• Journal of the Chinese Ceramic Society
  • Vol. 50, Issue 3, 661 (2022)
AN Zheyi* and ZHANG Nan
Author Affiliations
  • [in Chinese]
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    DOI: 10.14062/j.issn.0454-5648.20210750 Cite this Article
    AN Zheyi, ZHANG Nan. Scattering Techniques and Local Structures of Ferroelectric Perovskites[J]. Journal of the Chinese Ceramic Society, 2022, 50(3): 661 Copy Citation Text show less
    References

    [1] SCOTT J F. Applications of modern ferroelectrics[J]. Science, 2007, 315(5814): 954-959.

    [2] UCHINO K. Glory of piezoelectric perovskites[J]. Sci Technol Adv Mater, 2015, 16: 46001.

    [3] CLEGG W. X-ray crystallography[M]. Oxford: Oxford University Press, 2015.

    [4] KEEN D A, GOODWIN A L. The crystallography of correlated disorder[J]. Nature, 2015, 521(7552): 303-309.

    [5] LI F, ZHANG S, DAMJANOVIC D, et al. Local structural heterogeneity and electromechanical responses of ferroelectrics: learning from relaxor ferroelectrics[J]. Adv Funct Mater, 2018, 28(37): 1801504.

    [6] GOOSSENS D J. Local ordering in lead-based relaxor ferroelectrics[J]. Acc Chem Res, 2013, 46(11): 2597-2606.

    [7] EGAMI T. Local structure of ferroelectric materials[J]. Annu Rev Mater Res, 2007, 37(1): 297-315.

    [8] YOUNG R A. The Rietveld method[M]. Oxford: Oxford University Press, 1993.

    [9] EGAMI T, BILLINGE S J L. Underneath the Bragg peaks: structural analysis of complex materials[M]. 2nd ed. Oxford: Pergamon, 2012.

    [10] FRIEDRICH W. Rntgenstrahlinterferenzen[J]. Phys Z., 1913, 14: 1079-1087.

    [11] WELBERRY T R. One hundred years of diffuse X-ray scattering[J]. Metall and Mat Trans A, 2014, 45(1): 75-84.

    [12] HOWARD C J, STOKES H T. Structures and phase transitions in perovskites - A group-theoretical approach[J]. Acta Cryst A, 2005, 61(1): 93-111.

    [13] STOKES H T, KISI E H, HATCH D M, et al. Group-theoretical analysis of octahedral tilting in ferroelectric perovskites [J]. Acta Cryst B, 2002, 58: 934-938.

    [14] BILLINGE S J L, LEVIN I. The problem with determining atomic structure at the nanoscale[J]. Science, 2007, 316(5824): 561-565.

    [15] COMèS R, LAMBERT M, GUINIER A. Désordre linéaire dans les cristaux (cas du silicium, du quartz, et des pérovskites ferroélectriques)[J]. Acta Cryst A, 1970, 26(2): 244-254.

    [16] COCHRAN W. Crystal stability and the theory of ferroelectricity[J]. Phys Rev Lett, 1959, 3(9): 412-414.

    [17] PASCIAK M, WELBERRY T R. Diffuse scattering and local structure modeling in ferroelectrics[J]. Z Kristallogr Cryst Mater, 2011, 226(2): 113-125.

    [19] ZHANG N, YOKOTA H, GLAZER A M, et al. The missing boundary in the phase diagram of PbZr1-xTixO3[J]. Nat Commun, 2014, 5: 5231.

    [20] BURNS G, DACOL F H. Crystalline ferroelectrics with glassy polarization behavior[J]. Phys Rev B, 1983, 28(5): 2527-2530.

    [21] CROSS L E. Relaxor ferroelectrics[J]. Ferroelectrics, 1987, 76(1): 241-267.

    [23] BOKOV A A, YE Z-G. Recent progress in relaxor ferroelectrics with perovskite structure[J]. J Mater Sci, 2006, 41(1): 31-52.

    [24] NOHEDA B, COX D E, SHIRANE G, et al. Phase diagram of the ferroelectric relaxor (1-x)PbMg1/3Nb2/3O3-xPbTiO3[J]. Phys Rev B, 2002, 66(9): 092105.

    [25] PARK S-E, SHROUT T R. Ultrahigh strain and piezoelectric behavior in relaxor based ferroelectric single crystals[J]. J Appl Phys, 1997, 82(4): 1804-1811.

    [26] QIU C, WANG B, ZHANG N, et al. Transparent ferroelectric crystals with ultrahigh piezoelectricity[J]. Nature, 2020, 577(7790): 350-354.

