Microstructures and properties of high-entropy alloys

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Abstract

This paper reviews the recent research and development of high-entropy alloys (HEAs). HEAs are loosely defined as solid solution alloys that contain more than five principal elements in equal or near equal atomic percent (at.%). The concept of high entropy introduces a new path of developing advanced materials with unique properties, which cannot be achieved by the conventional micro-alloying approach based on only one dominant element. Up to date, many HEAs with promising properties have been reported, e.g., high wear-resistant HEAs, Co1.5CrFeNi1.5Ti and Al0.2Co1.5CrFeNi1.5Ti alloys; high-strength body-centered-cubic (BCC) AlCoCrFeNi HEAs at room temperature, and NbMoTaV HEA at elevated temperatures. Furthermore, the general corrosion resistance of the Cu0.5NiAlCoCrFeSi HEA is much better than that of the conventional 304-stainless steel. This paper first reviews HEA formation in relation to thermodynamics, kinetics, and processing. Physical, magnetic, chemical, and mechanical properties are then discussed. Great details are provided on the plastic deformation, fracture, and magnetization from the perspectives of crackling noise and Barkhausen noise measurements, and the analysis of serrations on stress–strain curves at specific strain rates or testing temperatures, as well as the serrations of the magnetization hysteresis loops. The comparison between conventional and high-entropy bulk metallic glasses is analyzed from the viewpoints of eutectic composition, dense atomic packing, and entropy of mixing. Glass forming ability and plastic properties of high-entropy bulk metallic glasses are also discussed. Modeling techniques applicable to HEAs are introduced and discussed, such as ab initio molecular dynamics simulations and CALPHAD modeling. Finally, future developments and potential new research directions for HEAs are proposed.

Introduction

Recently, high-entropy alloys (HEAs) have attracted increasing attentions because of their unique compositions, microstructures, and adjustable properties [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31]. They are loosely defined as solid solution alloys that contain more than five principal elements in equal or near equal atomic percent (at.%) [32]. Normally, the atomic fraction of each component is greater than 5 at.%. The multi-component equi-molar alloys should be located at the center of a multi-component phase diagram, and their configuration entropy of mixing reaches its maximum (R Ln N; R is the gas constant and N the number of component in the system) for a solution phase. These alloys are defined as HEAs by Yeh et al. [2], and named by Cantor et al. [1], [33] as multi-component alloys. Both refer to the same concept. There are also some other names, such as multi-principal-elements alloys, equi-molar alloys, equi-atomic ratio alloys, substitutional alloys, and multi-component alloys.

Cantor et al. [1], [33] pointed out that a conventional alloy development strategy leads to an enormous amount of knowledge about alloys based on one or two components, but little or no knowledge about alloys containing several main components in near-equal proportions. Theoretical and experimental works on the occurrence, structure, and properties of crystalline phases have been restricted to alloys based on one or two main components. Thus, the information and understanding are highly developed on alloys close to the corners and edges of a multi-component phase diagram, with much less knowledge about alloys located at the center of the phase diagram, as shown schematically for ternary and quaternary alloy systems in Fig. 1.1. This imbalance is significant for ternary alloys but becomes rapidly much more pronounced as the number of components increases. For most quaternary and other higher-order systems, information about alloys at the center of the phase diagram is virtually nonexistent except those HEA systems that have been reported very recently.

In the 1990s, researchers began to explore for metallic alloys with super-high glass-forming ability (GFA). Greer [29] proposed a confusion principle, which states that the more elements involved, the lower the chance that the alloy can select viable crystal structures, and thus the greater the chance of glass formation. Ma et al. [3] found that the best glass former is not exactly at the eutectic composition, and has a shift towards the high-entropy zone in the phase diagram. Recently, Takeuchi et al. [34] reported a high-entropy bulk metallic glass (BMG), which can have a critical size over 10 mm. Zhao et al. [35] and Gao et al. [36] reported a high-entropy BMG, which can be plastically deformed at room temperature. However, for some HEAs, their GFA is rather low, and they can only form solid-solutions even though the cooling rate is very high, e.g., alloys of CuCoNiCrAlFeTiV, FeCrMnNiCo, CoCrFeNiCu, AlCoCrFeNi, NbMoTaWV, etc. [1], [2], [12], [13], [14].

