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Effect of charge order transition on tunneling resistance in Pr_(0.6)Ca_(0.4)MnO_3/Nb-doped SrTiO_3 heterojunction
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作者 王登京 马俊杰 +2 位作者 王妹 汪汝武 李云宝 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第5期485-489,共5页
An oxide p-n heterojunction composed of Pro.6Ca0.4MnO3 film, with a charge order (CO) transition, and lwt% Nb- doped SrTiO3 substrate is fabricated, and the transport properties of the interface are experimentally s... An oxide p-n heterojunction composed of Pro.6Ca0.4MnO3 film, with a charge order (CO) transition, and lwt% Nb- doped SrTiO3 substrate is fabricated, and the transport properties of the interface are experimentally studied. The rectifying behavior of the junction, well described by the Newman equation, is observed, indicating that tunneling is the dominant process by which the carriers pass through the interface. Above and below the CO transition temperature, satisfactory linear dependencies of junction resistance on temperature are observed, but the slopes of the two resistance-temperature relations are different. The CO process is believed to be relevant to this difference. 展开更多
关键词 MANGANITE HETEROJUNCTION TUNNELING charge order transition
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The Major Power Diplomacy with Chinese Characteristics in the Transition of International Order
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作者 Qiu Huafei Zhou Chunning 《Contemporary International Relations》 2017年第4期138-162,共25页
The early 21st century finds great change in international order. China's foreign relations have entered a new phase where its driving force is rapidly rising for the emerging countries and new global economic govema... The early 21st century finds great change in international order. China's foreign relations have entered a new phase where its driving force is rapidly rising for the emerging countries and new global economic govemance mechanism is gradually established. To follow the trend of the times, China has actively participated in global economic govemance and supply of public goods. China' s foreign relations present a new vision, idea and strategy under the leadership of President Xi Jinping. It is a new starting point for China to further integrate itself into the world and open itself wider to the world. China takes an active part to participate in global governance and plays an important role in the issues of economic integration, environmental governance, climate change, nuclear nonproliferation, energy crisis, intemet security and anti-terrorism, especially anti-terrorism. This article explains the performance of international relations in current transition order and tries to tackle prior (and in some ways more intractable) issues and to analyze the internal logics and external environment of impact of multi-polarization on China's major power diplomacy with its characteristics in the transition of International order. 展开更多
关键词 Major power diplomacy Chinese characteristics transition order
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Magnetic phase transitions and large mass enhancement in single crystal CaFe_4 As_3
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作者 Zhang Xiao-Dong Wu Wei +1 位作者 Zheng Ping Luo Jian-Lin 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第1期12-17,共6页
High quality single crystal CaFe4As3 was grown by using the Sn flux method. Unlike layered CaFe2As2, CaFe4As3 crystallizes in an orthorhombic three-dimensional structure. Two magnetic ordering transitions are observed... High quality single crystal CaFe4As3 was grown by using the Sn flux method. Unlike layered CaFe2As2, CaFe4As3 crystallizes in an orthorhombic three-dimensional structure. Two magnetic ordering transitions are observed at - 90 K and - 27 K, respectively. The high temperature transition is an antiferromagnetic(AF) ordering transition. However, the low temperature transition shows complex properties. It shows a ferromagnetic-like transition when a field is applied along b-axis, while antiferromagnetism-like transition when a field is applied perpendicular to b-axis. These results suggest that the low temperature transition at 27 K is a first-order transition from an AF state to a canted AF state. In addition, the low temperature electron specific heat coefficient reaches as high as 143 mJ/mol.K2, showing a heavy fermion behavior. 展开更多
关键词 antiferromagnetic ordering transition ferromagnetic ordering transition canted antifer-romagnetic state
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Electrical Neutrality and Symmetry Restoring Phase Transitions at High Density in a Two-Flavor Nambu-Jona-Lasinio Model
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作者 WANG Xiao-Ming ZHOU Bang-Rong 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第6期1081-1087,共7页
