Influence of Uniaxial Tensile Stress on the Mechanical and Piezoelectric Properties of Short-period Ferroelectric Superlattice
© The Author(s) 2009
Received: 23 September 2009
Accepted: 16 November 2009
Published: 28 November 2009
Tetragonal ferroelectric/ferroelectric superlattice under uniaxial tensile stress along the c axis is investigated from first principles. We show that the calculated ideal tensile strength is 6.85 GPa and that the superlattice under the loading of uniaxial tensile stress becomes soft along the nonpolar axes. We also find that the appropriately applied uniaxial tensile stress can significantly enhance the piezoelectricity for the superlattice, with piezoelectric coefficient d33 increasing from the ground state value by a factor of about 8, reaching 678.42 pC/N. The underlying mechanism for the enhancement of piezoelectricity is discussed.
Ferroelectrics, which can convert mechanical to electrical energy (and vice versa) have wide applications in medical imaging, telecommunication and ultrasonic devices, the physical properties of which are sensitive to external conditions, such as strain, film thickness, temperature, electric and magnetic fields [1–3]. BaTiO3 (BTO) and PbTiO3 (PTO), as prototype ferroelectric materials and simple systems, have been intensively studied [4, 5]. It is known that the ferroelectricity arises from the competition of short-range repulsions which favor the paraelectric cubic phase and Coulomb forces, which favor the ferroelectric phase [6, 7]. As the pressure increases, the short-range repulsions increase faster than the Coulomb forces, leading to the reduced ferroelectricity. Accompanied with the suppression of ferroelectricity, the piezoelectricity decreases and even disappears. However, recent studies have shown that the noncollinear polarization rotation, occurring at phase transition pressure, can result in the giant piezoelectric response [8, 9]. In contrast to previous theoretical studies of the effects of epitaxial strain on the spontaneous polarization of ferroelectric thin films, we have systematically studied the influence of uniaxial and in-plane epitaxial strains on the mechanical and piezoelectric properties of perovskite ferroelectrics [10–15]. So far, there has been no previous work on the effect of uniaxial tensile strains on the mechanical and piezoelectric properties of short-period BTO/PTO superlattices.
Ferroelectric superlattices composed of alternating epitaxial oxides ultrathin layers are currently under intensive study due to their excellent ferroelectric and piezoelectric properties . Ferroelectricity can be induced in superlattice in spite of the paraelectric nature of and . This is because the coincidence of the positive and negative charge centers is destroyed in the superlattice and electric dipoles are induced. Moreover, ferroelectricity can be enhanced in ferroelectric superlattices in certain stacking sequences . The overall polarization of three-component SrTiO3(STO)/BTO/PTO ferroelectric superlattices can also be improved by increasing the number of BTO and PTO layers . Thanks to the periodic nature, it is possible to study the effect of uniaxial or biaxial strains on the properties of ferroelectric superlattices from first principles.
In this work, we perform total energy as well as linear response calculations to study the effect of uniaxial tensile stress along the c axis on the mechanical and piezoelectric properties of short-period BTO/PTO superlattice. We show the mechanical properties by calculating the ideal tensile strength, elastic constants and valence charge density at different strains. We also show the influence of uniaxial stress on the piezoelectricity. To reveal the underlying mechanisms, we study the effects of uniaxial tensile stress on the atomic displacements and Born effective charges, respectively.
Our calculations are performed within the local density approximation (LDA) to the density functional theory (DFT) as implemented in the plane-wave pseudopotential ABINIT package . To ensure good numerical convergence, the plane-wave energy cutoff is set to be 80 Ry, and the Brillouin zone integration is performed with 6 × 6 × 6 k-meshpoints. The norm-conserving pseudopotentials generated by the OPIUM program are tested against the all-electron full-potential linearized augmented plane-wave method [20, 21]. The orbitals of Ba 5s25p66s2, Pb 5d106s26p2, Ti 3s23p63d24s2 and O 2s22p4 are explicitly included as valence electrons. The dynamical matrices and Born effective charges are computed by the linear response theory of strain type perturbations, which has been proved to be highly reliable for ground state properties [22–24]. The polarization is calculated by the Berry-phase approach . The LDA is used instead of the generalized gradient approximation (GGA) because the GGA is found to overestimate both the equilibrium volume and strain for the perovskite structures . The piezoelectric strain coefficients , where e is the piezoelectric stress tensor and the elastic compliance tensor s is the reciprocal of the elastic stiffness tensor c (Roman indexes from 1 to 3, and Greek ones from 1 to 6).
