A solid-on-solid–type model was proposed in order to provide a unified description of both the surface reconstruction and roughening phase transitions. A low-temperature domain-wall analysis reveals the presence of several incommensurate phases, separated by continuous phase transitions, for all temperatures > 0. True commensurate order develops only at 0, a pseudo commensurate-incommensurate transition at > 0, and a high-temperature roughening transition terminated the sequence of incommensurate phases. The resulting phase diagram could apply to the description of the pure and alloyed noble-metal [110] solid-vapour interface structure.

Sequence of Incommensurate Phases in a Model of Surface Reconstruction and Roughening. G.Jug, E.Tosatti: Physical Review B, 1990, 42, 969-72