Single and binary two-dimensional (2D) films of Pb and Sn on Ag(1 1 1) prepared at room temperature have been investigated using low-energy electron diffraction (LEED) and scanning tunneling microscopy. (root 28 x root 28)-Pb is observed in addition to (root 3 x root 3)-Pb at coverages higher than 0.35 ML. The nominal coverages for the (root 28 x root 28)-Pb and (root 3 x root 3)-Pb structures are determined to be 0.68 and 1/3 ML, respectively. The (1 x 1)-Sn structure is formed at coverages less than 1 ML. Both Pb and Sn films forma hexagonal close-packed structure on Ag(1 1 1). When the Sn coverage increases to more than 1 ML, excess Sn atoms form a (root 3 x root 3) structure on the (1 x 1)-Sn surface. The 2D binary films exhibit an incommensurate structure close to (root 13 x root 13) at Pb and Sn coverages of 0.5 and 0.25 ML, respectively. Atomic-resolution STM images exhibit a hexagonal close-packed structure. From the DFT total energy calculations, it is concluded that the Pb and Sn atoms of the ("root 13 x root 13") structure do not form an ordered alloy but, rather, form a solid solution alloy. From these results, it is concluded that the binary 2D films also follow the Hume-Rothery rule. (C) 2015 Elsevier B.V. All rights reserved.