Flexoelectricity in Bulk and Nanoscale Polar and Non-Polar Dielectrics

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Abstract:

Piezoelectricity (PE) is defined as the polarization under homogeneous application of stress on polar/non-centrosymmetry/no-inversion symmetry dielectrics, whereas it has been commonly accepted that flexoelectricity (FLX) is the induced polarization due to strain gradient in any polar/nonpolar dielectrics, the latter effect is universal and can be generated in any materials under inhomogeneous stress. Flexoelectricity is inversely proportional to the size of materials and devices which further suggests that giant FLX effects may develop in nanoscale materials. Flexoelectricity represents the polarization due to strain gradient and have significant effects on the functional properties of nanoscale materials, epitaxial thin films, one-dimensional structure with various shape and size, liquid crystals, polymers, nanobio-hybrid materials, etc. Till late sixties, very few works on flexoelectricity have been reported due to very weak magnitude compared to piezoelectricity. Advancement in nanoscale materials and device fabrication process and highly sophisticated electronics with detection of data with high signal to noise ratio lead the scientists/researchers to get several orders of higher flexoelectric coefficients compared to the proposed theoretical limits. Recently, giant FLX have been observed in nanoscale materials and their magnitudes are six to seven orders larger than the theoretical limits. In this review article, we describe the basic mechanism of flexoelectricity, brief history of discovery, theoretical modeling, experimental procedures, and results reported by several authors for bulk and nanoscale ferroelectric and dielectric materials.

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Solid State Phenomena (Volume 232)

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213-233

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June 2015

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[1] S. Xu, Y. Qin, C. Xu, Y. Wei, R. Yang, Z. L. Wang, Self-powered nanowire devices, Nat. Nanotech. 5 (2010) 366-373.

DOI: 10.1038/nnano.2010.46

Google Scholar

[2] T. D. Nguyen, J. M. Nagarah, Y. Qi, S. S. Nonnenmann , A. V. Morozov , S. Li , C. B. Arnold, M. C. McAlpine, Wafer-Scale Nanopatterning and Translation into High-Performance Piezoelectric Nanowires, Nano Lett. 10 (2010) 4595–4599.

DOI: 10.1021/nl102619c

Google Scholar

[3] Y. Qi, N. T. Jafferis, K. Lyons Jr., C. M. Lee, H. Ahmad, M. C. McAlpine, Piezoelectric Ribbons Printed onto Rubber for Flexible Energy Conversion, Nano Lett. 10 (2010) 524.

DOI: 10.1021/nl903377u

Google Scholar

[4] S. M. Kogan, Piezoelectric effect during inhomogeneous deformation and acoustic scattering of carriers in crystals, Sov. Phys. Solid State 5(10) (1964) 2069–70; see also E.V. Bursian and O. L. Zaikovskii, Sov. Phys. Solid State 10 (1968) 1121.

Google Scholar

[5] J. F. Scott, Lattice perturbations in CaWO4 and CaMoO4, J. Chem. Phys. 48 (1968) 874.

Google Scholar

[6] V. L. Indenbom, E. B. Loginov, M. A. Osipov, Flexoelectric effect and crystal structure, Kristalografija 26 (1981) 1157-62.

Google Scholar

[7] M. Marvan, A. Havr´anek, Flexoelectric effect in elastomers, Progr. Colloid Polym. Sci. 78 (1988) 33–36.

Google Scholar

[8] A. K. Tagantsev, Pyroelectric, Piezoelectric, flexoelectric, and thermal polarization effects in ionic crystals, Sov. Phys. Usp. 30 (1987) 588–603.

DOI: 10.1070/pu1987v030n07abeh002926

Google Scholar

[9] R. Resta, Towards a bulk theory of flexoelectricity, Phys. Rev. Lett. 105 (2010) 127601-4.

Google Scholar

[10] A. K. Tagantsev, Piezoelectricity and flexoelectricity in crystalline dielectrics, Phys. Rev. B 34 (1986) 5883–5888.

DOI: 10.1103/physrevb.34.5883

Google Scholar

[11] P. Zubko, G. Catalan, A. Buckley, P. R. L. Welche, J. F. Scott, Strain-Gradient-Induced Polarization in SrTiO3 Single Crystals, Phys. Rev. Lett. 99 (2007) 167601-4.

DOI: 10.1103/physrevlett.100.199906

Google Scholar

[12] P. Zubko, G. Catalan, A. K. Tagantsev, Flexoelectric Effect in Solids, Annu. Rev. Mater. Res. 43 (2013) 387–421.

