The Free Energy Simulation Approach to Grain Boundary Segregation In Cu-Ni
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THE FREE ENERGY SIMULATION APPROACH TO GRAIN BOUNDARY SEGREGATION IN Cu-Ni H. Y. Wang* R. Najafabadi* D. J. Srolovitz* and R. LeSar** *University of Michigan, Dept. of Materials Science and Engineering, Ann Arbor, MI 48109 **Los Alamos National Laboratory, Theoretical Division, Los Alamos, NM 87545 ABSTRACT A new, accurate method for determining equilibrium segregation to defects in solids is employed to examine the segregation of Cu to grain boundaries in Cu-Ni alloys. The results are in very good agreement with the ones given by Monte Carlo. This method is based upon a point approximation for the configurational entropy, an Einstein model for vibrational contributions to the free energy. To achieve the equilibrium state of a defect in an alloy the free energy is minimized with respect to atomic coordinates and composition of each site at constant chemical potential. One of the main advantages this new method enjoys over other methods such as Monte Carlo, is the efficiency with which the atomic structure of a defect, segregation and thermodynamic properties can be determined. The grain boundary free energy can either increase or decrease with increasing temperature due to the competition between energetic and configurational entropy terms. In general, the grain boundary free energy increases with temperature when the segregation is strongest. INTRODUCTION Grain boundaries play a major role in determining such properties as strength, toughness, electrical resistivity, band structure, diffusivity, etc. in polycrystalline materials. In many cases, small changes in the composition of a material are known to produce large changes in those physical phenomena which are controlled by interfaces. Small changes in bulk composition can lead to extraordinarily changes in the composition in the vicinity of the grain boundary. These changes, in turn, can lead to large modifications of the grain boundary structure and grain boundary thermodynamics. For pure materials, atomistic simulations can be used to determine the structure of an interface by minimizing the internal energy with respect to atomic positions at T=0 OK. At T > 0, molecular dynamics (MD) or Monte Carlo (MC) simulation methods are traditionally used. Recent developments in Monte Carlo simulation methods have extended this method to alloy systems where the local composition may vary during the course of the simulation. This has led to the first atomistic studies of equilibrium segregation to interfaces [1]. While this method does yield equilibrium interfacial structure and composition, it has never been successfully applied to the determination of the thermodynamic properties of grain boundaries. Additionally, these types of Monte Carlo simulation require substantial computational resources and hence this method is generally limited to supercomputer applications. In order to perform systematic studies of grain boundary structure and their thermodynamic properties in alloy systems, we have extended our previously introduced free energy simulation approach [2] to the
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