Correlation between structure, energy, and ideal cleavage fracture for symmetrical grain boundaries in fcc metals

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Abstract
The misorientation phase space for symmetrical grain boundaries is explored by means of atomistic computer simulations, and the relationship between the tilt and twist boundaries in this three-parameter phase space is clucidated. The so-called random-boundary model (in which the interactions of atoms across the interface are assumed to be entirely random) is further developed to include relaxation of the interplanar spacings away from the grain boundary. This model is shown to include fully relaxed free surfaces naturally, thus permitting a direct comparison of the physical properties of grain boundaries and free surfaces, and hence the determination of ideal cleavage-fracture energies of grain boundaries. An extensive comparison with computer-simulation results for symmetrical tilt and twist boundaries shows that the random-boundary model also provides a good description of the overall structure-energy correlation for both low- and high-angle tilt and twist boundaries. Finally, the role of the interplanar spacing parallel to the grain boundary in both the grain-boundary and cleavage-fracture energies is elucidated.