A general research on chiral symmetry restoring phase transitions at zero temperature and finite chemical potentials under electrical neutrality condition has been conducted in a Nambu-Jona-Lasinio model to describe t... A general research on chiral symmetry restoring phase transitions at zero temperature and finite chemical potentials under electrical neutrality condition has been conducted in a Nambu-Jona-Lasinio model to describe twoflavor normal quark matter. Depending on whether mo/A, the ratio of dynamical quark mass in vacuum and the 3D momentum cutoff in the loop integrals, is less or greater than 0.413, the phase transition will be of the second or first order. A complete phase diagram of u quark chemical potential versus mo is given. With the electrical neutrality constraint, the region where the second order phase transition happens will be wider than the one without electrical neutrality limitation. The results also show that, for the value ofmo/A from QCD phenomenology, the phase transition must be of the first order. 展开更多
关键词 normal quark matter electrical neutrality Nambu-Jona-Lasinio model high density chiral symmetry restoring first and second order phase transitions
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NANOGrav results and dark first order phase transitions 被引量:1
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作者 Andrea Addazi Yi-Fu Cai +2 位作者 Qingyu Gan Antonino Marciano Kaiqiang Zeng 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS CSCD 2021年第9期9-14,共6页
The recent NANOGrav evidence of a common-source stochastic background provides a hint to gravitational waves(GW)radiation from the Early Universe.We show that this result can be interpreted as a GW spectrum produced f... The recent NANOGrav evidence of a common-source stochastic background provides a hint to gravitational waves(GW)radiation from the Early Universe.We show that this result can be interpreted as a GW spectrum produced from first order phase transitions(FOPTs)around a temperature in the keV-MeV window.Such a class of FOPTs at temperatures much below the electroweak scale can be naturally envisaged in several warm dark matter models such as Majoron dark matter. 展开更多
关键词 gravitational waves first order phase transitions warm dark matter effective field theory
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Order in Transitional China and Its Institutional Logic 被引量:1
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作者 He Yanling Wang Guanglong 《Social Sciences in China》 2017年第2期56-75,共20页
The development of order in transitional China is not merely a matter of institutional supply, hut also a matter of defining the state's special roles and functions in the transition period. Since reform and opening ... The development of order in transitional China is not merely a matter of institutional supply, hut also a matter of defining the state's special roles and functions in the transition period. Since reform and opening up, China has sought to realize the twin governance aims of high speed development of the socialist economy and maintenance of stability, which require that the state simultaneously undertake the dual roles of modern government and national capital. The consequent adjustments to the governance structure are expressed in the state's devolution of power to the market while reserving government pricing power; devolution of power to local governments while reserving power over central tasks; and affirming social rights while reserving the power to approve social organizations. At the institutional level, the externalities produced by this "quasi-decentralized governance structure" are marked by the shrinkage of arrangements for collective welfare, the absence of mechanisms for routine security in ordinary life, and the development of mechanisms that allow the government to profit from the market. This may result in the instrumentalization of government functions and the capitalization of public power, producing imbalances in the distribution of social rights, wealth and risk, or in other words, social instability. 展开更多
关键词 order in transitional China incidents of unrest governance structure
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Connection between Physical Properties in Homologous Series of Molecular Systems 被引量:1
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作者 Dolomatov Michail Yurievich Dezortsev Sergey Vladislavovich 《Journal of Chemistry and Chemical Engineering》 2013年第6期566-572,共7页
The connections between different physical-chemical properties in homologous molecular series are analyzed from the quantum-mechanic and the algebraic theory points of view and are explained by influence of the gage t... The connections between different physical-chemical properties in homologous molecular series are analyzed from the quantum-mechanic and the algebraic theory points of view and are explained by influence of the gage to the quantum electronic continuum. The connection between quantum and macroscopic properties of the substances is confirmed in homologous series of n-alkanes. Linear correlation between the coefficient of magnetization and energy of the highest occupied molecular orbital in homologous series of n-alkanes C2-C10 is established. The connection between diamagnetic and electronic characteristics of n-alkanes with the temperatures of the first order phase transitions (melting point) and other physical-chemical properties were discovered. The nature of interconnection between critical and diamagnetic properties of n-alkanes C2-C10 and results of previous works allow to suppose significant role of the spin interactions in electronic continuum states along the process of the first order phase transitions. 展开更多
关键词 N-ALKANES electronic structure physical-chemical properties band gap width first order phase transitions coefficient ofmagnetization.
