Density Functional Theory Calculations of Properties of the Grain Boundaries in Aluminum
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Density Functional Theory Calculations of Properties of the Grain Boundaries in Aluminum Marek Muzyk and Krzysztof J. Kurzydlowski Warsaw University of Technology, Faculty of Materials Science and Engineering, Woloska 141, 02-507 Warsaw, Poland ABSTRACT The Density Functional Theory has been used to analyze an inter-granular segregation of Cu and Mg. The stability of Cu and Mg atoms in the aluminum matrix, intermetallic phases and symmetric twist grain boundaries has been compared. The quantitative description of solubility of Cu and Mg atoms in the nano-crystalline aluminum has been proposed. The calculations have been carried out to investigate the properties of symmetric twist boundaries in aluminum with and without Cu/Mg atoms. The phenomena of are discussed and its effect on the stability of precipitates containing these elements.
INTRODUCTION Aluminum alloys are widely used in industry due to their low density and high strength, imparted among others by grain boundary strengthening and/or precipitations hardening. Copper and magnesium are the important alloying elements added to the aluminum matrix, which form Al2Cu and Al3Mg2 phase [1], respectively. These inter-metallic phases have low enthalpies of mixing, which make them energetically favorable with respect to solid solutions of Cu and Mg in Al. However, it has been experimentally found that Cu in aluminum may segregate to grain boundaries [2,3]. The resulting depletion of Cu near to the grain boundaries may have important implications to the structure/properties of Al-Cu alloys. This in particular applies to nano-grain size aluminum alloys, in which the grain boundaries account for significant specific volume of the material. Assuming that the grain size is 100 nm and the thickness of the grain boundary is 1 nm one can estimate, that the volume friction of grain boundaries is 3%. Such a volume friction may in an extreme case absorb nearly all alloying additions in Al alloys, especially that distance to nearest grain boundary is for grain size of 100 nm below 50 nm. This calls for more in-depth evaluation of driving forces governing grain boundary segregation. The phenomena of solute segregations has been described by Suzuki [4,5] (it is called Suzuki effect or segregation), and has been used to describe nanoprecipitation in Al-Ag system [6]. In this work the segregation of Cu and Mg to the grain boundaries in aluminum was analyzed using the Density Functional Theory (DFT).
MODELING The calculations described below have been based on DFT as implemented in the Vienna Abinitio Simulation Package (VASP) [7]. These calculations were performed using the projector augmented wave (PAW) potentials and the generalized gradient approximation (GGA), with the
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electron exchange-correlation described by Pardew-Burke-Ernzerhof parameterization (PBE) [8]. The Fermi smearing of the electronic occupancy with 0.2 eV and the plane wave cut-off energy of 350 eV were employed. The Monkhorst-Pack scheme [9] was used to sample the Brillouin zone, with 0.26 ǖ spacing in t
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