Interactions between grain boundary faceting, migration, and grain rotation: color group and molecular dynamics simulation approaches
Color group theory and molecular dynamics (MD) simulations were used to study the faceting and rotation of grains in nanocrystalline materials and their interactions. Color group arguments were used to determine symmetry-dictated extrema with respect to misorientation of the grains and with respect to grain boundary normal orientations. MD simulations were used to study the evolution of the system and to elucidate the interactions between grain rotation and faceting in nano-scale systems. The systems of study were fcc bicrystalline systems with two grains sharing their  directions. Two geometric parameters were studied: the misorientation between two grains with a common rotation axis in the  direction of both grains, and the grain boundary normal orientation of fcc (110) tilt grain boundaries.The symmetry-dictated extremum (SDE) with respect to misorientation around both grains'  direction is 90 degrees. The SDE with respect to GB normal orientations for (110) tilt GBs are located on top of the color and classical mirror planes of their dichromatic patterns.By using periodic boundary conditions and a cylindrical embedded grain structure in our simulations, grains are only free to vary the misorientation between grains around the common  direction, and the normal of the grain boundaries are always perpendicular to both grains  direction. All SDE studied in our simulation are observed to be local energy minimum states. We observed the systems reducing their excess energy through three main modes: forming facets at the boundaries, rotating between the two grains, and reduction of grain boundary area through grain shrinkage.Facets are formed in low-energy grain boundaries and oscillating rotation occurred when the initial misorientation was not a SDE. A new algorithm was developed to quantitatively measure the grain rotation. The ovsered rotations are not rigid-body rotations and have strong interaction with faceting. Systems with lower energy facets rotate less. Low energy facets are also impede the continuous rotation and shrinkage of the grains. Embedded grains with higher energy facets shrink faster. Grains shrink layer by layer through formation of stacking faults and movement of dislocations.