Universal thermodynamic framework for quasi-van der Waals epitaxy

Abstract: van der Waals (vdW) epitaxy is conventionally regarded as a rotation-free and strain-free growth mode driven by weak, isotropic interactions, yet many interfaces paradoxically exhibit strictly locked orientations that defy standard surface-energy models. We resolve this inconsistency by establishing a unified quantitative framework for 2D-3D systems, in which strong electrostatic and chemical interactions compete with entropic forces. We introduce a two-tier descriptor set-the predictive index (I_pre) and the thermodynamic locking criterion (I_lock)-to quantify the energetic sufficiency for locked epitaxy. Our theory accurately predicted the competitive interactions at the interface within the 2D-3D system, precisely characterized whether the epitaxial layer underwent free growth or was constrained in a locked growth mode, demonstrating robust consistency with diverse experimental observations. This framework unifies orientation selection in 3D-on-2D films and rotational locking in 2D-on-3D layers within a single-phase diagram. Our work provides a generalizable, predictive route to controlling epitaxial orientation across a broad spectrum of layered heterostructure