    [27] LI F, ZHANG S, YANG T, et al. The origin of ultrahigh piezoelectricity in relaxor-ferroelectric solid solution crystals[J]. Nat Commun, 2016, 7: 13807.

    [28] LI F, LIN D, CHEN Z, et al. Ultrahigh piezoelectricity in ferroelectric ceramics by design[J]. Nat Mater, 2018, 17(4): 349-354.

    [29] LIU Q, ZHANG Y, GAO J, et al. High-performance lead-free piezoelectrics with local structural heterogeneity[J]. Energy Environ Sci, 2018, 11(12): 3531-3539.

    [30] DAVIES P K, WU H, BORISEVICH A Y, et al. Crystal chemistry of complex perovskites: new cation-ordered dielectric oxides[J]. Annu Rev Mater Res, 2008, 38(1): 369-401.

    [31] PHELAN D, STOCK C, RODRIGUEZ-RIVERA J A, et al. Role of random electric fields in relaxors[J]. Proc Natl Acad Sci USA, 2014, 111(5): 1754-1759.

    [32] SETTER N, CROSS L E. The contribution of structural disorder to diffuse phase transitions in ferroelectrics[J]. J Mater Sci, 1980, 15(10): 2478-2482.

    [33] SETTER N, CROSS L E. The role of B-site cation disorder in diffuse phase transition behavior of perovskite ferroelectrics[J]. J Appl Phys, 1980, 51(8): 4356-4360.

    [34] BURSILL L A, QIAN H, PENG J, et al. Observation and analysis of nanodomain textures in the dielectric relaxor lead magnesium niobate[J]. Physica B Condens Matter, 1995, 216(1/2): 1-23.

    [36] AKBAS M A, DAVIES P K. Thermally induced coarsening of the chemically ordered domains in Pb(Mg1/3Nb2/3)O3 (PMN)-based relaxor ferroelectrics[J]. J Am Ceram, 2000, 83(1): 119-123.

    [37] CANTONI M, BHARADWAJA S, GENTIL S, et al. Direct observation of the B-site cationic order in the ferroelectric relaxor Pb(Mg13Ta23)O3[J]. Ferroelectrics, 2004, 96(7): 3870-3875.

    [38] MONTGOMERY J K, AKBAS M A, DAVIES P K. 1:1 Ordered domain growth in Pb(Mg1/3Ta2/3)O3-La(Mg2/3Ta1/3)O3 relaxor ferroelectric perovskites[J]. J Am Ceram, 1999, 82(12): 3481-3484.

    [39] WANG C, FU Z, ZHANG N, et al. Determination of chemical ordering in the complex perovskite Pb(Cd1/3Nb2/3)O3[J]. IUCrJ, 2018, 5(6): 808-815.

    [40] CABRAL M J, ZHANG S, DICKEY E C, et al. Gradient chemical order in the relaxor Pb(Mg13 Nb23)O3[J]. Appl Phys Lett, 2018, 112(8): 82901.

    [41] GLAZER A M. The classification of tilted octahedra in perovskites[J]. Acta Cryst B, 1972, 28(11): 3384-3392.

    [42] CORKER D L, GLAZER A M, DEC J, et al. A re-investigation of the crystal structure of the perovskite pbzro3 by X-ray and neutron diffraction[J]. Acta Cryst B, 1997, 53(1): 135-142.

    [43] BAK P. Commensurate phases, incommensurate phases and the devil's staircase[J]. Rep Prog Phys, 1982, 45(6): 587-629.

    [46] MA T, FAN Z, XU B, et al. Uncompensated polarization in incommensurate modulations of perovskite antiferroelectrics[J]. Phys Rev Lett, 2019, 123(21): 217602.

    [47] BURKOVSKY R G, BRONWALD I, ANDRONIKOVA D, et al. Triggered incommensurate transition in PbHfO3[J]. Phys Rev B, 2019, 100(1): 014107.

    [48] VIEHLAND D, DAI X H, LI J F, et al. Effects of quenched disorder on La-modified lead zirconate titanate: Long- and short-range ordered structurally incommensurate phases, and glassy polar clusters[J]. J Appl Phys, 1998, 84(1): 458-471.

    [49] BRAGG W L. The diffraction of short electromagnetic waves by a crystal[J]. 1913, 17: 43-57.

    [50] LAUE M V. Rntgenstrahlinterferenz und Mischkristalle[J]. Ann Phys, 1918, 361(15): 497-506.

