundaries in the RHEA with higher Ti content. For the as-cast RHEAs, the fracture strain increases by ~ 6.6% and the uniform plastic strain increases by ~ 5.9% at the compression test due to the increase of Ti content. Our work offers a reference for the composition design of RHEAs and makes a preliminary exploration of the optimization of the microstructures and mechanical properties.展开更多
The effect of Mn element on shock response of CoCrFeNiMnx high entropy alloys(HEAs)are investigated using molecular dynamics simulations.Structural analysis shows that Mn-rich CoCrFeNiMnx HEA has a larger average atom...The effect of Mn element on shock response of CoCrFeNiMnx high entropy alloys(HEAs)are investigated using molecular dynamics simulations.Structural analysis shows that Mn-rich CoCrFeNiMnx HEA has a larger average atomic volume.The elastic properties of CoCrFeNiMnx HEAs under various hydrostatic pressures are studied,revealing that the elastic modulus decreases with increasing of Mn content.The shock thermodynamic parameters are quantitatively analyzed.The Mn-dependent shock Hugoniot relationship of CoCrFeNiMnx HEAs is obtained:Us=1.25+(5.21–0.011x)Up.At relatively high shock pressure,the increase in Mn content promotes the formation of clustered BCC structures and hinders the development of dislocations.In addition,more FCC structures in Mn-rich CoCrFeNiMnx HEAs transform into disordered structures during spallation.Spall strength decreases with increasing Mn content.This study can provide a reference for the design and application of CoCrFeNiMn HEAs under shock loading.展开更多
High-entropy alloys(HEAs)are a promising solution for large-scale hydrogen storage(H-storage)and are therefore receiving increasing attention from the materials science community.In this study,we systematically invest...High-entropy alloys(HEAs)are a promising solution for large-scale hydrogen storage(H-storage)and are therefore receiving increasing attention from the materials science community.In this study,we systematically investigated the microstructures and H-storage properties of V_(35)Ti_(35)Cr_(10) Fe_(10)M_(10)(M=Mn,Co,Sc,or Ni)HEAs prepared by arcmelting.The cast HEAs were found to be nanocrystalline.The crystal lattice parameters and hydrogen absorption energies of the alloys were calculated using density functional theory(DFT)calculations.The alloys can be fully activated in just one cycle of hydrogen absorption/desorption under mild conditions,after which they reach hydrogen absorption saturation in approximately 100 s at ambient temperature.The hydrogenation kinetics of the HEAs are approximately five times higher than that of conventional solid-solution alloys with a body-centered cubic(BCC)structure.By performing in-situ hydriding differential scanning calorimetry in combination with DFT calculations,we revealed that the alloys are more susceptible to hydrogenation than traditional BCC structural alloys.The H-storage capacity of V_(35)Ti_(35)Cr_(10) Fe_(10)M_(10) alloys at ambient temperature was higher than that of HEAs reported in the literature.Quasi-in-situ X-ray diffraction characterization of the HEAs’hydrogenation revealed a phase transition process from a BCC to facecentered cubic,passing through a pseudo-BCC structure.Our work introduces a new perspective for designing alloys with ultrafast hydrogen absorption kinetics and high capacity for large-scale,room-temperature-applicable H-storage.展开更多
To enhance the microbiologically influenced corrosion(MIC)resistance of FeCoNiCrMn high entropy alloy(HEAs),a series of Fe_(x)Cu_((1−x))CoNiCrMn(x=1,0.75,0.5,and 0.25)HEAs were prepared.Microstructural characteristics...To enhance the microbiologically influenced corrosion(MIC)resistance of FeCoNiCrMn high entropy alloy(HEAs),a series of Fe_(x)Cu_((1−x))CoNiCrMn(x=1,0.75,0.5,and 0.25)HEAs were prepared.Microstructural characteristics,corrosion behavior(morphology observation and electrochemical properties),and antimicrobial performance of Fe_(x)Cu_((1−x))CoNiCrMn HEAs were evaluated in a medium inoculated with typical corrosive microorganism Pseudomonas aeruginosa.The aim was to identify copper-containing FeCoNiCrMn HEAs that balance corrosion resistance and antimicrobial properties.Results revealed that all Fe_(x)Cu_((1−x))CoNiCrMn(x=1,0.75,0.5,and 0.25)HEAs exhibited an FCC(face centered cubic)phase,with significant grain refinement observed in Fe_(0.75)Cu_(0.25)CoNiCrMn HEA.Electrochemical tests indicated that Fe_(0.75)Cu_(0.25)CoNiCrMn HEA demonstrated lower corrosion current density(i_(corr))and pitting potential(E_(pit))compared to other Fe_(x)Cu_((1−x))CoNiCrMn HEAs in P.aeruginosa-inoculated medium,exhibiting superior resistance to MIC.Anti-microbial tests showed that after 14 d of immersion,Fe_(0.75)Cu_(0.25)CoNiCrMn achieved an antibacterial rate of 89.5%,effectively inhibiting the adhesion and biofilm formation of P.aeruginosa,thereby achieving resistance to MIC.展开更多
