Solubility of Boron, Carbon, and Nitrogen in Transition Metals: Getting Insight into Trends from First-Principles Calculations

Efficient chemical vapor deposition synthesis of two-dimensional (2D) materials such as graphene, boron nitride, and mixed BCN systems with tunable band gaps requires precise knowledge of the solubility and mobility of B/C/N atoms in the transition metals (TMs) used as substrates for the growth. Yet, surprisingly little is known about these quantities either from experiments or simulations. Using first-principles calculations, we systematically study the behavior of B/C/N impurity atoms in a wide range of TMs. We compute formation energies of B/C/N interstitials and demonstrate that they exhibit a peculiar but common behavior for TMs in different rows of the periodic table, as experimentally observed for C. Our simulations indicate that this behavior originates from an interplay between the unit cell volume and filling of the d-shell electronic states of the metals. We further assess the vibrational and electronic entropic contributions to the solubility, as well as the role of anharmonic effects. Finally, we calculate the migration barriers, an important parameter in the growth kinetics. Our results not only unravel the fundamental behavior of interstitials in TMs but also provide a large body of reference data, which can be used for optimizing the growth of 2D BCN materials.