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