A one-dimensional model of atoms, such as xenon, adsorbed on a periodic substrate, such as graphite. This model, which can be used to investigate the nature of the lattice formed by the adsorbed gas, was invented in 1938 by Y. I. Frenkel and T. Kontorowa and independently in 1949 by F. C. Frank and J. H. Van der Merwe. A feature of the analysis is that it involves a devil’s staircase. The Frenkel–Kontorowa model can be used to investigate the phase transition between a commensurate lattice and an incommensurate lattice.