    [51] DEBYE P. Interferenz von Rntgenstrahlen und Wrmebewegung[J]. Ann Phys, 1913, 348(1): 49-92.

    [52] FAXéN H. Die bei Interferenz von Rntgenstrahlen durch die Wrmebewegung entstehende zerstreute Strahlung[J]. Ann Phys, 1917, 359(24): 615-620.

    [53] FAXéN H. Die bei interferenz von rntgenstrahlen infolge der wrmebewegung entstehende streustrahlung[J]. Z Physik, 1923, 17(1): 266-278.

    [54] WALLER I. Zur Frage der Einwirkung der wrmebewegung auf die interferenz von rntgenstrahlen[J]. Z Physik, 1923, 17(1): 398-408.

    [55] BRILLOUIN L. Diffusion de la lumière et des rayons X par un corps transparent homogène[J]. Ann Phys, 1922, 9(17): 88-122.

    [56] WELBERRY T R. Diffuse X-ray scattering and models of disorder [M]. Oxford: Oxford University Press, 2010.

    [57] TANAKA I, YAO M, SUZUKI M, et al. An automatic diffraction data collection system with an imaging plate[J]. J Appl Cryst, 1990, 23(4): 334-339.

    [58] BARNA S L, SHEPHERD J A, TATE M W, et al. Characterization of a prototype pixel array detector (PAD) for use in microsecond framing time-resolved X-ray diffraction studies[J]. IEEE Trans Nucl Sci, 1997, 44(3): 950-956.

    [59] BROENNIMANN C, EIKENBERRY E F, HENRICH B, et al. The PILATUS 1M detector[J]. J Synchrotron Radiat, 2006, 13(2): 120-130.

    [60] FRSTER A, BRANDSTETTER S, SCHULZE-BRIESE C. Transforming X-ray detection with hybrid photon counting detectors[J]. Philos Trans A Math Phys Eng Sci, 2019, 377(2147): 20180241.

    [61] BOYSEN H, ADLHART W. Resolution corrections in diffuse scattering experiments[J]. J Appl Cryst, 1987, 20(3): 200-209.

    [62] ESTERMAN M A, SCHEIDEGGER S, REIFLER H, et al. A helium beam path for an imaging-plate detector system[J]. J Appl Cryst, 1997, 30(6): 1165-1166.

    [63] BOSAK A, CHERNYSHOV D, VAKHRUSHEV S, et al. Diffuse scattering in relaxor ferroelectrics: true three-dimensional mapping, experimental artefacts and modelling[J]. Acta Cryst A, 2012, 68(1): 117-123.

    [64] AEBISCHER A, HOSTETTLER M, HAUSER J, et al. Structural and spectroscopic characterization of active sites in a family of light-emitting sodium lanthanide tetrafluorides[J]. Angew Chem Int Ed Eng, 2006, 45(17): 2802-2806.

    [65] DYADKIN V, PATTISON P, DMITRIEV V, et al. A new multipurpose diffractometer PILATUS@SNBL[J]. J Synchrotron Radiat, 2016, 23(3): 825-829.

    [66] MIHAILOVA B, ANGEL R J, Welsch A-M, et al. Pressure-induced phase transition in PbSc0.5Ta0.5O3 as a model Pb-based perovksite-type relaxor ferroelectric[J]. Phys Rev Lett, 2008, 101(1): 17602.

    [67] MALIBERT C, DKHIL B, KIAT J M, et al. Order and disorder in the relaxor ferroelectric perovskite (PSN): Comparison with simple perovskites and[J]. J Phys Condens Matter, 1997, 9(35): 7485-7500.

    [68] TAKESUE N, FUJII Y, ICHIHARA M, et al. Self-accommodation of ionic size-effect atomic displacements in antiferroelectric order in relaxor lead scandium Niobate[J]. Phys Rev Lett, 1999, 82(18): 3709-3712.

    [69] MAIER B, MIHAILOVA B, PAULMANN C, et al. Effect of local elastic strain on the structure of Pb-based relaxors: A comparative study of pure and Ba- and Bi-doped PbSc0.5Nb0.5O3[J]. Phys Rev B, 2009, 79(22): 224108.

    [70] CHAABANE B, KREISEL J, DKHIL B, et al. Pressure-induced suppression of the diffuse scattering in the model relaxor ferroelectric PbMg(1/3)Nb(2/3)O3[J]. Phys Rev Lett, 2003, 90(25): 257601.

    [71] XU G, ZHONG Z, BING Y, et al. Electric-field-induced redistribution of polar nano-regions in a relaxor ferroelectric[J]. Nat Mater, 2006, 5(2): 134-140.