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Multiple magnetic transitions and magnetocaloric effect of Tb_(4)Coln alloy 被引量:1
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作者 Remya U.D. Arun K. +4 位作者 Swathi S. Athul S.R. Andrea Dzubinska Marian Reiffers Nagalakshmi R. 《Journal of Rare Earths》 SCIE EI CAS CSCD 2023年第11期1721-1727,I0003,共8页
We report on the magnetic,magnetocaloric,thermal,and electrical transport properties of Tb_(4)Coln alloy,which crystallizes in two phases,Tb_6Co_(2.1)In_(0.8)(space group Immm)and Tb_(2)In_(0.9)Co_(0.1)(space group P6... We report on the magnetic,magnetocaloric,thermal,and electrical transport properties of Tb_(4)Coln alloy,which crystallizes in two phases,Tb_6Co_(2.1)In_(0.8)(space group Immm)and Tb_(2)In_(0.9)Co_(0.1)(space group P6_(3)/mmc),respectively.The alloy reveals three successive magnetic transitions around T_(1)(163 K),T_(2)(50 K),and T_(3)(29 K),respectively,associated with paramagnetic to ferromagnetic transition and two sequential antiferromagnetic transitions.The low-temperature transition T_(3) follows the first-order magnetic behavior and exhibits the field-induced magnetic transition.Meanwhile,T_(2) and T_(1) are found to be second-order in nature which opens a possibility for hysteresis-free magnetocaloric application.The magnetocaloric properties are determined using different magnetocaloric figures of merits such as-ΔS_(M),ΔT_(ad).RCP,and TEC(10).Additionally,the universal curve behavior in the isothermal entropy change unveils the variation in critical exponents around T_(1) and T_(2) due to the magnetic inhomogeneity in the alloy.Besides,the electrical transport properties of the metallic alloy denote the maximum magnetoresistance of-10%around T_(1). 展开更多
关键词 Multiple magnetic transitions order of magnetic transition Magnetocaloric effect MAGNETORESISTANCE Universal curve behavior Rare earths
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Magnetic properties and magnetocaloric effect in compound PrFe_(12)B_6
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作者 王芳 沈保根 +4 位作者 张健 孙继荣 张健 孟凡斌 李养贤 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第6期513-517,共5页
Magnetic properties and magnetocaloric effect of compound PrFe12B6 are investigated. The coexistence of hard phase PrFe12B6 and soft phase α-Fe causes interesting phenomena on the curves for the temperature dependenc... Magnetic properties and magnetocaloric effect of compound PrFe12B6 are investigated. The coexistence of hard phase PrFe12B6 and soft phase α-Fe causes interesting phenomena on the curves for the temperature dependence of magnetization. PrFe12B6 experiences a first order phase transition at the Curie temperature 206 K, accompanied by an obvious lattice contraction, which in turn results in a large magnetic entropy change. The Maxwell relation fails to give the correct information about magnetic entropy change due to the first order phase transition nature. The large magnetic entropy changes of PrFe12.3B4.7 obtained from heat capacity method are 11.7 and 16.2 J/kg.K for magnetic field changes of 0-2 T and 0-5 T respectively. 展开更多
关键词 magnetic properties magnetic entropy change first order phase transition
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Dynamic ordering transitions in charged solid
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作者 Jian Sun Jiasen Niu +5 位作者 Yifan Li Yang Liu LNPfeiffer KWWest Pengjie Wang Xi Lin 《Fundamental Research》 CAS 2022年第2期178-183,共6页
The phenomenon of group motion is common in nature,ranging from the schools of fish,birds and insects,to avalanches,landslides and sand drift.If we treat objects as collectively moving particles,such phenomena can be ... The phenomenon of group motion is common in nature,ranging from the schools of fish,birds and insects,to avalanches,landslides and sand drift.If we treat objects as collectively moving particles,such phenomena can be studied from a physical point of view,and the research on many-body systems has proved that marvelous effects can arise from the simplest individuals.The motion of numerous individuals presents different dynamic phases related to the ordering of the system.However,it is usually difficult to study the dynamic ordering and its transitions through experiments.Electron bubble states formed in a two-dimensional electron gas,as a type of electron solids,can be driven by an external electric field and provide a platform to study the dynamic collective behaviors.Here,we demonstrate that the noise spectrum is a powerful method to investigate the dynamics of bubble states.We observed not only the phenomena of dynamically ordered and disordered structures,but also unexpected alternations between them.Our results show that a dissipative system can convert between chaotic structures and ordered structures when tuning global parameters,which is concealed in conventional transport measurements of resistance or conductance.Moreover,charging the objects to study the electrical noise spectrum in collective motions can be an additional approach to revealing dynamic ordering transitions. 展开更多
