Reply to “comment on: ‘surface miscibility gaps in CuAg alloys by Y. Liu and P. Wynblatt’ by J. du Plessis”

As pointed out by du Plessis in his comments [1] on our recent papers [2,3], the issues he raises do not pertain to the results reported in those papers, but rather to our "explanation". Our experimental paper [3] merely reported some interesting experimental results without providing any significant interpretation. Detailed interpretation is currently under preparation and will be developed in a future paper [4]. Our modeling paper [2] included some preliminary interpretation based on Helms' analysis [5] of this type of surface phase transition. In both of those papers, however, we clearly referred to the phenomena observed as phase transitions associated with a miscibility gap. This seems to be the principal bone of contention in du Plessis' comments, as he takes the view that no miscibility gap is involved in the transitions we have observed by both modeling and experimental approaches. At first sight it might seem that this disagreement is primarily a matter of semantics. Du Plessis insists that the terminology "miscibility gap" should be reserved for the case of a closed system when a single-phase solution becomes unstable, due to the appearance of a second minimum in the free energy versus composition curve below a certain "critical" temperature. The case we have studied in the papers in question [2,3] is also one where a single phase becomes unstable as a result of the development of a second minimum in the free energy versus composition curve, below some critical temperature; but, as correctly pointed out by du Plessis, the phenomenon we have observed occurs at a segregated surface, which must be considered to be an open system in contact with an infinite (bulk) reservoir of the components of the solution. Thus, it might appear as though the issue revolves around the definition of what might appropriately be referred to as a miscibility gap. However, we will demonstrate here that the locus of points at which the transition occurs in a system consisting of an open surface in contact with an infinite reservoir, coincides exactly with the miscibility gap which may be calculated for a closed two-dimensional system. In order to accomplish this, we must first clarify a misconception in du Plessis' discussion of the problem in his comments [1], and one which is discussed more fully in a previous publication [6]. The issue has to do with the so-called "double branch of solutions" (displayed in fig. 1 of ref. [1]) which du Plessis introduces in the description of the transition [6]. His argument given for the existence of the two branches can be explained by considering fig. 1, which represents a plot of the surface tension versus surface atom fraction (in du Plessis' formalism the extrema in surface tension are shown to correspond to extrema in the total free energy of the system). In the figure, curve T~ represents the system at temperature T z where free energies (surface tensions) at the two minima are equal, and curve T 2 represents the system at temperature T 2 where the region of negative curvature between the two minima has just disappeared. Du Plessis asserts that if the system exists in the state corresponding to the left