High entropy alloys(HEAs),especially refractory HEAs,have become a subject of interest in the past years due to their exceptional properties in terms of high-temperature strength,corrosion resistance,radiation toleran...High entropy alloys(HEAs),especially refractory HEAs,have become a subject of interest in the past years due to their exceptional properties in terms of high-temperature strength,corrosion resistance,radiation tolerance,etc.under extreme environments.While the phase formation of these alloys significantly affects their properties.If the phase of HEAs can be forecasted before the experiments,the material design process can be greatly accelerated.The phase formation study of HEAs mainly relied on trial-and-error experiments and multi-scale computational simulations such as calculation of phase diagrams(CALPHAD) and density functional theory(DFT).However,those methods require massive time,man-power,and resources.As a highly efficient tool,machine learning(ML) method has been developed and applied to predict the phase formation of HEAs very recently.This review provided a comprehensive overview and analysis of the most recent research work in this area.First,we introduce ML methodologies applied in HEAs’ phase prediction in terms of principles,database,algorithm,and validation.We then summarize recent applications of the ML method in the phase prediction of HEAs.In the end,we propose possible solutions to the current problems and future research pathways for various challenges in the phase prediction of HEAs using ML.展开更多
A mathematical formula of high physical interpretation,and accurate prediction and large generaliza-tion power is highly desirable for science,technology and engineering.In this study,we performed a domain knowledge-g...A mathematical formula of high physical interpretation,and accurate prediction and large generaliza-tion power is highly desirable for science,technology and engineering.In this study,we performed a domain knowledge-guided machine learning to discover high interpretive formula describing the high-temperature oxidation behavior of FeCrAlCoNi-based high entropy alloys(HEAs).The domain knowledge suggests that the exposure time dependent and thermally activated oxidation behavior can be described by the synergy formula of power law multiplying Arrhenius equation.The pre-factor,time exponent(m),and activation energy(Q)are dependent on the chemical compositions of eight elements in the FeCrAlCoNi-based HEAs.The Tree-Classifier for Linear Regression(TCLR)algorithm utilizes the two exper-imental features of exposure time(t)and temperature(T)to extract the spectrums of activation energy(Q)and time exponent(m)from the complex and high dimensional feature space,which automatically gives the spectrum of pre-factor.The three spectrums are assembled by using the element features,which leads to a general and interpretive formula with high prediction accuracy of the determination coefficient R^(2)=0.971.The role of each chemical element in the high-temperature oxidation behavior is analytically illustrated in the three spectrums,thereby the discovered interpretative formula provides a guidance to the inverse design of HEAs against high-temperature oxidation.The present work demonstrates the sig-nificance of domain knowledge in the development of materials informatics.展开更多
Herein,we trained machine learning(ML)model to quickly and accurately conduct the strength prediction of refractory high entropy alloys(RHEAs)matrix.Gradient Boosting(GB)regression model shows an outstanding performan...Herein,we trained machine learning(ML)model to quickly and accurately conduct the strength prediction of refractory high entropy alloys(RHEAs)matrix.Gradient Boosting(GB)regression model shows an outstanding performance against other ML models.In addition,the heat of fusion and atomic size difference is shown to be paramount to the strength of the high entropy alloys(HEAs)matrix.In addition,we discussed the contribution of each feature to the solid solution strengthening(SSS)of HE As.The excellent predictive accuracy shows that the GB model can be efficient and reliable for the design of RHEAs with desired strength.展开更多
Searching for single-phase solid solutions(SPSSs)in high-entropy alloys(HEAs)is a prerequisite for the intentional design and manipulation of microstructures of alloys in vast composition space.However,to date,reporte...Searching for single-phase solid solutions(SPSSs)in high-entropy alloys(HEAs)is a prerequisite for the intentional design and manipulation of microstructures of alloys in vast composition space.However,to date,reported SPSS HEAs are still rare due to the lack of reliable guiding principles for the synthesis of new SPSS HEAs.Here,we demonstrate an ensemble machine-learning method capable of discovering SPSS HEAs by directly predicting quinary phase diagrams based only on atomic composition.A total of 2198 experimental structure data are extracted from as-sputtered quinary HEAs in the literature and used to train a random forest classifier(termed AS-RF)utilizing bagging,achieving a prediction accuracy of 94.6%compared with experimental results.The AS-RF model is then utilized to predict 224 quinary phase diagrams including∼32,000 SPSS HEAs in Cr-Co-Fe-Ni-Mn-Cu-Al composition space.The extrapolation capability of the AS-RF model is then validated by performing first-principle calculations using density functional theory as a benchmark for the predicted phase transition of newly predicted HEAs.Finally,interpretation of the AS-RF model weighting of the input parameters also sheds light on the driving forces behind HEA formation in sputtered systems with the main contributors being:valance electron concentration,work function,atomic radius difference and elementary symmetries.展开更多
