Plane-wave-basis pseudopotential calculations of the surface relaxations of Ti(0001) and Zr(0001)

The relaxations of the Ti(0001) and Zr(0001) surfaces are studied using the plane-wave-basis pseudopotential method within the local-density approximation. We find that the first interlayer spacings of Ti(0001) and Zr(0001) are contracted with respect to the bulk spacings by 6.8% and 6.1%, respectively. Such large relaxations for the close-packed surfaces of Ti and Zr are in good agreement with recent linear-augmented-planewave calculations. In addition, we predict a weak vibrational effect on the surface relaxation of Zr(0001) by considering the free energy in the quasiharmonic approximation. This result can be attributed to a very strong bonding between the first-and second-layer Zr atoms as a consequence of the bond-order-bond-length correlation.