目录结构

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参考文献

1 Introduction▲
2 Computational and experimental methods▲
3 Results and discussion▲
3.1 UW interface structure and preference site
3.2 Vacancy formation energy and diffusion energy barrier
3.3 Adhesion of U/W interface
3.4 Analysis of electronic structure
4 Conclusion▲
图表▲

Rare Metals2018年第9期

First principles application for mechanical properties of Ti-doped W particles enhanced U matrix composite

Jian-Bo Qi Li-Li Ru Guang-Xin Wu Jie-Yu Zhang Kuo-Chih Chou

State Key Laboratory of Advanced Special Steel,Shanghai University

Institute of Metallurgy,China North Nuclear Fuel Co. Ltd

Department of Physical Chemistry,University of Science and Technology Beijing

作者简介：*Guang-Xin Wu,e-mail:gxwu@shu.edu.cn;

收稿日期：27 February 2014

基金：financially supported by the National Natural Science Foundation of China(Nos.51074103 and 51104098);shanghai university scientific selection and cultivation for outstanding young teachers in special fund and Innovation Program of Shanghai University (SDCX2012011);

First principles application for mechanical properties of Ti-doped W particles enhanced U matrix composite

Jian-Bo Qi Li-Li Ru Guang-Xin Wu Jie-Yu Zhang Kuo-Chih Chou

State Key Laboratory of Advanced Special Steel,Shanghai University

Institute of Metallurgy,China North Nuclear Fuel Co. Ltd

Department of Physical Chemistry,University of Science and Technology Beijing

Abstract：

The stability, bonding, work of adhesion and electronic structure of the U/W interface with and without Ti were investigated by first principles to explore the mechanical properties of W particles enhanced U-Ti alloy matrix composite as a construction material. The calculated results indicate that the preferable orientation of the U/W interfacial structure is (001)_u/(11 0)_w crystallographic plane, Ti atoms originating from U slab are prone to diffuse into W slab through the interface, and additional Ti in U matrix is the stronger adhesion to W, with an ideal work of adhesion of 6.93 J·m^-2 for U-Ti/W interface, relative to the value of 6.72 J·m^-2 for clean U/W interface. The stronger adhesion performance is due to the increase in valence electron hybridization for U-Ti/W compared with U/W interface, as evidenced by the characteristic of the local density of states for the interfacial atoms.

Keyword：

First principles; U/W interface; Diffuse; Work of adhesion; Electronic structure;

Received： 27 February 2014

1 Introduction

As a radioactive element found early,uranium (U) occupies an important position all the time in nuclei energy field.At the same time,with the accelerating development of nuclei energy,further rigorous requirements to the mechanical properties of uranium matrix materials including high strength,heat resisting and rupture resistant are put forward.The stability of uranium decreases obviously within the reactor temperature range of 723-923 K;meanwhile,the mechanical properties become bad and cannot be improved even through heat treatment or deformation processing method.In this case,the alloying method can solve the problem.Kim et al. [ 1] investigated some commonly alloying elements of uranium,such as Mo,Ti,Nb,Zr and Cr.These elements have relatively large solubility in hightemperature phase ofγ-U (from 1047.8 to 1405.3 K,bcc crystal structure),form continuous solid solution in a wide range of temperatures [ 2] ,and hardly dissolve in room temperature phase ofα-U (≤940.7 K,orthorhombic crystal structure).According to the study of Udy and Boulger [ 3] ,a small additional amount of Ti after heat treatment(quenching,aging) can greatly improve the mechanical properties of uranium.The temperature of the reactor beyond 923 K should use uranium matrix composites because the performance of uranium alloy cannot yet meet the surrounding environmental requirements.As a kind of metal with high elastic modulus,high melting point,good thermal shock property and corrosion resistance,tungsten (W) has higher strength and thermal stability compared with uranium.Therefore,it is widely applied in nuclear power industry as a high-temperature construction material.Some former researchers [ 4, 5, 6, 7, 8] studied thermodynamics about uranium and tungsten reactive features.It is known that tungsten cannot form the intermetallic compound brittle phase with uranium at high temperature.Interface between uranium and tungsten will not form a strong combination,which will lead to fracture.At the same time,the density of tungsten is about19 g·cm^-3,close to uranium,which is prone to the uniform distribution of tungsten in uranium and good consistency of physical and chemical properties in integrated material.At present,the effect mechanisms for mechanical properties of U matrix after adding W and Ti are still not clear.So the study mainly focuses on mechanical effects of adding Ti to W particles reinforced U matrix composite.

