Kinetics of Surface Segregation in Metallic Alloys with First-Principles Interaction Parameters
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ABSTRACT We report the results of Monte Carlo simulations of the kinetics of surface segregation at the (001) face of CuNi and MoW alloys. These two systems were selected because they are based on different lattice structures and show contrasting segregation behavior: CuNi exhibits a monotonic profile, while that of MoW is oscillatory. To describe the energetics we have determined a set of effective cluster interactions (ECI) which govern the ordering or clustering tendencies of these alloys. The ECI were obtained by means of tight-binding electronic structure calculations in which no adjustable or experimentally determined parameters were used. Equilibrium segregation profiles are calculated and a series of quenches are performed. The layer concentrations are studied as a function of time and the existence of metastable phases in the surface region is investigated. INTRODUCTION Many effects in materials science are the result of a subtle interplay of electronic structure and statistical physics. Surface segregation is no exception: band structure effects must provide the driving force that, in thermodynamic equilibrium, causes one species to preferentially occupy surface sites. One of the great successes of the quantum theory of solids in recent years has been the determination of the relevant interaction parameters from first principles for numerous systems. This has allowed researchers to relate these microscopic quantities to macroscopic ones, such as surface tensions which were historically used to understand the segregation phenomenon [1]. Moreover, the parameters thus obtained could be used as input in truncated Ising models, which had been central to many phenomenological model studies [2]. However, the ensuing Hamiltonians are more complex than just a simple nearest-neighbor pair-interaction model: the interactions are in general concentration-dependent and one needs to include point-energies as well as further-neighbor or higher-order cluster interactions. A detailed discussion of the formalism may be found elsewhere [3, 4]. The present work focuses on two interesting alloy systems: CuNi and MoW. The former has been the subject of several studies [4, 5] and is revisited here since separate investigations have produced conflicting findings: although all authors agree that Cu segregates strongly to the surface, one group of studies obtains a monotonic segregation profile, while others find an oscillating approach to the bulk concentration. This disagreement for a relatively simple alloy illustrates the complexity of the surface segregation problem. The second system studied is the bcc-based MoW alloy [6]. This material is of interest because it exhibits an apparently contradictory phenomenon: an oscillating segregation profile accompanied by bulk phase separation. Confirmation of the latter is hard to come by, though, since in the bulk experiment shows a continuous series of solid solutions, but theory predicts a miscibility gap at very low temperatures, too low to be observed directly. While the study of t
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