ABSTRACT
Liquids or molten metals are important in many industrial re–ning, smelting, and casting processes, as well as in numerous scienti–c applications (e.g., [1,2]). From the point of view of research, free surfaces (or equivalently the liquid-vapor transition zones) of liquid metals have provided signi–cant interest for experimental and
5.1 Introduction .................................................................................................. 135 5.2 Liquid Metal Surfaces: Transverse Surface Structure .................................. 137
5.2.1 Summary of Experiments on Liquid Metal Surfaces ....................... 137 5.2.2 Simulations Viewpoint ..................................................................... 139
5.2.2.1 Layering against Hard Wall ............................................... 139 5.2.2.2 Geometrical Rearrangement to Increase Density at the
Surface ............................................................................... 140 5.2.2.3 Friedel Oscillations in Electronic Density Pro–le ............. 140 5.2.2.4 Surface Layering without Metallic Interactions: Ratio
of Melting to Critical Temperatures ................................... 141 5.3 Density Functional Theory-Based Molecular Dynamics Simulations ......... 141
5.3.1 Density Functional Theory ............................................................... 142 5.3.1.1 Ensemble Density Functional Theory ............................... 143
5.3.2 Orbital-Free Molecular Dynamics.................................................... 144 5.3.3 Ensemble DFT-Based Molecular Dynamics Simulations of
Liquid Metal Surfaces ...................................................................... 145 5.3.3.1 Free Sodium Surfaces ........................................................ 145 5.3.3.2 Introducing a Thin Rigid Wall into Liquid Sodium .......... 151 5.3.3.3 Friedel Oscillations in Sodium .......................................... 152
5.4 In-Plane Ordering ......................................................................................... 154 5.5 Summary ...................................................................................................... 158 References .............................................................................................................. 159
theoretical study for several years, in addition to the focus on other interfaces incorporating a liquid metal component. A major reason for this is that these surfaces display properties that are more complex than those of the surfaces of ionic and dielectric liquids. The atomic structure of the surface of a simple dielectric liquid is generally believed to be relatively straightforward, exempli–ed by a monotonic decrease in the transverse density pro–le from the bulk liquid density to the vapor density. The situation is more complex across the transition zone of a liquid metal; this is particularly apparent in the density pro–le, which displays oscillations on the liquid side of the interface (see Figure 5.1). A density pro–le containing such oscillations is indicative of the formation of atomic layers. In the liquid, where the atoms undergo diffusive motion, the layers will exist as preferential regions with higher or lower densities (corresponding respectively to maxima and minima in the density pro–le). At a fundamental level, the differences seen between the structures of the surfaces of liquid dielectrics and liquid metals re™ect the behaviors of the microscopic interactions across the different interfaces. In the case of a dielectric, the nature of the interatomic interactions may not need to change a great deal across the interface, for instance, being van der Waals bonding in both the liquid and vapor phases of the material [3]. In the liquid metal case, there has to be a substantial
change in the nature of the interatomic interactions across the surface, as the bonding changes from metallic in the liquid part to dispersive-type interactions between the atoms in the vapor part. These fundamental differences at the microscopic level mean that atomistic simulations, which are able to provide insight at this level, have an extremely useful role to play.