DOI: 10.1146/annurev-matsci-071312-121634

Google Scholar

[13] W. Ma, L. E. Cross, Observation of the flexoelectric effect in relaxor Pb ( Mg 1/3 Nb 2/3) O3 ceramics, Appl. Phys. Lett. 78 (2001) 2920–2921.

DOI: 10.1063/1.1356444

Google Scholar

[14] W. Ma, L. E. Cross, Strain-gradient-induced electric polarization in lead zirconate titanate ceramics, Appl. Phys. Lett. 82 (2003).

DOI: 10.1063/1.1570517

Google Scholar

[15] A. Biancoli, C. M. Fancher, J. L. Jones, D. Damjanovic, Breaking of macroscopic centric symmetry in paraelectric phases of ferroelectric materials and implications for flexoelectricity, Nat. Materials. 14 (2015) 224-229.

DOI: 10.1038/nmat4139

Google Scholar

[16] O. Aktas, M. A. Carpenter, E. K. H. Salje, Polar precursor ordering in BaTiO3 detected by resonant piezoelectric spectroscopy, Appl. Phys. Lett. 103 (2013) 142902-4.

DOI: 10.1063/1.4823576

Google Scholar

[17] A. N. Morozovska, E. A. Eliseev, S. V. Kalinin, L. Q. Chen, V. Gopalan, Surface polar states and pyroelectricity in ferroelastics induced by flexo-roto field, Appl. Phys. Lett. 100 (2012) 142902.

DOI: 10.1063/1.3701152

Google Scholar

[18] W. Kleemann, F. J. Schafer, M. D. Fontana, Crystal optical studies of spontaneous and precursor polarization in KNbO3, Phys. Rev. B 30 (1984) 1148-1154.

Google Scholar

[19] J. Narvaez, G. Catalan, Origin of the enhanced flexoelectricity of relaxor ferroelectrics Appl. Phys. Lett. 104 (2014) 162903.

DOI: 10.1063/1.4871686

Google Scholar

[20] R. Maranganti, P. Sharma, Atomistic determination of flexoelectric properties of crystalline dielectrics, Phys. Rev. B 80 (2009) 054109.

DOI: 10.1103/physrevb.80.054109

Google Scholar

[21] J. Hong, G. Catalan, J. F. Scott, E. Artacho, The flexoelectricity of barium and strontium titanates from first principles, J. Phys.: Condens. Matter 22 (2010) 112201.

DOI: 10.1088/0953-8984/22/11/112201

Google Scholar

[22] J. Hong, D. Vanderbilt, First-principles theory and calculation of flexoelectricity, Phys. Rev. B 88 (2013) 174107.

Google Scholar

[23] P. Hana, Study of Flexoelectric Phenomenon from Direct and from Inverse Flexoelectric Behavior of PMNT Ceramic, Ferroelectrics 351 (2007) 196–203.

DOI: 10.1080/00150190701354281

Google Scholar

[24] S. E. Park, T. R. Shrout, Ultrahigh strain and piezoelectric behavior in relaxor based ferroelectric single crystals, J. Appl. Phys. 82 (1997) 1804–1811.

DOI: 10.1063/1.365983

Google Scholar

[25] A. A. Bokov, Z. G. Ye, Recent progress in relaxor ferroelectrics with perovskite structure, J. Mater. Sci. 41 (2006) 31–52.

DOI: 10.1007/s10853-005-5915-7

Google Scholar

[26] M. Correa, A. Kumar, S. Priya, R. S. Katiyar, J. F. Scott, Phonon anomalies and phonon-spin coupling in oriented PbFe0. 5Nb0. 5O3 thin films, Physical Review B 83(1) (2011) 014302.

Google Scholar

[27] Y. Qi, J. Kim, T. D. Nguyen, B. Lisko, P. K. Purohit, M. C. McAlpine, Enhanced Piezoelectricity and Stretchability in Energy Harvesting Devices Fabricated from Buckled PZT Ribbon, Nano Lett. 11 (2011) 1331.

DOI: 10.1021/nl104412b

Google Scholar

[28] F. C. Frank, On the theory of liquid crystals, Discuss. Faraday Soc. 25(1) (1958) 19–28, doi: 10. 1039/DF9582500019.

Google Scholar

[29] R. B. Meyer, Piezoelectric effects in liquid crystals, Phys. Rev. Lett. 22(18) (1969) 918–921.

