Normal-incidence standing x-ray wavefield (NISXW) measurements have been made of the local adsorption site of Rb on Al(111) surfaces, particularly in an ordered ( square root 3* square root 3)R30 degrees phase, as a function of the sample temperature during adsorption or subsequent annealing. The results confirm the a top-site occupation for low-temperature (around 150 K) preparation, but show that room-temperature preparation leads to a structure having Rb atoms in surface substitutional sites. The overall structural situation is therefore essentially the same as that found previously by low-energy electron diffraction LEED for the Al(111)( square root 3* square root 3)R30 degrees -K phases. However, experiments involving annealing of the low-temperature prepared surface to room temperature indicate that only a small part of the surface easily transforms to the higher-temperature form, and indeed there is evidence that even in room-temperature preparations some fraction of the adsorbed atoms may remain in atop sites. The apparent conflict of this result with that from recent photoemission core-level shift and LEED data is discussed.