The yield strength of the body-centered cubic (BCC) HEAs can be rather high [12], usually comparable to BMGs [12]. Moreover, the high strength can be kept up to 800 K or higher for some HEAs based on 3d transition metals [14]. In contrast, BMGs can only keep their high strength below their glass-transition temperature.

Being different from the conventional alloys, compositions in HEAs are complex due to the equi-molar concentration of each component. Yeh [37] summarized mainly four core effects for HEAs, that is: (1) Thermodynamics: high-entropy effects; (2) Kinetics: sluggish diffusion; (3) Structures: severe lattice distortion; and (4) Properties: cocktail effects. We will discuss these four core effects separately.

The high-entropy effects, which tend to stabilize the high-entropy phases, e.g., solid-solution phases, were firstly proposed by Yeh [9]. The effects were very counterintuitive because it was expected that intermetallic compound phases may form for those equi- or near equi-atomic alloy compositions which are located at the center of the phase diagrams (for example, a monoclinic compound AlCeCo forms in the center of Al–Ce–Co system [38]). According to the Gibbs phase rule, the number of phases (P) in a given alloy at constant pressure in equilibrium condition is:P=C+1-Fwhere C is the number of components and F is the maximum number of thermodynamic degrees of freedom in the system. In the case of a 6-component system at given pressure, one might expect a maximum of 7 equilibrium phases at an invariant reaction. However, to our surprise, HEAs form solid-solution phases rather than intermetallic phases [1], [2], [4], [17]. This is not to say that all multi-components in equal molar ratio will form solid solution phases at the center of the phase diagram. In fact, only carefully chosen compositions that satisfy the HEA-formation criteria will form solid solutions instead of intermetallic compounds.

The solid-solution phase, according to the classical physical-metallurgy theory, is also called a terminal solid solution. The solid-solution phase is based on one element, which is called the solvent, and contains other minor elements, which are called the solutes. In HEAs, it is very difficult to differentiate the solvent from the solute because of their equi-molar portions. Many researchers reported that the multi-principal-element alloys can only form simple phases of body-centered-cubic (BCC) or face-centered-cubic (FCC) solid solutions, and the number of phases formed is much fewer than the maximum number of phases that the Gibbs phase rule allows [9], [23]. This feature also indicates that the high entropy of the alloys tends to expand the solution limits between the elements, which may further confirm the high-entropy effects.

The high-entropy effect is mainly used to explain the multi-principal-element solid solution. According to the maximum entropy production principle (MEPP) [39], high entropy tends to stabilize the high-entropy phases, i.e., solid-solution phases, rather than intermetallic phases. Intermetallics are usually ordered phases with lower configurational entropy. For stoichiometric intermetallic compounds, their configurational entropy is zero.

Whether a HEA of single solid solution phase is in its equilibrium has been questioned in the scientific community. There have been accumulated evidences to show that the high entropy of mixing truly extends the solubility limits of solid solution. For example, Lucas et al. [40] recently reported absence of long-range chemical ordering in equi-molar FeCoCrNi alloy that forms a disordered FCC structure. On the other hand, it was reported that some equi-atomic compositions such as AlCoCrCuFeNi contain several phases of different compositions when cooling slowly from the melt [15], and thus it is controversial whether they can be still classified as HEA. The empirical rules in guiding HEA formation are addressed in Section 2, which includes atomic size difference and heat of mixing.

The sluggish diffusion effect here is compared with that of the conventional alloys rather than the bulk-glass-forming alloys. Recently, Yeh [9] studied the vacancy formation and the composition partition in HEAs, and compared the diffusion coefficients for the elements in pure metals, stainless steels, and HEAs, and found that the order of diffusion rates in the three types of alloy systems is shown below:HEAs<stainless steels<pure metals

The sluggish diffusion effect is usually used to explain the formation of nano-sized precipitations, because the nuclei are easier to form but grow slowly, as shown in Fig. 1.2 on an as-cast CuCoNiCrFe alloy [2]. In the figure, nano-precipitates with a size of 7–50 nm in diameter, close to the FCC phase in a spinodal plate appear, as shown in Fig. 1.2B(b). Fig. 1.2 also shows that the microstructures of certain HEAs are usually very complicated, which can include nano-precipitates, ordered solid-solution phases, disordered solid-solution phases, and even amorphous phases. This feature is due to the fact that the interactions between the principal elements and the content of all the elements are very high.

