A pseudoatom theory for the liquid-vapor interface of simple metals: computer simulation studies of sodium and cesium

This paper describes a theory of the structure of the liquid–vapor interface of simple metal. The atomic motion is described by an effective Hamiltonian for the ions in an inhomogeneous metal. The ‘‘pseudoatom’’ Hamiltonian is derived by evaluating the electronic free energy of the metal to second order in the electron–ion pseudopotential. The model is completed by an approximate treatment of the metal–nonmetal transition which must occur in the traversal of the liquid–vapor interface. Using the derived effective Hamiltonian, Monte Carlo simulations of liquid sodium and cesium have been carried out. The Monte Carlo algorithm used is much more sophisticated than that employed in conventional simulations of liquids since the effective ion–ion interaction is density and position (relative to the surface) dependent, and therefore must be recalculated with each Monte Carlo displacement to insure convergence to a self-consistent effective Hamiltonian and density distribution. Monte Carlo simulations of bulk liquid sodium and cesium yield pair correlation functions which are in excellent agreement with experimental data. The simulations of the liquid–vapor interface reveal considerable structure, in the form of stable density oscillations extending several atomic layers into the bulk liquid; the spacing characteristic of this structure is about one atomic diameter. The existence of this ordering is traced to the variation in the surface zone of the so-called structure-independent energy component of the effective Hamiltonian. A less robust, more model dependent, result of the simulations is the prediction that there is a partial monolayer of ‘‘hybrid-state’’ species, neither metallic nor vaporized, adsorbed on the liquid metal surface. The existence of these hybrid-state atoms is a consequence of our treatment of the metal–nonmetal transition. The implications of our results for the interpretation of the surface properties of liquid metals are briefly discussed.