Surface energies and relaxation of NiCoCr and NiFeX (X = Cu, Co or Cr) equiatomic multiprincipal element alloys from first principles calculations

Abstract

First principles calculations of the energies and relaxation of unreconstructed low-index surfaces, i.e. (001), (011) and (111) surfaces, in NiCoCr and NiFeX (X = Cu, Co or Cr) equiatomic multi-principal element alloys (MPEAs) are presented. The calculations were conducted for 12-layer slabs represented by special quasi-random supercells using the projector augmented wave method within the generalized gradient approximation. While experimental predictions are unavailable for comparison, the calculated surface energies agree fairly well with those from thermodynamic modeling and a bond-cutting model. In addition, the calculations unveil an important surface structure, namely, that the topmost surface layer is in contraction except for the (001) surface of NiFeCr alloy, the next layer below is in extension, and the bulk spacing is gradually recovered from the subsequent layers down. Additionally, the surface contraction is the most pronounced on the (011) plane, being about 4%–10% relative to the bulk spacings. The results presented here can provide an understanding of surface-controlled phenomena such as corrosion, catalytic activities and fracture properties in these equiatomic MPEAs.