New Perturbation Method for Predicting Solute Segregation Energies for Symmetric Tilt Grain Boundaries
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New Perturbation Method for Predicting Solute Segregation Energies for Symmetric Tilt Grain Boundaries Shijing Lu and Donald W. Brenner Department of Material Science and Engineering, Raleigh, NC 27695-7907, U.S.A. ABSTRACT Solute atoms in dilute alloys have been shown to segregate at grain boundaries and stabilize them against grain growth. At present, most theories of the stabilization of nanostructured alloys do not account for the detailed atomic structure of the interfaces, but instead rely on averaged segregation energies. One of the reasons for this is the daunting task of determining segregation energies for a large number of possible sites in a given microstructure. We have developed a new approach to predicting and organizing interface structures in alloys that takes advantage of perturbation techniques and a disclination structural units model (DSUM) developed previously to describe grain boundary structure and properties in pure systems. The fundamental idea is to treat dilute alloys as a perturbed form of the pure metal systems whose energy can be determined by the DSUM. This paper introduces this method and gives a preliminary validation by comparing segregation energies for zirconium solute segregating to a grain boundary in copper calculated via the perturbation method and full atomistic simulations. INTRODUCTION It is well established that for many dilute metal alloys solute atoms tend to segregate to the grain boundaries, and that this segregation can profoundly affect the micro-structure, mechanical and chemical properties in the form of altered recrystallization, grain boundary faceting, corrosion and embrittlement. Solute segregation to grain boundaries can also help stabilize nanostructured metals against grain growth. The degree of solute segregation is conventionally quantified by a parameter called the grain boundary enrichment ratio , which is defined as the molar content of solute at a grain boundary to the bulk solute molar content . As an example the grain boundary enrichment ratio of zirconium in pure copper at 1254K has been measured to be as high as .1 According to theoretical work done by Seah and Mclean et al1,2, the degree of segregation of solute atoms can be linked to the free energy change associated with moving a solute atom from the bulk to a grain boundary by the expression (1)
where is the molar content of solute if all atoms of the grain boundary monolayer are replaced by solute atoms. Mclean made the simplifying assumption that the energy gain from segregation is due exclusively to the total release of strain energy associated with solute atoms in the bulk 3. Making an analogy between solute segregates in a pure metal system and a misfit sphere in an elastic continuum yields
(2)
where and are the solute bulk modulus and radius of the solute atoms, respectively, and and are the matrix shear modulus and atom radius, respectively. While this expression has been successfully used,4,5 it ignores changes in chemical bonding for a solute atom in the bulk and in the grain boun
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