The severe lattice-distortion effect is usually compared with the one dominant element alloys, where the lattice site is occupied mainly by the dominant constituent. For HEAs, each element has the same possibility to occupy the lattice site, if ignoring chemical ordering. Since the size of different elements can be very different in some cases, this can lead to the severe lattice distortion. This effect is well confirmed by the ultrahigh strength of the BCC HEAs [11]. Yeh et al. [41] studied the anomalous decrease in X-ray diffraction (XRD) intensities of the CuNiAlCoCrFeSi alloy systems with multi-principal elements. A series of CuNiAlCoCrFeSi alloys with a systematic addition of principal elements from pure element to seven elements was investigated for the quantitative analysis of XRD intensities. The variation of XRD peak intensities of the alloy system is similar to that caused by thermal effects, but the intensities further drop beyond the thermal effect with increasing the number of constituent principal elements. An intrinsic lattice distortion effect caused by the addition of multi-principal elements with different atomic sizes is expected for the anomalous decrease in the XRD intensities. The mathematical treatment of this distortion effect for the modification of the XRD structure factor is formulated to be similar to that of the thermal effect, as shown in Fig. 1.3 [41]. The larger roughness of the atomic planes makes the intensity of the XRD for HEAs much lower than that for the single-element solid.

The severe lattice distortion is also used to explain the high strength of HEAs, especially the BCC-structured HEAs [4], [12], [23]. The severe lattice-distortion effect is also related to the tensile brittleness and the slower kinetics of HEAs [2], [9], [11]. However, the authors also noticed that single-phase FCC-structured HEAs have very low strength [7], which certainly cannot be explained by the severe lattice distortion argument. Fundamental studies in quantification of lattice distortion of HEAs are needed.

The cocktail-party effect was usually used as a term in the acoustics field, which have been used to describe the ability to focus one’s listening attention on a single talker among a mixture of conversations and background noises, ignoring other conversations. For metallic alloys, the effect indicates that the unexpected properties can be obtained after mixing many elements, which could not be obtained from any one independent element. The cocktail effect for metallic alloys was first mentioned by Ranganathan [42], which has been subsequently confirmed in the mechanical and physical properties [12], [13], [15], [18], [35], [43].

The cocktail effect implies that the alloy properties can be greatly adjusted by the composition change and alloying, as shown in Fig. 1.4, which indicates that the hardness of HEAs can be dramatically changed by adjusting the Al content in the CoCrCuNiAlx HEAs. With the increase of the Al content, the phases change from FCC to BCC + FCC and then to BCC structures. As a result, the lattice constants for both the BCC and FCC structures increase, and the hardness of the alloys increases. Fig. 1.5 presents the change of hardness as a function of the Al content for the Cu-free CoCrFeNiAlx HEAs [44]. The hardness of the FCC phase does not vary too much with changing the Al content from 0 to 0.45, while the hardness of the BCC phase decreases from about HV 538 to HV 480 as the Al content increases from 0.88 to 2.0. Moreover, the two phase region of FCC + BCC structures becomes much narrower for CoCrFeNiAlx than CoCrCuFeNiAlx indicating that Cu stabilizes the FCC phase. But caution should be addressed here for Cu: Cu tends to segregate and form very Cu-rich phase(s) in CoCrCuFeNiAlx [15], [45]. Cu forms isomorphous solid solution with Ni but it is insoluble in Co, Cr and Fe; it dissolves about 20 at.% Al but also forms various stable intermetallic compounds with Al.

