研究生: |
張景翔 Chang, Ching-Hsiang |
---|---|
論文名稱: |
利用壓電力顯微鏡探討鈮酸鹽之一維奈米線結構的區域壓電特性 Local Piezoelectric Characterization of Alkaline Niobate 1-Dimensional Nanostructures Measured by Piezoresponse Force Microscope |
指導教授: |
李紫原
Lee, Chi-Young |
口試委員: |
裘性天
Chiu, Hsin-Tien 林諭男 Lin, I-Nan 李紫原 Lee, Chi-Young 張裕煦 Chang, Yu-Hsu |
學位類別: |
碩士 Master |
系所名稱: |
工學院 - 材料科學工程學系 Materials Science and Engineering |
論文出版年: | 2012 |
畢業學年度: | 100 |
語文別: | 中文 |
論文頁數: | 129 |
中文關鍵詞: | 鈮酸鉀 、鈮酸鈉 、奈米 、壓電力顯微鏡 、鐵電 |
外文關鍵詞: | potassium niobate, sodium niobate, PFM |
相關次數: | 點閱:3 下載:0 |
分享至: |
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本研究將以掃描探針顯微鏡 (SPM) 分析鈮酸鉀與鈮酸鈉的一維奈米結構,了解其在奈米尺度下所表現的鐵電特性。實驗首以微米級五氧化二鈮與不同金屬氫氧化物,如氫氧化鉀或氫氧化納,進行反應,在回流環境下進行合成,分別獲得鈮酸鉀與鈮酸鈉水合物 (SOMS) 的奈米線 (KNbO3 寬 50-100 nm,長0.2-3 μm ; Na2Nb2O6.H2O 寬 200-500 um 長 5-10 um),後者經過退火處理可成為斜方晶的鈮酸鈉奈米線。所得生成產物經分散後,利用掃描探針顯微鏡的探針施加直流電與交流電並量測其單一奈米線所產生之形變,亦稱為壓電力顯微技術,探討奈米材料的鐵電疇分佈、偏壓極化與局部電滯現象,並結合穿透式電子顯微鏡、X光繞射分析與相關文獻以了解晶格結構與退火製程之關係。
研究證實鈮酸鉀奈米線有自發極化的現象,另外則發現鈮酸鈉奈米線所表現的鐵電特性,不同於文獻記載的傳統塊材反鐵電性表現,未經過電場高溫極化即具有區域鐵電特性,在施加平行軸向偏壓後以側向壓電力顯微鏡觀測可明顯觀察到延奈米線軸向 [100] 呈週期性排列的電域疇,平均d33=3.25 pm/V,與鐵電性的鈮酸鉀奈米線 (d33 = 7.32 pm/V) 的壓電性略有不同。
The piezoelectricity of potassium and sodium niobate 1-Dimensional nanostructurs was examined by scanning probe microscope (SPM). Metal oxides with different morphologies were obtained by refluxing micro-sized niobium oxide (Nb2O5) with alkali metal hydroxides, potassium hydroxide (KOH) or sodium hydroxide (NaOH), for several days. Firstly, ferroelectric potassium niobate (KNbO3 with 50~100 nm diameter and 0.2-3.0 µm length) and non-ferroelectric sodium niobate hydrate nanowires, sandia octahedral molecular sieves (SOMS), (Na2Nb2O6.H2O with 200~500 nm diameter and 5~10 µm length), were obtained. Then, orthorhombic sodium niobate nanowires were produced from wiry SOMS by annealing above 400 ºC.
Piezoelectric characterization was performed by piezoresponse force microscopy (PFM), responding the local vibrations induced by an AC power or combine with DC power applied between the conductive SPM tip and the bottom electrode of the sample. Ferroelectric properties including domain distribution, local polarization and hysteresis phenomenon under nano-scale were studied in detail.
The results show the spontaneous polarization of ferroelectricity KNbO3 nanowires, with maximum piezoelectric coefficient about 7.9 pmV; while NaNbO3 nanowires exhibited a local piezoelectric phenomenon, which was absent in its un-poled anti-ferroelectric bulk material. The domain distribution (dzz = 0.5~4.0 pmV) along the nanowire axis periodicity, as an electric field parallels to the axis direction was applied. According to transmission electron microscopy (TEM) and X-ray diffraction studies, wiry NaNbO3 was along the [100] axis. Additionally, wiry NaNbO3 obtained at lower anneal temperature possess more oxygen vacancy. The domain wall of wiry NaNbO3 changes under an applied voltage difficultly.
