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An electronic origin to the oscillatory segregation behavior in Ni-Cr and other BCC defects in FCC metals

Ni-Cr alloys exhibit oscillatory segregation behaviors near low index surfaces, in which the preferred segregation species changes from Ni in the first layer to Cr in the second layer. In many dilute-alloy systems, this oscillatory pattern is attributed to the elastic release of stresses in the local lattice around the segregating solute or impurity atom. These stresses are mostly thought to originate from mismatches in the atomic size of the solute and host atoms. In Ni-Cr alloys, however, an appreciable mismatch in atomic size is not present, leading to questions about the origins of the oscillatory behavior in this alloy. Therefore, using density functional theory, we have modeled the segregation of a single Cr atom in the and surfaces of FCC Ni, an alloy which exhibits this oscillatory behavior. Using Bader charge analysis, we show that the negative energy correlates directly with the amount of charge on the Cr atom. As Ni atoms strip valence charge from the Cr, the Cr contracts slightly in size. The greatest contraction and highest positive charge for the Cr occurs when it is in the second layer of the surface where the system exhibits the oscillating negative segregation energy. We then find that this behavior persists in other alloy systems (Ag-Nb, Cu-Cr, Pt-Nb, and Pt-V), which exhibit similar atomic radii and electronegativity differences between host and solute to Ni-Cr. These represent alloys in which the host metal exhibits an FCC ground-state structure while the solute metal exhibits a BCC ground-state structure.

36 MATERIALS SCIENCE↗

Materials Data on VPt2 by Materials Project

VPt2 crystallizes in the orthorhombic Immm space group. The structure is three-dimensional. V4+ is bonded in a distorted q6 geometry to ten equivalent Pt2- atoms. There are eight shorter (2.72 Å) and two longer (2.87 Å) V–Pt bond lengths. Pt2- is bonded to five equivalent V4+ and seven equivalent Pt2- atoms to form a mixture of distorted face, edge, and corner-sharing PtV5Pt7 cuboctahedra. There are a spread of Pt–Pt bond distances ranging from 2.70–2.80 Å.

36 MATERIALS SCIENCE↗

Materials Data on V3Pt by Materials Project

V3Pt crystallizes in the cubic Pm-3n space group. The structure is three-dimensional. V is bonded in a 6-coordinate geometry to two equivalent V and four equivalent Pt atoms. Both V–V bond lengths are 2.41 Å. All V–Pt bond lengths are 2.69 Å. Pt is bonded to twelve equivalent V atoms to form a mixture of edge and face-sharing PtV12 cuboctahedra.

36 MATERIALS SCIENCE↗

Materials Data on VPt by Materials Project

PtV is Tetraauricupride structured and crystallizes in the tetragonal P4/mmm space group. The structure is three-dimensional. V2+ is bonded to eight equivalent Pt2- atoms to form distorted VPt8 hexagonal bipyramids that share corners with sixteen equivalent PtV8Pt4 cuboctahedra, corners with eight equivalent VPt8 hexagonal bipyramids, edges with eight equivalent PtV8Pt4 cuboctahedra, edges with twelve equivalent VPt8 hexagonal bipyramids, and faces with six equivalent VPt8 hexagonal bipyramids. All V–Pt bond lengths are 2.74 Å. Pt2- is bonded to eight equivalent V2+ and four equivalent Pt2- atoms to form distorted PtV8Pt4 cuboctahedra that share corners with twelve equivalent PtV8Pt4 cuboctahedra, corners with sixteen equivalent VPt8 hexagonal bipyramids, edges with eight equivalent PtV8Pt4 cuboctahedra, edges with eight equivalent VPt8 hexagonal bipyramids, and faces with ten equivalent PtV8Pt4 cuboctahedra. All Pt–Pt bond lengths are 2.70 Å.

36 MATERIALS SCIENCE↗

Materials Data on VPt3 by Materials Project

Pt3V is Uranium Silicide-like structured and crystallizes in the tetragonal I4/mmm space group. The structure is three-dimensional. V2+ is bonded to twelve Pt+0.67- atoms to form VPt12 cuboctahedra that share corners with four equivalent VPt12 cuboctahedra, corners with eight equivalent PtV4Pt8 cuboctahedra, edges with eight equivalent VPt12 cuboctahedra, edges with sixteen equivalent PtV4Pt8 cuboctahedra, faces with four equivalent VPt12 cuboctahedra, and faces with fourteen PtV4Pt8 cuboctahedra. There are four shorter (2.75 Å) and eight longer (2.78 Å) V–Pt bond lengths. There are two inequivalent Pt+0.67- sites. In the first Pt+0.67- site, Pt+0.67- is bonded to four equivalent V2+ and eight Pt+0.67- atoms to form distorted PtV4Pt8 cuboctahedra that share corners with twelve equivalent PtV4Pt8 cuboctahedra, edges with eight equivalent VPt12 cuboctahedra, edges with sixteen PtV4Pt8 cuboctahedra, faces with four equivalent VPt12 cuboctahedra, and faces with fourteen PtV4Pt8 cuboctahedra. There are four shorter (2.75 Å) and four longer (2.78 Å) Pt–Pt bond lengths. In the second Pt+0.67- site, Pt+0.67- is bonded to four equivalent V2+ and eight equivalent Pt+0.67- atoms to form distorted PtV4Pt8 cuboctahedra that share corners with four equivalent PtV4Pt8 cuboctahedra, corners with eight equivalent VPt12 cuboctahedra, edges with twenty-four PtV4Pt8 cuboctahedra, faces with six equivalent VPt12 cuboctahedra, and faces with twelve PtV4Pt8 cuboctahedra.

