We have used low energy electron microscopy to monitor the high-temperature behavior of surface phases in the Co͞Si(111) system at submonolayer coverages. We observe a reversible phase separation from a disordered "͑1 3 1͒" phase to well-defined coexisting regions of ordered ͑7 3 7͒-reconstructed and disordered phases. The transition temperature is depressed by nearly 200 ± C by the addition of 0.1 monolayer of cobalt. The shape of the coverage-temperature phase boundary allows us to estimate the latent heat of the ͑7 3 7͒ order-disorder transition. [S0031-9007(97)03320-6] PACS numbers: 68.35.Rh, 81.30.Hd, 82.65.Dp Surface effects in bulk alloying systems is a topic of long-standing interest, with important fundamental and practical aspects such as surface segregation, grain boundary embrittlement, impurity gettering, and faceting behavior. More recently, studies of heteroepitaxial growth have highlighted the importance of understanding the thermodynamics of coupling between overlayers and substrate. In view of the above, and the ubiquity of compositional phase separations in bulk systems, it is perhaps surprising to find no report in the literature of two-dimensional (2D) phase separation of a surface segregant. One reason for this is that surface segregants in most systems are essentially equilibrated with the bulk at temperatures of interest. This results in a single-phase surface structure at all temperatures, even though the surface may exhibit a phase transition in which coverage increases suddenly below a critical temperature, following a miscibility gap phase diagram [1]. A second reason may be that it is experimentally difficult to observe phase separation with diffraction techniques, which are almost exclusively used for such studies. On the other hand, phase separation is directly observable using surface imaging techniques such as low energy electron microscopy (LEEM), which is capable of distinguishing phases with differing atomic structure, with approximately 100 Å lateral resolution, high contrast, and at high temperature [2]. In this paper, we report direct LEEM observations of a reversible phase separation between ordered and disordered 2D phases for a prototype metal-semiconductor system, Co͞Si(111).Previously, Bennett et al., using scanning tunneling microscopy (STM) and medium energy ion scattering (MEIS) found that a remarkably stable "ring-cluster" (RC) structure exists for all group VIII metals adsorbed on Si(111), with each RC consisting of a single metal atom in a substitutional silicon site plus an overlying ring of six silicon adatoms [3]. In the case of cobalt an ordered arrangement of RC's with a ͑ p 7 3 p 7 ͒R19.1 ± unit cell forms at the close-packed density of 1 7 ML. At lower coverages a disordered, or "͑1 3 1͒," variable density lattice gas arrangement of RC's exists at domain boundaries of the ͑7 3 7͒ reconstruction. It was not clear from STM "quench and look" observations whether these structures exist at high temperature or what their interactions might be.As we describe be...