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.