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The role of Hume-Rothery's rules play in the MAX phases formability

MAX phases are a family of layered, hexagonal-structure ternary carbides or nitrides of a transitional metal and an A-group element. What makes this type of material fascinating and potentially useful is their remarkable combinations of metallic and ceramic characteristics; as well as the indispensable role in 'top-down' synthesis of their 2D counterparts, MXenes. To enhance the efficiency in the successful search for potential novel MAX phases, the main efforts could go toward creating an informationprediction system incorporating all MAX phases' databases, as well as generally valid principles and the high-quality regularities. In this work, we employ structure mapping methodology, which has shown its merit of being useful guides in materials design, with Hume-Rothery parameters to provide guiding principles in the search of novel MAX phases. The formable/non-formable data on MAX phases can be ordered within a twodimensional plot by using proposed expression of geometrical and electron concentration factors.