![]() ![]() N α and N β are the numbers of atoms inside the regions spanned by the crossing vectors. ![]() Their sum in the reference state is a DSC lattice vector. ![]() BC and DA are the lattice vectors of the upper and lower grains, respectively. AB and CD are the crossing vectors of the GB phases α and β, respectively. (a) A general Burgers circuit ABCD around a GB phase junction in the deformed state. In general, different Burgers vectors can be obtained between the same GB phases by changing the bicrystals original dimensions. In this construction, the magnitude of the Burgers vector of the junction depends on the sizes and shapes of the reference bicrystals shown in (a). In an infinitely large system, the blue and orange GB structures would converge to their undistorted dimensions, shown in (a) and (b), infinitely far away from the junction. Here we assume that the system has a finite size. Both GB structures are elastically distorted compared to (a) and (b). (c) GB phase junction is formed by elastically deforming both bicrystals so the lattice planes in the bulk can be connected. The bulk lattice planes cannot be joined because they generally mismatch. (b) An attempt to form a GB phase junction using the reference bicrystals results in a closure failure. (a) Bicrystals with different GB structures, shown in blue and orange, have different dimensions in the reference state. The proposed analysis quantifies b and therefore makes it possible to calculate the elastic part of the energy of these defects, evaluate their contribution to the nucleation barrier during GB phase transformations, and treat elastic interactions with other defects.Ĭlosure failure. These expressions provide a connection between GB phase transformations driven by the GB free energy difference and the motion of GB junctions under applied normal and shear stresses. We derive expressions for the normal and tangential components of b in terms of the DSC lattice vectors and the non-DSC part due to Δ N * and additional GB excess properties, including excess volume and shears. In the boundaries studied, the latter component dominates and even changes the sign of b. We show that, in general, the normal component of b is not equal to the difference in the GB excess volumes but contains another contribution from the numbers of GB atoms per unit area Δ N * required to transform one GB phase into another. The Burgers vectors of these junctions cannot be described by the displacement shift complete (DSC) lattice alone. We apply a general Burgers circuit analysis to calculate the Burgers vectors b of junctions in two Σ 5 Cu boundaries previously simulated with molecular dynamics. While regular GB disconnections have been characterized for a variety of interfaces, GB phase junctions formed by GBs with different structures and different numbers of excess atoms have not been previously studied. We analyze the dislocation content of grain boundary (GB) phase junctions, i.e., line defects separating two different GB phases coexisting on the same GB plane. ![]()
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