    [72] STOCK C, XU G, GEHRING P M, et al. Neutron and X-ray diffraction study of cubic[111]field-cooled Pb(Mg13Nb23)O3[J]. Ferroelectrics, 2007, 76(6): 064122.

    [73] YOU H, ZHANG Q M. Diffuse X-ray scattering study of lead magnesium niobate single crystals[J]. Phys Rev Lett, 1997, 79(20): 3950-3953.

    [74] XU G, SHIRANE G, COPLEY J R D, et al. Neutron elastic diffuse scattering study of Pb(Mg1/3Nb2/3)O3[J]. Phys Rev B, 2004, 69(6): 64112.

    [76] WELBERRY T R, GUTMANN M J, WOO H, et al. Single-crystal neutron diffuse scattering and Monte Carlo study of the relaxor ferroelectric PbZn1/3Nb2/3O3(PZN)[J]. J Appl Cryst, 2005, 38(4): 639-647.

    [77] HLINKA J, KAMBA S, PETZELT J, et al. Diffuse scattering in Pb(Zm1/3Nb2/3)O3 with 8 PbTiO3 by quasi-elastic neutron scattering[J]. J Phys Condens Matter, 2003, 15(24): 4249-4257.

    [78] XU G, ZHONG Z, BING Y, et al. Ground state of the relaxor ferroelectric Pb(Zn1/3Nb2/3)O3[J]. Phys Rev B, 2003, 67(10): 104102.

    [79] XU G, ZHONG Z, HIRAKA H, et al. Three-dimensional mapping of diffuse scattering in Pb(Zn1/3Nb2/3)O3-xPbTiO3[J]. Phys Rev B, 2004, 70(14): 144410.

    [80] ZHANG N, PASCIAK M, GLAZER A M, et al. A neutron diffuse scattering study of PbZrO3 and Zr-rich PbZr1-xTixO3[J]. J Appl Cryst, 2015, 48: 1637-1644.

    [82] AN Z, YOKOTA H, ZHANG N, et al. Multiple structural components and their competition in the intermediate state of antiferroelectric Pb(Zr,Ti)O3[J]. Phys Rev B, 2021, 103(5): 054113.

    [83] VAKHRUSHEV S B, ANDRONIKOVA D, BRONWALD I, et al. Electric field control of antiferroelectric domain pattern[J]. Phys Rev B, 2021, 103(21): 214108.

    [84] WELBERRY T R. Multi-site correlations and the atomic size effect[J]. J Appl Cryst, 1986, 19(5): 382-389.

    [85] K. HUANG. X-Ray Reflexions from Dilute Solid Solutions[J]. Proc R Soc Lond A Math Phys Sci, 1947, 190(1020): 102-117.

    [86] BURKOVSKY R G, BRONWALD Y A, FILIMONOV A V, et al. Structural heterogeneity and diffuse scattering in morphotropic lead zirconate-titanate single crystals[J]. Phys Rev Lett, 2012, 109(9): 97603.

    [87] PROFFEN T, NEDER R B. DISCUS: A program for diffuse scattering and defect-structure simulation[J]. J Appl Cryst, 1997, 30(2): 171-175.

    [88] PADDISON J AM. Ultrafast calculation of diffuse scattering from atomistic models [J]. Acta Cryst A, 2019, 75(1): 14-24.

    [89] SIMONOV A, WEBER T, STEURER W. Yell: a computer program for diffuse scattering analysis via three-dimensional delta pair distribution function refinement[J]. J Appl Cryst, 2014, 47(3): 1146-1152.

    [90] METROPOLIS N, ROSENBLUTH A W, ROSENBLUTH M N, et al. Equation of state calculations by fast computing machines[J]. J Chem Phys, 1953, 21(6): 1087-1092.

    [91] WELBERRY T R, GOOSSENS D J. The interpretation and analysis of diffuse scattering using Monte Carlo simulation methods[J]. Acta Cryst A, 2008, 64(1): 23-32.

    [92] MCGREEVY R L, PUSZTAI L. Reverse Monte Carlo simulation: a new technique for the determination of disordered structures[J]. Mol Simul, 1988, 1(6): 359-367.

    [93] WELBERRY T R, PROFFEN T. Analysis of diffuse scattering from single crystals via the reverse Monte Carlo Technique. I. Comparison with direct Monte Carlo[J]. J Appl Cryst, 1998, 31(3): 309-317.