DOI: 10.1103/physrevlett.22.918

Google Scholar

[30] J. Prost, J. P. Marcerou, On the microscopic interpretation of flexoelectricity, J. Phys. France 38(3) (1977) 315–324.

DOI: 10.1051/jphys:01977003803031500

Google Scholar

[31] E. V. Bursian, O. I. Zaikovski, Changes in the curvature of a ferroelectric film due to polarization, Sov. Phys. -Solid State 10 (1968) 1121-1124.

Google Scholar

[32] Y. Luo, Y. Luo, X. Li, L. Chang, W. Gao, G. Yuan, J. Yin and Z. Liu, Upward ferroelectric self-poling in (001) oriented PbZr0. 2Ti0. 8O3 epitaxial films with compressive strain, AIP Adv. 3 (2013) 122101.

DOI: 10.1063/1.4840595

Google Scholar

[33] J. Fousek, L. E. Cross, D. B. Litvin, Possible piezoelectric composites based on the flexoelectric effects, Mater. Lett. 39 (1999) 287-291.

DOI: 10.1016/s0167-577x(99)00020-8

Google Scholar

[34] D. Lee, A. Yoon, S. Y. Jang, J. G. Yoon, J. S. Chung, M. Kim, J. F. Scott, T. W. Noh, Giant flexoelectric effect in ferroelectric epitaxial thin films, Phys. Rev. Lett. 107 (2011) 057602.

DOI: 10.1103/physrevlett.107.057602

Google Scholar

[35] D. Lee, TW. Noh, Giant flexoelectric effect through interfacial strain relaxation, Philos. Trans. R. Soc. Lond. Ser. A 370 (2012) 4944–57.

DOI: 10.1098/rsta.2012.0200

Google Scholar

[36] A. K. Tagantsev, A. S. Yurkov, Flexoelectric effect in finite samples, Appl. Phys. Lett. 112, (2012) 044103.

DOI: 10.1063/1.4745037

Google Scholar

[37] B. Jaffe, W. Cook, H. Jaffe, Piezoelectric Ceramics, Academic Press, New York, (1971).

Google Scholar

[38] R. Pelrine, R. Kornbluh, Q. Pei, J. Joseph, High-Speed Electrically Actuated Elastomers with Strain Greater Than 100%, Science 287 (2000) 836.

DOI: 10.1126/science.287.5454.836

Google Scholar

[39] J. Y. Fu, W Zhu, N. Li, L. E. Cross, Experimental studies of the converse flexoelectric effect induced by inhomogeneous electric field in a barium strontium titanate composition, J. Appl. Phys. 100(2) (2006) 024112.

DOI: 10.1063/1.2219990

Google Scholar

[40] K. B. Tolpygo, Long wavelength oscillations of diamond-type crystals including long range forces, Sov. Phys. Sol. State 4 (1963) 1297.

Google Scholar

[41] V. S. Mashkevich, Sov. Phys. JETP 9, (1959) 1237.

Google Scholar

[42] P. V. Yudin, A. K. Tagantsev, Fundamentals of flexoelectricity in solids, Nanotechnology 24 (2013) 43.

DOI: 10.1088/0957-4484/24/43/432001

Google Scholar

[43] J. Hong, D. Vanderbilt , First-principles theory of frozen-ion flexoelectricity, Phys. Rev. B 84 (2011) 180101.

DOI: 10.1103/physrevb.84.180101

Google Scholar

[44] G. Catalan, L. J. Sinnamon, J. M. Gregg, The effect of flexoelectricity on the dielectric properties of inhomogeneously strained ferroelectric thin films, J. Phys.: Condens. Matter 16 (2004) 2253–2264.

DOI: 10.1088/0953-8984/16/13/006

Google Scholar

[45] G. Catalan, B. Noheda, J. McAneney, L. J. Sinnamon, J. M. Gregg, Strain gradients in epitaxial ferroelectrics, Phys. Rev. B 72 (2005) 020102 R.

DOI: 10.1103/physrevb.72.020102

Google Scholar

[46] J. F. Scott, Flexoelectric spectroscopy, J. Phys.: Condens. Matter 25 (2013) 331001.

Google Scholar

[47] R. Maranganti, N. D. Sharma, P. Sharma, Electromechanical coupling in nonpiezoelectric materials due to nanoscale nonlocal size effects: Green's function solutions and embedded inclusions, Phys. Rev. B 74 (2006) 014110.

