Examination of computed aluminum grain boundary structures and energies that span the 5D space of crystallographic character

Relative Grain Boundary Energies from Triple Junction Geometry: Limitations to Assuming the Herring Condition in Nanocrystalline Thin Films

“…In both presented films, at the highest population misorientation (60°|[111], Σ3), Figure 7d (8d) show a deep minimum at the coherent twin position of (111), and a band of generally higher relative energy and a corresponding deficit in population is seen along the (111) tilt boundaries, as is predicted for fcc materials. Furthermore, the calculated relative energies show general agreement with the energies calculated via MD [34,35], and plotted in 7g (8g). Fig.…”

“…Least squares fit lines are plotted in the same color as their corresponding misorientation, including two regimes for the Σ3 boundaries. energies calculated by molecular dynamics [34,35], as in Figure 10, the inverse correlation shows no such discontinuities for Σ3 boundaries, or any of the other selected boundary misorientations. While the relative energies extracted under the assumption of local equilibrium at the junctions do not reproduce trends observed in other systems, when the boundary energies computed by Homer et al [34,35] are compared to nanocrystalline experimental populations, the inverse relationship is observed.…”

“…energies calculated by molecular dynamics [34,35], as in Figure 10, the inverse correlation shows no such discontinuities for Σ3 boundaries, or any of the other selected boundary misorientations. While the relative energies extracted under the assumption of local equilibrium at the junctions do not reproduce trends observed in other systems, when the boundary energies computed by Homer et al [34,35] are compared to nanocrystalline experimental populations, the inverse relationship is observed. Figure 10 shows the population values, read from the GBCD, plotted against the corresponding energy for each boundary considered by Homer et al [34,35].…”

“…Furthermore, there are sharp minima present in the Al Σ7 relative GBEDs at arbitrary locations, which neither correspond to features in the GBCDs, nor to features found in bulk fcc materials' relative energy functions (e.g. nickel [21]), nor to features calculated by MD [34,35]. Finally, for boundaries with misorientation axes other than [111], the extracted relative energies shows virtually no correlation with GBCD, correlation with the GBEDs of other fcc materials [21], nor MD calculated energies, as can be seen qualitatively in Figures 7c,f, and i and 8c,f, and i, representing distributions for the Σ11 boundaries.…”

“…Finally, the absolute energies computed via molecular dynamics simulations are plotted in the third column (g-i). Note the minima at the (111) twist position for the Σ3 and Σ7 misorientations, with minimum values of 75 mJ/m 2 and 271 mJ/m 2 respectively, which are vanishingly narrow in the plots due to the limited sampling of the 5D space by the MD calculations [34,35]. Further, the appearance of the Σ7 symmetry is affected by the contouring between sparse points during plotting.…”