عنوان مقاله [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.
 H. Li, Z.D. Deng, T.J. Carlson, Piezoelectric materials used in underwater acoustic transducers, Sensor Letters 10 (2012) 679-697.
 B. Jaffe, R. Roth, S. Marzullo, Piezoelectric properties of lead zirconate‐lead titanate solid‐solution ceramics, Journal of Applied Physics 25 (1954) 809-810.
 P. Panda, B. Sahoo, PZT to lead free piezo ceramics: a review, Ferroelectrics 474 (2015) 128-143.
 D. Fu, M. Itoh, S.-y. Koshihara, Crystal growth and piezoelectricity of BaTiO3–CaTiO3 solid solution, Applied Physics Letters 93 (2008) 012904.
 W. Liu, X. Ren, Large piezoelectric effect in Pb-free ceramics, Physical Review Letters 103 (2009) 257602.
 Y. Guo, K.-i. Kakimoto, H. Ohsato, Phase transitional behavior and piezoelectric properties of (Na0.5K0.5)NbO3–LiNb3 ceramics, Applied physics letters 85 (2004) 4121-4123.
 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.
 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.
 R. Nunes, X. Gonze, Berry-phase treatment of the homogeneous electric field perturbation in insulators, Physical Review B 63 (2001) 155107.
 K.M. Rabe, P. Ghosez, First-principles studies of ferroelectric oxides, Physics of Ferroelectrics 105 (2007) 117-174.
 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.
 M. Born, K. Huang, Dynamical theory of crystal lattices, Clarendon press, (1954).
 P. Ghosez, J.-P. Michenaud, X. Gonze, Dynamical atomic charges: The case of ABO3 compounds, Physical Review B 58 (1998) 6224.
 R. King-Smith, D. Vanderbilt, Theory of polarization of crystalline solids, Physical Review B 47 (1993) 1651.
 R. Resta, Macroscopic polarization in crystalline dielectrics: the geometric phase approach, Reviews of Modern Physics 66 (1994) 899.
 R. Resta, M. Posternak, A. Baldereschi, Towards a quantum theory of polarization in ferroelectrics: The case of KNbO3, Physical Review Letters 70 (1993) 1010.
 D. Vanderbilt, R. King-Smith, Electric polarization as a bulk quantity and its relation to surface charge, Physical Review B 48 (1993) 4442.
 J. Zak, Berry’s phase for energy bands in solids, Physical Review Letters 62 (1989) 2747.
 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.
 W. Zhong, R. King-Smith, D. Vanderbilt, Giant LO-TO splittings in perovskite ferroelectrics, Physical Review Letters 72 (1994) 3618.
 P. Hohenberg, W. Kohn, Inhomogeneous electron gas, Physical Review 136 (1964) B864.
 W. Kohn, L.J. Sham, Self-consistent equations including exchange and correlation effects, Physical Review 140 (1965) A1133.
 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.
 X. Gonze, Perturbation expansion of variational principles at arbitrary order, Physical Review A 52 (1995) 1086.
 D. Hamann, M. Schlüter, C. Chiang, Norm-conserving pseudopotentials, Physical Review Letters 43 (1979) 1494.
 J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Physical Review Letters 77 (1996) 3865.
 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.
 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.
 R. Vali, Structural phases of SrHfO3, Solid state communications 148 (2008) 29-31.
 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.