Incoherent interfacial energy from first-principles

Incoherent interfaces are ubiquitous in materials, yet their interfacial properties remain poorly understood. Due to the high computational cost, density functional theory (DFT) studies are typically restricted to coherent or semicoherent interfaces. In this work, we propose a novel approach to estimate incoherent interfacial energies within a DFT-accessible supercell size. Based on the so-called “incoherent γ-surface” concept, we first develop a classical-model-potential-based framework to capture the evolution of the one-dimensional (1D) incoherent γ-surface with increasing cell size. The method is then extended to the Ni/Ni₃Nb interface in a quasi-1D configuration, and further to a fully two-dimensional case of the Cu–Nb incoherent interface possessing very different lattice mismatches along the two in-plane directions. All investigated systems exhibit a consistent smoothing behavior of the γ-surface with increasing cell size. Moreover, the average value of the incoherent γ-surface is demonstrated to be a robust estimator for the incoherent interfacial energy, which is shown to converge rapidly even at small cell sizes. This work extends the applicability of first-principles methods to ideal incoherent interfaces and deepens the understanding of the coherent versus incoherent γ-surface concepts.