Low-index surface energies, cleavage energies, and surface relaxations for crystalline NiAl from first-principles calculations
NiAl surfaces frequently serve as a platform for studying a broad range of physical and chemical phenomena including chemisorption, catalysis, oxidation, alloy growth, and surface nanostructure formation. Knowledge of precise values for low-index surface energies of NiAl, the most fundamental quantities characterizing surface thermodynamics, is often invaluable for understanding of these phenomena. In all previous analyses for NiAl(100) and NiAl(111), Ni- and Al-terminations are not distinguished, and half of the cleavage energy (or equivalently, the average of the surface energies of two differently terminated surfaces) is always identified as the "surface energy". No values are available for individual surface energies of Ni- or Al-terminated NiAl(100) or NiAl(111) surfaces, whereas knowledge of only cleavage energy is often insufficient for analyzing surface-associated behavior. In this work, we perform extensive first-principles density-functional-theory (DFT) calculations for surface energies and cleavage energies of NiAl(110), NiAl(100) and NiAl(111) by considering the chemical-potential-based formulations to clarify the ambiguity in their surface energies and cleavage energies. We obtain a surface-energy phase diagram for these three low-index surfaces versus the relevant chemical potential, as well as the chemical-potential-dependent Wulff plots for NiAl crystal equilibrium shapes. We also provide the surface-relaxation information from our DFT calculations for comparison with previous experimental data.