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Abstract: We perform first-principles density-functional theory (DFT) calculations to resolve the controversy of off-stoichiometry of Q-phase in Al-Cu-Mg-Si system. We compute the single and multiple defect energies (vacancy-vacancy, anti-site–vacancy, anti-site–anti-site) at 0 K and finite temperatures to understand the gap between DFT-predicted lowest energy structure and experimentally observed various stoichiometries of Q-phase. We find that i) the stoichiometry of Al4Cu2Mg8Si7 observed by Arnberg can be explained by the single anti-site defect of Al on Mg site, ii) the stoichiometry of Al5Cu2Mg8Si6 observed by Phragmen can be understood by the multiple anti-site defects of Al on Mg site and Al on Si site, iii) the physical size effect is important in determining the defect formation energetics under a similar chemistry (i.e., composition) of Q-phase. We believe that the proposed defect energetic information and mechanism will be useful to design Q-phase strengthened aluminum alloys based on Integrated Computational Materials Engineering (ICME).