Extra variable in grain boundary description

Grain boundaries (GBs) in crystalline materials are traditionally described by five crystallographic angles, which are assumed to fully define the GB structure and energy. It has recently been realized that variations in the atomic density lambda in the GB region can drastically alter the GB structure and cause transformations between different GB phases. Here we extend the previous studies of Cu Sigma 5 GBs by computing the structures and energies of a set of [001] symmetrical tilt GBs over the entire angular range by allowing arbitrary variations in.. The results confirm the existence of stable and metastable phases in all GBs studied here. There are three types of structural units that can describe all GB structures obtained in this work. The work demonstrates that. should be added to the description of GBs as an extra thermodynamic parameter that helps predict the GB phases and transformations among them.