Prediction of Energies of <100> Tilt Boundaries in Al-Pb Alloy
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1056-HH01-10
PREDICTION OF ENERGIES OF TILT BOUNDARIES IN Al-Pb ALLOY Y. Purohit, D. L. Irving, R. O. Scattergood, and D. W. Brenner Materials Science and Engineering, North Carolina State University, Raleigh, NC, 27695
ABSTRACT Energies for symmetric tilt grain boundaries in pure Al and in Al with substitutional Pb defects at coincident sites along the grain boundaries were calculated using a modified embedded atom method potential and density functional theory. The agreement between the analytic potential, the first principles calculations and experiment is reasonably good for the pure system. For the Al-Pb system both the analytic potential and first principles calculations predict that Pb segregation to the interface is energetically preferred compared to the dilute solution. The application of a disclination structural unit model to calculating grain boundary energies over the entire range of tilt angles is also explained. INTRODUCTION In a recent study, Monte Carlo simulations were used to investigate the structures and energies of Pb impurities in an aluminum bicrystal containing two complementary Σ5 {210} tilt grain boundaries [1]. Interatomic interactions in the Al-Pb alloy system were described using a modified embedded atom method (MEAM) potential [2] with parameters fit to the results of density functional theory (DFT) calculations on two hypothetical Al-Pb binary alloys. These simulations, and subsequent calculations of the energies of Pb clusters in an Al matrix with the same potential function, predict a preference for the segregation of Pb atoms to grain boundaries compared to the formation of embedded Pb clusters with diameters less than about 4 nm. This preference for grain boundary segregation is consistent with experimental z-contrast transmission electron micrographs of Al-Pb nanoalloys that indicate Pb dispersed on grain boundaries [3]. According to Weismuller and others [4-5], the segregation of impurities with limited solubilities to grain boundaries can reduce the grain boundary energy and therefore help to stabilize the structures against grain growth. A reduction of grain boundary energy with an increasing number of Pb atoms on the grain boundary was predicted by our calculations, with a negative energy with respect to the ideal dilute solid solution predicted when more than 50 percent of the coincident sites per unit grain boundary area are replaced by Pb atoms. This result suggests that Pb impurities can stabilize grains in Al against grain growth.
Motivated by the above findings using a MEAM potential, we report in this paper the results of DFT calculations of the energy of two high symmetry tilt grain boundaries in Al with and without Pb at the interface. The DFT energies confirm the stabilization of grain boundaries in Al due to Pb segregation with respect to the ideal solid solution predicted by the MEAM. Also reported is the application of a disclination structural unit model (DSUM) for calculating energies of Al tilt grain boundaries over a complete range of angle with and with
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