MAEAM Simulation On The Formation And Migration Of The Vacancies In BCC Transition Metals

Vacancy is one kind of the crystal defects in metals. The existence of the vacancy in metals and at the surface affects directly the physical, chemical and mechanical properties of the metals. The migration of vacancy is the dominant mechanism of atom transport or diffusion in processes like solid phase transformation,crack formation and expanding, dislocation and interface migration. Many surface phenomena such as diffusion, surface roughening and segregation, oxidation, corrosion and crystal growth are directly referred to the vacancy at the surfaces. So many experimental and theories methods have been developed to study it.In this paper, the formation energy of mono-vacancy, both the formation and binding energies of the di- and tri-vacancies in the bulk, the formation energy of a single vacancy and an vacancy-adatom pair at the uppermost layers of the three low-index surfaces ((100), (110) and (111)), and the formation, migration and self-diffuse activation energies of a single vacancy in W (001), W (110) and Fe (111) surfaces for BCC transition metals have been calculated by using the modified analytical embedded-atom method (MAEAM). From the energy minimization, the favorable stable configuration of di- and tri-vacancies in the bulk, the favorable formation of the vacancy-adatom pair at the three low-index surfaces and the favorable formation and migration mechanism of the vacancy in the W (001), W (110) and Fe (111) surface layers are discussed in detail. The results are shown in the following.(1) The favorable configuration of the di-vacancy and tri-vacancy respectively is the first-nearest-neighbor (FN) or the second-nearest-neighbor (SN) di-vacancy and the [112] tri-vacancy constructed by two firs- and one second-neighbor vacancies. It is indicated that there is a concentration tendency for vacancies in BCC metals.(2) The formation energies of a single vacancy or an vacancy-adatom pair are different for different metals and they are all decreased in sequence of (111)→(100)→(110) surfaces for each metal, that is E_v¹¹¹ï¼œE_v¹⁰⁰＜E_v¹¹⁰, E_v+ad¹¹¹ï¼œE_v+ad¹⁰⁰＜E_v+ad¹¹⁰ So for BCC metals, the larger the interplanar spacing (or the atomic area density) is, the higher the formation energy of a single vacancy or an vacancy-adatom pair is; The negative values of the formation energy for a single vacancy or an vacancy-adatom pair are obtained in the (111) surface, this implies that the formation of these defects is spontaneous and natural; For each low-index surface of each metal, the formation energy of an vacancy-adatom pair is always lower than that of a single vacancy, which shown the formation of vacancy-adatom pair is more energetically favorable than that of the vacancy for the BCC transition metals.(3) For the W (001), W (110) and Fe (111) surfaces, it is easier for a vacancy to form and to migrate in the first intra-layer respectively. This is in agreement with the fact of experiment that the vacancy has the largest concentration in the first layer. For the vacancy in the first four layers of W (001), the first second layers of W (110) and the first sixth layers of Fe (111) are all favorably migrate to the upper layers. However, the vacancy in the fifth and sixth layers of W (001) and in the eighth, ninth and tenth layers of Fe (111) migrate favorably to the lower layers, in the third layer of W (110), it migrate favorably to the lower layers or in the intra-layer. Of course, in the seventh layer of W (001), the fourth layer of W (110) and the tenth layer of Fe (111), the vacancy migration is the same with that in the bulk. So the vacancy migration in BCC transition metals surfaces is completely different with the vacancy migration in the bulk because of the surface effect.