基金financially supported by the National Natural Science Foundation of China(Nos.51971017,52271003,52071024,52001184,and 52101188)the National Science Fund for distinguished Young Scholars,China(No.52225103)+3 种基金the Funds for Creative Research Groups of China(No.51921001)the National Key Research and Development Program of China(No.2022YFB4602101)the Projects of International Cooperation and Exchanges NSFC(No.52061135207)the Fundamental Research Funds for the Central Universities,China(No.FRF-TP-22-130A1)。
文摘Short-range ordering(SRO)is one of the most important structural features of high entropy alloys(HEAs).However,the chemical and structural analyses of SROs are very difficult due to their small size,complexed compositions,and varied locations.Transmission electron microscopy(TEM)as well as its aberration correction techniques are powerful for characterizing SROs in these compositionally complex alloys.In this short communication,we summarized recent progresses regarding characterization of SROs using TEM in the field of HEAs.By using advanced TEM techniques,not only the existence of SROs was confirmed,but also the effect of SROs on the deformation mechanism was clarified.Moreover,the perspective related to application of TEM techniques in HEAs are also discussed.
基金financially supported by Ministry of Science and Higher Education of the Russian Federation(Grant No.FENU-2023-0013)。
文摘The high entropy alloys(HEAs)are the newly developed high-performance materials that have gained significant importance in defence,nuclear and aerospace sector due to their superior mechanical properties,heat resistance,high temperature strength and corrosion resistance.These alloys are manufactured by the equal mixing or larger proportions of five or more alloying elements.HEAs exhibit superior mechanical performance compared to traditional engineering alloys because of the extensive alloying composition and higher entropy of mixing.Solid state welding(SSW)techniques such as friction stir welding(FSW),rotary friction welding(RFW),diffusion bonding(DB)and explosive welding(EW)have been efficiently deployed for improving the microstructural integrity and mechanical properties of welded HEA joints.The HEA interlayers revealed greater potential in supressing the formation of deleterious intermetallic phases and maximizing the mechanical properties of HEAs joints.The similar and dissimilar joining of HEAs has been manifested to be viable for HEA systems which further expands their industrial applications.Thus,the main objective of this review paper is to present a critical review of current state of research,challenges and opportunities and main directions in SSW of HEAs mainly CoCrFeNiMn and Al_xCoCrFeNi alloys.The state of the art of problems,progress and future outlook in SSW of HEAs are critically reviewed by considering the formation of phases,microstructural evolution and mechanical properties of HEAs joints.
基金supported by the National Science Foundation under Grant No.CMMI-1762190The research was performed in part in the Nebraska Nanoscale Facility:National Nanotechnology Coordinated Infrastructure and the Nebraska Center for Materials and Nanoscience (and/or NERCF),which are supported by the National Science Foundation under Award ECCS:2025298+1 种基金the Nebraska Research Initiativesupported by the U.S.Department of Energy,Office of Nuclear Energy under DOE Idaho Operations Office Contract DE-AC07-051D14517 as part of a Nuclear Science User Facilities experiment。
文摘W-based WTaVCr refractory high entropy alloys (RHEA) may be novel and promising candidate materials for plasma facing components in the first wall and diverter in fusion reactors. This alloy has been developed by a powder metallurgy process combining mechanical alloying and spark plasma sintering (SPS). The SPSed samples contained two phases, in which the matrix is RHEA with a body-centered cubic structure, while the oxide phase was most likely Ta2VO6through a combined analysis of X-ray diffraction (XRD),energy-dispersive spectroscopy (EDS), and selected area electron diffraction (SAED). The higher oxygen affinity of Ta and V may explain the preferential formation of their oxide phases based on thermodynamic calculations. Electron backscatter diffraction (EBSD) revealed an average grain size of 6.2μm. WTaVCr RHEA showed a peak compressive strength of 2997 MPa at room temperature and much higher micro-and nano-hardness than W and other W-based RHEAs in the literature. Their high Rockwell hardness can be retained to at least 1000°C.
