Long-range force and interfacial energy between dissimilar metals

Abstract

The Lifshitz theory is applied to calculate the long-range dispersion force between two semi-infinite half planes of dissimilar metals. It is shown that the asymptotic form of the force F, for large separation d between the half planes is F = C 12/ d 3, where an explicit expression is given for C 12 in terms of the two plasma frequencies ω p2 and ω p1 of the interacting metals. Attention is then given to the contributions to the interfacial energy of the composite system. In an ideal situation, in which the two metals had (a) the same crystal structure, (b) identical lattice parameters and (c) no charge transfer, the interfacial energy is the sum σ 1 + σ 2 of the surface energies of the two pure metals involved. It is argued that the charge transfer contribution (c) takes the form ( Δ W) 2/ ρ 2 l c, where Δ W is the difference in work functions of the two pure metals and l c is a characteristic length. Contributions arising from departures for ideal lattice matching, embodied in point (b) above can be estimated from the isothermal compressibility, κ T, of the pure metals. Further, invoking for a pure metal the known approximate relation that σκ T ∼ 1 A ̊ . this lattice mismatch contribution is expressed again in terms of surface energies. It will usually alter the contribution σ 1 + σ 2 of ine interfacial energy by a multiplying factor less than, but quite near to unity.