In the metal matrix composites (MMCs),interface forms between hard particles and soft metal matrix,and its structure and performance are key factors to form the best comprehensive properties and give full play to the functions of composite [ 9] .Its structure and properties play a decisive role in the distribution of stress and strain,thermal expansion,load transfer and fracture process in MMCs.Further studies on the influences of performance,optimization,stability and control approach on interface structure [ 10] were investigated based on the interface rational structure,law of interface reaction and interface microstructure.At present,the researchers are scarcely concerning U-W composite and its interface,especially the theoretical research of the material.Until now,the experimental study of interface is difficult due to the limitation of experimental methods.Particularly for some nuclear and high chemical active materials,it is hard to determine or observe interface properties directly.So the density functional theory (DST) was used via implementing first principles calculation to investigate the interface structure and mechanical properties;meanwhile,the results were verified by energy-dispersive spectroscopy (EDS) method.

2 Computational and experimental methods

Owing to the periodicity of interface,all structures were fully relaxed with respect to volume and Z axis orientation at cell internal atomic coordinates.The total energies of the interface were calculated using density functional theory (DFT)and plane-wave pseudopotential methods [ 11, 12] .The convergence of results with respect to energy cutoff and kpoints was carefully considered.A plane-wave basis set was used with an energy cutoff of 400 eV to represent the KohnSham wave functions.Calculation was implemented in the Vienna ab initio simulation package (VASP) code [ 13] based on DFT.The generalized gradient approximation (GG A) and Perdew-Burke-Ernzerhof (PBE) [ 14] functions were applied to the electron exchange and correlation,using Blochl all electron projector augmented wave (PAW) method [ 15] ,as implemented by Kresse and Joubert [ 16] .

In order to establish the validity of the ab initio approach,the bulk lattice constant and some properties of the interface,namely the optimized bulk,the interface relaxation and surface energy were calculated prior to considering the work of adhesion and the electronic structure.The traditional four atoms orthorhombicα-U and bcc-W cells were fully relaxed for structure optimization [ 17] ,and the kinetic energy cutoff andk-point sampling were tested.The test results show that a kinetic energy cutoff of 400 eV for all calculations is appropriate.Cells converged total energies and force change for each atom are less than 0.1 meV and 0.1 eV·nm^-1,respectively.The first Brillouin zone k-points were sampled according to Monkhorst-Pack scheme with 9×4×5 and11×11×11 mesh,respectively.It was pointed out that GGA method was improved greatly than LDA in dealing with the outer electrons containing f orbital electrons [ 18] .The lattice parameters of the orthorhombicα-U were calculated to be a=0.2797 nm,b=0.5892 nm,c=0.4891 nm and bcc-W were a=b=c=0.3179 nm with GGA-PAW method.The equilibrium primitive unit cell volumes were 0.02015 and 0.01606 nm³,respectively.These results were in agreement with the pseudopotential results of the others [ 19, 20, 21, 22, 23] ,as well as experimental results in Refs. [ 24, 25] .Similarly,for bcc-W,GGA results were more in agreement with the experimental value of0.3165 nm than those of LDA.The more calculation details are as follows.

Before experiment,W powder morphology and granularity size were measured by VEGA 3 XMU scanning electron microscope (SEM) attached with Bruker energydispersive spectrum (EDS),voltage 30 kV and secondary electron.The morphology of tungsten powder is shown in Fig.1.Most particles demonstrate polyhedron shape.The value of granularity test is listed in Table 1,the average grain size and mid-value size are about 8.23 and 6.40μm,respectively.At the range of granularity,tungsten powder has fewer defects.In experimental process,moderate tungsten powder was placed into a crucible first,and then U

Fig.1 Secondary electron image of tungsten particles

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Table 1 Tungsten powder granularity

bulk or U-Ti alloy bulk was added for vacuum induction melting.Temperature was up to 1330℃for 20 min of heat preservation and pouring subsequently,and then outage cooling.Wire cutting sample was 2.0 mm×2.0 mm×1.5 mm in dimension grinded with SiC abrasive papers (400-2000meshes).The long flannelette with 1.0-μm diamond abrasive paste was used to final grinded step for mechanical polishing.EDS,back-scattering and mapping tests were carried,and the voltage was 20 kV for the detection of pure U matrix additive W particles composite.

