Extracting Relative Grain Boundary Energies from Triple Junction Geometry in Nanocrystalline Thin Films—Effect of Film Geometry on Interfacial Equilibrium

Grain boundary character distributions (GBCD) and relative grain boundary energy distributions (GBED) are routinely calculated from 3D serial-section electron backscatter diffraction (EBSD) data from microcrystalline bulk samples, and are consistently found to be inversely correlated. The GBEDs are calculated based on triple junction geometry and the assumption of force balance via the Herring condition. For nanocrystalline thin films, precession electron diffraction (PED) has proven an effective method to measure the GBCD, but the GBED has not been reconstructed. In the work reported here, we adapt the established energy reconstruction method to PED data from films with columnar grain structures, where serial sectioning is not required to determine boundary inclination. For a 40 nm-thick, sputter-deposited, nanocrystalline tungsten film, the relative GBED obtained by this method does not correlate to grain boundary energies which are interpolated with Read-Shockley-Wolf (RSW) functions from molecular dynamics calculations. Furthermore, while the boundary populations in this data-set have been previously demonstrated to show both an inverse log-linear correlation with the RSW-calculated energies and a clear correlation to the GBCD of comparable microcrystalline bcc materials, the populations of boundaries show no inverse relationship to the relative energies obtained here. This failure indicated that the assumed Herring condition does not successfully relate triple junction geometry and boundary energy in this system, and thus cannot be used to extract relative boundary energies. This film had not experienced grain growth, however, and so its structure may reflect a metastable state. To address this, a set of aluminum samples were also examined: a film in its as-deposited state and after 30 and 150 minutes at 400°C. Here, the film experiences significant grain growth, with equivalent circle diameter of mean area increasing by more than 40% after 150 minutes of annealing. Still, when the relative energies are reconstructed from the data-set the inverse relationship with population is not recovered, even when accounting for certain boundaries (i.e. coherent twins) which are not likely perpendicular to the plane of the film. When compared to aluminum grain boundary energies recently calculated with molecular dynamics, the populations show an obvious inverse trend with energy, in line with the previously reported correlation of the nanocrystalline GBCD to the bulk microcrystalline results. The failure of the energy reconstruction model to reproduce the expected trends likely implies that the assumed conventional Herring condition of force balance is not an appropriate avenue for energy extraction in thin films, indicating that the Herring equation does not fully specify the geometry at triple junctions in these systems. While boundary character follows well established thermodynamic expectations, this result points to other factors, including those related to thin film geometry, which must play a significant role in determining triple junction geometry in these spatially constrained systems.