| In the last few decades, there have been tremendous advances in the performance of metallic materials by using computer simulation. Accompanied by the continuous progress of computational method in materials design, a series of methods has been established to simulate the properties of the bcc transitional metals and their alloys. We can not only continue to optimize the material design models through computer simulations, but also save experimental materials by virtual experiments, so as to improve the efficiency of material use and open a new way for the material design.There are many varieties of computer simulation methods for the calculation of material properties. Embedded atom method (EAM) has attracted considerable interests for the past30years because of its convenience and agreement with experimental results in the calculation of the properties of metal and intermetallic compounds. It is known that four levels of EAM methods such as the original EAM proposed by Daw and Baskes, the analytic EAM (AEAM) by Johnson, the modified EAM (MEAM) by Baskes and the modified analytic EAM (MAEAM) by Zhang et al. exist. MAEAM is convenient in the calculation of alloy properties and can resolve the negative Cauchy pressure problem of Johnson’s model. To improve the exactness of the calculation results of this method, the farther neighbor atoms are considered by Hu and Shu. But this MAEAM still has some points to improve, including the properties of the end parts the derivatives of the pair potential function, the structure stabilities of noble metals, and the misfitting problem of the calculation results of energy differences between several structures.In the original MAEAM calculation, the results of structure energy differences misfit the experiment data for several bcc metals, because its model parameters are fitted without any consideration for these differences. Firstly, In the present paper, the traditional MAEAM theory considering farther neighbor atoms is modified. We not only adopt an end processing function and an enhanced smooth continuous condition, but also adjust model parameters of multi-body potential by fitting cohesion energies, mono-vacancy formation energies, Rose equation curves for total energy as a function of lattice parameter, energy differences between several model structures, elastic parameters, equilibrium conditions of crystals. In order to resolve the misfitting problem between calculated results and experimental data for the energy differences between several structures of transition metals, input physical data include one of these differences. Two model parameters become unnecessary because of the adoption of the end processing function. Through adusting one of these two parameters, the many-body potential becomes fit to the structure energy difference.Secondly, the structural stabilities, the phonon spectra, the densities of states and the lattice specific heats are studied with the new MAEAM multi-body potential for seven bcc metals. The results are in good agreement with experimental values and other calculation results, although there are still some defects in the results of some individual metals, the calculation results of various physical properties are consistent with the experimental variation rules on the whole, which demonstrates the application of the new MAEAM potential function may lead to the better simulation of material properties and materials design.Thirdly, we study the vacancy properties of seven bcc metals. We refer and make better the calculation methods of Zhang Bang Wei et al. in the calculation of the properties of mono-and bi-vacancies, and determine migration saddle points by calculating the distribution of migration energies around the migration atom in the study of the properties of bi-vacancy migrations. Our calculation results of mono-vacancy formation and diffusion energies agreed with the experimental results, and better than other model results. The results of bi-vacancy formation, combination, migration and diffusion energies fit the calculation results based on the other models very well.In summary, a modified MAEAM theory is used in the study of the physical properties of bcc metals. The calculations fully demonstrate the structure stabilities, the lattice dynamical properties, the lattice specific heats and the vacancy properties of pure bcc metals, which ensured the effectiveness of our MAEAM multi-body potentials and calculation methods considering farther neighbor atoms. |
