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采用基于密度泛函理论的第一性原理超原胞方法和虚晶近似方法, 在局域密度近似和广义梯度近似下系统研究了三方相和四方相 PbZr0.5Ti0.5O3的能量稳定性、原子结构以及电子结构. 计算结果表明三方相的能量比四方相低, 说明三方相结构更加稳定, 并且发现利用广义梯度近似计算的结构参数与实验值符合得更好. 电子结构表明, 两种相的Ti/Zr的3d电子和O的2p电子间存在明显的轨道杂化, 并且Ti-O之间的作用比Zr-O作用更强；Pb的6s和5d电子与O的2s和2p电子也分别存在轨道杂化. 而三方相中Pb的5d电子与O的2s电子杂化比四方相更强, 进一步说明三方相比四方相结构更加稳定.The energetic stability, the structural and the electronic properties of rhombohedral and tetragonal PbZr0.5Ti0.5O3 are systematically investigated by the first-principles plane-wave pseudopotential and the virtual crystal approximation (VCA) based on the density functional theory, within the frameworks of local density approximation (LDA) and generalized gradient approximation (GGA). Our calculation results show that the total energy of the rhombohedral phase is lower than that of the tetragonal phase, which suggests that the rhombohedral structure is more energetically stable than the tetragonal one. Furthermore, the structural parameters calculated in the GGA are well consistent with experimental values. From the analysis of electronic structure, we can find the strong hybridization between Ti/Zr d and O 2p both in two phases. Furthermore the hybridization between Ti-O is stronger than that between Zr-O; there also exists the hybridization between Pb s, d and O 2s, 2p. Moreover, the hybridization between Pb 5d and O 2s in the rhombohedral phase is stronger than that in the tetragonal phase, which indicates that the rhombohedral phase is more stable than the tetragonal phase.
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Keywords:
- PZT /
- rhombohedral phase /
- tetragonal phase /
- density functional theory
[1] Scott J F 1998 Ferroelectrics Review 1 1
[2] Uchino K 1996 Piezoelectric Actuators and Ultrasonic Motors (Kluwer Academic Publishers, Boston)
[3] Cohen R E 1992 Nature (London) 358 136
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[14] Lin H B, Cao M S, Yuan J,Wang D W, Zhao Q L,Wang F C 2008 Chin. Phys. B 17 4323
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[16] Segall M D, Lindan P L D, Probert M J, Pickard C J, Hasnip P J, Clark S J, Payne M C 2002 J. Phys. Condens. Matter 14 2717
[17] Milman V, Winkler B, White J A, Pickard C J, Payne M C, Akhmatskaya E V, Nobes R H 2000 Int. J. Quantum. Chem. 77 895
[18] Ceperley D M, Alder B J 1980 Phys. Rev. Lett. 45 566
[19] Perdew J P, Zunger A 1981 Phys. Rev. B 23 5048
[20] Perdew J P, Wang Y 1986 Phys. Rev. B 33 8800
[21] Vanderbilt D 1990 Phys. Rev. B 41 7892
[22] Nordheim L 1931 Ann. Phys. 9 607
[23] Jirak Z, Kala T 1988 Ferroelectrics 82 79
[24] Frantti J, Lappalainen J, Eriksson S, Lantto V, Nishio S, Kakihana M, Ivanov S, Rundlöf H 2000 Jpn. J. Appl. Phys. I 39 5697
[25] Yoshihiro K, Shinobu A, Akikatsu S, Jimpei H, Eiji N, Masaki T, Makoto S 2001 Phys. Rev. Lett. 87 217061
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[1] Scott J F 1998 Ferroelectrics Review 1 1
[2] Uchino K 1996 Piezoelectric Actuators and Ultrasonic Motors (Kluwer Academic Publishers, Boston)
[3] Cohen R E 1992 Nature (London) 358 136
[4] Al-Zein A, Fraysse G, Rouquete J, Papet P, Haines J, Hehlen B, Levelut C, Aquilanti G, Joly Y 2010 Phys. Rev. B 81 174110
[5] Yokota H, Zhang N, Taylor A E, Thomas P A, Glazer A M 2009 Phys. Rev. B 80 104109
[6] Schierholz R, Fuess H 2008 Phys. Rev. B 78 024118
[7] Jaffe B, Cook W R, Jaffe H 1971 Piezoelectric Ceramics (Acadermic Press London)
[8] Zhang D Q, Liu H T, Cao M S 2006 Journal of Functional Material 37 1213(in Chinese) [张德庆, 刘海涛, 曹茂盛 2006 功能材料 37 1213]
[9] Wang D W, Jin H B, Yuan J,Wen B L, Zhao Q L, Zhang D Q, Cao M S 2010 Chin. Phys. Lett. 27 047701
[10] Wang D W, Zhang D Q, Yuan J, Zhao Q L, Liu H M, Wang Z Y, Cao M S 2009 Chin. Phys. B 18 2596
[11] Zhang D Q, Wang D W, Yuan J, Zhao Q L, Wang Z Y, Cao M S 2008 Chin. Phys. Lett. 25 4410
[12] Duan Z X, Yuan J, Zhao Q L, Liu H M, Lin H B, Zhang W T, Cao M S 2008 Chin. Phys. Lett. 25 1472
[13] Liu H M, Zhao Q L, Cao M S, Yuan J, Duan Z X, Qiu C J 2008 Chin. Phys. Lett. 25 4128
[14] Lin H B, Cao M S, Yuan J,Wang D W, Zhao Q L,Wang F C 2008 Chin. Phys. B 17 4323
[15] Meng X J, Cheng J G, Li B, Tang J, Ye H J, Guo S L, Zhu J H 2000 Acta Phys. Sin. 49 811(in Chinese) [孟祥建, 程建功, 李标, 唐军, 叶红娟, 郭少令, 褚君浩 2000 49 811]
[16] Segall M D, Lindan P L D, Probert M J, Pickard C J, Hasnip P J, Clark S J, Payne M C 2002 J. Phys. Condens. Matter 14 2717
[17] Milman V, Winkler B, White J A, Pickard C J, Payne M C, Akhmatskaya E V, Nobes R H 2000 Int. J. Quantum. Chem. 77 895
[18] Ceperley D M, Alder B J 1980 Phys. Rev. Lett. 45 566
[19] Perdew J P, Zunger A 1981 Phys. Rev. B 23 5048
[20] Perdew J P, Wang Y 1986 Phys. Rev. B 33 8800
[21] Vanderbilt D 1990 Phys. Rev. B 41 7892
[22] Nordheim L 1931 Ann. Phys. 9 607
[23] Jirak Z, Kala T 1988 Ferroelectrics 82 79
[24] Frantti J, Lappalainen J, Eriksson S, Lantto V, Nishio S, Kakihana M, Ivanov S, Rundlöf H 2000 Jpn. J. Appl. Phys. I 39 5697
[25] Yoshihiro K, Shinobu A, Akikatsu S, Jimpei H, Eiji N, Masaki T, Makoto S 2001 Phys. Rev. Lett. 87 217061
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