Segregation of niobium solute in nickel toward grain boundaries and free surfaces

Abstract

The spatial redistribution of niobium atoms near the (100) and (111) free surfaces and selected grain boundaries (GBs) of pure nickel has been considered in the low niobium concentration limit. There is one key difference between the situation for placing a niobium atom at a free surface and at a GB. At the free surface, an energetic compromise is required between having space for the large niobium atom and being able to place that atom at a position of high electron density. For a GB, no such compromise is required. An extremely interesting feature is the presence of a region around the third layer of (111) and the fourth layer of (100) free surfaces where the substitutional internal energy reverses its sign. The authors’ simulations show a significant depletion in concentration of niobium immediately at free surfaces. However, under the first two or three layers of pure nickel, there exists a niobium-enriched region with a strongly temperature-dependent concentration. This predicted nonmonotonic distribution of niobium in the surface region may be important for many applications and calls for experimental confirmation. In contrast, at the grain boundaries, the concentration of niobium, which is pertinent to GB oxidation embrittlement, is predicted to be much higher than in the bulk. It monotonically decreases with the distance from the GB until reaching the bulk value. The calculation of the free energy uses atomistic potentials based on ab initio quantum mechanical calculations, includes lattice relaxation around niobium atoms by using molecular dynamics (with 1440 or 2880 atoms in the modeling cell), and includes vibrational entropy phenomenologically within the local harmonic approximation. The entire approach is ab initio based and does not require any empirical information.