MAX phases – Past, present, and future: From traditional ternary compounds to advanced chemical ordering in multinary compounds

MAX phases are atomically laminated materials that combine metallic and ceramic characteristics and serve as precursors for two-dimensional MXenes. Their chemistry has expanded rapidly from ternary compounds to solid solutions, medium- and high-entropy compositions, and structures with chemical order. Herein we list more than 500 experimentally realized MAX phases and review how elemental distribution adds a design variable beyond overall composition. Emphasis is on chemically ordered MAX phases, including out-of-plane ordered ( o -MAX), in-plane ordered ( i -MAX), and super-ordered ( s -MAX) structures, with a summary of their synthesis, composition and structure, characterization, thermodynamic stability, and design rules. We discuss challenges associated with distinguishing ideal order, disorder and states in between, and introduce a site-occupation-based framework to describe the collective degree of chemical order, including off-stoichiometry and intermixing. We also propose a notation that enables chemically ordered and disordered MAX phases to be distinguished directly from their reported composition, including means for describing degree of intermixing and site occupancy. Furthermore, we discuss how chemical order in precursors can be inherited, modified, or converted into metal and vacancy order in MXenes, with consequences for, e.g., electrochemical and catalytic functionality. Finally, we identify the central challenges in the field, from quantitative determination of chemical order across length scales to predictive control of chemical order during synthesis. By linking composition, atomic arrangements, and functionality across both MAX phases and derived MXenes, chemical order and disorder provide a framework for moving beyond compositional exploration toward rational design of layered materials with targeted properties.