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 usin g 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 s urfaces of Ti and Zr are in good agreement with recent linear-augmente d-planewave calculations. In addition, we predict a weak vibrational e ffect on the surface relaxation of Zr(0001) by considering the free en ergy 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.