FACE-DEPENDENT HAMAKER CONSTANTS AND SURFACE MELTING OR NONMELTING OFNONCUBIC CRYSTALS

Surface melting is strongly influenced by long-range dispersion forces which crucially control the thickness l of the liquid layer that form s at the crystal surface, through a free-energy term of asymptotic for m V (l) = H/l2. In isotropic crystals, the face-independent Hamaker co nstant H is usually calculated by a well-known formula by Lifshitz et al. that relates dispersion forces to the optical conductivity of the solid and the liquid. In this paper we generalize this result to aniso tropic crystals specializing in uniaxial crystal surfaces normal or pa rallel to the optical c axis, and to surfaces of orthorhombic biaxial crystals normal to one principal axis. The main result is that the Ham aker constant becomes face dependent, and may, in principle, even chan ge sign from one face to another. Using experimental data for frequenc y-dependent dielectric constants we have calculated Hamaker constants of the main faces for some low-melting-point anisotropic metals, namel y, alpha-Ga,beta-Sn, and Cd. It is found that H is negative and large for all faces of alpha-Ga, implying surface nonmelting. Values found f or different faces of beta-Sn are moderately negative, and those for C d are marginally positive. The search for surface nonmelting or meltin g on these metals should be interesting in light of these results.