关键词 Two-dimensional system Electron solid Dynamic ordering transition Noise spectrum measurement Collective motion
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Quasinormal Modes of Phantom Scalar Perturbation in Background of Reissner-Nordstrom Black Hole
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作者 潘启沅 苏汝铿 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第2期221-226,共6页
We have investigated the quasinormal modes (QNMs) of phantom scalar perturbation in a Reissner Nordstr6m (RN) background. We find that the dependence of Q, NMs on the mass of the field for the phantom perturbation... We have investigated the quasinormal modes (QNMs) of phantom scalar perturbation in a Reissner Nordstr6m (RN) background. We find that the dependence of Q, NMs on the mass of the field for the phantom perturbation is totally different from that of usual massive perturbation. However, we obtain the same critical value of the overtone number for an angular quantum number from which the mass will begin to have a reverse effect on the real part of QNM frequencies and the perturbation-independent relation between the Q, NMs and the second order thermodynamic phase transition. 展开更多
关键词 quasinormal modes phantom scalar perturbation second order thermodynamic phase transition
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Representations of Free Groups on Rational Line Q
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作者 Bing-xin Lu Zuo-tong Zhu 《Advances in Manufacturing》 2000年第2期101-105,共5页
A.M.W. Glass and S.H.McCleary have given the 2 transitive representation of the countable free l group F η(1<η≤ω 0 ).In this paper we shall give the highly ordered transitive representation of count... A.M.W. Glass and S.H.McCleary have given the 2 transitive representation of the countable free l group F η(1<η≤ω 0 ).In this paper we shall give the highly ordered transitive representation of countable free groups on the rational line Q, which generalizes their results. As applications,we obtain the highly ordered transitive representation for the direct product of countable free groups,and the inverse limit of countable free groups must be an action on the set Q. 展开更多
关键词 free group highly ordered transitive representation direct product of groups inverse limit of free groups
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A NEW PANSYSTEMS RESEARCH ABOUT BINARY RELATION ′S TRANSITIVITY
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作者 吴守志 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1994年第11期1081-1085,共5页
Because of. the great needs both for the research of pansystem mathematics andfor the analysis of general things' mechanism, this paper discusses the binary relation,stransitivity confined to multirelation. The so... Because of. the great needs both for the research of pansystem mathematics andfor the analysis of general things' mechanism, this paper discusses the binary relation,stransitivity confined to multirelation. The so-called g-transitvity- a completelynew concept about transitivity- is introduced and its basic properties are investigated.The study shows that it is not only g-transitivity a generalization of traditionaltransitivity, quasi-transitivity, seml-order, quasi-order and other panorder, but alsoincludes many important concepts such as closeness, convexity, topology, duality as itsspecial cases. 展开更多
关键词 pansystems theory relation panorder. order. transitivity.quasi-transitivity `g-transitivity
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Superconductivity in self-flux-synthesized single crystalline R2Pt3Ge5(R=La,Ce,Pr)
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作者 盛琪 张建 +4 位作者 黄百畅 丁兆峰 彭小冉 谭程 殳蕾 《Chinese Physics B》 SCIE EI CAS CSCD 2017年第5期357-361,共5页
