Calculation of the surface energy of hcp metals by using the modified embedded atom method

With MEAM, the surface energies of three kinds of representative surfaces, (h 0 l), (h h l) and (h k 0) belong to [0 1 0], [11¯0] and [0 0 1] crystal band, respectively, have been calculated for 13 closed-packed hexagonal (hcp) metals Co, Dy, Er, Gd, Ho, Mg, Nd, Pr, Re, Sc, Tb, Tl and Zr. For all 13 hcp metals, the basal plane (0 0 1) has the minimum surface energy. So from surface energy minimization, the (0 0 1) texture should be favored in the hcp films, this is consistent with the experimental results. The fact that the short termination corresponds to much lower surface energy than long one implies the former is more stable for those surfaces having two possible terminations. Such as the prism plane (1 0 0), only the short termination was observed in experiment.