文摘High entropy alloys usually show good weldability.The weldability problems of high entropy alloys are segregation,cracks,and hardening or softening of weld,etc.When an Al_(x)CoCrFeNi alloy is welded,Al and Ni will segregate to the interdendritic region in the weld,but the degree of segregation is less than that of the base metal.When an Al_(x)CoCrCu_(x)FeNi alloy or a CoCrCu_(x)FeNi alloy is welded,Cu tends to segregate to the interdendritic region in the weld.Increasing the cooling rate of the welding process,such as with laser welding,is conducive to reducing the segregation in the weld.The segregation in the weld and the heat affected zone,especially the segregation of Cu,will lead to the generation of hot cracks.Hot cracking is the main form of cracking in high entropy alloys joints.Welding will lead to changes in the hardness of the weld.The main factors affecting the hardness change are the grain sizes and the precipitations.With laser welding,if the base metal is cold rolled,the hardness of the weld will decrease.If the base metal is hot rolled and annealed or cast,the hardness of the weld will increase.With TIG welding,the hardness of the weld is usually lower than that of the base metal,unless the grain of the base metal is particularly coarse before welding.With friction stir welding,recrystallization and grain refinement occur in the stir zone,and the hardness of the stir zone will be significantly improved no matter the original base metal is cold rolled or cast.
文摘FeNiCrCoSi_(x) and FeNiCrCoTi_(x)(x=0,0.3,0.6,and 0.9 wt.%)high entropy alloys(HEAs)were prepared via the powder metallurgy technique.A homogenous distribution of the elements in all alloys due to the formation of a solid solution phase is observed.The density and hardness of the prepared HEAs are improved by Si and Ti additions,compared to FeNiCrCo HEA.The wear rate of the prepared alloys was studied at different loads and the results indicate that the alloys that contain 0.3 wt.%Si and 0.9 wt.%Ti have the lowest wear rates.X-ray diffraction,SEM,and EDX were used to understand the phases,grain sizes,and microstructures in different investigated HEAs.The effects of Si and Ti content on the corrosion behavior and surface morphologies of sintered FeNiCrCoSi_(x) and FeNiCrCoTi_(x) HEAs were studied by immersion in H_(2)SO_(4),HNO_(3),and HCl solutions.Uniform corrosion and localized pitting are observed in different sizes in the corrosive media used.Because of the smaller pit size and the reduced pit density,the FeNiCrCoSi_(0.3) HEA has an excellent microstructure.
基金Funded by the National Natural Science Foundation of China(No.51405510)。
文摘High entropy alloys(HEAs)possess good mechanical properties and a wide range of industrial applications.In this paper,phase formation prediction theory,microstructure,properties and preparation methods of light-weight HEAs(LWHEAs)were reviewed.The problems and challenges faced by LWHEAs development were analyzed.The results showed that many aspects are still weak and require investigation for future advanced alloys,such as clarification of the role of entropy in phase formation and properties of HEAs,improved definition and different generations division of HEAs,close-packed hexagonal(HCP)phase structure prediction and corresponding alloy design and fabrication.Finally,some suggestions were presented in this paper including in-depth research on formation mechanism of multi-component alloy phase and strengthening of large-scale HEA preparation methods via technology compounding and 3D printing technology.Also,there is a need for more research on the in-situ preparation of HEA coatings and films,as well as developing LWHEAs with superior strength and elevated temperature resistance or ultra-low temperature resistance to meet the requirements of future engineering applications.
基金This research is financially supported by the National Key Research and Development Program of China(Grant Nos.2017YFB1103900 and 2018YFB1107701)the Fundamental Research Funds for the Central Universities(Grant No.2042019kf0015)+1 种基金the Key R&D projects of Sichuan Province(Grant No.2020YFSY0054)the National Natural Science Foundation of China(Grant No.51605343).
