Elsevier

Acta Materialia

Volume 59, Issue 18, October 2011, Pages 7022-7028
Acta Materialia

First-principles-based mesoscale modeling of the solute-induced stabilization of 〈1 0 0〉 tilt grain boundaries in an Al–Pb alloy

https://doi.org/10.1016/j.actamat.2011.07.056Get rights and content

Abstract

A first-principles disclination structural units (DSUM) model was used to calculate the energies of 12 〈0 0 1〉 symmetric tilt grain boundaries in Al for a pure system and a system in which Pb atoms substitute for Al at one-half of the lattices sites along the interfacial plane. The grain boundaries are modeled as disclination dipole walls with energies given as a weighted sum of individual disclination energies determined from special low-sigma structures, elastic terms and disclination core energies. Predictions of the DSUM using the bulk Al shear modulus and Poisson’s ratio in the elastic and core energy terms are found to be comparable to energies for fully atomistic simulations calculated using a modified embedded-atom method (MEAM) potential. No relation between grain boundary energies in pure Al and the degree of stabilization due to Pb doping was found. The DSUM parameterized to density functional theory calculations predicts a ∼50% reduction in the energy anisotropy with respect to angle due to doping compared to the pure system, while MEAM calculations yield no appreciable reduction in the energy anisotropy.

Section snippets

Motivation and background

Nanocrystalline materials with grain sizes less than ∼100 nm have been of keen interest to the materials community because of their potential for unique and technologically important combinations of ductility, toughness, hardness and strength [1], [2], [3], [4]. These materials, however, are prone to grain growth at lower temperatures than conventional materials, which limits their service temperatures and expected lifetimes. Grain growth can be slowed (or even eliminated) either kinetically,

First-principles disclination structural units model

The SUM describes the structure of a grain boundary at an arbitrary tilt angle as a linear combination of structural units taken from high-symmetry (low-sigma) grain boundaries at special angles that bound the tilt angle of interest. In the implementation of the SUM using disclination defects, the junctions where different types of structural units meet are represented as partial disclinations of strength ± w = (θ1 − θ2), where θ is the tilt angle. The energy of an intermediate grain boundary is then

Details of the calculations

Energies for the grain boundaries at the low-sigma structures that are used to determine the structural unit energies were calculated using an analytic MEAM potential [15], [16] and with DFT calculations. The analytic interatomic potential was also used to calculate energies of grain boundaries at select intermediate angles to evaluate the accuracy of the FP-DSUM results. Each atomic system used periodic boundaries in all three directions, and contained two grain boundaries. To create the

Results

Plotted in the top panel of Fig. 1 are the grain boundary energies calculated using the MEAM and the DSUM as a function of tilt angle. The triangles correspond to pure Al; the open triangles are from the DSUM while the closed triangles represent full atomistic simulations at the low-sigma grain boundaries from which the disclination energies are obtained. The squares and circles correspond to the grain boundaries doped with substitutional Pb atoms calculated with the DSUM and MEAM,

Conclusions

The DSUM has been used to calculate and analyze the enhanced stability of tilt grain boundaries in Al by the substitution of 50% of the Al atoms at the grain boundary interfacial plane with Pb atoms. This work was motivated by experimental observations of Pb at grain boundaries in nanocrystalline Al [7], and by a desire to expand the understanding of driving forces and trends in grain boundary stabilization via doping [5]. Using an analytic MEAM potential for Al–Pb, predictions of the DSUM were

Acknowledgements

This work was initiated under a National Science Foundation NIRT Grant and completed with support from the Office of Naval Research Grant N00014-10-1-0168. Airat Nazarov, Doug Irving and Carl Koch are thanked for helpful discussions.

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