Two-dimensional freezing in the liquid–vapor interface of a dilute Pb:Ga alloy

Abstract

We report the results of x-ray reflectivity and grazing incidence x-ray diffraction studies of the liquid-vapor interface of a dilute alloy of Pb in Ga over the temperature range of 23-76°C. Our data show that the liquid-vapor interface of this alloy is stratified for several atomic diameters into the bulk liquid and that a monolayer of Pb forms the outermost stratum of the interface. Over the temperature range of 23-56°C, the monolayer of Pb is in an ordered hexagonal phase. At about 58°C, this monolayer undergoes a first-order transition to a hexatic phase, which remains stable to 76°C. An analogy between the observed transition and the firstorder melting transition in a one-component classical plasma is suggested.T he existence of a composition difference between the liquidvapor interface and the bulk liquid phase of a binary mixture has been known since the work of Gibbs (see, e.g., ref. 1). However, it is only in the last few years that information about the atomic structure of that interface has become available. Theoretical studies of the liquid-vapor interfaces of pure metals and binary alloys (2-13) lead to the following predictions: (i) the (longitudinal) distribution of density along the normal to the interface is stratified for several atomic diameters into the bulk liquid, and (ii) the species in excess in the liquid-vapor interface of a dilute binary alloy forms a monolayer that is the outermost layer of that interface. Recent x-ray reflectivity (XR) and grazing incidence x-ray diffraction (GIXD) studies of the liquidvapor interfaces of several pure metals and binary alloys have confirmed these predictions (14-27). In this paper, we report the results of XR and GIXD studies of the liquid-vapor interface of a dilute alloy of Pb in Ga over the temperature range of 23-76°C. These experiments explore the possibility of using the monolayer of the segregated species to study phase transitions in a quasi two-dimensional system. Our data suggest that the Pb monolayer that forms the outermost stratum of the liquid-vapor interface of the alloy is in a hexatic phase from 60°C to 76°C and that it undergoes a first-order two-dimensional hexatic-to-hexagonal solid transition in the vicinity of 58°C. Over the temperature range of 23-56°C, the range of the translational order in the hexagonal Pb monolayer is greater than our instrumental resolution. Experimental Methods and ResultsThe high-vacuum sample chamber used for our experiments has been described elsewhere (24-27), as have the x-ray surface scattering spectrometer and the detection electronics used. We merely note that the sample chamber contains a residual gas analyzer to monitor the vacuum, an Auger spectrometer to monitor the liquid sample surface composition, and an ion gun and a sweep arm to clean the liquid sample surface. Two liquid alloy samples with slightly different compositions were studied. The results obtained from x-ray diffraction and XR studies of these samples were the same; thus, we focus attention on one of them: 0.054 atomic percent Pb...

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