3 Results and discussion

3.1 UW interface structure and preference site

The interface between matrix and reinforced particles has relatively intricate structure due to low symmetric orthorhombicα-U and high symmetric bcc-W.Building surface has a variety of options,including how to cut the surface of the matrix and reinforced particles,as well as how to build them together.With respect to W particles reinforced U matrix composite,several low miller index structures were studied.First of all,no doped Ti atom clean U/W interface was selected and calculated.The lattice parameters of U and W are different in leading to lattice mismatch.Because the W(110) crystal plane is known to be stable in the respective bulk materials,this orientation is expected to appear in the interface formation.So the bcc unit cell of tungsten is cleaved by the (110) plane and reconstructs another slab structure along the[110]crystallography direction,and the lattice constants are a=c= =0.4496 nm,b=b_bulk=0.3179 nm.To make the lattice mismatch as small as possible,orthorhombicα-U,(001) and (010) cleave slabs were built,respectively.Then according to above slab,W(110) 2×2 slab five layers with oa-U(001) 3×1 slab six layers,and W(110)2×3 slab five layers withα-U(010) 3×2 slab eight layers superlattice structure U/W interface were built,respectively.A 3×5×1 mesh was used for thek-points sampling,and both of interfaces carried out structural optimization.The total energies of the W(110)/U(001) and W(110)/U(010) interfaces are-905.14 and-899.75 eV,respectively.These two structures have the same crystal systems and can get W(110)/U(001) interface which has lower energy.W(110)/U(001) interface is more stable than W(110)/U(010) interface.The interface structure is shown in Fig.2.The U-W interface spacing takes different values of 0.21,0.23,0.24,0.25 and 0.26 nm,respectively,to verify the reasonable distance.Relaxation continues until the optimization is completed and the lowest energy interface is the reasonable distance,0.24 nm,as listed in Table 2.According to the computational result and Zarshenas,investigation [ 23] ,a crystal orientation of W(110)/α-U(001) was selected.Although other kinds of interface orientations between bcc-W and orthorhombicα-U can be presented,it is believed that the primary bonding can be characterized by a model as investigated in this study.From what was discussed above,in the following calculation,the W(110)/U(001) interface structure with interface spacing of 0.24 nm can be used to investigate the theoretical work of adhesion and Griffith fracture work of interface as the basis of judging the mechanical performance of the material.

In addition,the mechanical properties of U matrix-doped Ti atoms W(110)/UTi(001) interface were studied.Owing to relatively low Ti content (from 0.95 wt%to 1.30 wt%),one Ti atom with interface condition was calculated in the system and the total energies of Ti atom in the interface and bulk are—905.14 and—897.35 eV,respectively.It can be seen that Ti atoms are apt to segregation in U/W interface.

3.2 Vacancy formation energy and diffusion energy barrier

The vacancy formation energy is defined as the energy needed to remove an atom from the host material and place it into a reservoir of the same atomic species.With respect to the issue of atoms diffusion within UW and Ti-doped U/W interface,due to that the vacancy diffusion energy barrier is the lowest for substitution atoms,the vacancy diffusion is the main diffusion way.Therefore,two aspects are mainly considered,the interface vacancy formation energy ( )and diffusion energy barrier (E_a) [ 26, 27, 28] .Vacancy formation energy of interface atoms is described by:

Fig.2 U/W interface structure:a U(001)/W(110) interface and b U(010)W(110) interface

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Table 2 Relationship of interface spacing and total energy (E_tot) for UW interface

where E_vis and E_ps are the total energies of the slab with a metal atom vacancy and perfect slab,respectively;μ_va is the chemical potential of a metal vacancy atom removed from slab.The chemical potential is defined as the Gibbs free energy per atom in the atomic reservoir [ 29] .The energy per atom in bulk of equilibrium state is often taken as the reference energy for describing the chemical potential,and therefore,the calculated chemical potentials for species U,W and Ti are-11.14,-12.83 and-7.77 eV,respectively.Furthermore,for the vacancy diffusion mechanism,the driving force of interfacial atom is the chemical potential differences value of element both sides of the interface.For the interface layer between uranium matrix and tungsten particles,when one atom diffuses from original site to a vacancy of another slab at the interface,the diffusion energy barrier (E_a) is qualitative given by:

where,U_host andμ_d are the chemical potentials of matrix atom and diffusion atom,respectively.The results are given in Table 3 and clearly the diffusion energy barrier of U atom is less than that of W atom.So within U/W interface structure,U atoms are apt to diffuse to W(110) slab but W atoms are difficult to diffuse to U(001) slab.After adding Ti and forming solid solution,computational and E_a are1.27 and 0.62 eV,respectively.It can be seen that doped Ti atom escapes away from its original site and forms vacancy more difficultly than U atom ( of 0.94 eV).However,Ti atom possesses lower diffusion energy barrier than U and W atoms,which indicates that Ti atoms are easier to diffuse.

