سهم اتم‌های Sr و Hf در پاسخ پیزوالکتریک 3SrHfO چهارکنجی

افشاری, مجید; شاهمیرزایی, حسین

doi:10.22055/jrmbs.2019.14831

سهم اتم‌های Sr و Hf در پاسخ پیزوالکتریک 3SrHfO چهارکنجی

نوع مقاله : مقاله پژوهشی کامل

نویسندگان

¹ گروه علوم پایه، دانشگاه فرهنگیان، تهران، ایران

² دانشگاه صنعتی مالک اشتر، شیراز، ایران

10.22055/jrmbs.2019.14831

چکیده

در این مقاله با استفاده از محاسبات اصول اولیه، مبتنی بر نظریه‌ی اختلالی تابعی چگالی، سهم هر یک از اتم‌های Sr و Hf در خواص پیزوالکتریکی 3SrHfO در ساختار چهارکنجی با گروه فضایی mm4P و در حالت پایه مورد بررسی قرار گرفت. ثابت‌های شبکه، بارهای مؤثر بورن، ثابت پیزوالکتریک و سهم اتم‌های Sr و Hf در مقدار قطبش و ثابت پیزوالکتریک کل محاسبه شدند. نتایج نشان می‌دهد که این ترکیب در ساختار مورد نظر خاصیت پیزوالکتریسیته دارد و قطبش و پیزوالکتریسیته این ترکیب عمدتاً از اتم Hf ناشی می‌شود. اثر تغییر ثابت شبکه c بر قطبش و ثابت پیزوالکتریک نیز بررسی شد. مشخص شد که با افزایش پارامتر شبکه c، قطبش و ثابت پیزوالکتریک افزایش می‌یابد و سهم ناشی از اتم Sr در ثایت پیزوالکتریک به ازای Å 5/4c= به 50 درصد مقدار کل می‌رسد. این تغییرات به پیوند کووالانسی قابل ملاحظه میان اتم‌های Sr و O نسبت داده می-شود.

کلیدواژه‌ها

عنوان مقاله [English]

Sr and Hf contributions to piezoelectric response of tetragonal SrHfO3

نویسندگان [English]

Majid Afshari ¹
Hossein Shahmirzaee ²

¹ Department of Basic Science, Farhangian University, Tehran, Iran

² Malek Ashtar university, Shiraz, Iran

چکیده [English]

In this paper, the contribution of Sr and Hf atoms in piezoelectric properties of tetragonal SrHfO3 with P4mm space group, were investigated by using first principle calculations based on density functional perturbation theory. Lattice constants, Born effective charges, piezoelectric constant and Sr and Hf contributions in total polarization and piezoelectric coefficient were calculated. Our results show that tetragonal SrHfO3 has piezoelectric property and its polarization and piezoelectricity mainly come from Hf atoms. The effect of lattice constant changes on polarization and piezoelectric constant were also studied. It was found that polarization and piezoelectric constant enhance by increasing lattice parameter and at c=4.5 Å, Sr atom contributes 50% of the total piezoelectric constant. This behavior assigns to significant covalent bonding between Sr and surrounding O atoms.

کلیدواژه‌ها [English]

piezoelectricity
Born effective charge
density functional perturbation theory
piezoelectric constant
lead free piezoelectric

مراجع

[1] H. Li, Z.D. Deng, T.J. Carlson, Piezoelectric materials used in underwater acoustic transducers, Sensor Letters 10 (2012) 679-697.

[2] B. Jaffe, R. Roth, S. Marzullo, Piezoelectric properties of lead zirconate‐lead titanate solid‐solution ceramics, Journal of Applied Physics 25 (1954) 809-810.

[3] P. Panda, B. Sahoo, PZT to lead free piezo ceramics: a review, Ferroelectrics 474 (2015) 128-143.

[4] D. Fu, M. Itoh, S.-y. Koshihara, Crystal growth and piezoelectricity of BaTiO₃–CaTiO₃ solid solution, Applied Physics Letters 93 (2008) 012904.

[5] W. Liu, X. Ren, Large piezoelectric effect in Pb-free ceramics, Physical Review Letters 103 (2009) 257602.

