However until now combined influence on SAV

However, until now combined influence on SAV of H and other light elements such as C, O and N as well as trapping of H atoms by the monovacancy in the Ti lattice were poorly studied. At the same time the possibility of such influence is indicated by experimental data on Al lattice with C and H impurities [33]. Number of pores is increased after preliminary annealing. In this connection, in the present article, we investigate combined influence of H, C, N and O atoms on the formation of their complexes with monovacancy and vacancy formation energy from first principles (ab initio). The investigation was performed for FCC Al and HCP Ti lattices, their alloys being widely used because of their high specific strength and corrosion resistance.
Calculation method Calculations were performed in the framework of the density functional theory (DFT) [34,35] within the generalized gradient approximation (GGA) using the functional of Perdew et al. [36,37] for description of the exchange-correlation energy and the projected augmented wave (PAW) method [38] as implemented in ABINIT code [39]. Point defects were considered within supercell model. The list of point defects included an impurity pacap in the interstitial site, a monovacancy and monovacancy-impurity complexes. Brillouin-zone (BZ) integrals were approximated using the special k-point sampling of Monkhorst and Pack [40]. Full energies of supercells were calculated after relaxation to equilibrium positions of atoms and volumes at 0K. Relaxation was performed in several steps. Initial configurations included an impurity atom in the center of a monovacancy and the impurity atom in the center of interstitial site of the HCP lattice. Molecular-dynamics modeling were performed for initial configurations using Verlet algorithm [41] at 300K and consecutive cooling down to 100K using Nose–Hoover thermostat [42]. Final equilibrium configurations were determined by relaxation of supercells with the Broyden–Fletcher–Goldfarb–Shanno mеthod [43] to the energy minimum at 0K. The relaxation was stopped when all forces acting on the atoms were converged to within 2.5meV/Å. The favorable occupation site of an impurity is defined by a difference of solution energies of this impurity at different positions (Δ. The solution energy is calculated by the following formula: where E[+] are the total energies of the system with n atoms of metal M (M=Ti, Al) when atom X is at tetrahedral (T) or octahedral (O) interstitial site, E[] is the energy of pure system with n atoms of metal M, E[] is the energy of molecule X2 (X=H, C, N and O) in the vacuum or in the case of carbon – the energy of graphene cell with two atoms. In the case of vacancy-impurity system, the stability of each configuration is defined by the binding energy which was calculated by the following formula: where is the total energy of the supercell with n atoms of metal M (M=Al, Ti) and the impurity X in the T/O site (X=H, C, N and O), E[] is the total energy of the supercell with n atoms of metal, E[V+−1] is the total energy of the supercell with (n−1) metal atoms and one vacancy, E[/–V+−1] is the total energy of the supercell with the complex X – vacancy and (n−1) metal atoms. In the case of the X–(H–V) complexes V is replaced by (H–V) in this equation. Formation vacancy energies were calculated as follows:
Here and [X] are vacancy formation energies in pure metal and in the metal with (X–V) complexes, correspondingly. In the case of the (X–(H–V)) complexes H must be additionally subtracted from . Ismer et al. [32] suggested to determine changing of the energetic characteristics of (V–nH) complex (a vacancy and n atoms of hydrogen) stepwise form by adding impurity atoms one by one. Using this approach we can write the cohesive energy between a hydrogen atom and the (V–(n–1)H) complex as follows: where E[V–(n–1)H+1] is the total energy of the supercell with (V–(n–1)H) complex, E[V–nH+1] is the total energy of the supercell with (V–nH) complex.