Quasiharmonic free energy and derivatives for slabs: oxide surfaces at elevated temperatures

The work of Taylor et nl. [Phys. Rev. B 56, 14380 (1997)], which calculates the free energy of three-dimensional periodic crystals and its analytic derivatives with respect to all the external and internal degrees of freedom using lattice statics and lattice dynamics in the quasiharmonic approximation, is extended to lattices which are periodic in only two dimensions. Derivatives are calculated by means of first-order perturbation theory and detailed expressions for all the lattice sums required are presented. The method is used to calculate the temperature variation of the surface free energy, surface structure, and density of states of some representative oxide surfaces. These include the (100) and (110) surfaces of MgO, the (100) surface of NiO, the (111) surface of Li2O and the microfaceted (110) sur face of MgO. For these systems, surface free energies decrease slightly over the range of temperatures for which the quasiharmonic approximation holds. [S0163-1829(99)01310-7].