Valence Bond Structures And Phase Stability Of Refractory Metals (W, Mo, Ta, Nb) And Their Binary Alloys

The valence bond structures and phase stability of refractory metals (W, Mo, Ta, Nb) and their binary alloys have been systematically studied and analyzed under the framework of systematic science of metallic materials.Based on the one-atom self-consistency method for determining the valence and bond structures of metal, the energy and shape (ES) method has been brought forward. New progress has been made in the theory. The VB structures are determined with the unity of lattice constant and energy minimization. To take Al, Ti and Cu as an example, the ES method is introduced in detail. The VB structures of Al, Ti, and Cu are determined. This method overcomes the problem of multiple solutions and the difficult selection of basic states. The results are more refined and reliable.The valence bond structure of refractory metals (W, Mo, Ta, Nb) is redetermined at room temperature and at ambient pressure using the ES method. The results are more refined than Pauling's and Brewer's. The properties (melting point, Young's module, rigid module, elastic module, Brinell hardness, electrical and thermal conductivity) of refractory metals (W, Mo, Ta, Nb) are quantitatively analysed by their bond valence structures. It is studied that temperature and pressure have influence on the valence bond structure of refractory metals (W, Mo, Ta, Nb). It is found that the valence electrons e_c (d_c, s_c and p_c), bond energy and bond valence decrease while near free electrons e_f, bond length and single-bond radius increases with increasing temperature. Overall, the temperature dependent valence structure of refractory metals (W, Mo, Ta, Nb) is not a drastic change within the range of solid phase. The covalent electrons e_c (d_c, s_c and p_c) and bond valence increase while near free electrons e_f, bond length, single-bond radius and bond energy decreases with increasing pressure. The electron distributions are more localized and the bonding character becomes more covalent bonding with increasing pressure.According to characteristic crystal theory, the valence bond structures and phase stability of Ta-W, Nb-Mo and Ta-Mo system have been studied systematically. The atom volume interacting function and energy interacting function between atoms in disordered Ta-W, Nb-Mo and Ta-Mo system with bcc structure are determined for the ninth function. The valence bond structures of and characteristic crystal sequences with bcc structure in Ta-W, Nb-Mo and Ta-Mo system are obtained. Applying the characteristic atom arranging designing technique based on the characteristic crystal theory, the relationship curve of valence bond structures varying with the alloy concentration of disordered bcc A2 and the typical ordered phases, such as bcc B2, DO₃ A₃B and DO₃ AB₃, in Ta-W, Nb-Mo and Ta-Mo system have been calculated. When disordered bcc A2 is transformed into ordered bcc B2, DO₃ A₃B or DO₃ AB₃, the covalent electrons, bonding electrons and cohesive energy increase, the near free electrons, bond length and atomic volume decrease.Applying statistic thermodynamics based on the characteristic crystal model, the thermodynamic properties of Ta-W, Nb-Mo and Ta-Mo system have been studied. The Gibbs free energies of liquid,disordered bcc phase and ordered phases of the Ta-Mo system are described. The phase diagram of Ta-W, Nb-Mo and Ta-Mo system with liquidus, solidus and ordered phases areas is assessed and predicted. The calculated liquidus and solidus are in agreement with experimental information and other assessed papers, moreover, the evaluated results about ordered phases are better than that of first principle. The enthapy of formation of ordered bcc B2, DO₃ A₃B and DO₃ AB₃ and order-disorder A2-B2 transition temperatures in the Ta-W, Nb-Mo and Ta-Mo alloys have been analyzed. Ta-Mo alloys is the strongest, Ta-W alloys is the weakest in atom interaction.