Fig. 1.6 exhibits the hardness of some reported HEAs in the descending order with stainless steels as benchmark. The MoTiVFeNiZrCoCr alloy has a very high value of hardness of over 800 HV while CoCrFeNiCu is very soft with a value of less than 200 HV. Fig. 1.7 compares the specific strength, which is defined by the yield strength over the density of the materials, and the density among HEAs, BMGs, conventional alloys, polymers and foam materials [5]. We can see that HEAs have densities close to the steel but have high values of specific strength (yield strength/density). This is partially because our recently-reported HEAs usually contain mainly the late transitional elements whose density is on the high side. The lightweight HEAs have much more potential because lightweight elements can be used and the density of the resultant alloys will be lowered significantly. Fig. 1.8 shows the specific-yield strength of HEAs vs. Young’s modulus compared with conventional alloys. As can be seen, HEAs exhibit the highest specific strength and their Young’s modulus can be varied in a very large range. This observation may indicate that the modulus of HEAs can be more easily adjusted than conventional alloys. In addition to the high specific strength, other properties such as high hydrogen storage property are also reported [46].

To understand the fundamentals of HEAs is a challenge to the scientists in materials science and related fields because of lack of thermodynamic and kinetic data for multi-component systems in the center of phase diagrams. The phase diagrams are usually available only for the binary and ternary alloys. For HEAs, no complete phase diagrams are currently available to directly assist designing the alloy with desirable micro- and nanostructures. Recently, Yang and Zhang [28] proposed the Ω parameter to design the solid-solution phase HEAs, which should be used combing with the parameter of atomic-size difference. This strategy may provide a starting point prior to actual experiments. The plastic deformation and fracture mechanisms of HEAs are also new because the high-entropy solid solutions contain high contents of multi-principal elements. In single principal-element alloys, dislocations dominate the plastic behavior. However, how dislocations interact with highly-disordered crystal lattices and/or chemical disordering/ordering will be an important factor responsible for plastic properties of HEAs. Interactions between the other crystal defects, such as twinning and stacking faults, with chemical/crystal disordering/ordering in HEAs will be important as well.

For conventional alloys that contain a single principal element, the main mechanical behavior is dictated by the dominant element. The other minor alloying elements are used to enhance some special properties. For example, in the low-carbon ferritic steels [47], [48], [49], [50], [51], [52], [53], [54], [55], [56], [57], [58], [59], the main mechanical properties are from the BCC Fe. Carbon, which is an interstitial solute element, is used for solid-solution strengthened steels, and also to enhance the martensite-quenching ability which is the phase-transformation strengthening. The main properties of steels are still from Fe. For aluminum alloys [60] and titanium alloys [61], their properties are mainly related to the dominance of the elemental aluminum and titanium, respectively.

Intermetallic compounds are usually based on two elements, e.g., Ti–Al, Fe3Al, and Fe3Si. Intermetallic compounds are typically ordered phases and some may have strict compositional range. The Burgers vectors of the ordered phases are too large for the dislocations to move, which is the main reason why intermetallic phases are usually brittle. However, there are many successful case studies to improve the ductility of intermetallic compound by micro-alloying, e.g., micro-alloying of B in Ni3Al [62], and micro-alloying of Cr in Fe3Al [63], [64].

Amorphous metals usually contain at least three elements although binary metallic glasses are also reported, and higher GFA can be obtained with addition of more elements, e.g., ZrTiCuNiBe (Vit-1), PdNiCuP, LaAlNiCu, and CuZrAlY alloys [65], [66], [67], [68], [69]. Amorphous metals usually exhibit ultrahigh yield strength, because they do not contain conventional any weakening factors, such as dislocations and grain boundaries, and their yield strengths are usually three to five times of their corresponding crystalline counterpart alloys. There are several models that are proposed to explain the plastic deformation of the amorphous metal, including the free volume [70], a shear-transformation-zone (STZ) [71], more recently a tension-transition zone (TTZ) [72], and the atomic-level stress [73], [74]. The micro-mechanisms of the plastic deformation of amorphous metals are usually by forming shear bands, which is still an active research area till today. However, the high strength of amorphous alloys can be sustained only below the glass-transition temperature (Tg). At temperatures immediately above Tg, the amorphous metals will transit to be viscous liquids [68] and will crystallize at temperatures above the first crystallization onset temperature. This trend may limit the high-temperature applications of amorphous metals. The glass forming alloys often are chemically located close to the eutectic composition, which further facilitates the formation of the amorphous metal–matrix composite. The development of the amorphous metal–matrix composite can enhance the room-temperature plasticity of amorphous metals, and extend application temperatures [75], [76], [77], [78].

