Near-Equilibrium Solubility of Nanocrystalline Alloys

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Near-Equilibrium Solubility of Nanocrystalline Alloys Alexander Kirchner , Thomas Riedl, Konrad Eymann, Michael Noethe, and Bernd Kieback Institute of Materials Science, Technische Universität, 01062 Dresden, Germany ABSTRACT Grain boundaries are the dominating type of defect in nanocrystalline materials. Understanding their properties is crucial to the comprehension of nanocrystalline materials behavior. A facile thermodynamic model for alloy grain boundaries is developed. The macroscopic analysis is based on established descriptions of metallic solutions and the universal equation of state at negative pressure, using mainly parameters obtainable from measurements on macroscopic samples. The free energy of atoms in grain boundaries is derived as a function of excess volume, composition, and temperature. Interfacial enrichment is computed using equilibrium conditions between bulk phase and grain boundaries. The excess volume of symmetric ‹100› tilt grain boundaries in Cu as a common system is obtained by atomistic computer simulation. In a general case the predictions of the proposed model are compared to experimental grain boundary segregation data, yielding a good match. The near-equilibrium solubility of Ag in nanocrystalline Cu and of Cu in nanocrystalline Fe is calculated. INTRODUCTION The energetic situation of atoms occupying positions in grain boundaries (GBs) is distinctly different from those in an undisturbed crystal. As the fraction of atoms located in GBs is approximately 3G / D with G being the GB width and D the grain size, their contribution to the overall thermodynamic properties can be neglected in coarse grained materials. The properties of nanocrystalline (nc) materials, however, increasingly deviate from those of coarsegrained materials with diminishing grain size. For many aspects this effect becomes noticeable at grain sizes smaller than 20 nm. To describe the thermodynamic properties of nc elemental metals Fecht [1] and Wagner [2] constructed a model of GBs. In that the GBs are approximated by a uniformly dilated lattice retaining the symmetry of the bulk material. This very simplistic view neglects the complex reality of GBs such as changed coordination and different sites. Yet this model correctly describes the measured increase in the heat capacity and thermal expansion as well as the reduction of the elastic moduli. In a previous work the above mentioned model has been extended to binary alloys and the condition for equilibrium between bulk and GB established [3]. In the present contribution molecular statics simulation is used to elucidate the excess volume of Cu GBs. Thereafter an empirically found correlation between bulk solubility and GB enrichment is modeled in terms of this theory. Two binary systems will be used to demonstrate the calculation of solubility in nc alloys in dependence of grain size.

Corresponding author. Email: [email protected].

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THEORY Thermodynamic Model of Alloy Grain Boundaries The thermodynamic description is based upon a model for press