文摘High entropy alloys(HEAs)with multi-component solid solution microstructures have the potential for large-scale industrial applications due to their excellent mechanical and functional properties.However,the mechanical properties of HEAs limit the selection of processing technologies.Additive manufacturing technology possesses strong processing adaptability,making itthe best candidate method to overcome this issue.This comprehensive review examines the current state of selective laser melting(SLM)of HEAs.Introducing SLM to HEAs processing is motivated by its high quality for dimensional accuracy,geometric complexity,surface roughness,and microstructure.This review focuses on analyzing the current developments and challenges in SLM of HEAs,including defects,microstructures,and properties,as well as strengthing prediction models of fabricated HEAs.This review also offers directions for future studies to address existing challenges and promote technological advancement.
基金Supported by the National Natural Science Foundation of China under Grant No 51571127
文摘Effects of Ti addition on the microstructures and mechanical properties of AICrFeNiMo0.5 Tix (x = 0, 0.25, 0.4, 0.5, 0.6, 0.75) high entropy alloys (HEAs) are investigated. All these HEAs of various Ti contents possess dual BCC structures, indicating that Ti addition does not induce the formation of any new phase in these alloys. As Ti addition x varies from 0 to 0.75, the Vickers hardness (HV) of the alloy system increases from 623.7HV to 766.2HV, whereas the compressive yield stress firstly increases and then decreases with increasing x above 0.5. Meanwhile, the compressive ductility of the alloy system decreases with Ti addition. The AlCrFeNiMo0.5 Ti0.6 and AlCrFeNiMo0.5Ti0.75 HEAs become brittle and fracture with very limited plasticity. In the AlCrFeNiMo0.5Tix HEAs, the AlCrFeNiMoo.5 HEA possesses the highest compressive fracture strength of 4027 MPa and the largest compressive plastic strain of 27.9%, while the AlCrFeNiMo0.5 Ti0.5 HEA has the highest compressive yield strength of 2229 MPa and a compressive plastic strain of 10.1%. The combination of high strength and large plasticity of the AICrFeNiMoo.sTix (x = 0, 0.25, 0.4, 0.5) HEAs demonstrates that this alloy system is very promising for engineering applications.
基金Project(51671217)supported by the National Natural Science Foundation of ChinaProject(CX2017B047)supported by the Program of Innovation for Postgraduate of Hunan Province,China
文摘Refractory high entropy alloys have superior mechanical properties at high temperatures, and the oxidation behavior of these alloys is very important. The present work investigated the high temperature oxidation behavior of three alloys with compositions of TiNbTa0.5Zr, TiNbTa0.5ZrAl and TiNbTa0.5ZrAlMo0.5, and the effects of alloying elements were discussed. Results indicated that the oxidation rates of the TiNbTa0.5Zr and TiNbTa0.5ZrAl alloys are controlled by diffusion, and obey the exponential rule. However, the oxidation rate of the TiNbTa0.5ZrAlMo0.5 alloy is controlled by interface reaction, and obeys the linear rule. The addition of Al leads to a better oxidation resistance by forming a protective oxide scale. However, the protection of Al-rich scale is weakened by the addition of Mo. Extensive pores and cracks occur in the oxide scale of the TiNbTa0.5ZrAlMo0.5 alloy, resulting in a significant decrease in oxidation resistance.
基金The authors are grateful for the financial supports from the National Natural Science Foundation of China(51825401 and 52001114)the State Key Laboratory of Materials Processing and Die&Mould Technology(P2020-023)the Guangdong Introducing Innovative and Entrepreneurial Teams,China(2016ZT06G025).
文摘To study the effects of La on the microstructure and mechanical properties of refractory high entropy alloys,NbMoTiVSi0.2 alloys with different La contents were prepared.Phase constitution,microstructure evolution,compressive properties and related mechanisms were systematically studied.Results show that the alloys with La addition are composed of BCC solid solution,eutectic structure,MSi2 disilicide phase and La-containing precipitates.Eutectic structure and most of La precipitates are formed at the grain boundaries.Disilicide phase is formed in the grains.La can change the grain morphologies from dendritic structure to near-equiaxed structure,and the average grain size decreases from 180 to 20μm with the increase of La content from 0 to 0.5 at.%.Compressive testing shows that the ultimate strength and the yield strength increase with the increase of La content,which is resulted from the grain boundary strengthening.However,they cannot be greatly improved because of the formation of MSi2 disilicide phase with low strength.The ductility decreases with the increase of La content,which is due to the La precipitates and brittle MSi2 disilicide phase.