For HEAs, their properties can be different from any of the constituent elements. The structure types are the dominant factor for controlling the strength or hardness of HEAs [5], [12], [13]. The BCC-structured HEAs usually have very high yield strengths and limited plasticity, while the FCC-structured HEAs have low yield strength and high plasticity. The mixture of BCC + FCC is expected to possess balanced mechanical properties, e.g., both high strength and good ductility. Recent studies show that the microstructures of certain “HEAs” can be very complicated since they often undergo the spinodal decomposition, and ordered, and disordered phase precipitates at lower temperatures. Solution-strengthening mechanisms for HEAs would be much different from conventional alloys. HEAs usually have high melting points, and the high yield strength can usually be sustained to ultrahigh temperatures, which is shown in Fig. 1.9 for refractory metal HEAs. The strength of HEAs are sometimes better than those of conventional superalloys [14].

Mechanical properties include the Young’s modulus, yield strength, plastic elongation, fracture toughness, and fatigue properties. For the conventional one-element principal alloys, the Young’s modulus is mainly controlled by the dominant element, e.g., the Young’s modulus of Fe-based alloys is about 200 GPa, that of Ti-based alloys is approximately 110 GPa, and that of Al-based alloys is about 75 GPa, as shown in Fig. 1.8.

In contrast, for HEAs, the modulus can be very different from any of the constituent elements in the alloys [79], and the moduli of HEAs are scattered in a wide range, as shown in Fig. 1.8. Wang et al. [79] reported that the Young’s modulus of the CoCrFeNiCuAl0.5 HEA is about 24.5 GPa, which is much lower than the modulus of any of the constituent elements in the alloy. It is even lower than the Young’s modulus of pure Al, about 69 GPa [80]. On the other hand, this value needs to be verified using other methods including impulse excitation of vibration.

It has been reported that the FCC-structured HEAs exhibit low strength and high plasticity [13], while the BCC-structured HEAs show high strength and low plasticity at room temperature [12]. Thus, the structure types are the dominant factor for controlling the strength or hardness of HEAs. For the fracture toughness of the HEAs, there is no report up to date.

It has been verified that not all the alloys with five-principal elements and with equi-atomic ratio compositions can form HEA solid solutions. Only carefully chosen compositions can form FCC and BCC solid solutions. Till today there is no report on hexagonal close-packed (HCP)-structured HEAs. One reason is probably due to the fact that a HCP structure is often the stable structure at low temperatures for pure elements (applicable) in the periodic table, and that it may transform to either BCC or FCC at high temperatures. Most of the HEA solid solutions are identified by trial-and-error experiments because there is no phase diagram on quaternary and higher systems. Hence, the trial-and error approach is the main way to develop high-performance HEAs. However, some parameters have been proposed to predict the phase formation of HEAs [17], [22], [28] in analogy to the Hume-Rothery rule for conventional solid solution.

The fundamental thermodynamic equation states:G=H-TSwhere H is the enthalpy, S is the entropy, G is the Gibbs free energy, and T is the absolute temperature. From Eq. (1-2), the TS term will become significant at high temperatures. Hence, preparing HEAs from the liquid and gas would provide different kinds of information. These techniques may include sputtering, laser cladding, plasma coating, and arc melting, which will be discussed in detail in the next chapter. For the atomic-level structures of HEAs, the neutron and synchrotron diffraction methods are useful to detect ordering parameters, long-range order, and short-range ordering [81].

For HEAs, entropy effects are the core to their formation and properties. Some immediate questions are: (1) How can we accurately predict the total entropy of HEA phase? (2) How can we predict the phase field of a HEA phase as a function of compositions and temperatures? (3) What are the proper modeling and experimental methods to study HEAs? To address the phase-stability issue, thermodynamic modeling is necessary as the first step to understand the fundamental of HEAs. The typical modeling techniques to address thermodynamics include the calculation of phase diagram (CALPHAD) modeling, first-principle calculations, molecular-dynamics (MD) simulations, and Monte Carlo simulations.

Kao et al. [82] using MD to study the structure of HEAs, and their modeling efforts can well explain the liquid-like structure of HEAs, as shown in Fig. 1.10. Grosso et al. [83] studied refractory HEAs using atomistic modeling, clarified the role of each element and their interactions, and concluded that 4- and 5-elements alloys are possible to quantify the transition to a high-entropy regime characterized by the formation of a continuous solid solution.