36 MATERIALS SCIENCE↗

Materials Data on VPt3 by Materials Project

Pt3V is Uranium Silicide structured and crystallizes in the cubic Pm-3m space group. The structure is three-dimensional. V2+ is bonded to twelve equivalent Pt+0.67- atoms to form VPt12 cuboctahedra that share corners with twelve equivalent VPt12 cuboctahedra, edges with twenty-four equivalent PtV4Pt8 cuboctahedra, faces with six equivalent VPt12 cuboctahedra, and faces with twelve equivalent PtV4Pt8 cuboctahedra. All V–Pt bond lengths are 2.78 Å. Pt+0.67- is bonded to four equivalent V2+ and eight equivalent Pt+0.67- atoms to form distorted PtV4Pt8 cuboctahedra that share corners with twelve equivalent PtV4Pt8 cuboctahedra, edges with eight equivalent VPt12 cuboctahedra, edges with sixteen equivalent PtV4Pt8 cuboctahedra, faces with four equivalent VPt12 cuboctahedra, and faces with fourteen equivalent PtV4Pt8 cuboctahedra. All Pt–Pt bond lengths are 2.78 Å.

36 MATERIALS SCIENCE↗

Materials Data on V3Pt by Materials Project

V3Pt is Uranium Silicide structured and crystallizes in the cubic Pm-3m space group. The structure is three-dimensional. V is bonded to eight equivalent V and four equivalent Pt atoms to form distorted VV8Pt4 cuboctahedra that share corners with twelve equivalent VV8Pt4 cuboctahedra, edges with eight equivalent PtV12 cuboctahedra, edges with sixteen equivalent VV8Pt4 cuboctahedra, faces with four equivalent PtV12 cuboctahedra, and faces with fourteen equivalent VV8Pt4 cuboctahedra. All V–V bond lengths are 2.71 Å. All V–Pt bond lengths are 2.71 Å. Pt is bonded to twelve equivalent V atoms to form PtV12 cuboctahedra that share corners with twelve equivalent PtV12 cuboctahedra, edges with twenty-four equivalent VV8Pt4 cuboctahedra, faces with six equivalent PtV12 cuboctahedra, and faces with twelve equivalent VV8Pt4 cuboctahedra.

36 MATERIALS SCIENCE↗

Materials Data on VPt by Materials Project

PtV is beta-prime cadmium gold structured and crystallizes in the orthorhombic Pmma space group. The structure is three-dimensional. V2+ is bonded in a 8-coordinate geometry to eight equivalent Pt2- atoms. There are a spread of V–Pt bond distances ranging from 2.68–2.81 Å. Pt2- is bonded to eight equivalent V2+ and four equivalent Pt2- atoms to form a mixture of distorted corner, edge, and face-sharing PtV8Pt4 cuboctahedra. There are two shorter (2.71 Å) and two longer (2.81 Å) Pt–Pt bond lengths.

36 MATERIALS SCIENCE↗

Materials Data on VPt3 by Materials Project

Pt3V crystallizes in the trigonal R-3m space group. The structure is three-dimensional. V2+ is bonded in a distorted hexagonal planar geometry to six equivalent Pt+0.67- atoms. All V–Pt bond lengths are 2.64 Å. There are four inequivalent Pt+0.67- sites. In the first Pt+0.67- site, Pt+0.67- is bonded in a 12-coordinate geometry to three equivalent V2+ and three equivalent Pt+0.67- atoms. All Pt–Pt bond lengths are 2.92 Å. In the second Pt+0.67- site, Pt+0.67- is bonded to twelve Pt+0.67- atoms to form a mixture of edge, face, and corner-sharing PtPt12 cuboctahedra. All Pt–Pt bond lengths are 2.77 Å. In the third Pt+0.67- site, Pt+0.67- is bonded in a 12-coordinate geometry to three equivalent V2+ and three equivalent Pt+0.67- atoms. All Pt–V bond lengths are 2.64 Å. All Pt–Pt bond lengths are 2.92 Å. In the fourth Pt+0.67- site, Pt+0.67- is bonded to sixteen Pt+0.67- atoms to form a mixture of edge, face, and corner-sharing PtPt16 cuboctahedra. There are a spread of Pt–Pt bond distances ranging from 2.77–5.54 Å.

36 MATERIALS SCIENCE↗

Materials Data on VPt8 by Materials Project

Pt8V crystallizes in the tetragonal I4/mmm space group. The structure is three-dimensional. V5+ is bonded to twelve Pt+0.62- atoms to form VPt12 cuboctahedra that share corners with eight equivalent PtV2Pt10 cuboctahedra, faces with two equivalent VPt12 cuboctahedra, and faces with twelve equivalent PtV2Pt10 cuboctahedra. There are eight shorter (2.74 Å) and four longer (2.75 Å) V–Pt bond lengths. There are two inequivalent Pt+0.62- sites. In the first Pt+0.62- site, Pt+0.62- is bonded to two equivalent V5+ and ten Pt+0.62- atoms to form distorted PtV2Pt10 cuboctahedra that share corners with two equivalent VPt12 cuboctahedra, corners with four equivalent PtV2Pt10 cuboctahedra, edges with twelve equivalent PtV2Pt10 cuboctahedra, faces with three equivalent VPt12 cuboctahedra, and faces with seven equivalent PtV2Pt10 cuboctahedra. There are a spread of Pt–Pt bond distances ranging from 2.70–2.89 Å. In the second Pt+0.62- site, Pt+0.62- is bonded in a distorted single-bond geometry to one V5+ and six equivalent Pt+0.62- atoms.

36 MATERIALS SCIENCE↗