Melting of quasi-two-dimensional crystalline Pb supported on liquid Ga

Experimental studies have shown that the Pb monolayer that segregates in the PbGa alloy liquid-vapor interface forms a two-dimensional hexagonal crystal that melts at 341 K, and it has been speculated that the disordered phase formed is hexatic. This paper reports the results of simulation studies of the in-plane structure of the outermost stratum of the liquid-vapor interface of a dilute Pb in Ga alloy. These simulations are based on four major improvements to a previous study. First, the simulation studies involve considerably more atoms and considerably longer equilibration runs than considered in the previous work of Chekmarev, Oxtoby, and Rice. Second, a more accurate nonlocal pseudopotential representation of the interactions in the system is used. Third, the amplitude of the out-of-plane motion of the Pb atoms is constructed to have the observed value. Fourth, an approximation to the role of the liquid Ga substrate is provided by adding a layer of Ga atoms to the layer of Pb atoms. The results of our simulation studies show that the Ga layer adjacent to the Pb layer has a profound influence on that layer's properties. In particular, it is shown that in the two-layer PbGa system the Pb layer forms, at low temperature, a stable two-dimensional crystal on top of liquid Ga. This two-dimensional crystal melts at a temperature close to that found experimentally. It is found that the crystalline Pb layer is transformed to the liquid state via two intermediate hexatic phases that differ in the magnitude of the bond orientation order. Each of the phase transitions along this melting pathway is first order. The temperature range over which each hexatic phase is stable is small. The profound influence of out-of-plane motion is demonstrated by a comparison of the results of simulations of a quasi-two-dimensional (Q2D) and of a strictly two-dimensional monolayer of Pb. The melting transition in the Q2D one-layer system is first order, directly to the liquid, with no intervention of a hexatic phase. The melting transition in the strictly 2D system involves two stages: a first-order transition to an intermediate hexatic phase followed by melting of the hexatic to a liquid phase. The latter transition is continuous over a small temperature range. An examination of the role of defects in the melting process reveals a picture rather different from that postulated in the Kosterlitz-Thouless-Halperin-Nelson-Young theory of 2D melting.