DOI: 10.1103/physrevb.74.014110

Google Scholar

[48] A. K. Tagantsev, Electric polarization in crystals and its response to thermal and elastic perturbations, Phase Transit 35(3–4) (1991) 119–203.

DOI: 10.1080/01411599108213201

Google Scholar

[49] L. E. Cross, Flexoelectric effect, Journal of Materials Science 63 (2006) 4153.

Google Scholar

[50] A. Klic, M. Marvan, Theoretical Study of the Flexoelectric Effect Based on a Simple Model of Ferroelectric Material, Integrated Ferroelectric 63 (2004) 155.

DOI: 10.1080/10584580490459341

Google Scholar

[51] M. Gharbi, Z. H. Sun, P. Sharma, K. White, S. El-Borgi, Flexoelectric properties of ferroelectrics and the nanoindentation size-effect, International Journal of Solids and Structures 48 (2011) 249–256.

DOI: 10.1016/j.ijsolstr.2010.09.021

Google Scholar

[52] T. Kato, N. Mizoshita, K. Kishimoto, Functional liquid-crystalline assemblies: self-organized soft materials, Angew. Chem. Int. Ed. Engl 45 (2006) 38.

DOI: 10.1002/anie.200501384

Google Scholar

[53] S. Baskaran, X. He, Y. Wang, J. Y. Fu, Strain gradient induced electric polarization in α-phase polyvinylidene fluoride films under bending conditions, J. Appl. Phys. 111 (2012) 014109.

DOI: 10.1063/1.3673817

Google Scholar

[54] S. Baskaran, N. Ramachandran, X. He, S. Thiruvannamalai, H. J. Lee , H. Heo , Q. Chen , J. Y. Fu , Giant flexoelectricity in polyvinylidene fluoride films. Phys. Lett. A 375 (2011) (2082).

DOI: 10.1016/j.physleta.2011.04.011

Google Scholar

[55] A. G. Petrov, Flexoelectricity of model and living membranes, Biochim. Biophys. Acta 1561 (2002) 1.

Google Scholar

[56] A. Y. Borisevich, E. A. Eliseev , A. N. Morozovska , C. J. Cheng , J. Y. Lin , Y. H. Chu, D. Kan , I. Takeuchi , V. Nagarajan , S. V. Kalinin , Atomic-scale evolution of modulated phases at the ferroelectric–antiferroelectric morphotropic phase boundary controlled by flexoelectric interaction, Nat. Commun. 3 (2012).

DOI: 10.1038/ncomms1778

Google Scholar

[57] S. P. Alpay, I. B. Misirlioglu, V. Nagarajan, R. Ramesh, Can interface dislocations degrade ferroelectric properties?, Appl. Phys. Lett. 85 (2004) 2044.

DOI: 10.1063/1.1788894

Google Scholar

[58] A. K. Tagantsev, G. Gerra, Interface-induced phenomena in polarization response of ferroelectric thin films, J. Appl. Phys. 100 (2006) 051607.

DOI: 10.1063/1.2337009

Google Scholar

[59] M. W. Chu, I. Szafraniak , R. Scholz, C. Harnagea, D. Hesse , M. Alexe, U. Gosele, Impact of misfit dislocations on the polarization instability of epitaxial nanostructured ferroelectric perovskites, Nat. Mater. 3 (2004) 87.

DOI: 10.1038/nmat1057

Google Scholar

[60] A. Gruverman , A. Kholkin , A. Kingon , H. Tokumoto, Asymmetric nanoscale switching in ferroelectric thin films by scanning force microscopy, Appl. Phys. Lett. 78 (2001) 2751.

DOI: 10.1063/1.1366644

Google Scholar

[61] K. Abe, N. Yanase, T. Yasumoto, T. Kawakubo, Voltage shift phenomena in a heteroepitaxial BaTiO3 thin film capacitor, J. Appl. Phys. 91 (2002) 323.

DOI: 10.1063/1.1426249

Google Scholar

[62] T. D. Nguyen, S. Mao, Y. Yeh, P. K. Purohit, and M. C. McAlpine, Nanoscale Flexoelectricity, Adv. Mater. 25 (2013) 946–974.

DOI: 10.1002/adma.201203852

Google Scholar

[63] A. Kumar, C. Rinaldi, R. S. Katiyar, J. F. Scott, Strain induced artificial multiferroicity in Pb(Zr0. 53Ti0. 47)O3/Pb(Fe0. 66W0. 33)O3 layered nanostructure at ambient temperature", Recent Developments in Ferroelectric Nanostructures and Multilayers, J. Mater. Sci. 44 (2009).

