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We identify and characterize a two-dimensional phase transition in a layer of Sn on Cu͑100͒. The stable phase at room temperature has a ͑3 ͱ 2 ϫ ͱ 2͒R45°structure. Above ϳ360 K, a new phase with ͑ ͱ 2 ϫ ͱ 2͒R45°structure is formed. The high-temperature phase exhibits a quasi-two-dimensional free-electron surface band, with Fermi surface nesting in excellent agreement with the three-times larger periodicity of the low-temperature phase. A momentum-dependent band gap opens along the nested areas of the Fermi surface in the low-temperature phase. The phase transition is a clear experimental confirmation of the role of Fermisurface gapping and nesting in the stabilization of a commensurate two-dimensional phase, which is interpreted as a charge-density wave.

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The surface phase Sn/ Cu͑100͒-͑3 ͱ 2 ϫ ͱ 2͒R45°exhibits a temperature induced phase transition to a ͑ ͱ 2 ϫ ͱ 2͒R45°phase above 360 K. We report an angle-resolved photoemission study of the two-dimensional Fermi surface of the low-temperature phase. The Fermi surface is formed by folding of a quasi-twodimensional surface band and presents three contours. It is characterized by gaps appearing in optimally nested regions of one of the contours, whereas other sections remain ungapped. We address the origin of the folding and of the surface phase transition, which is attributed to the formation of a surface charge density wave.

The application of genetic algorithms to the analysis of surface x-ray diffraction data is discussed and the implementation of a genetic algorithm of evolutionary type is described in detail. The structure of Sn/Cu(100)-[Formula: see text] is determined on the basis of surface x-ray diffraction data analysed using this algorithm. The results are compared to previous findings using other techniques.