Section snippets

Thermodynamics

Thermodynamics mainly addresses the relationship among the macroscopic variables, such as temperature, volume, and pressure, which describes physical properties of material bodies and heat radiation. The chemical thermodynamics study the role of entropy in chemical reactions. Statistical thermodynamics or statistical mechanics give explanations of macroscopic thermodynamics by statistical predictions of the collective motion of particles based on the mechanics of their microscopic behavior [84].

Kinetics and alloy preparation

Thermodynamics, as mentioned in the former section, mainly addresses the stability of the state, and does not concern the rate, time, and routes. The kinetics in materials science is defined as the process of the materials transition from one state to another, with time. There is also another term, dynamics, which is mainly used for mechanical behavior, and conventionally related to the loading speed and time. Thus, the kinetics for HEAs in this section will focus on the mobility of the

Properties

The constitution of materials science usually contains four components, which forms the materials science tetrahedron. They include: (1) compositions and structures; (2) processing; (3) properties; and (4) performance. Sometimes, the characterization or the modeling and simulation can also be thought as the center of the tetrahedron. In this chapter, the mechanical, physical, and chemical properties of HEAs are described as follows.

Serrations and deformation mechanisms

According to Sethna, Dahmen et al. [155], [156], [157], [158], [159], [160], crackling noise arises when a system responds to slowly changing external conditions through discrete, impulsive events spanning a broad range of sizes. For example, when a magnetic tape is slowly magnetized by an external magnetic field, the process happens in avalanches, “Barkhausen noise” of reorienting magnetic domains that range from the microscopic to macroscopic scale in size. The avalanche size and duration

Glass formation in high-entropy alloys

High-entropy bulk metallic glasses (BMGs) can be referred to BMGs with an equal-atomic or near equal atomic composition. These BMGs have not only large high glass-forming ability (GFA), but also very high entropy of mixing. Consequently, the high-entropy BMGs are a special class of BMGs which have both strong topological disorder and chemical disorder.

Recently, Lucas et al. have verified that HEAs indeed lack the long-range chemical order [40]. In this regard, the high-entropy BMGs may have

Modeling and simulations

Largely due to the complexity of the multi-component system and disordered solid-solution structure in HEAs, predictive computational modeling of HEAs is very challenging. As a result, there are few theoretical reports on HEAs available in the open literature. However, there are increasing interests in computational modeling of HEAs to study the structure (including defects), thermodynamics, kinetics, and mechanical properties. For example, Kao et al. [247] simulated the structures of HEAs

Future development and research

HEAs are based on the multi-principal elements concept, which has stimulated rising interests for basic science and applications. The potential applications of HEAs are mainly based on their unique properties. Their excellent high-temperature properties may provide the potential to replace the Ni-based superalloy, e.g., AlCoCrFeNi, which is expected to be of lighter weight and lower cost. It is also reported that HEAs can be used as thermal barrier coatings for the Ti-based alloys and a

Summary

As a new class of materials that contain multi-principal-elements, HEAs have demonstrated unique and attractive engineering properties. The present paper has reviewed the formation criteria, thermodynamics, processing, kinetics, mechanical properties, and computer modeling of HEAs, as summarized as follows:

The four core effects of the HEAs have been summarized to understand the HEAs; the parameters, such as, enthalpy of mixing, atomic size difference, Ω, VEC, have been used to predict the phase

Disclaimer

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific

Acknowledgements

The authors are indebted to Prof. G.L. Chen, who passed away in 2011, for his pioneering work in HEAs and academic guidance. The authors are also grateful to Prof. W.K. Wang, Prof. W.H. Wang, Prof. Y. Li, Prof. H.A. Davies, Prof. Z.Q. Sun, Prof. T.G. Nieh, Prof. X.D. Hui, Prof. J.P. Lin, Dr. Y.Q. Cheng, and Dr. G.Y. Wang for valuable discussion, comments and advices. Z.Y. is grateful to the financial support of the National Natural Science Foundation of China (Grant Nos. 50971019, 51010001 and

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