All-electron local-density determination of the surface energy of transition metals: W(001) and V(001)

The surface energies of W(001) and V(001) are determined theoretically within local-density-functional theory employing the all-electron full-potential linearized augmented-plane-wave method. The calculated values are 5.1 J/${\mathrm{m}}^2$ for W(001)—in good agreement with experiment—and 3.4 J/${\mathrm{m}}^2$ for V(001). Multilayer surface-relaxation calculations show that the surface-relaxation energy is small and amounts to only a few percent of the surface energy. The surface entropy at sufficient high temperatures for the W(001) surface, as deduced from a comparison of our calculated result and high-temperature experimental surface-energy values, is large (1.5×${10}^{\mathrm{-}3}$ J/${\mathrm{m}}^2$ deg).