In order to study the basic superconductivity properties of R2Pt3Ge5, we synthesized the single crystalline samples by the Pt–Ge self-flux method. R2Pt3Ge5(R = La, Ce) were also grown for a systematic study. Zero-r... In order to study the basic superconductivity properties of R2Pt3Ge5, we synthesized the single crystalline samples by the Pt–Ge self-flux method. R2Pt3Ge5(R = La, Ce) were also grown for a systematic study. Zero-resistivity was observed in both the La-and Pr-based samples below the reported superconducting transition temperatures. However, magnetic susceptibility measurements showed low superconductivity volume fractions in both La2Pt3Ge5 and R2Pt3Ge5(less than2%). Ce2Pt3Ge5 did not show any signature of superconductivity. From the specific heat measurements, we did not observe a superconducting transition peak in R2Pt3Ge5, suggesting that it is not a bulk superconductor. The magnetic susceptibility and heat capacity measurements revealed two antiferromagnetic(AFM) orders in R2Pt3Ge5 at T(N1)= 4.2 K and T(N2)= 3.5K, as well as a single AFM transition at TN= 3.8 K in Ce2Pt3Ge5. 展开更多
关键词 crystalline superconductor susceptibility signature resistivity magnetization Curie impurity orders transitions
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New Kinetics Equation for Stress Relaxation of Semi-crystalline Polymers below Glass Transition Temperature
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作者 Cheng Zhang Li-Hai Cai +2 位作者 Bao-Hua Guo Bing Miao Jun Xu 《Chinese Journal of Polymer Science》 SCIE EI CAS CSCD 2022年第12期1662-1669,I0010,共9页
The stress relaxation of semi-crystalline nylon 1010 cannot be fitted by the Kohlrausch-Williams-Watts formula when the experiments were performed at pre-yielding regime below the glass transition temperature.We study... The stress relaxation of semi-crystalline nylon 1010 cannot be fitted by the Kohlrausch-Williams-Watts formula when the experiments were performed at pre-yielding regime below the glass transition temperature.We study this problem and identify the two-step mechanism of stress relaxation.At short time scale,relaxation is fast,dominated by stress biased thermal fluctuation with a fixed short-range length scale(activation volume).At long time scale,relaxation is slow due to the emergence of a cooperative long-range length scale determined by the stress fluctuation.The cooperative length scale is proportional to the reciprocal of stress and the amplitude of stress fluctuation is the product of stress and activation volume.Based on this two-step mechanism,we propose a new kinetics equation to capture the stress relaxation effectively,where the short time relaxation is described by an Eyring-like local activation and the long-time relaxation is captured by a cooperative excitation process resorting to an extension from the random first order transition theory.Our equation fits the experimental data well and can serve as a model to guide the related experiments of relaxation processes in crystalline solids. 展开更多
关键词 Stress relaxation Semi-crystalline polymers Kohlrausch-Williams-Watts(KWW)equation Random first order transition(RFOT)theory
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CROWDING EFFECT INDUCED PHASE TRANSITION OF AMPHIPHILIC DIBLOCK COPOLYMER IN SOLUTION
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作者 Zhu Liu Zhi-Bin Jiang +3 位作者 Hong Yang Shu-Ming Bai 汪蓉 薛奇 《Chinese Journal of Polymer Science》 SCIE CAS CSCD 2013年第11期1491-1500,共10页
The crowding agent induced phase transition of amphiphilic block copolymers in solution was explicitly considered. The influence of the size and the volume fraction of the crowding agent on the phase separation of amp... The crowding agent induced phase transition of amphiphilic block copolymers in solution was explicitly considered. The influence of the size and the volume fraction of the crowding agent on the phase separation of ampbiphilic diblock copolymers is investigated by using self-consistent field theory (SCFT) method. The concentration of the disorder to order transition of the block copolymer decreases when the size of the crowding agent is larger than that of the solvent. The higher volume fraction of the crowding agent will induce the transition of the block copolymer from disorder to order state at a lower concentration. The relation between the size and the volume fraction of the crowding agent is elucidated. When the size of the crowding agent is larger, its volume fraction of the disorder to order transition of the block copolymer will be lower. The conformation of the crowding agent considered as a polymer chain is also studied and compared. 展开更多
关键词 Crowding agent Disorder to order transition Block copolymer.
