Vacancies in Metals: From First-Principles Calculations to Experimental Data

Abstract

We have revealed, and resolved, an apparent inability of density functional theory, within the local density and generalized gradient approximations, to describe vacancies in Al accurately and consistently. The shortcoming is due to electron correlation effects near electronic edges and we show how to correct for them. We find that the divacancy in Al is energetically unstable and we show that anharmonic atomic vibrations explain the non-Arrhenius temperature dependence of the vacancy concentration.

First-Principles Study of the Stability and Interfacial Bonding of Tilt and Twist Grain Boundaries in Al and Cu

“…The present features of significant charge accumulations for local regions formed by less-coordinated or greatly distorted atoms are general features observed in distorted or defective configurations in Al such as point defects 6,7) and surfaces. 33) In a single vacancy in Al, the first shell is strengthened by charge accumulation among less-coordinated atoms, which stabilizes a single vacancy against a divacancy.…”

“…There emerges a hypothesis that the covalent nature of valence electrons in Al 5) may generally reduce defect energies, namely stabilize defective structures via electronic and atomic behavior of reconstruction as observed in ab initio calculations of Al surfaces 33) or point defects. 6,7) This problem will be discussed again later.…”

“…For example, the vacancy formation energy is experimentally 1.03 eV, 26) 1.19 eV, 27) or 1.30 eV 28) for Cu, in contrast to 0.68 eV for Al (52{66% of Cu), 29) which are well reproduced by recent ab initio calculations. 6,7,30) Recent ab initio calculations also indicate that the surface energy of Cu (110) is 0.901 eV per surface atom in contrast to 0.708 eV (78%) for Al(110). 31,32) Thus the present results of the smaller boundary energies for Al than for Cu are consistent with other types of defect energies.…”

“…4) Recently, the origin of the different SFEs has been explained by the different bonding nature. 5) In Al, sp electrons reveal rather covalent or directional-bonding features in deformed or defective configurations 6,7) in contrast to rather isotropic metallic bonding of Cu with a closed-shell d-band. More distant inter-atomic interactions in Al via such sp electrons generate a substantial energy difference between fcc and hcp structures, while the structural difference over the 2nd neighbors is not so sensitive in Cu with short-ranged inter-atomic interactions, resulting in much larger SFE for Al.…”

Diffusion quantum Monte Carlo study of the equation of state and point defects in aluminum

“…Our DMC calculations of the defect properties of aluminum include the simplest point defect, the vacancy for which numerous DFT 7-9 and experimental results [10][11][12][13][14] are available. We compute the nearest-neighbor divacancy binding energy, a defect that DFT calculations 7,15 have found to be unstable. Since this instability is counter to both experimental studies 11,16 and simple bond counting arguments 17 it is important to perform calculations of this defect with DMC, a method that unlike DFT, does not rely on approximations for exchange and correlation.…”