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A first-principles density functional approach is used to study the electronic and the elastic properties of Nb_(15) X (X=Ti,Zr,Hf,V,Ta,Cr,Mo,and W) alloys.The elastic constants c 11 and c 12,the shear modulus C,and the elastic modulus E 100 are found to exhibit similar tendencies,each as a function of valence electron number per atom (EPA),while c44 seems unclear.Both c 11 and c12 of Nb 15 X alloys increase monotonically with the increase of EPA.The C and E 100 also show similar tendencies.The elastic constants (except c44) increase slightly when alloying with neighbours of a higher d-transition series.Our results are supported by the bonding density distribution.When solute atoms change from Ti(Zr,Hf) to V(Ta) then to Cr(Mo,W),the bonding electron density between the central solute atom and its first neighbouring Nb atoms is increased and becomes more anisotropic,which indicates the strong interaction and thus enhances the elastic properties of Nb-Cr(Mo,W) alloys.Under uniaxial 100 tensile loading,alloyed elements with less (more) valence electrons decrease (increase) the ideal tensile strength.
A first-principles density functional approach is used to study the electronic and the elastic properties of Nb_ (15) X (X = Ti, Zr, Hf, V, Ta, Cr, Mo, and W) and c 12, the modulus of elasticity E 100 are found to exhibit similar tendencies, each as a function of valence electron number per atom (EPA), while c44 seems unclear. Both c 11 and c12 of Nb 15 X alloys increase monotonically with the increase of EPA. The C and E 100 also show similar similar to that ofdenhance constants (except c44) increase slightly when alloying with neighbors of a higher d-transition series.Our results are supported by the bonding density distribution. When solute atoms change from Ti (Zr, Hf) to V (Ta) then to Cr (Mo, W), the bonding electron density between the central solute atom and its first neighbor Nb atoms is increased and becomes more anisotropic, which indicates the strong interaction and thus enhances the elastic properties of Nb-Cr (Mo, W) alloys. Under uniaxial 100 t ensile loading, alloyed elements with less (more) valence electrons decrease (increase) the ideal tensile strength.