To our knowledge, the present work is the first report of the preparation of NaNbO3 nanowires as well as the determination of piezoelectricity. Here we able to image domain in those nanowires with PFM, both lattice contribution and domain wall contribution to piezoelectric were observed. Lateral mode PFM revealed preferred polarization orientation and strong imprint in NaNbO3 nanowires.
(1) J. Curie, P. Curie, “Development by pressure of polar electricity in hemihedral crystals with inclined faces”, Bull. Soc. Min. France, 1880, 3, 90
(2) J. Valasek, “Piezoelectric and allied phenomena in Rochelle salt”, Phys. Rev., 1920, 15, 537
(3) S. Roberts, “Dielectric and piezoelectric properties of barium titanate”, Phys. Rev., 1947, 71, 890
(4) M. E. Lines, A. M. Glass, “Principles and applications of ferroelectrics and related materials”, Clarendon Press: Oxford, U.K., 1977
(5) G. A. Smolenskii, “Ferroelectrics and related materials”, Gordon and Breach: Amsterdam, 1984
(6) J. F. Scott, C. A. Pazdearaujo, “Ferroelectric memories”, Science, 1989, 246,1400
(7) Y. Saito, H. Takao, T. Tani, T. Nonoyama, K. Takatori, T. Homma, T. Nagaya, M. Nakamura, “Lead-free piezoceramics”, Nature, 2004, 432, 84
(8) P. Baettig, C. F. Schelle, R. LeSar, U. V. Waghmare, N. A. Spaldin, “Theoretical prediction of new high-performance lead-free piezoelectrics”, Chem. Mater., 2005, 17, 1376
(9) R.-J. Xie, Y. J. Akimune, “Lead-free piezoelectric ceramics in the (1-x)Sr2NaNb5O15–xCa2NaNb5O15 (0.05≤x≤0.35) system”, Mater. Chem., 2002, 12, 3156
(10) Cross, E., “Materials science-Lead-free at last”, Nature, 2004, 432, 24
(11) W. Kobayashi, I. Terasaki, “CaCu3Ti4O12/CaTiO3 composite dielectrics: Ba/Pb-free dielectric ceramics with high dielectric constants”, Appl. Phys. Lett., 2005, 87, 032902
(12) L. A. Reznichenko, L. A. Shilkina, A. V. Turik, S. I. Dudkina, “Giant piezoelectric anisotropy in sodium niobate with a composite-like structure”, Tech. Phys., 2002, 47, 206
(13) T. Hungria, L. Pardo, A. Moure, A. J. Castro, “Effect of mechanochemical activation on the synthesis of NaNbO3 and processing of environmentally friendly piezoceramics”, Alloy. Compd., 2005, 395, 166
(14) M. Anliker, H. R. Brugger, W. Kanzig, “Behavior of colloidal ferroelectrics, Barium titante BaTiO3”, Helv. Phys. Acta., 1954, 27, 99
(15) Y. Shiratori, A. Magrez, J. Dornseiffer, F. H. Haegel, C. Pithan, R. Waser, “Microemulsion mediated synthesis of nanocrystalline (Kx,Na1-x)NbO3 powders”, J. Phys. Chem. B, 2005, 190, 20122
(16) G. Arlt, D. Hennings, G. With, “Dielectric properties of fine‐grained barium titanate ceramics”, J. Appl. Phys., 1985, 58, 1619
(17) K. Ishikawa, K. Yoshikawa, N. Okada, “Size effect on the ferroelectric phase transition in PbTiO3 ultrafine particles”, Rhys. Rev. B, 1988, 37, 5852
(18) E. Soergel, “Piezoresponse force microscopy”, J. Phys. D: Appl. Phys., 2011, 44, 464003
(19) P. Güthner, K. Dransfeld, “Local poling of ferroelectric polymers by scanning force microscopy”, Appl. Phys. Lett., 1992, 61, 1137
(20) A. Gruverman, O. Auciello, R. Ramesh, H. Tokumoto, “Scanning force microscopy of domain structure in ferroelectric thin films: imaging and control”, Nanotechnology, 1997, 8, 38
(21) M. Abplanalp, L. M. Eng, P. Günter, “Mapping the domain distribution at ferroelectric surfaces by scanning force microscopy”, Appl. Phys. A: Mater. Sci., 1998, 66, 231
