Dislocations and the commensurate-incommensurate transition in two dimensions

The stability of weakly incommensurate two-dimensional solid phases described by periodic arrays of discommensurations has been investigated. It is shown that incommensurate phases consisting of a small number of possible commensurate domains of either the striped or honeycomb type are unstable with respect to the spontaneous creation of dislocations. Such phases are consequently "liquids," with exponential decay of correlations. The consequences of these results on the phase diagram of overlayers and the relation with experiment is discussed.