Asymmetric tilt grain boundary structure and energy in copper and aluminum

M. A. Tschopp, D. L. McDowell, Philosophical Magazine, 87, 3871-3892 (2007).

Atomistic simulations were employed to investigate the structure and energy of asymmetric tilt grain boundaries in Cu and Al. In this work, we examine the Sigma 5 and Sigma 13 systems with a boundary plane rotated about the < 100 > h imisorientation axis, and the Sigma 9 and Sigma 11 systems rotated about the < 110 > h imisorientation axis. Asymmetric tilt grain boundary energies are calculated as a function of inclination angle and compared with an energy relationship based on faceting into the two symmetric tilt grain boundaries in each system. We find that asymmetric tilt boundaries with low index normals do not necessarily have lower energies than boundaries with similar inclination angles, contrary to previous studies. Further analysis of grain boundary structures provides insight into the asymmetric tilt grain boundary energy. The Sigma 5 and Sigma 13 systems in the < 100 > h system agree with the aforementioned energy relationship; structures confirm that these asymmetric boundaries facet into the symmetric tilt boundaries. The Sigma 9 and Sigma 11 systems in the < 110 > h system deviate from the idealized energy relationship. As the boundary inclination angle increases towards the Sigma 9 ( 221) and Sigma 11 ( 332) symmetric tilt boundaries, the minimum energy asymmetric boundary structures contain low index 111 and 110 planes bounding the interface region.

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