(22) J. Muñoz-Saldaña, M. J. Hoffmann, G. A. Schneider, “Ferroelectric domains in coarse-grained lead zirconate titanate ceramics characterized by scanning force microscopy”, J. Mater. Res., 2003, 18, 1777
(23) H. Ko, K. Ryu, H. Park, C. Park, D. Jeon, Y. K. Kim, J. Jung, D.-K. Min, Y. Kim, H. N. Lee, Y. Park, H. Shin, S. Hong, “High-resolution field effect sensing of ferroelectric charges”, Nano Lett., 2011, 11, 1428
(24) K. Uchino, “Ferroelectric Devices”, Marcel Dekker, Inc. New York, 2000
(25) B. Jaffe, W. R. Cook, H. Jaffe, “Piezoelectric Ceramics”, Academic Press, Inc., Londin 1970
(26) K. G. Deshmukh, S. G. Ingle, “Interferometric studies of domain structures in potassium niobate single crystals”, J. phys. D.: Appl. Phys., 1971, 4,124
(27) E. Wiessendanger, “Domain structures in orthorhombic KNbO3 and characterisation of single domain crystals”, Czech. J. Phys. B, 1973, 23, 91
(28) P. Paruch, T. Giamachi, J. M. Triscone, “Domain wall roughness in epitaxial ferroelectric Pb(Zr0.2Ti0.8)O3 thin films”, Phys. Rev. Lett., 2005, 94, 197601
(29) L. A. Reznitchenko, A. V. Turik, E. M. Kuznetsova, V. P. Sakhnenko, “Piezoelectricity in NaNbO3 ceramics”, J. Phys.: Condens. Matter, 2001, 13, 3875
(30) E. Ringgaard, T. Wurlitzer, “Lead-free piezoceramics based on alkali niobates”, J. Eur. Ceram. Soc., 2005, 25, 2701
(31) Y. P. Guo, K. Kakimoto, H. Ohsato, “(Na0.5K0.5)NbO3-LiTaO3 lead-free piezoelectric ceramics”, Mater. Lett., 2005, 59, 241
(32) C.-R. Cho, I. Katardjiev, M. Grishin, A. Grishin, “Na0.5K0.5NbO3 thin films for voltage controlled acoustoelectric device applications”, Appl. Phys. Lett., 2002, 80, 3171
(33) F. Jona, G. Shirane, R. Pepinsky, “Optical study of PbZrO3 and NaNbO3 single crystals”, Phys. Rev., 1955, 97, 1584
(34) S. K. Mishra, N. Choudhury, S. L. Chaplot, P. S. R. Krishna, R. Mittal, “Competing antiferroelectric and ferroelectric interactions in NaNbO3: Neutron diffraction and theoretical studies”, Phys. Rev. B, 2007, 76, 024110
(35) S. K. Mishra, R. Mittal, V. Yu. Pomjakushin, S. L. Chaplot, “Phase stability and structural temperature dependence in sodium niobate: A high-resolution powder neutron diffraction study”, Phys. Rev. B, 2011, 83, 134105
(36) Y. I. Yuzyuk, P. Simon, E. Gagarina, L. Hennet, D. Thiaudi`ere, V. I. Torgashev, S. I. Raevskaya, I. P. Raevskii, L. A. Reznitchenko, J. L. Sauvajol, “Modulated phases in NaNbO3: Raman scattering, synchrotron x-ray diffraction, and dielectric investigations”, J. Phys.: Condens. Matter, 2005, 17, 4977
(37) A. D. Handoko, K. L. Gregory, “One-dimensional perovskite nanostructures”, Sci. Adv. Mater., 2010, 2, 16
(38) P. M. Rørvik , T. Grande , M.-A. Einarsrud, “One-dimensional nanostructures of ferroelectric perovskites”, Adv. Mater., 2011, 23, 4007
(39) Y. Deng, J. L. Wang, K. R. Zhu, M. S. Zhang, J. M. Hong, Q. R. Gu, Z. Yin, “Synthesis and characterization of single-crystal PbTiO3 nanorods”, Mater. Lett., 2005, 59, 3272
(40) Y. C. Choi, J. Kim, S. D. Bu, “Template-directed formation of functional complex metal-oxide nanostructures by combination of sol–gel processing and spin coating”, Mater. Sci. and Eng.: B, 2006, 133, 245
(41) Z. Hua, P. Yang, H. Huang, J. Wan, Z.-Z. Yu, S. Yang, M. Lu, B. Gu, Y. Du, ““Sol-gel template synthesis and characterization of magnetoelectric CoFe2O4/Pb(Zr0.52Ti0.48)O3 nanotubes”, Mater. Chem. Phys., 2008, 107, 541
(42) X. Y. Zhang, J. Y. Dai, C. W. Lai, “Synthesis and characterization of highly ordered BiFeO3 multiferroic nanowire arrays”, Prog. Solid State Chem., 2005, 33, 147
