A quantitative understanding of homogeneity ranges and the thermodynamic stability of vacancy formation in MAX phases is essential for tailoring their properties, yet a comprehensive link between atomic-scale energetics and macroscopic phase behavior has remained elusive. In this work, we bridge this gap by integrating density functional theory (DFT) calculations with the Calphad (Calculation of Phase Diagrams) approach to investigate the Ti-Al-C-N system. Our results demonstrate that the X-sublattice (C, N) in Tin+1AlXn phases (n = 1-3) can accommodate extensive vacancy solubility ranging from 13% to 30%, whereas vacancies on the Al-sublattice are energetically unfavorable under equilibrium conditions. By incorporating DFT-derived mixing enthalpies and vacancy formation energies into the thermodynamic model, we successfully reproduce experimental isothermal sections and quaternary phase equilibria, resolving long-standing literature discrepancies regarding the stoichiometry of carbonitride solid solutions. Furthermore, we apply the framework to describe constrained equilibria in nanoscale TiN/TiAl and Ti/AlN multilayers, accurately predicting phase evolution and defect concentrations in thin film systems where global equilibrium is kinetically hindered. This work provides a roadmap for defect engineering in MAX phases and establishes a predictive framework for designing parent materials to tailor the chemistry and active-site density of derived two-dimensional MXenes.
Funding Agencies|Swedish Research Council [2023-04833, 2025-06131, 2022-06725]; Swedish Research Council [2023-04833] Funding Source: Swedish Research Council