Small size atoms like boron, nitrogen, oxygen, and carbon form interstitial in transition metals. The solubility of oxygen in Ti, Zr, a nd Hf is up to 33, 29, and 20 at. % respectively, at room temperature [1]. High solubility is attributed to the small distortion oxygen interstitials exert on these metals [2]. Similarly higher solubility of C in FCC Fe compared to BCC Fe is attributed to a small amount of strain exerted by C on Fe. But C and N interstitials prefer to be at the tetrahedral position compared to the octahedral position in metals like Pt [3]. Although the lattice parameter of Pt is much smaller than that of Ti, N prefers to occupy an octahedral position in Ti while it prefers to occupy a tetrahedral position in Pt. This observation is counterintuitive to the established notion, that distortion plays a major role in the stability of interstitials. In this work, we explore the role of the distortion and electronic binding energy of boron, oxygen, nitrogen, and carbon interstitials and their relative stability in the octahedral and tetrahedral, and substitutional sites in bulk and at the surfaces.
We show that distortion alone does not play a role in the preference of a site of solute atoms. These results help us understand the limitations of the thumb rule (larger atoms will occupy a larger site, and smaller ones will occupy smaller sites) and the size of space available at various sites in Fe. While B follows the thumb rule, the genesis of O's occupation of the Octa site lies in the strong bonding to Fe in the Octa environment. We showed that B does not bind strongly to Fe, and its stability is dictated by distortion alone, which could explain the preference of B to segregate at large open volumes, like grain boundary. C, N, and O form strong bonds with Fe and have strong environmental dependence. O bonding at the Octa site is strong enough to overcome the largest distortion among various sites in bulk Fe and stabilize there. We also show that solute atoms could not be assumed to be a hard-sphere with fixed volume as suggested by calculated radii. We show that the si ze of the atom changes when placed in different sites in Fe, this is due to different amount of charge transfer from Fe to solute atoms.
Interstitial formation energy of oxygen atoms at their most preferred site in TM elements become more positive, as one move from left to right in the periodic table. Interstial formation energy is positive for Ni, Cu, Mo, W, Re, Os, Ir, Ru, Rh, Pd, Ag, Pt, and Au. As the volume available at either octahedral or tetrahedral site in TM decreases as one move from left to right, one would expect that more positive interstitial formation energy is due to large distortion energy. But we found that oxygen prefers tetrahedral sites in Mo, Ru, Rh, Pd, Ta, W, Re, Os, Ir, Pt, and Au, where distortion energy is higher. This suggest that distortion energy alone does not control preference for a site. In fact, for In, Pt, and Au electronic binding energy is positive at both octahedral and tetrahedral site, oxygen is stable at tetrahedral site because electronic binding energy is less positive at tetrahedral site.
We find that adsorption energy of oxygen, on the surfaces is more negative than their formation energies at most stable site in the bulk. This is due to both low distortion energy at the surface and more negative electronic binding energy at the surface. This is particularly important for elements that have positive interstials formation energy in the bulk. Adsorption energy of oxygen on surface of all these elements is negative. This suggests that oxygen will adsorb on the surface but will not from interstial in the bulk. This explains why metals like, Ti, Zr, Hf, V, Nb, Ta forms oxygen solid solution while other TM do not. But catalytic metals like, Pt, Pd, Cu, Ni does facilitate catalytic reactions by adsorption of oxygen on the surface but oxygen does not get absorbed in the bulk.
[1] R.W. Cahn, P. Haasen, Physical Metallurgy, fourth ed., North-Holland Publishing Company, Amsterdam, 1996.
[2] A. v. Ruban, V.I. Baykov, B. Johansson, V. v. Dmitriev, M.S. Blanter, Oxygen and nitrogen interstitial ordering in hcp Ti, Zr, and Hf: An ab initio study, Phys Rev B 82 (2010) 134110.
[3] Xiaohui Hu, Torbjö rn Bjö rkman, Harri Lipsanen, Litao Sun, Arkady V. Krasheninnikov, “Solubility of Boron, Carbon, and Nitrogen in Transition Metals: Getting Insight into Trends from First-Principles Calculations” J. Phys. Chem. Lett. 6, 3263−3268, 2015.