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• Effects of Zn content on the stability of T-phase are addressed. • The defect properties and bonding characteristics of T-phase are investigated. • The preference of vacancy formation at A-sites under Zn-poor condition is verified. • Cu and Ag can promote the precipitation of T-phase, due to deep orbital hybridizations. In the development process of crossover aluminum alloys, T-Mg 32 (Al, Zn) 49 phases play a significant role in the precipitation strengthening effect. However, comprehensive understandings of the structural characteristics, interactions among alloying elements, mechanical property dependence on composition variation, effects of doping and defects etc. are still inadequate. A combination of density functional theory (DFT) calculations and special quasi-random structures (SQSs) was applied to investigate the formation energies, lattice parameters, electronic structures and mechanical properties of the disordered T-phases, as well as the effects of possible defects and alloying elements. The formation energy and lattice constant of the T-phase gradually vary from 0 to –0.12 eV/atom and from 1.460 to 1.405 nm, respectively, with increasing Zn contents. Zn-3 d orbitals exhibit stronger hybridization with Al-3 s than Mg-3 s orbitals, and this is further enhanced by increasing Zn contents, leading to improved covalency and mechanical properties of the T-phase. The T-phases show good ductility according to the Poisson's ratio ν , Cauchy's pressure and G/B. The A site is more favorable to remain vacant in Al-rich and Zn-poor environments, which is consistent with the previous experimental observations. For alloying elements, Zn atoms tends to occupy Al atoms at the B, C and F sites and Mg atoms at the G sites. Both Cu and Ag elements can decrease the formation energy of T-phases and possibly produce a greater number of T-phases during the precipitation process. The effect of Ag is more significant relative to Cu due to the deeper orbital hybridization. The computational results show good agreement with previous experimental data and provide new insights into the compositional design of new Al-Mg-Zn alloys. [ABSTRACT FROM AUTHOR]