基金National Natural Science Foundation of China(Grant Nos.U2141205,51775525,52175369,52005465,52025041 and 52174294)Fast Support Program(Grant No.80923020405)Beijing Nova Program from Beijing Municipal Science&Technology Commission(Grant No.Z201100006820094).
文摘Owing to superior comprehensive performance than conventional superalloys at high temperature,refractory high entropy alloy(RHEA)is becoming a promising candidate for the next generation high-temperature material.Herein,contemporary aspects of corresponding development of RHEAs are reviewed to discuss various factors affecting the organization structure and service performance.It mainly covers alloying system and strengthening mechanism,the preparation method,plastic deformation and the related mechanism,as well as microstructure control by heat treatment.Firstly,the alloy systems and strengthening mechanism are introduced.This is followed by different preparation methods and the comparison of strengths and shortcomings based on different RHEAs.Then,hot deformation behavior and plastic deformation under different loadings are analyzed.Based on this,the influence of heat treatment on microstructures prior to and after the deformation is further summarized.Finally,some important research areas to be carried out in future are pointed out.This review will give a deep understanding of the effects of different factors on the service performance and provide scientific guide in designing RHEAs with improved performance.
基金the Foundation for Innovative Research Groups of the National Natural Science Foundation of China(No.51621004)the National Natural Science Foundation of China(Nos.12072109,51871092,and 11772122)。
文摘High entropy alloys(HEAs)attract remarkable attention due to the excellent mechanical performance.However,the origins of their high strength and toughness compared with those of the traditional alloys are still hardly revealed.Here,using a microstructure-based constitutive model and molecular dynamics(MD)simulation,we investigate the unique mechanical behavior and microstructure evolution of FeCoCrNiCu HEAs during the indentation.Due to the interaction between the dislocation and solution,the high dislocation density in FeCoCrNiCu leads to strong work hardening.Plentiful slip systems are stimulated,leading to the good plasticity of FeCoCrNiCu.The plastic deformation of FeCoCrNiCu is basically affected by the motion of dislocation loops.The prismatic dislocation loops inside FeCoCrNiCu are formed by the dislocations with the Burgers vectors of a/6[112]and a/6[112],which interact with each other,and then emit along the<111>slip direction.In addition,the mechanical properties of FeCoCrNiCu HEA can be predicted by constructing the microstructure-based constitutive model,which is identified according to the evolution of the dislocation density and the stress-strain curve.Strong dislocation strengthening and remarkable lattice distortion strengthening occur in the deformation process of FeCoCrNiCu,and improve the strength.Therefore,the origins of high strength and high toughness in FeCoCrNiCu HEAs come from lattice distortion strengthening and the more activable slip systems compared with Cu.These results accelerate the discovery of HEAs with excellent mechanical properties,and provide a valuable reference for the industrial application of HEAs.
文摘Here, the composition of TaMoNbZrTiAl refractory high entropy alloy (RHEA) is optimized by increasing Ti content to improve its mechanical property especially the ductility, through comparing two RHEAs with different Ti content. The RHEAs contain two body-centered-cubic (BCC) phases. The BCC phase in the dendritic region is rich in Ta, Mo and Nb, and the BCC phase in the interdendritic region is enriched in Zr, Ti and Al. The as-cast RHEA with a higher Ti content remains dendritic microstructures, and Ti is mainly enriched in the interdendritic region. After annealing treatment at 1300 ℃ for 48 h, the dendritic microstructures change into equiaxed-grain morphology, accompanied by needle-like micron precipitates at grain boundaries in the RHEA with higher Ti content. For the as-cast RHEAs, the fracture strain increases by ~ 6.6% and the uniform plastic strain increases by ~ 5.9% at the compression test due to the increase of Ti content. Our work offers a reference for the composition design of RHEAs and makes a preliminary exploration of the optimization of the microstructures and mechanical properties.
基金Project supported by the National Natural Science Foundation of China(Grant No.11802139).
文摘The effect of Mn element on shock response of CoCrFeNiMnx high entropy alloys(HEAs)are investigated using molecular dynamics simulations.Structural analysis shows that Mn-rich CoCrFeNiMnx HEA has a larger average atomic volume.The elastic properties of CoCrFeNiMnx HEAs under various hydrostatic pressures are studied,revealing that the elastic modulus decreases with increasing of Mn content.The shock thermodynamic parameters are quantitatively analyzed.The Mn-dependent shock Hugoniot relationship of CoCrFeNiMnx HEAs is obtained:Us=1.25+(5.21–0.011x)Up.At relatively high shock pressure,the increase in Mn content promotes the formation of clustered BCC structures and hinders the development of dislocations.In addition,more FCC structures in Mn-rich CoCrFeNiMnx HEAs transform into disordered structures during spallation.Spall strength decreases with increasing Mn content.This study can provide a reference for the design and application of CoCrFeNiMn HEAs under shock loading.
