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 = C₁₂/d³, where an explicit expression is given for C₁₂ 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 σ₁ + σ₂ of the surface energies of the two pure metals involved. It is argued that the charge transfer contribution (c) takes the form (ΔW)²/ρ²l_c, where ΔW 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 $\text{σκ}{}_{\mathrm{<mtext>T</mtext>}}\text{∼ 1}\text{A}\text{̊}$. this lattice mismatch contribution is expressed again in terms of surface energies. It will usually alter the contribution σ₁ + σ₂ of ine interfacial energy by a multiplying factor less than, but quite near to unity.