    [94] PROFFEN T, WELBERRY T R. Analysis of diffuse scattering from single crystals via the reverse Monte Carlo technique. II. The Defect Structure of Calcium-Stabilized Zirconia[J]. J Appl Cryst, 1998, 31(3): 318-326.

    [96] GANESH P, COCKAYNE E, AHART M, et al. Origin of diffuse scattering in relaxor ferroelectrics[J]. Phys Rev B, 2010, 81(14): 144102.

    [97] FRIEDRICH W, KNIPPING P, LAUE M. Interferenzerscheinungen bei Rntgenstrahlen[J]. Ann Phys, 1913, 346(10): 971-988.

    [98] FRIEDRICH W. Eine neue Interferenzerscheinung bei Rntgenstrahlen[J]. Phys Z, 1913, 14: 317-319.

    [99] DEBYE P. Zerstreuung von Rntgenstrahlen[J]. Ann Phys, 1915, 351(6): 809-823.

    [100] BASAK S, CLARKE R, NAGEL S R. Pair distribution function and its relation to the glass transition in an amorphous alloy[J]. Phys Rev B, 1979, 20(8): 3388-3390.

    [102] FARROW C L, JUHAS P, LIU J W, et al. PDFfit2 and PDFgui: computer programs for studying nanostructure in crystals[J]. J Phys Condens Matter, 2007, 19(33): 335219.

    [103] KEEN D A. A comparison of various commonly used correlation functions for describing total scattering[J]. J Appl Cryst, 2001, 34(2): 172-177.

    [105] KEEN D A. Total scattering and the pair distribution function in crystallography[J]. Crystallogr Rev, 2020, 26(3): 143-201.

    [106] FISCHER H E, CUELLO G J, PALLEAU P, et al. D4c: A very high precision diffractometer for disordered materials[J]. Appl Phys A, 2002, 74(0): s160-s162.

    [107] DAY P, ENDERBY J, WILLIAMS W, et al. Scientific Reviews: GEM: The general materials diffractometer at ISIS-multibank capabilities for studying crystalline and disordered materials[J]. Neutron News, 2004, 15(1): 19-23.

    [108] HANNON A C. Results on disordered materials from the GEneral materials diffractometer, GEM, at ISIS[J]. Nucl Instrum Methods Phys Res B, 2005, 551(1): 88-107.

    [109] SMITH R I, HULL S, TUCKER M G, et al. The upgraded Polaris powder diffractometer at the ISIS neutron source[J]. Rev Sci Instrum, 2019, 90(11): 115101.

    [110] Diamond Light Source. XPDF (I15-1). [OL]. [2021-08-28]. https://www.diamond.ac.uk/Instruments/Crystallography/I15-1.html.

    [111] Advanced Photon Source. 11-ID-B.[OL]. [2021-08-28]. https://www. aps.anl.gov/Beamlines/Directory/Details?beamline_id=16.

    [112] HOU D, ZHAO C, PATERSON A R, et al. Local structures of perovskite dielectrics and ferroelectrics via pair distribution function analyses[J]. J Eur Ceram Soc, 2018, 38(4): 971-987.

    [113] SOPER A K. GudrunN and GudrunX: programs for correcting raw neutron and X-ray diffraction data to differential scattering cross section[M]. Science and Technology Facilities Council, 2011.

    [114] JUHáS P, DAVIS T, FARROW C L, et al. PDFgetX3: A rapid and highly automatable program for processing powder diffraction data into total scattering pair distribution functions[J]. J Appl Cryst, 2013, 46(2): 560-566.

    [115] JUHáS P, LOUWEN J N, VAN EIJCK L, et al. PDFgetN3: Atomic pair distribution functions from neutron powder diffraction data using ad hoc corrections[J]. J Appl Cryst, 2018, 51(5): 1492-1497.

    [116] DOVE M T, TUCKER M G, KEEN D A. Neutron total scattering method: simultaneous determination of long-range and short-range order in disordered materials[J]. Eur J Mineral, 2002, 14(2): 331-348.

    [117] EREMENKO M, KRAYZMAN V, GAGIN A, et al. Advancing reverse Monte Carlo structure refinements to the nanoscale[J]. J Appl Cryst, 2017, 50(6): 1561-1570.

    [118] EREMENKO M, KRAYZMAN V, BOSAK A, et al. Local atomic order and hierarchical polar nanoregions in a classical relaxor ferroelectric[J]. Nat Commun, 2019, 10(1): 2728.

    [119] ZHANG Y, EREMENKO M, KRAYZMAN V, et al. New capabilities for enhancement of RMCProfile: Instrumental profiles with arbitrary peak shapes for structural refinements using the reverse Monte Carlo method[J]. J Appl Cryst, 2020, 53(6): 1509-1518.

