Relying on Frenkel Kontorova (FK) models of diatomic chains of increasing levels of complexity, this study presents an overall view of the diversity of structural effects that a compound (oxide) chain supported on a metal may display and helps assigning them to precise microscopic mechanisms. At each stage, the models are solved numerically, in order to provide phase diagrams as a function of chain-substrate interaction and misfit. Analytic derivations of transition lines are also provided within the continuum approximation. Their predictions are shown to quantitatively account for the numerical results, thus showing the validity of the continuum approximation in the misfit range under consideration. The present study thus extends our knowledge of the FK model by specifically focusing on diatomic chains and brings new information on a potentially interesting system which experimentalists just start being able to synthesize-oxide chains on metal substrates. (C) 2013 AIP Publishing LLC.