(43) F. Teng, S. Liang, B. Gaugeu, R. Zong, W. Yao, Y. Zhu, “Carbon nanotubes-templated assembly of LaCoO3 nanowires at low temperatures and its excellent catalytic properties for CO oxidation”, Catal. Commun., 2007, 8, 1748
(44) U. A. Joshi, S. Yoon, S. Baik, J. S. Lee, “Surfactant-free hydrothermal synthesis of highly tetragonal barium titanate nanowires: a structural investigation”, J. Am. Ceram. Soc., 2006, 110, 12249
(45) J.-F. Liu, X.-L. Li, Y.-D. Li, “Novel synthesis of polymorphous nanocrystalline KNbO3 by a low temperature solution method”, J. Nanosci, Nanotechnol., 2002, 2, 617
(46) G. Suyal, E. Colla, R. Gysel, M. Cantoni, N. Setter, “Piezoelectric response and polarization switching in small anisotropic perovskite particles”, Nano Lett., 2004, 4, 1339
(47) A. Magrez, E. Vasco, J. W. Seo, C. Dieker, N. Setter, L. Forro, “Growth of Single Crystalline KNbO3 Nanostructures”, J. Phys. Chem. B, 2006, 110, 58
(48) H. Zhu, Z. Zheng, X. Gao, Y. Huang, Z. Yan, J. Zou, H. Yin, Q. Zou, S. H. Kable, J. Zhao, Y. Xi, W. N. Marten, R. L. Frost, “Structural evolution in a hydrothermal reaction between Nb2O5 and NaOH solution: from Nb2O5 grains to microporous Na2Nb2O6•⅔H2O fibers and NaNbO3 cubes”, J. Am. Chem. Soc., 2006, 128, 2373
(49) T.-Y. Ke, H-A. Chen, H.-S. Sheu, J-W Yeh, H-N Lin, C.-Y. Lee, H.-T. Chiu, “Sodium niobate nanowire and its piezoelectricity”, J. Phys. Chem. C, 2008, 112, 8827
(50) Y. Qin, X. Wang, Z. L. Wang, “Microfibre-nanowire hybrid structure for energy scavenging”, Nature, 2008, 451, 809
(51) Z. L. Wang, “Towards self-powered nanosystems: from nanogenerators to nanopiezotronics”, Adv. Funct. Mater., 2008, 18, 3553.
(52) S. N. Cha, J.-S. Seo, S. M. Kim, H. J. Kim, Y. J. Park, S.-W. Kim, J. M. Kim, Adv. Mater., “Sound-driven piezoelectric nanowire-based nanogenerators”, 2010, 22, 4726.
(53) B. Kumar, S.-W. Kim, “Recent advances in power generation through piezoelectric nanogenerators”, J. Mater. Chem., 2011, 21, 18946
(54) J. H. Jung, M. Lee, J.-I. Hong, Y. Ding, C.-Y. Chen, L.-J. Chou, Z. L. Wang, ACS Nano, 2011, 5, 10041
(55) W. Kanzig, “Ferroelectrics and Antiferroelectrics” Academic, New York, 1957
(56) K. Uchino, E. Sadanaga, T. Hirose, “Dependence of the crystal structure on particle size in barium titanate”, J. Am. Ceram. Soc., 1989, 72, 1555
(57) K. Seagusa, W. E. Rhine, H. K. Bowen, J. Am. Ceram. Soc., “Effect of composition and size of crystallite on crystal phase in lead barium titanate”, 1993, 76 1505
(58) M.-H. Lee, A. Halliyal, R. E. Newnham, “Poling studies of piezoelectric composites prepared by coprecipitated PbTiO3 powder”, Ferroelectrics, 1988, 87, 71
(59) W. Y. Shih, W. H. Shih, I. A. Aksay, “Dependence of the ferroelectric transition of small batio3 paticles: effect of depolarization”, Phys. Rew. B, 1994, 50, 15575
(60) F. Jona, G. Shirane, “Ferroelectric crystal”, Dover, New York, 1962
(61) A. Schilling, R. M. Bowman, G. Catalan, J. F. Scott, J. M. Gregg, “Morphological control of polar orientation in single-crystal ferroelectric nanowires”, Nano Lett., 2007, 7, 3787
(62) M. McMillen, R. G. P. McQuaid, S. C. Haire, C. D. McLaughlin, L. W. Chang, A. Schilling, J. M. Gregga, “The influence of notches on domain dynamics in ferroelectric nanowires”, Appl. Phys. Lett., 2010, 96, 042904
(63) P. Ayyub, S. Chattopadhyay, R. Pinto, M. S. Multani, “Ferroelectric behavior in thin films of antiferroelectric materials”, Phys. Rev. B, 1998, 57, 5559