    [120] HARADA J, AXE J D, SHIRANE G. Neutron-scattering study of soft modes in cubic BaTiO3[J]. Phys Rev B, 1971, 4(1): 155-162.

    [121] COMèS R, LAMBERT M, GUINIER A. The chain structure of BaTiO3 and KNbO3[J]. Solid State Commun, 1968, 6(10): 715-719.

    [122] BUSSMANN-HOLDER A, BEIGE H, VLKEL G. Precursor effects, broken local symmetry, and coexistence of order-disorder and displacive dynamics in perovskite ferroelectrics[J]. Phys Rev B, 2009, 79(18): 184111.

    [123] STERN E A. Character of order-disorder and displacive components in barium titanate[J]. Phys Rev Lett, 2004, 93(3): 37601.

    [124] ZALAR B, LAGUTA V V, BLINC R. NMR evidence for the coexistence of order-disorder and displacive components in barium titanate[J]. Phys Rev Lett, 2003, 90(3): 37601.

    [125] SENN M S, KEEN D A, LUCAS T C A, et al. Emergence of long-range order in BaTiO3 from local symmetry-breaking distortions[J]. Phys Rev Lett, 2016, 116(20): 207602.

    [126] JIANG L, MITCHELL D C, DMOWSKI W, et al. Local structure of NaNbO3: A neutron scattering study[J]. Phys Rev B, 2013, 88(1): 14105.

    [127] JAFFE B, ROTH R S, MARZULLO S. Piezoelectric properties of lead zirconate-lead titanate solid-solution ceramics[J]. J Appl Phys, 1954, 25(6): 809-810.

    [128] JAFFE B, COOK W R, JAFFE H. Piezoelectric Ceramics[M]. Academic Press: New York, 1971.

    [130] TESLIC S, EGAMI T, VIEHLAND D. Local atomic structure of PZT and PLZT studied by pulsed neutron scattering[J]. J Phys Chem Solids, 1996, 57(10): 1537-1543.

    [131] TESLIC S, EGAMI T, VIEHLAND D. Structural instabilities in PZT[J]. Ferroelectrics, 1997, 194(1): 271-285.

    [132] DMOWSKI W, EGAMI T, FARBER L, et al. Structure of Pb(Zr, Ti)O3 near the morphotropic phase boundary[J]. AIP Conf Proc, 2001, 582: 33-44.

    [133] GRINBERG I, COOPER V, RAPPE A. Oxide chemistry and local structure of PbZrxTi1-xO3 studied by density-functional theory supercell calculations[J]. Phys Rev B, 2004, 69(14): 144118.

    [134] ZHANG N, YOKOTA H, GLAZER A M, et al. Local-scale structures across the morphotropic phase boundary in PbZr1-xTixO3[J]. IUCrJ, 2018, 5(1): 73-81.

    [135] VAKHRUSHEV S, ANDRONIKOVA D A, CHERNYSHOV D Y, et al. X-ray scattering by antiphase ferroelectric domain walls in the antiferroelectric phase of the PbZr0.985Ti0.015O3 [C]// Internet of things, smart spaces, and next generation networks and systems: 18th International Conference, NEW2AN 2018, and 11th Conference, ruSMART 2018, St. Petersburg, Russia, 2018: 683-690.

    [136] KO J H, GóRNY M, MAJCHROWSKI A, et al. Mode softening, precursor phenomena, and intermediate phases in PbZrO3[J]. Phys Rev B, 2013, 87(18): 184110.

    [137] TESLIC S, EGAMI T. Atomic structure of PbZrO3 determined by pulsed neutron diffraction[J]. Acta Cryst B, 1998, 54(6): 750-765.

    [138] FUJISHITA H, HOSHINO S. A study of structural phase transitions in antiferroelectric PbZrO3 by neutron diffraction[J]. J Phys Soc Jpn, 1984, 53(1): 226-234.

    [139] ANDRONIKOVA D A, BRONWALD I A, LEONTYEV N G, et al. Structural peculiarities of the intermediate phase in Zr-rich lead zirconate titanate[J]. Phys Solid State, 2019, 61(10): 1772-1778.

    [140] BURKOVSKY R G, BRONWALD I, ANDRONIKOVA D, et al. Critical scattering and incommensurate phase transition in antiferroelectric PbZrO3 under pressure[J]. Sci Rep, 2017, 7: 41512.

