Core shift controls grain boundary energy scaling in Cu and Al

Grain boundary energies in different elements are correlated. The proportional scaling constants relating the \nenergies of crystallography-equivalent boundaries in any two f.c.c. elements are nearly constant, with the notable \nexception of aluminum where these constants are known to vary significantly. However, the origins of the \nexceptional behavior of aluminum are not understood. Previously, we reported that for fcc metals there is a \npreference for tilt boundaries to shift their tilt axis across the (110) plane towards [112] and to ultimately form \nlow energy [112] core shifted boundaries (CSBs). By comparing grain boundary energies in copper and \naluminum with different tilt axes in (110) plane, we now report the existence of a well-defined scaling behavior \nfor the case of low angle boundaries. In contrast, the scaling constant for high angle boundaries is essentially \nfixed regardless of their tilt axis shift. This results in a gradual change in the scaling constants from low angle to \nhigh angle boundaries, which is responsible for the apparent exceptional scaling behavior found in aluminum. An \nanalysis of structure evolution during core shifting points to the significance of boundary-core dissociation, a \nform of correlated relaxation of individual atoms at boundaries, in controlling the scaling of boundary energies.