(64) Y. I. Yuzyuk, A. Shakhovoy, S. I. Raevskaya, I. P. Raevski, M. El Marssi, M. G. Karkut, P. Simon, “Ferroelectric Q-phase in a NaNbO3 epitaxial thin film”, Appl. Phys. Lett., 2010, 96, 222904
(65) C. Yan, L. Nikolova, A. Dadvand, C. Harnagea, A. Sarkissian, D. F. Perepichka, D. Xue, F. Rosei, “Multiple NaNbO3/Nb2O5 heterostructure nanotubes: a new class of ferroelectric/semiconductor nanomaterials”, Adv. Mater., 2010, 22, 1741
(66) G. Binnig, H. Rohrer, “Scanning tunneling microscopy”,Physica, 1984, 127B, 37
(67) G. Binnig H. Rohrer, “In touch with atoms”, Rev. Mod. Phys., 1999, 71, 324
(68) R. J. Colton, A. Engel, J. E. Frommer, H. Gaub, A. Gerirth, R. Guckenbbrger, W. Heckl, B. Parkinson, J. Rabe, “Procedures in Scanning Probe Microscopies”, Wiley, New York, 1998
(69) G. Binnig, H. Rohrer, Ch. Gerber, E. Weibel, “Tunneling through a controllable vacuum gap”, Appl. Phys. Lett., 1981, 40, 178
(70) G. Binning, H. Rohrer, Ch. Gerber, E. Weibel, “Surface studies by scanning tunneling microscopy”, Phys. Rev. Lett., 1982, 49, 57
(71) J. A. Kubb, Y. R. Wang, W. J. Greene, “Fabry-Pérot transmission resonances in tunneling microscopy”, Phys. Rev. B, 1991, 43, 9346
(72) G. Binnig. C. F. Quate, Ch. Gerber, “Atomic force microscope”,Phys. Rev. Lett., 1986 56, 930
(73) S. Yamazoe, H. Sakurai, T. Saito, T. Wada, “Observation of domain structure in 001 orientated NaNbO3 films deposited on (001)SrTiO3 substrates by laser beam scanning microscopy”, Appl. Phys. Lett., 2010, 96, 092901
(74) R.-P. Herber, G. A. Schneider, S. Wagner, M. J. Hoffmann, “Characterization of ferroelectric domains in morphotropic potassium sodium niobate with scanning probe microscopy”, Appl. Phys. Lett., 2007, 90, 252905
(75) H. Birk, J. Glatz-Reichenbach, L. Jie, E. Schreck, K. Dransfeld, “The local piezoelectric activity of thin polymer films observed by scanning tunneling microscopy”, J. Vac. Sci. Technol. B, 1991, 9, 1162
(76) A. Gruverman, O. Auciello, H. Tokumoto, “Scanning force microscopy for the study of domain structure in ferroelectric thin films”, J. Vac. Sci. Technol. B, 1996, 14, 602
(77) S. V. Kalinin, B. J. Rodriguez, S. Jesse, J. Shin, A. P. Baddorf, P. Gupta, H. Jain, D. B. Williams, A. Gruverman, “Vector Piezoresponse Force Microscopy”, Microsc. Microanal., 2006, 12, 206
(78) W. S. Yun, J. J. Urban, Q. Gu, H. Park, “Ferroelectric properties of individual barium titanate nanowires investigated by scanned probe microscopy”, Nano Lett., 2002, 2, 447
(79) J. Wang, C. Stampfer, C. Roman, W. H. Ma, N. Setter, C. Hierold, “Piezoresponse force microscopy on doubly clamped KNbO3 nanowires”, Appl. Phys. Lett., 2008, 93, 223101
(80) J. Y. Jo, P. Chen, R. J. Sichel, S.-H. Baek, R. T. Smith, N. Balke, S. V. Kalinin, M. V. Holt, J. Maser, K. Evans-Lutterodt, C.-B. Eom, P. G. Evans, “Structural consequences of ferroelectric nanolithography”, Nano Lett., 2011, 11, 3080
(81) M.-H. Zhao, Z.-L. Wang, S. X. Mao, “Piezoelectric characterization of individual zinc oxide nanobelt probed by piezoresponse force microscope”, Nano Lett., 2004, 4, 587
(82) T. Jungk, A. Hoffmann, E. Soergel, “Influence of the inhomogeneous field at the tip on quantitative piezoresponse force microscopy”, Appl. Phys. A, 2007, 86, 353
(83) K. Matsumoto, Y. Hiruma, H. Nagata, T. Takenaka, “Piezoelectric properties of pure and Mn-doped potassium niobate ferroelectric ceramics”, Jpn. J. Appl. Phys., 2006, 46, 4479.
