First-Principles Study of Mechanical Properties of Pb(Zr<sub>x</sub>Ti<sub>1−x</sub>)O<sub>3</sub> in the Cubic and Tetragonal Phase
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<...
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MDPI AG
2025-02-01
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| Series: | Crystals |
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| Online Access: | https://www.mdpi.com/2073-4352/15/2/160 |
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| author | Xudong Ran Shaolan Zhou Shaowen Zhou Wei Lei Lin Xiang Yang Wu Bingfei Hu Jianquan Tao Qiang Chen |
| author_facet | Xudong Ran Shaolan Zhou Shaowen Zhou Wei Lei Lin Xiang Yang Wu Bingfei Hu Jianquan Tao Qiang Chen |
| author_sort | Xudong Ran |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-2f0e3a9b8b5441adae2b56a35fc771eb |
| institution | DOAJ |
| issn | 2073-4352 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Crystals |
| spelling | doaj-art-2f0e3a9b8b5441adae2b56a35fc771eb2025-08-20T03:12:14ZengMDPI AGCrystals2073-43522025-02-0115216010.3390/cryst15020160First-Principles Study of Mechanical Properties of Pb(Zr<sub>x</sub>Ti<sub>1−x</sub>)O<sub>3</sub> in the Cubic and Tetragonal PhaseXudong Ran0Shaolan Zhou1Shaowen Zhou2Wei Lei3Lin Xiang4Yang Wu5Bingfei Hu6Jianquan Tao7Qiang Chen8Southwest Technology and Engineering Research Institute, Chongqing 400039, ChinaSouthwest Technology and Engineering Research Institute, Chongqing 400039, ChinaSchool of Information Engineering, Chongqing Jianzhu College, Chongqing 400074, ChinaSouthwest Technology and Engineering Research Institute, Chongqing 400039, ChinaSouthwest Technology and Engineering Research Institute, Chongqing 400039, ChinaSouthwest Technology and Engineering Research Institute, Chongqing 400039, ChinaSouthwest Technology and Engineering Research Institute, Chongqing 400039, ChinaSouthwest Technology and Engineering Research Institute, Chongqing 400039, ChinaSouthwest Technology and Engineering Research Institute, Chongqing 400039, ChinaIn 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.https://www.mdpi.com/2073-4352/15/2/160first principlesPb(Zr<sub>x</sub>Ti<sub>1−x</sub>)O<sub>3</sub>cubic and tetragonal phasesmechanical properties |
| spellingShingle | Xudong Ran Shaolan Zhou Shaowen Zhou Wei Lei Lin Xiang Yang Wu Bingfei Hu Jianquan Tao Qiang Chen First-Principles Study of Mechanical Properties of Pb(Zr<sub>x</sub>Ti<sub>1−x</sub>)O<sub>3</sub> in the Cubic and Tetragonal Phase Crystals first principles Pb(Zr<sub>x</sub>Ti<sub>1−x</sub>)O<sub>3</sub> cubic and tetragonal phases mechanical properties |
| title | First-Principles Study of Mechanical Properties of Pb(Zr<sub>x</sub>Ti<sub>1−x</sub>)O<sub>3</sub> in the Cubic and Tetragonal Phase |
| title_full | First-Principles Study of Mechanical Properties of Pb(Zr<sub>x</sub>Ti<sub>1−x</sub>)O<sub>3</sub> in the Cubic and Tetragonal Phase |
| title_fullStr | First-Principles Study of Mechanical Properties of Pb(Zr<sub>x</sub>Ti<sub>1−x</sub>)O<sub>3</sub> in the Cubic and Tetragonal Phase |
| title_full_unstemmed | First-Principles Study of Mechanical Properties of Pb(Zr<sub>x</sub>Ti<sub>1−x</sub>)O<sub>3</sub> in the Cubic and Tetragonal Phase |
| title_short | First-Principles Study of Mechanical Properties of Pb(Zr<sub>x</sub>Ti<sub>1−x</sub>)O<sub>3</sub> in the Cubic and Tetragonal Phase |
| title_sort | first principles study of mechanical properties of pb zr sub x sub ti sub 1 x sub o sub 3 sub in the cubic and tetragonal phase |
| topic | first principles Pb(Zr<sub>x</sub>Ti<sub>1−x</sub>)O<sub>3</sub> cubic and tetragonal phases mechanical properties |
| url | https://www.mdpi.com/2073-4352/15/2/160 |
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