基金supported by the Natural Science Foundation of Inner Mongolia,China(grant nos.2022MS05011,2020LH01006,and 2022FX02)the National Natural Science Foundation of China(grant nos.52261041 and 51961032)+1 种基金the Major Science and Technology Project of Inner Mongolia(grant no.2021ZD0029)the Fundamental Research Funds for Inner Mongolia University of Science&Technology(grant no.2023QNJS119).
文摘High-entropy alloys(HEAs)are a promising solution for large-scale hydrogen storage(H-storage)and are therefore receiving increasing attention from the materials science community.In this study,we systematically investigated the microstructures and H-storage properties of V_(35)Ti_(35)Cr_(10) Fe_(10)M_(10)(M=Mn,Co,Sc,or Ni)HEAs prepared by arcmelting.The cast HEAs were found to be nanocrystalline.The crystal lattice parameters and hydrogen absorption energies of the alloys were calculated using density functional theory(DFT)calculations.The alloys can be fully activated in just one cycle of hydrogen absorption/desorption under mild conditions,after which they reach hydrogen absorption saturation in approximately 100 s at ambient temperature.The hydrogenation kinetics of the HEAs are approximately five times higher than that of conventional solid-solution alloys with a body-centered cubic(BCC)structure.By performing in-situ hydriding differential scanning calorimetry in combination with DFT calculations,we revealed that the alloys are more susceptible to hydrogenation than traditional BCC structural alloys.The H-storage capacity of V_(35)Ti_(35)Cr_(10) Fe_(10)M_(10) alloys at ambient temperature was higher than that of HEAs reported in the literature.Quasi-in-situ X-ray diffraction characterization of the HEAs’hydrogenation revealed a phase transition process from a BCC to facecentered cubic,passing through a pseudo-BCC structure.Our work introduces a new perspective for designing alloys with ultrafast hydrogen absorption kinetics and high capacity for large-scale,room-temperature-applicable H-storage.
基金supported by the China Postdoctoral Science Foundation(No.2022M720401)the Postdoctoral Research Foundation of Shunde Innovation School,University of Science and Technology Beijing(No.2022BH007)the National Natural Science Foundation of China(No.52301074).
文摘To enhance the microbiologically influenced corrosion(MIC)resistance of FeCoNiCrMn high entropy alloy(HEAs),a series of Fe_(x)Cu_((1−x))CoNiCrMn(x=1,0.75,0.5,and 0.25)HEAs were prepared.Microstructural characteristics,corrosion behavior(morphology observation and electrochemical properties),and antimicrobial performance of Fe_(x)Cu_((1−x))CoNiCrMn HEAs were evaluated in a medium inoculated with typical corrosive microorganism Pseudomonas aeruginosa.The aim was to identify copper-containing FeCoNiCrMn HEAs that balance corrosion resistance and antimicrobial properties.Results revealed that all Fe_(x)Cu_((1−x))CoNiCrMn(x=1,0.75,0.5,and 0.25)HEAs exhibited an FCC(face centered cubic)phase,with significant grain refinement observed in Fe_(0.75)Cu_(0.25)CoNiCrMn HEA.Electrochemical tests indicated that Fe_(0.75)Cu_(0.25)CoNiCrMn HEA demonstrated lower corrosion current density(i_(corr))and pitting potential(E_(pit))compared to other Fe_(x)Cu_((1−x))CoNiCrMn HEAs in P.aeruginosa-inoculated medium,exhibiting superior resistance to MIC.Anti-microbial tests showed that after 14 d of immersion,Fe_(0.75)Cu_(0.25)CoNiCrMn achieved an antibacterial rate of 89.5%,effectively inhibiting the adhesion and biofilm formation of P.aeruginosa,thereby achieving resistance to MIC.