To calculate the uniaxial tensile stress σ33, we apply a small strain increment η3 along the c axis and then conduct structural optimization for the lattice vectors perpendicular to the c axis, and all the internal atomic positions until the two components of stress tensor (i.e., σ11 and σ22) are smaller than 0.05 GPa. The strain is then increased step by step. Since , the elastic constants satisfy η3/η1≈ − (c11 + c12)/c13 under the loading of uniaxial tensile strain applied along the c axis, where the strains η i are calculated by η1 = η2 = (a − a0)/a0 and η3 = (c − c0)/c0, with and being the lattice constants of the unstrained superlattice structure. We have examined the accuracy of our calculations by studying the influence of different strains on the properties of BTO and PTO, respectively [12–15].
Results and Discussion
In summary, we have studied the influence of uniaxial tensile stress applied along the c axis on the mechanical and piezoelectric properties of short-period BTO/PTO superlattice using first-principles methods. We show that the calculated ideal tensile strength is 6.850 GPa and that the superlattice under the loading of uniaxial tensile stress becomes soft along the nonpolar axes. We also find that the appropriately applied uniaxial tensile stress can significantly enhance the piezoelectricity for the superlattice. Our calculated results reveal that it is the drastic increase in atomic displacements along the c axis that leads to the increase in polarization and that the enhancement of piezoelectricity is attributed to the change in the magnitude of polarization with the stress. Our work suggests a way of enhancing the piezoelectric properties of the superlattices, which would be helpful to enhance the performance of the piezoelectric devices.
The work is supported by the National Natural Science Foundation of China under Grant Nos. 10425210, 10832002 and 10674177, the National Basic Research Program of China (Grant No. 2006CB601202), and the Foundation of China University of Mining and Technology.
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
- Lines ME, Glass AM: Principles and Applications of Ferroelectrics and Telated Materials. Clarendon, Oxford; 1979.Google Scholar
- Uchino K: Piezoelectric Actuators and Ultrasonic Motors. Kluwer, Boston; 1996.View ArticleGoogle Scholar
- Zhu Z, Zhang H, Tan M, Zhang X, Han J: J. Phys. D: Appl. Phys.. 2009, 41: 215408. Bibcode number [2008JPhD...41u5408Z] Bibcode number [2008JPhD...41u5408Z] 10.1088/0022-3727/41/21/215408View ArticleGoogle Scholar
- Zhong W, Vanderbilt D, Rabe KM: Phys. Rev. B. 1995, 52: 6301. COI number [1:CAS:528:DyaK2MXotVSls7o%3D]; Bibcode number [1995PhRvB..52.6301Z] 10.1103/PhysRevB.52.6301View ArticleGoogle Scholar
- Salehi H, Shahtahmasebi N, Hosseini SM: Eur. Phys. J. B. 2003, 32: 177. COI number [1:CAS:528:DC%2BD3sXjs1ygtbY%3D]; Bibcode number [2003EPJB...32..177S] 10.1140/epjb/e2003-00086-6View ArticleGoogle Scholar
- Samara GA, Sakudo T, Yoshimitsu K: Phys. Rev. Lett.. 1975, 35: 1767. COI number [1:CAS:528:DyaE28XmvVSkuw%3D%3D]; Bibcode number [1975PhRvL..35.1767S] 10.1103/PhysRevLett.35.1767View ArticleGoogle Scholar
- Cohen RE: Nature. 1992, 358: 136. COI number [1:CAS:528:DyaK38Xlt1amtL4%3D]; Bibcode number [1992Natur.358..136C] 10.1038/358136a0View ArticleGoogle Scholar
- Fu H, Cohen RE: Nature. 2000, 403: 281. COI number [1:CAS:528:DC%2BD3cXns1CisA%3D%3D]; Bibcode number [2000Natur.403..281F] 10.1038/35002022View ArticleGoogle Scholar
- Wu Z, Cohen RE: Phys. Rev. Lett.. 2005, 95: 037601. Bibcode number [2005PhRvL..95c7601W] Bibcode number [2005PhRvL..95c7601W] 10.1103/PhysRevLett.95.037601View ArticleGoogle Scholar