Further analysis as below is the diffusion effect by combining EDS results.As shown in Fig.3,the experimental temperature is from 1300 to 1350℃and it can be seen that the boundary of W particles is exactly W element distribution boundary,that is,W atoms hardly diffuse to U matrix.From U element distribution image,it can be clearly seen that the green spacing increases between W particles,U atoms diffuse to W particles inside,and the diffusion distance is about 0.5μm.In addition,the observed interface between W particles and U matrix is clear and clean where precipitation emerged cannot be found.And there is no crackle existing in the morphology.

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Table 3 Vacancy formation energy (Ey) and diffusion energy barrier(E_a) of cleave slab

Figure 4 is the back-scattering image and corresponding EDS analyses.U and Ti atoms can diffuse to W bulk,as shown in Fig.4b,c.On the contrary,W atoms cannot diffuse to U matrix (Fig.4f).Experimental temperature is from 1400 to 1450℃.Figure 4d,e indicates that W bulk boundary recrystallization happens and brittle phase forms in this temperature range.The tensile strength limitation is 450 MPa via detecting and that of U matrix is798 MPa,showing that the mechanical property declines.To sum up,the composite temperature and time should be strictly controlled in the process of preparation composite materials.

3.3 Adhesion of U/W interface

Work of adhesion and Griffith fracture work are important indexes to measure coherent strength and toughness of interface.According to this point,clean U/W interface and UTi/W interface of adding Ti in U matrix between U matrix and W particles were investigated,respectively.Before and after adding Ti,work of adhesion for interface can be obtained by Eqs.(3) and (4) [ 30, 31, 32] ,respectively.

where E(Xsur) and E(Ysur) are total energies of complete interface removed W slab or U slab,respectively;E(fully relaxed U/W) and E(fully relaxed UTi/W) are total energies of fully relaxed clean U/W interface and containing Ti UTi/W interface;A is area of interface.In Eq.(3),it represents the work of adhesion for no diffusion as X is U and Y is W,or U atom diffused to W as X is U and Y is U-doped W.In Eq.(4),it represents the work of adhesion for no diffusion as X is UTi and Y is W,or Ti atom diffused to W as X is U and Y is Ti-doped W.

Fig.3 Back-scattering and mapping images of pure U matrix additive W particles composite at temperature range of 1300-1350℃:a W particles distribution (gray color),b W element distribution (blue) and c U element distribution (green)

Fig.4 Back-scattering a and corresponding (Points 1-5) EDS analyses b-f of U-0.95 wt%Ti alloy additive W composite at temperature range of 1400-1450℃

Griffith fracture work (W_Grif) is an approximation to strength and toughness of an interface.It is defined as the energy needed (per unit area) to separate reversibly an interface into two free surfaces.According to this definition,the fracture work of interface related to the crystal plane can be estimated as W_Grif～2γ,whereγis surface energy,and clean U(001)/W(110) and Ti-doped UTi(001)/W(110) surface energy (γ_c)and (γ_d) can be obtained by Eqs.(5) and (6),respectively.

where E_slab and are the total energies of unrelaxed clean slab and UTi solid solution slab,respectively;,U_bulk, and represent the chemical potentials of clean bulk,U bulk and Ti bulk,respectively;N,N_U and N_Tirepresent total atom number of clean slab,U slab and doped Ti atom,respectively.The total interface area is given by A and factor 2 accounts for splitting between the two identical surfaces in the supercell;ΔH_f is the formation enthalpy of UTi solid solution at 0 K as shown in Eq.(7) [ 27] :

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Table 4 Work of adhesion (E_ad) and Griffith fracture work (W_Grif) of interface (J·m^-2)

where E_tot(UTi) is the total energy of UTi solid solution that contains the same atom number with slab.E_tot(U) and E_tot(Ti) are the total energies of U and Ti atoms in solid solution,respectively.Therefore,Griffith fracture work of U/W and UTi/W interface can be described,respectively,by [ 32, 33] :

The calculated results are shown in Table 4.It can be seen that work of adhesion and Griffith fracture work are improved from 6.72 and 5.10 J·m^-2 to 7.01 and 5.37 J·m^-2respectively,after adding Ti and no diffusion.It indicates that the interface bonding strength increases and the fracture toughness improves.The work of adhesion increases from6.93 to 7.11 J·m^-2 if Ti and U atoms diffuse to W side,which further improves the bonding strength of interface.

