Full spectral calculation of non-retarded Hamaker constants for ceramic systems from interband transition strengths

Abstract

The van der Waals (vdW) interaction is one of the key terms in the force balances dictating wetting behavior and intergranular film thicknesses. The characteristics of thin intergranular or surficial glass films are of increasing importance due to their role in determining the properties of polycrystalline ceramics. The Hamaker constant scales the London dispersion force part of the vdW interaction for a particular configuration of grains and films and is a direct function of the interband optical properties of the interatomic bonds of the materials. For ceramics, much previous work focused on simplified models, such as the Tabor-Winterton approximation (TWA), to determine Hamaker constants based on refractive indices. Herein we develop full spectral calculations of the Hamaker constants for various ceramic systems using experimentally determined interband transition strengths (ĵcv(ω)) to directly derive the London dispersion spectra (ε2(ξ)) from which spectral difference functions lead to direct determination of the Hamaker constants. The results affirm the expectation that transitions involving valence electrons provide the predominant contribution to the dispersion forces for the compounds examined. Calculations have been done for the planar case of a gap between two semi-infinite bodies containing either vacuum or an intervening glassy layer. The results indicate that the TWA is useful for oxides with relatively low refractive indices, i.e., n ~ 1.4–;1.8. However, when any of the materials have larger indices, this approximation becomes inexact, and no obvious, simple correction to the TWA gives uniformly good results, as the behavior differs for simple covalent materials and for oxides with partially filled d-shells but having similar refractive indices. An important consequence is that Hamaker constants are smaller for such high index materials, especially oxides, with intervening glassy films than might be expected from approximations. Calculations have also been done for two other geometries, i.e., for an intervening film with a layer of a third material at both interfaces and for glass coated free surfaces. The former of these provides first insights regarding the behavior with nonuniform films which often differs markedly from that expected for homogeneous films of the same average composition.