基金supported by Faculty Startup Fund in the New York State College of Ceramics at Alfred University。
文摘High entropy alloys(HEAs),especially refractory HEAs,have become a subject of interest in the past years due to their exceptional properties in terms of high-temperature strength,corrosion resistance,radiation tolerance,etc.under extreme environments.While the phase formation of these alloys significantly affects their properties.If the phase of HEAs can be forecasted before the experiments,the material design process can be greatly accelerated.The phase formation study of HEAs mainly relied on trial-and-error experiments and multi-scale computational simulations such as calculation of phase diagrams(CALPHAD) and density functional theory(DFT).However,those methods require massive time,man-power,and resources.As a highly efficient tool,machine learning(ML) method has been developed and applied to predict the phase formation of HEAs very recently.This review provided a comprehensive overview and analysis of the most recent research work in this area.First,we introduce ML methodologies applied in HEAs’ phase prediction in terms of principles,database,algorithm,and validation.We then summarize recent applications of the ML method in the phase prediction of HEAs.In the end,we propose possible solutions to the current problems and future research pathways for various challenges in the phase prediction of HEAs using ML.
基金financially supported by the National Key Re-search and Development Program of China(No.2018YFB0704400)the Key Program of Science and Technology of Yunnan Province(No.202002AB080001-2)+1 种基金the Key Research Project of Zhejiang Laboratory(No.2021PE0AC02)the Shanghai Pujiang Program(No.20PJ1403700).
文摘A mathematical formula of high physical interpretation,and accurate prediction and large generaliza-tion power is highly desirable for science,technology and engineering.In this study,we performed a domain knowledge-guided machine learning to discover high interpretive formula describing the high-temperature oxidation behavior of FeCrAlCoNi-based high entropy alloys(HEAs).The domain knowledge suggests that the exposure time dependent and thermally activated oxidation behavior can be described by the synergy formula of power law multiplying Arrhenius equation.The pre-factor,time exponent(m),and activation energy(Q)are dependent on the chemical compositions of eight elements in the FeCrAlCoNi-based HEAs.The Tree-Classifier for Linear Regression(TCLR)algorithm utilizes the two exper-imental features of exposure time(t)and temperature(T)to extract the spectrums of activation energy(Q)and time exponent(m)from the complex and high dimensional feature space,which automatically gives the spectrum of pre-factor.The three spectrums are assembled by using the element features,which leads to a general and interpretive formula with high prediction accuracy of the determination coefficient R^(2)=0.971.The role of each chemical element in the high-temperature oxidation behavior is analytically illustrated in the three spectrums,thereby the discovered interpretative formula provides a guidance to the inverse design of HEAs against high-temperature oxidation.The present work demonstrates the sig-nificance of domain knowledge in the development of materials informatics.
基金supported by the Faculty Startup Fund in the New York State College of Ceramics at Alfred University。
文摘Herein,we trained machine learning(ML)model to quickly and accurately conduct the strength prediction of refractory high entropy alloys(RHEAs)matrix.Gradient Boosting(GB)regression model shows an outstanding performance against other ML models.In addition,the heat of fusion and atomic size difference is shown to be paramount to the strength of the high entropy alloys(HEAs)matrix.In addition,we discussed the contribution of each feature to the solid solution strengthening(SSS)of HE As.The excellent predictive accuracy shows that the GB model can be efficient and reliable for the design of RHEAs with desired strength.
基金We acknowledge support from the National Natural Science Foundation of China(Nos.52271006,22173047)the Fundamental Research Funds for the Central Universities(Nos.30922010716,30920041116,0920021159,and 30919011405).
文摘Searching for single-phase solid solutions(SPSSs)in high-entropy alloys(HEAs)is a prerequisite for the intentional design and manipulation of microstructures of alloys in vast composition space.However,to date,reported SPSS HEAs are still rare due to the lack of reliable guiding principles for the synthesis of new SPSS HEAs.Here,we demonstrate an ensemble machine-learning method capable of discovering SPSS HEAs by directly predicting quinary phase diagrams based only on atomic composition.A total of 2198 experimental structure data are extracted from as-sputtered quinary HEAs in the literature and used to train a random forest classifier(termed AS-RF)utilizing bagging,achieving a prediction accuracy of 94.6%compared with experimental results.The AS-RF model is then utilized to predict 224 quinary phase diagrams including∼32,000 SPSS HEAs in Cr-Co-Fe-Ni-Mn-Cu-Al composition space.The extrapolation capability of the AS-RF model is then validated by performing first-principle calculations using density functional theory as a benchmark for the predicted phase transition of newly predicted HEAs.Finally,interpretation of the AS-RF model weighting of the input parameters also sheds light on the driving forces behind HEA formation in sputtered systems with the main contributors being:valance electron concentration,work function,atomic radius difference and elementary symmetries.