    [141] VAKHRUSHEV S B, KVYATKOVSKY B E, NABEREZHNOV A A, et al. Glassy phenomena in disordered perovskite-like crystals[J]. Ferroelectrics, 1989, 90(1): 173-176.

    [142] HIROTA K, YE Z-G, WAKIMOTO S, et al. Neutron diffuse scattering from polar nanoregions in the relaxor Pb(Mg1/3Nb2/3)O3[J]. Phys Rev B, 2002, 65(10): 104105.

    [143] VAKHRUSHEV S B, NABEREZHNOV A A, OKUNEVA N M, et al. Determination of polarization vectors in lead magnoniobate[J]. Phys Solid State, 1995, 37(12): 1993-1997.

    [144] ZHAO J, GLAZOUNOV A E, ZHANG Q M, et al. Neutron diffraction study of electrostrictive coefficients of prototype cubic phase of relaxor ferroelectric PbMg1/3Nb2/3O3[J]. Appl Phys Lett, 1998, 72(9): 1048-1050.

    [145] BONNEAU P, GARNIER P, CALVARIN G, et al. X-ray and neutron diffraction studies of the diffuse phase transition in ceramics[J]. J Solid State Chem, 1991, 91(2): 350-361.

    [146] NABEREZHNOV A, VAKHRUSHEV S, DORNER B, et al. Inelastic neutron scattering study of the relaxor ferroelectric PbMg1/3Nb2/3O3 at high temperatures[J]. Eur Phys J B, 1999, 11(1): 13-20.

    [147] JEONG I K, DARLING T W, LEE J K, et al. Direct observation of the formation of polar nanoregions in Pb(Mg1/3Nb2/3)O3 using neutron pair distribution function analysis[J]. Phys Rev Lett, 2005, 94(14): 147602.

    [148] DMOWSKI W, VAKHRUSHEV S B, JEONG I-K, et al. Local lattice dynamics and the origin of the relaxor ferroelectric behavior[J]. Phys Rev Lett, 2008, 100(13): 137602.

    [149] WELBERRY T R, GOOSSENS D J, GUTMANN M J. Chemical origin of nanoscale polar domains in PbZn13Nb23O3[J]. Ferroelectrics, 2006, 74(22): 241.

    [150] XU G, GEHRING P M, SHIRANE G. Coexistence and competition of local- and long-range polar orders in a ferroelectric relaxor[J]. Phys Rev B, 2006, 74(10): 104110.

    [151] HLINKA J. Do we need the ether of polar nanoregions?[J]. J Adv Dielect, 2012, 02(02): 1241006.

    [152] COWLEY R A, GVASALIYA S N, LUSHNIKOV S G, et al. Relaxing with relaxors: A review of relaxor ferroelectrics[J]. Adv Phys, 2011, 60: 229-327.

    [153] GEHRING, PARK, SHIRANE. Soft phonon anomalies in the relaxor ferroelectric Pb(Zn1/3Nb2/3)0.92Ti0.08O3[J]. Phys Rev Lett, 2000, 84(22): 5216-5219.

    [154] GEHRING P M. Soft mode anomalies in the perovskite relaxor Pb(Mg1/3Nb2/3)O3 [J]. AIP Conf Proc, 2000: 314-322.

    [155] WAKIMOTO S, STOCK C, YE Z G, et al. Mode coupling and polar nanoregions in the relaxor ferroelectric Pb(Mg1/3Nb2/3)O3[J]. Phys Rev B, 2002, 66(22): 224102.

    [156] GEHRING P M, PARK S E, SHIRANE G. Dynamical effects of the nanometer-sized polarized domains in Pb(Zn1/3Nb2/3)O3[J]. Phys Rev B, 2001, 63(22): 224109.

    [157] TOMENO I, SHIMANUKI S, TSUNODA Y, et al. Lattice dynamics of disordered perovskite Pb(Zn1/3Nb2/3)O3[J]. J Phys Soc Jpn, 2001, 70(6): 1444-1447.

    [159] KOO T Y, GEHRING P M, SHIRANE G, et al. Anomalous transverse acoustic phonon broadening in the relaxor ferroelectric Pb(Mg1/3Nb2/3)0.8Ti0.2O3[J]. Phys Rev B, 2002, 65(14): 144113.

    [160] GEHRING P M, WAKIMOTO S, YE Z G, et al. Soft mode dynamics above and below the Burns temperature in the relaxor Pb(Mg1/3Nb2/3)O3[J]. Phys Rev Lett, 2001, 87(27): 277601.

    [161] HLINKA J, KAMBA S, PETZELT J, et al. Origin of the “Waterfall” effect in phonon dispersion of relaxor perovskites[J]. Phys Rev Lett, 2003, 91(10): 107602.