3.4 Analysis of electronic structure

The interaction levels of electrons among atoms decide the mechanical properties of interface in nature.So it is necessary to investigate the electronic structure of U/W interface with and without Ti atom.The density of states(DOS) and electronic density distribution were used to study valence electronic hybridization of interface.As shown in Figs.5 and 6,on the basis of above calculation,changes of mechanical properties with additive Ti were investigated.

Figures 5 and 6 show that the valence electrons of U atoms located in clean interface have strong localization and the hybridization effect is relatively feeble of U valence electrons.At the same time,it can be seen that valence electrons hybridization of U and W atoms is slightly stronger than that of U atoms in the interface layer.However,valence electrons localization of U atoms of Tidoped U/W interface decreases and the interaction effect of valence electrons improves among U atoms or W atoms,as well as between U atom and W atom.The valence electrons interaction between Ti and U atoms increases not much but that of Ti and W atoms increases more.

Valence electronic orbit is 5p65d46s2 with W atom and5f36d17s2 with U atom.It can be seen from DOS figure that the influence of U-5f orbital electrons cannot be neglected.In contrast,the DOS image with and without Ti can be obtained in either case of the range from-21.3 to-15.5 eV mainly dominated by U-6p orbital under the Fermi energy.Devoted by U-5f and W-5d,the clean U/W interface has the relatively higher eigenvalue (134.4states·eV^-1) of the DOS at the Fermi energy and the peak value is up to 135.6 eV that appears at-0.04 eV of the nearest to Fermi energy,which shows up stronger localization characteristic for valence electrons.Valence electrons hybridization is weak,and valence electrons are easily ruptured by interface.After a little Ti (about 0.95wt%,valence electrons orbit 3d24s2) doped,the eigenvalue(112.4 states·eV^-1) of the DOS is lower at the Fermi energy.By comparing with the DOS of clean interface,the peak value which is the nearest to Fermi energy (116.8 eV)shifts to lower energy (-0.21 eV) and becomes mild near the Fermi energy,its range is from-5 to 0 eV,which shows strong metallic bond character.U-5f/7s,Ti-3d/4s and W-5p/5d orbital hybridizations increase to some extent,indicating that the valence electrons localization decreases and the interaction effect increases.According to above analysis,it can be explained that Ti-doped interface has stronger adhesion performance,higher strength and better toughness.In other words,the interface is more stable.With the addition of Ti,bonding effects between TiW and U-W atoms of interface are more significant,and bonding strength and toughness of interface improve because of the change with interface electronic structure,consequently improving the mechanical properties of whole composite material.

Fig.5 DOS images of interface with and without Ti:a clean interface and b Ti-doped interface

Fig.6 Valence electron density distribution of U/W interface with and without Ti atom:a clean interface and b Ti-doped interface.Blue,green and red spheres indicating U,W and Ti atoms,respectively

4 Conclusion

In summary,a plane-wave pseudopotential method based on first principles is employed to study the electronic structure,diffusion and adhesion properties of U/W interface with and without Ti.For the clean U(001)/W(110)interface,by comparing with the diffusion barriers of all kinds of atoms,the results indicate that U atom is easy to diffuse to a vacancy of W bulk as a substitute atom but W atom is difficult to diffuse to U bulk.Computational results of work of adhesion with and without diffusion indicate that the diffusion improves the bonding strength of U/Winterface no matter Ti or U atom diffuses.Relative to the clean U/W interface,doped Ti can further improve the interface bonding strength and make the fracture toughness of interface better because of the strong valence electrons hybridization between Ti and U atoms or Ti and W atoms.Compared with no Ti-doped interface,the higher work of adhesion and Griffith fracture work can be also proved from the conclusions.In addition,computational diffusion barrier values show that Ti atom is easier to diffuse to W bulk than U atom,and interfacial work of adhesion as well as Griffith fracture work is higher compared with no diffusion interface.The results prove that the interfacial bonding strength and stability are improved further.

Acknowledgments The work was financially supported by the National Natural Science Foundation of China (Nos.51074103 and51104098) and shanghai university scientific selection and cultivation for outstanding young teachers in special fund and Innovation Program of Shanghai University (SDCX2012011).