Diffuse scattering from the liquid-vapor interfaces of diluteBi:Ga,Tl:Ga, andPb:Gaalloys

Abstract

As part of a study of the in-plane wave-vector $({q}_{xy})$ dependence of the effective Hamiltonian for the liquid-vapor interface, $H(q)$, the wave-vector dependences of diffuse x-ray scattering from the liquid-vapor interfaces of dilute alloys of Bi in Ga, Tl in Ga, and Pb in Ga have been measured. In these dilute alloys the solute component segregates as a monolayer that forms the outermost stratum of the liquid-vapor interfaces, and the density distribution along the normal to the interface is stratified. Over the temperature ranges that the alloy interfaces were studied, the Tl and Pb monolayers exhibit both crystalline and liquid phases while the Bi monolayer is always liquid. The diffuse scattering from the liquid-vapor interfaces of these alloys displays interesting differences with that from the liquid-vapor interface of pure Ga. The presence of a segregated monolayer of solute in the liquid-vapor interface of the alloy appears to slightly suppress the fluctuations in an intermediate wave-vector range in a fashion that preserves the validity of the macroscopic capillary wave model to smaller wavelengths than in pure liquid Ga, and there is an increase in diffuse scattering when the Tl and Pb monolayers melt. The surface intrinsic roughness from fitting the wave-vector dependence of surface tension is 5.0 pm for the $\mathrm{Tl}:\mathrm{Ga}$ alloy and 1.4 pm for the $\mathrm{Bi}:\mathrm{Ga}$ alloy. Also, a mode of excitation that contributes to diffuse scattering from the liquid-vapor interface of Pb in Ga, but does not contribute to diffuse scattering from the liquid-vapor interface of Ga, has been identified. It is proposed that this mode corresponds to the separation of the Pb and Ga layers in the regime $1\phantom{\rule{0.3em}{0ex}}{\mathrm{nm}}^{\ensuremath{-}1}\ensuremath{\leqslant}{q}_{xy}\ensuremath{\leqslant}10\phantom{\rule{0.3em}{0ex}}{\mathrm{nm}}^{\ensuremath{-}1}$.