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Phase transitions of two spin-1/2 Baxter–Wu layers coupled with Ising-type interactions
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作者 Wei Liu Zhengxin Yan Yixian Wang 《Communications in Theoretical Physics》 SCIE CAS CSCD 2021年第1期99-105,共7页
Using a Monte Carlo simulation and the single histogram reweighting technique,we study the critical behaviors and phase transitions of the Baxter-Wu(BW)model on a two-layer triangular lattice with Ising-type interlaye... Using a Monte Carlo simulation and the single histogram reweighting technique,we study the critical behaviors and phase transitions of the Baxter-Wu(BW)model on a two-layer triangular lattice with Ising-type interlayer couplings.Via the finite-size analysis,we obtain the transition temperatures and critical exponents at repulsive and attractive interlayer couplings.The data for the repulsive interlayer coupling suggest continuous transitions,and the critical behaviors are the same as those of the 2D BW model,belonging to the four-state Potts universality class.The reduced energy cumulants and the histograms reveal that attractive coupling leads to weak firstorder phase transitions.The pseudocritical exponents with the existence of the interlayer couplings indicate that the first-order transition is very close to the critical point of the 2D standard BW model. 展开更多
关键词 Baxter-Wu model Monte Carlo simulation critical behavior weak first order phase transition
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Ageing Hardening Mechanism and Corrosion Resistance in the Fe65Cr13Cu3(CoMnMoNiAlTi)19 Medium-Entropy Stainless Alloy 被引量:1
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作者 Ben-Qi Xu Hui Zhang +2 位作者 Dong Ma Qun-Shuang Ma Li-Zhai Pei 《Acta Metallurgica Sinica(English Letters)》 SCIE EI CAS CSCD 2021年第11期1601-1608,共8页
The ageing hardening mechanism of a newly designed Fe65Cr13Cu3(CoMnMoNiAlTi)19 medium-entropy stainless alloy(ME-SA)with a simple bcc solid solution matrix was studied.This kind of ME-SA possessed a higher ageing hard... The ageing hardening mechanism of a newly designed Fe65Cr13Cu3(CoMnMoNiAlTi)19 medium-entropy stainless alloy(ME-SA)with a simple bcc solid solution matrix was studied.This kind of ME-SA possessed a higher ageing hardness of approximately 584 HV and higher compressive stress and corrosion resistance than those of the conventional precipitation hardening stainless steel 17-4 PH(Cr17Ni4Cu4 Nb),which has comparable compressive strain.The well-dispersed B2-ordered phase in the cast state transformed to a D03 crystal structure with a higher ordering degree and reduced the precipitate size after ageing at 500℃,thus promoting a great ageing hardening effect. 展开更多
关键词 Medium-entropy stainless alloy ordered phase transition Aging hardening Corrosion resistance
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Charged pion condensation in anti-parallel electromagnetic fields and nonzero isospin density
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作者 Jingyi Chao Mei Huang Andrey Radzhabov 《Chinese Physics C》 SCIE CAS CSCD 2020年第3期101-110,共10页
The formation of charged pion condensate in anti-parallel electromagnetic fields and in the presence of the isospin chemical potential is studied in the two-flavor Nambu-Jona-Lasinio model.The method of Schwinger prop... The formation of charged pion condensate in anti-parallel electromagnetic fields and in the presence of the isospin chemical potential is studied in the two-flavor Nambu-Jona-Lasinio model.The method of Schwinger proper time is extended to explore the quantities in the off-diagonal flavor space,i.e.the charged pion.In this framework,π^± are treated as bound states of quarks and not as point-like charged particles.The isospin chemical potential plays the role of a trigger for charged pion condensation.We obtain the associated effective potential as a function of the strength of the electromagnetic fields and find that it contains a sextic term which possibly induces a weak first order phase transition.The dependence of pion condensation on model parameters is investigated. 展开更多
关键词 pion condensate electromagnetic fields weakly first order phase transition
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Statistical properties of quantum spectra in nuclei
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作者 吴锡真 张英逊 +3 位作者 顾建中 李祝霞 冯仁发 卓益忠 《Science China Mathematics》 SCIE 2001年第7期923-931,共9页
Some aspects of quantum chaos in a finite system have been studied based on the analysis of statistical behavior of quantum spectra in nuclei.The experiment data show the transition from order to chaos with increasing... Some aspects of quantum chaos in a finite system have been studied based on the analysis of statistical behavior of quantum spectra in nuclei.The experiment data show the transition from order to chaos with increasing excitation energy in spherical nuclei.The dependence of the order to chaos transition on nuclear deformation and nuclear rotating is described.The influence of pairing effect on the order to chaos transition is also discussed.Some important experiment phenomena in nuclear physics have been understood from the point of view of the interplay between order and chaos. 展开更多
关键词 transition from order to chaos Level spacing distribution Poincare section map Wigner distribution Poisson distribution
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