[6] Y. Guo, K.-i. Kakimoto, H. Ohsato, Phase transitional behavior and piezoelectric properties of (Na_0.5K_0.5)NbO₃–LiNb₃ ceramics, Applied physics letters 85 (2004) 4121-4123.

[7] J. Shi, I. Grinberg, X. Wang, A.M. Rappe, Atomic sublattice decomposition of piezoelectric response in tetragonal PbTiO₃, BaTiO₃, and KNbO₃, PhysicalReview B 89 (2014) 094105.

[8] M. De Jong, W. Chen, H. Geerlings, M. Asta, K.A. Persson, A database to enable discovery and design of piezoelectric materials, Scientific data 2 (2015) 150053.

[9] R. Nunes, X. Gonze, Berry-phase treatment of the homogeneous electric field perturbation in insulators, Physical Review B 63 (2001) 155107.

[10] K.M. Rabe, P. Ghosez, First-principles studies of ferroelectric oxides, Physics of Ferroelectrics 105 (2007) 117-174.

[11] X. Wu, D. Vanderbilt, D. Hamann, Systematic treatment of displacements, strains, and electric fields in density-functional perturbation theory, Physical Review B 72 (2005) 035105.

[12] M. Born, K. Huang, Dynamical theory of crystal lattices, Clarendon press, (1954).

[13] P. Ghosez, J.-P. Michenaud, X. Gonze, Dynamical atomic charges: The case of ABO₃ compounds, Physical Review B 58 (1998) 6224.

[14] R. King-Smith, D. Vanderbilt, Theory of polarization of crystalline solids, Physical Review B 47 (1993) 1651.

[15] R. Resta, Macroscopic polarization in crystalline dielectrics: the geometric phase approach, Reviews of Modern Physics 66 (1994) 899.

[16] R. Resta, M. Posternak, A. Baldereschi, Towards a quantum theory of polarization in ferroelectrics: The case of KNbO₃, Physical Review Letters 70 (1993) 1010.

[17] D. Vanderbilt, R. King-Smith, Electric polarization as a bulk quantity and its relation to surface charge, Physical Review B 48 (1993) 4442.

[18] J. Zak, Berry’s phase for energy bands in solids, Physical Review Letters 62 (1989) 2747.

[19] X. Gonze, B. Amadon, P.-M. Anglade, J.-M. Beuken, F. Bottin, P. Boulanger, F. Bruneval, D. Caliste, R. Caracas, M. Côté, ABINIT: First-principles approach to material and nanosystem properties, Computer Physics Communications 180 (2009) 2582-2615.

[20] W. Zhong, R. King-Smith, D. Vanderbilt, Giant LO-TO splittings in perovskite ferroelectrics, Physical Review Letters 72 (1994) 3618.

[21] P. Hohenberg, W. Kohn, Inhomogeneous electron gas, Physical Review 136 (1964) B864.

[22] W. Kohn, L.J. Sham, Self-consistent equations including exchange and correlation effects, Physical Review 140 (1965) A1133.

[23] S. Baroni, S. De Gironcoli, A. Dal Corso, P. Giannozzi, Phonons and related crystal properties from density-functional perturbation theory, Reviews of Modern Physics 73 (2001) 515.

[24] X. Gonze, Perturbation expansion of variational principles at arbitrary order, Physical Review A 52 (1995) 1086.

[25] D. Hamann, M. Schlüter, C. Chiang, Norm-conserving pseudopotentials, Physical Review Letters 43 (1979) 1494.

[26] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Physical Review Letters 77 (1996) 3865.

[27] Y. Duan, H. Shi, L. Qin, Studies of tetragonal PbTiO3 subjected to uniaxial stress along the c-axis, Journal of Physics: Condensed Matter 20 (2008) 175210.

[28] D. Cherrad, D. Maouche, Structural, electronic and optical properties of SrHfO 3 (I4/mcm, Imma, Cmcm, P4/mbm and P4mm) phases, Physica B: Condensed Matter 405 (2010) 3862-3868.

[29] R. Vali, Structural phases of SrHfO₃, Solid state communications 148 (2008) 29-31.

[30] M. Posternak, R. Resta, A. Baldereschi, Role of covalent bonding in the polarization of perovskite oxides: the case of KNbO₃, Physical Review B 50 (1994) 8911.