(84) H. Nagata, K. Matsumoto, T. Hirosue, Y. Hiruma, T. Takenaka, “Fabrication and electrical properties of potassium niobate ferroelectric ceramics”, Jpn. J. Appl. Phys., 2007, 46, 7084.
(85) A. Gruverman, B. J. Rodriguez, A. I. Kingon, R. J. Nemanich, A. K. Tagantsev, “Mechanical stress effect on imprint behavior of integrated ferroelectric capacitors”, Appl. Phys. Lett., 2003, 83, 728
(86) L. Liu, B. Li, D. Yu, Y. Cui, X. Zhou, W. Ding, “Temperature-induced solid-phase oriented rearrangement route to the fabrication of NaNbO3 nanowires”, Chem. Commun., 2010, 46, 427
(87) J. Chen, D. Feng, “TEM study of phases and domains in NaNbO3 at room temperature”, Phys. Stat. Sol., 1988, 109, 171
(88) J. Chen, D. Feng, “In situ TEM studies of para-ferro phase transitions in NaNbO3”, Phys. Stat. Sol., 1988, 109, 427
(89) J. Koruza, J. Tellier, B. Malič, V. Bobnar, M. Kosec, “Phase transitions of sodium niobate powder and ceramics, prepared by solid state synthesis”, J. Appl. Phys., 2010, 108, 113509
(90) Z. X. Shen, X. B. Wang, M. H. Kuok, S. H. Tang, “Raman scattering investigations of the antiferroelectric–ferroelectric phase transition of NaNbO3”, J. Raman Spectrosc., 1998, 29, 379.
(91) Z. X. Shen, X. B. Wang, S. H. Tang, M. H. Kuok, R. Malekfar, “High-pressure Raman study and pressure-induced phase transitions of sodium niobate NaNbO3. Journal of Raman Spectroscopy”, J. Raman Spectrosc., 2000, 31, 439
(92) R. J. C .Lima, P. T. C. Freire, J. M. Sasaki, A. P. Ayala, F. E. A. Melo, J. M. Filho, K. C. Serra, S. Lanfredi, M. H. Lente, J. A. J. Eiras, “Temperature-dependent Raman scattering studies in NaNbO3 ceramics”, Raman Spectrosc., 2002, 33, 669.
(93) Y. D. Juang, M. L. Hu, W. S. Tse, “Temperature dependent Raman scattering studies of Li0.02Na0.98NbO3”, J. Appl. Phys., 1994, 76, 3746
(94) C. L. Jia, S. B. Mi, K. Urban, I. Vrejoiu, M. Alexe, D. Hesse, “Effect of a single dislocation in a heterostructure layer on the local polarization of a ferroelectric layer”, Phys. Rev. Lett., 2009, 102, 117601
(95) S.Yamazoe, A. Kohori, H. Sakurai, T. Wada, Y. Kitanaka, Y. Noguchi, M. Miyayama, Applications of Ferroelectrics (ISAF/PFM), 2011 International Symposium on and 2011 International Symposium on Piezoresponse Force Microscopy and Nanoscale Phenomena in Polar Materials, Date of Conference: 24-27 July 2011
(96) D. Damjanovic, “Logarithmic frequency dependence of the piezoelectric effect due to pinning of ferroelectric-ferroelastic domain walls”, Phys. Rev. B, 1997, 55, 649
(97) H. Kronmuller, “Statistical theory of Rayleigh's law”, Z. Angew. Phys., 1970, 30, 9
(98) B. D .Begg, K. S. Finnie, E. R. Vance, “Raman study of the relationship between room-temperature tetragonality and the curie point of barium titanate”, J. Am. Ceram. Soc., 1996, 79, 2666