RETRACTED: Atomic scale interfacial and compositional characteristics of the σ and γ phases of Ni-based single-crystal superalloys (Retracted Article)

High-resolution transmission electron microscopy and high-angle annular dark-field imaging were used to study differences in the interfacial and compositional characteristics between the plate-shaped sigma and gamma phases in a Ni-based single-crystal superalloy. An atomic structural model of the interface between the sigma and gamma phases that includes a step was proposed. The a phase exhibits the following relationship with the matrix: [0 0 1](gamma)//[1 1 (2) over bar](sigma), ((2) over bar 2 0)(gamma)//((1) over bar 1 0)(sigma), ((2) over bar (2) over bar 0)(gamma)//(1 1 0)(sigma), [0 1 1](gamma)//[1 1 0](sigma), (1 (1) over bar 1)(gamma)//(0 0 (1) over bar)(sigma), The compositional characteristics of the sigma phase indicate that it is rich in high-Z elements (Z is the atomic number), especially the alloying element rhenium (Re). The impurity formation energies for the sigma and gamma phases doped with Re in different sublattices were investigated using the first-principles method based on the density functional theory. The bonding characteristics of the undoped and doped sigma and gamma phases were analyzed with the valence charge densities and the density of states. The results indicate that the alloying element Re, with a large atomic size, substitutes the W atom preferentially, owing to the nature of the bonding and the interstitial spaces in the crystal structure. (C) 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.