DOI: 10.1007/s10853-009-3503-y

Google Scholar

[64] S. H. Baek J. Park, D. M. Kim, V. A. Aksyuk et al, Giant Piezoelectricity on Si for Hyperactive MEMS, Science 334 (2011) 958.

Google Scholar

[65] A. Gruverman, B. J. Rodriguez, A. I. Kingon, R. J. Nemanich, A. K. Tagantsev, J. S. Cross, M. Tsukada, Mechanical stress effect on imprint behavior of integrated ferroelectric Capacitors , Appl. Phys. Lett. 83 (2003) 728.

DOI: 10.1063/1.1593830

Google Scholar

[66] J. F. Scott, C. A. Paz de Araujo , Ferroelectric Memories, Science 246 (1989) 1400.

Google Scholar

[67] I. B. Misirlioglu, A. L. Vasiliev, M. Aindow, S. P. Alpay, Strong degradation of physical properties and formation of a dead layer in ferroelectric films due to interfacial dislocations, Integr. Ferroelectr. 71 (2005) 67.

DOI: 10.1080/10584580590964709

Google Scholar

[68] L. W. Chang, M. McMillen, F. D. Morrison, J. F. Scott, J. M. Gregg, Size effects on thin film ferroelectrics: Experiments on isolated single crystal sheets, Appl. Phys. Lett. 93 (2008) 132904.

DOI: 10.1063/1.2990760

Google Scholar

[69] R. Hull, J. C. Bean, L. J. Peticolas, B. E. Weir, K. Prabhakaran, T. Ogino, Misfit Dislocation Propagation Kinetics in GexSi1-x/Ge(100) Heterostructures, Appl. Phys. Letter. 65 (1994) 327.

DOI: 10.1063/1.113023

Google Scholar

[70] J. Junquera, P. Ghosez, Critical thickness for ferroelectricity in perovskite ultrathin films, Nature 422 (2003) 506.

DOI: 10.1038/nature01501

Google Scholar

[71] L. E. Cross, Flexoelectric effects: Charge separation in insulating solids subjected to elastic strain gradients. J. Mater. Sci. 41 (2006) 53-63.

DOI: 10.1007/s10853-005-5916-6

Google Scholar

[72] J. Y. Fu, W. Zhu, N. Li, , N. B. Smith, L. E. Cross, Gradient scaling phenomenon in microsize flexoelectric piezoelectric composites. Appl. Phys. Lett. 91 (2007) 182910.

DOI: 10.1063/1.2800794

Google Scholar

[73] H. Kawai, The Piezoelectricity of Poly (vinylidene Fluoride), Jpn. J. Appl. Phys. 8 (1969) 975.

Google Scholar

[74] M. Schulz, M. Marvan, Theory of flexoelectric effect of polymer glasses, Colloid Polym. Sci. 269 (1991) 553.

DOI: 10.1007/bf00659908

Google Scholar

[75] J. Harden, M. Chambers, R. Verduzco, P. Luchette, J. T. Gleeson, S. Sprunt, A. Jakli , Giant flexoelectricity in bent-core nematic liquid crystal elastomers Appl. Phys. Lett. 96 (2010) 102907.

DOI: 10.1063/1.3358391

Google Scholar

[76] S. Baskaran, X. He, Q. Chen, J. Y. Fu, Experimental studies on the direct flexoelectric effect in α-phase polyvinylidene fluoride films, Appl. Phys. Lett. 98 (2011) 242901.

DOI: 10.1063/1.3599520

Google Scholar

[77] S. Poddar, Stephen Ducharme, Measurement of the flexoelectric response in ferroelectric and relaxor polymer thin films, Appl. Phys. Lett. 103 (2013) 202901.

DOI: 10.1063/1.4829622

Google Scholar

[78] A. K. Tagantsev, Zh. Eksp. Teor. Fiz. Vegard strains and Flexoelectric effect 88 (1985) 2108.

Google Scholar

[79] A. Jakli, Electro-mechanical effects in liquid crystals, Liq. Cryst. 37(6-7) (2010) 825-837.

Google Scholar

[80] M. Marvan, A. Havranek , Static volume flexoelectric effect in a model of linear chains, Solid State Communications 101 (1997) 493-496.

DOI: 10.1016/s0038-1098(96)00623-0

Google Scholar