  We present an x-ray reflectivity study of wetting at the free surface of the
binary liquid metal gallium-bismuth (Ga-Bi) in the region where the bulk phase
separates into Bi-rich and Ga-rich liquid phases. The measurements reveal the
evolution of the microscopic structure of wetting films of the Bi-rich,
low-surface-tension phase along different paths in the bulk phase diagram. A
balance between the surface potential preferring the Bi-rich phase and the
gravitational potential which favors the Ga-rich phase at the surface pins the
interface of the two demixed liquid metallic phases close to the free surface.
This enables us to resolve it on an Angstrom level and to apply a mean-field,
square gradient model extended by thermally activated capillary waves as
dominant thermal fluctuations. The sole free parameter of the gradient model,
i.e. the so-called influence parameter, $\kappa$, is determined from our
measurements. Relying on a calculation of the liquid/liquid interfacial tension
that makes it possible to distinguish between intrinsic and capillary wave
contributions to the interfacial structure we estimate that fluctuations affect
the observed short-range, complete wetting phenomena only marginally. A
critical wetting transition that should be sensitive to thermal fluctuations
seems to be absent in this binary metallic alloy.
