| 總結: | In this study, we employed the first-principles method based on density functional theory to calculate the elastic constants, bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio, and density of states for both cubic and tetragonal phases of Pb(Zr<sub>x</sub>Ti<sub>1−x</sub>)O<sub>3</sub>. The structural model of Pb(Zr<sub>x</sub>Ti<sub>1−x</sub>)O<sub>3</sub> was established using the virtual crystal approximation (VCA). Our results demonstrate that the VCA-calculated properties are in excellent agreement with other theoretical predictions and experimental data. As the Zr content increases, the lattice constants of both cubic and tetragonal Pb(Zr<sub>x</sub>Ti<sub>1−x</sub>)O<sub>3</sub> increase, while the c/a ratio initially decreases and subsequently increases. Both cubic and tetragonal Pb(Zr<sub>x</sub>Ti<sub>1−x</sub>)O<sub>3</sub> satisfy the Born stability criteria, indicating mechanical stability. For the cubic phase, the elastic constants, bulk modulus, and shear modulus decrease with increasing Zr content. In contrast, for the tetragonal phase, the elastic and shear moduli exhibit a non-monotonic trend, peaking at a Zr content of 0.5, where Pb(Zr<sub>0.5</sub>Ti<sub>0.5</sub>)O<sub>3</sub> demonstrates superior mechanical properties. A comparative analysis reveals that as Zr content increases, the cubic phase exhibits enhanced structural resilience, greater electronic structure stability, and increased anisotropy. These characteristics make cubic Pb(Zr<sub>x</sub>Ti<sub>1−x</sub>)O<sub>3</sub> more suitable for advanced manufacturing techniques such as additive manufacturing, offering enhanced design flexibility for ferroelectric materials.
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