Self-Propagating High-Temperature Synthesis as an Enabling Route for High-Entropy MAX Phases.

High-entropy MAX (HE-MAX) phases represent a new class of layered ceramics that combine the multi-principal-element chemistry of high-entropy materials with intrinsic damage tolerance, electrical conductivity, and multifunctionality of conventional MAX phases. Despite their promise, the synthesis of HE-MAX phases remains fundamentally constrained by sluggish multicomponent diffusion, narrow thermodynamic stability windows, and strong competition from thermodynamically favored binary and ternary carbides, borides, and nitrides. These challenges are further exacerbated by the volatility of A-site elements under near-equilibrium processing conditions. This review positions self-propagating high-temperature synthesis (SHS) as an energy-efficient, non-equilibrium processing route capable of stabilizing selected entropy-driven MAX chemistries through ultrafast thermal excursions and rapid quenching. A unified thermodynamic-kinetic framework is developed to elucidate the interplay among reaction enthalpy, configurational entropy, combustion wave sustainability, and phase evolution in HE-MAX systems. Predictions of thermochemical adiabatic temperature are systematically correlated with experimental SHS studies to delineate phase stability boundaries, stoichiometric sensitivity, and the roles of diluents and transient liquid formation. Finally, practical design principles for scalable SHS synthesis of HE-MAX phases are outlined, alongside strategies for their selective exfoliation into high-entropy MXenes and a critical assessment of their emerging functional applications.