This study systematically investigates the elastic anisotropy and thermodynamic properties of \(\:{{\upbeta\:}}_{1}^{{\prime\:}}\) phase in Mg-Zn alloys through first-principles calculations combined with Debye-Grüneisen theory. Three critical intermetallic phases - monoclinic Mg4Zn7, cubic MgZn2 (C-MgZn2), and hexagonal MgZn2 (H-MgZn2) phases were comparatively analyzed. Electronic structure analysis reveals that C-MgZn2 and H-MgZn2 exhibit stronger chemical bonding stability compared to Mg4Zn7. Phonon dispersion characteristics demonstrate distinct vibrational patterns: C-MgZn2 and Mg4Zn7 display enhanced phonon modes at both low and high frequency ranges, while H-MgZn2 shows predominant medium-frequency vibrational modes. Elastic anisotropy evaluation identifies Mg4Zn7 as moderately anisotropic, H-MgZn2 as significantly anisotropic, and C-MgZn2 as nearly isotropic. Thermodynamic analysis predicts superior thermal stability for C-MgZn2, evidenced by its highest Debye temperature (θd = 366 K), maximum sound velocity (vm=3.468 m/s), and minimal Grüneisen parameter (γ = 0.641), correlating with its exceptional thermal conductivity. In contrast, Mg4Zn7 exhibits the highest thermal expansion coefficient among the investigated phases. These findings establish fundamental structure-property relationships that advance the understanding of \(\:{{\upbeta\:}}_{1}^{{\prime\:}}\) phase stabilization mechanisms, providing critical guidance for designing high-performance Mg-Zn alloys through phase engineering strategies.
