Excess Volume at Grain Boundaries in hcp Metals
  The excess volume associated with grain boundaries represents a key structural parameter for the characterization of grain boundaries. It plays a critical role in segregation of impurity and alloy elements to grain boundaries, and influences significantly the mechanical and functional properties of materials. We have carried out first-principles density functional calculations on the atomic structure of the (10-12) coherent twin boundary in hexagonal close packed (hcp) Ti and Zr and the basal-prismatic boundary in Zn, Cd, and Zr. We find the calculated excess volume has a vanishing magnitude at the (10-12) coherent twin boundary in Ti and Zr; whereas it is remarkable at the basal-prismatic boundary in Zn, Cd, and Zr. 
J. L. Cao and W. T. Geng
cond-mat.mtrl-sci