  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.