- Sang Y, Liu B, Fang D: Chin. Phys. Lett.. 2008, 25: 1113. COI number [1:CAS:528:DC%2BD1cXksFSgs7o%3D]; Bibcode number [2008ChPhL..25.1113S] 10.1088/0256-307X/25/3/083View ArticleGoogle Scholar
- Ederer C, Spaldin NA: Phys. Rev. Lett.. 2005, 95: 257601. Bibcode number [2005PhRvL..95y7601E] Bibcode number [2005PhRvL..95y7601E] 10.1103/PhysRevLett.95.257601View ArticleGoogle Scholar
- Duan Y, Li J, Li S-S, Xia J-B, Chen C: J. Appl. Phys.. 2008, 103: 083713. Bibcode number [2008JAP...103h3713D] Bibcode number [2008JAP...103h3713D] 10.1063/1.2912721View ArticleGoogle Scholar
- Wang C, Duan Y, Chen C: Chin. Phys. Lett.. 2009, 26: 017203. Bibcode number [2009ChPhL..26a7203W] Bibcode number [2009ChPhL..26a7203W] 10.1088/0256-307X/26/1/017203View ArticleGoogle Scholar
- Duan Y, Shi H, Qin L: J. Phys.: Condens. Matter. 2008, 20: 175210. Bibcode number [2008JPCM...20q5210D] Bibcode number [2008JPCM...20q5210D] 10.1088/0953-8984/20/17/175210Google Scholar
- Duan Y, Qin L, Tang G, Chen C: J. Appl. Phys.. 2009, 105: 033706. Bibcode number [2009JAP...105c3706D] Bibcode number [2009JAP...105c3706D] 10.1063/1.3077231View ArticleGoogle Scholar
- Li Z, Lu T, Cao W: J. Appl. Phys.. 2008, 104: 126106. Bibcode number [2008JAP...104l6106L] Bibcode number [2008JAP...104l6106L] 10.1063/1.3053148View ArticleGoogle Scholar
- Neaton B, Rabe KM: Appl. Phys. Lett. 2003, 82: 1586. COI number [1:CAS:528:DC%2BD3sXhvV2ltrc%3D]; Bibcode number [2003ApPhL..82.1586N] 10.1063/1.1559651View ArticleGoogle Scholar
- Shah SH, Bristowe PD, Kolpak AM, Rappe AM: J. Mater. Sci.. 2008, 43: 3750. COI number [1:CAS:528:DC%2BD1cXlslajsLs%3D]; Bibcode number [2008JMatS..43.3750S] 10.1007/s10853-007-2212-7View ArticleGoogle Scholar
- Gonze X, Beuken J-M, Caracas R, Detraux F, Fuchs M, Rignanese G-M, Sindic L, Verstraete M, Zerah G, Jollet F, Torrent M, Roy A, Mikami M, Ghosez Ph, Raty J-Y, Allan DC: Comput. Mater. Sci.. 2002, 25: 478. 10.1016/S0927-0256(02)00325-7View ArticleGoogle Scholar
- Rappe AM, Rabe KM, Kaxiras E, Joannopoulos JD: Phys. Rev. B. 1990, 41: 1227. Bibcode number [1990PhRvB..41.1227R] Bibcode number [1990PhRvB..41.1227R] 10.1103/PhysRevB.41.1227View ArticleGoogle Scholar
- Singh DJ: Planewaves, Pseudopotential, and the LAPW Method. Kluwer, Boston, MA; 1994.View ArticleGoogle Scholar
- Gonze X, Lee C: Phys. Rev. B. 1997, 55: 10355. COI number [1:CAS:528:DyaK2sXivFOlsbs%3D]; Bibcode number [1997PhRvB..5510355G] 10.1103/PhysRevB.55.10355View ArticleGoogle Scholar
- Baroni S, de Gironcoli S, Dal Corso A, Giannozzi P: Rev. Mod. Phys.. 2001, 73: 515. COI number [1:CAS:528:DC%2BD3MXlvFKrtLc%3D]; Bibcode number [2001RvMP...73..515B] 10.1103/RevModPhys.73.515View ArticleGoogle Scholar
- Hamann DR, Wu X, Rabe KM, Vanderbilt D: Phys. Rev. B. 2005, 71: 035117. Bibcode number [2005PhRvB..71c5117H] Bibcode number [2005PhRvB..71c5117H] 10.1103/PhysRevB.71.035117View ArticleGoogle Scholar
- King-Smith RD, Vanderbilt D: Phys. Rev. B. 1993, 47: 1651. COI number [1:CAS:528:DyaK3sXlvFeiu7o%3D]; Bibcode number [1993PhRvB..47.1651K] 10.1103/PhysRevB.47.1651View ArticleGoogle Scholar
- Wu Z, Cohen RE, Singh DJ: Phys. Rev. B. 2004, 70: 104112. Bibcode number [2004PhRvB..70j4112W] Bibcode number [2004PhRvB..70j4112W] 10.1103/PhysRevB.70.104112View ArticleGoogle Scholar
- Alahmed Z, Fu H: Phys. Rev. B. 2008, 77: 045213. Bibcode number [2008PhRvB..77d5213A] Bibcode number [2008PhRvB..77d5213A] 10.1103/PhysRevB.77.045213View ArticleGoogle Scholar
- Cooper VR, Rabe KM: Phys. Rev. B. 2009, 79: 180101. Bibcode number [2009PhRvB..79r0101C] Bibcode number [2009PhRvB..79r0101C] 10.1103/PhysRevB.79.180101View ArticleGoogle Scholar