The molecular-scale structure and phase behavior of single-component Langmuir films of 4'-methyl-4-mercaptobiphenyl (MMB) and 4'-perfluoromethyl-4-mercaptobiphenyl (FMMB) on mercury were studied using surface tensiometry, grazing incidence X-ray diffraction, and X-ray reflectivity. At low coverages, a condensed but in-plane disordered single layer of surface-parallel molecules is found for both compounds. At high coverages, both compounds exhibit in-plane-ordered phases of standing-up molecules. For MMB, the biphenyl core dominates the structure, yielding a centered-rectangular unit cell with an area A(x) of 21.8 angstrom(2)/ molecule, with molecules tilted by similar to 14 degrees from the surface normal in the nearest-neighbor direction, and a coherence length xi of > 1000 angstrom for the crystalline domains. For FMMB, the perfluoromethyl group dominates the structure, yielding a hexagonal unit cell with untilted molecules, an area A(x) of 24.2 angstrom(2)/molecule, and a much smaller of similar to 110 angstrom. The structure is discussed in comparison with self-assembled monolayers of MMB on crystalline Au(111) and similar-length alkanethiolate SAMs on Au(111) and on mercury. The differences in the structure are discussed and traced to the differences in the substrate's surface structure, and in the molecular cross section and rigidity.