    [162] STOCK C, GEHRING P M, EWINGS R A, et al. Spontaneous decay of a soft optical phonon in the relaxor ferroelectric PbMg1/3Nb2/3O3[J]. Phys Rev Mater, 2018, 2(2): 830.

    [163] MANLEY M E, LYNN J W, ABERNATHY D L, et al. Phonon localization drives polar nanoregions in a relaxor ferroelectric[J]. Nat Commun, 2014, 5: 3683.

    [164] GEHRING P M, PARSHALL D, HARRIGER L, et al. Correspondence: Phantom phonon localization in relaxors[J]. Nat Commun, 2017, 8(1): 1935.

    [165] KROGSTAD M J, GEHRING P M, ROSENKRANZ S, et al. The relation of local order to material properties in relaxor ferroelectrics[J]. Nat Mater, 2018, 17: 718-724.

    [166] XU G, WEN J, STOCK C, et al. Phase instability induced by polar nanoregions in a relaxor ferroelectric system[J]. Nat Mater, 2008, 7(7): 562-566.

    [167] XU Z, WEN J, XU G, et al. Two-component model of the neutron diffuse scattering in the relaxor ferroelectric PZN-4.5%PT[J]. Phys Rev B, 2010, 82(13): 134124.

    [168] AKSEL E, FORRESTER J S, JONES J L, et al. Monoclinic crystal structure of polycrystalline Na0.5Bi0.5TiO3[J]. Appl Phys Lett, 2011, 98(15): 152901.

    [169] GORFMAN S, THOMAS P A. Evidence for a non-rhombohedral average structure in the lead-free piezoelectric material Na0.5Bi0.5TiO3[J]. J Appl Cryst, 2010, 43(6): 1409-1414.

    [170] KREISEL J, BOUVIER P, DKHIL B, et al. High-pressure x-ray scattering of oxides with a nanoscale local structure: Application to Na1/2Bi1/2TiO3[J]. Phys Rev B, 2003, 68(1): 14113.

    [171] GORFMAN S, KEEBLE D S, BOMBARDI A, et al. Topology and temperature dependence of the diffuse X-ray scattering in Na0.5Bi0.5TiO3 ferroelectric single crystals[J]. J Appl Cryst, 2015, 48(2002): 1543-1550.

    [172] DANIELS J E, JO W, RDEL J, et al. Structural origins of relaxor behavior in a 0.96(Bi1/2Na1/2)TiO3-0.04BaTiO3 single crystal under electric field[J]. Appl Phys Lett, 2011, 98(25): 252904.

    [173] GE W, LUO C, DEVREUGD C P, et al. Direct evidence of correlations between relaxor behavior and polar nano-regions in relaxor ferroelectrics: A case study of lead-free piezoelectrics Na0.5Bi0.5TiO3-x%BaTiO3[J]. Appl Phys Lett, 2013, 103(24): 241914.

    [175] KEEBLE D S, BARNEY E R, KEEN D A, et al. Bifurcated polarization rotation in bismuth-based piezoelectrics[J]. Adv Funct Mater, 2013, 23(2): 185-190.

    [176] DATTA K, NEDER R B, RICHTER A, et al. Adaptive strain prompting a pseudo-morphotropic phase boundary in ferroelectric (1-x)Na0.5Bi0.5TiO3-xBaTiO3[J]. Phys Rev B, 2018, 97(18): 184101.

    [177] USHER T-M, LEVIN I, DANIELS J E, et al. Electric-field-induced local and mesoscale structural changes in polycrystalline dielectrics and ferroelectrics[J]. Sci Rep, 2015, 5: 14678.

    [178] INGHAM B. X-ray scattering characterisation of nanoparticles[J]. Crystallogr Rev, 2015, 21(4): 229-303.

    [179] CHRISTIANSEN T L, COOPER S R, JENSEN K M O. There’s no place like real-space: Elucidating size-dependent atomic structure of nanomaterials using pair distribution function analysis[J]. Nanoscale Adv, 2020, 2(6): 2234-2254.

    [180] KORSUNSKIY V I, NEDER R B. Exact model calculations of the total radial distribution functions for the X-ray diffraction case and systems of complicated chemical composition[J]. J Appl Cryst, 2005, 38(6): 1020-1027.

    [181] I KORSUNSKIY V, NEDER R B, HOFMANN A, et al. Aspects of the modelling of the radial distribution function for small nanoparticles[J]. J Appl Cryst, 2007, 40(6): 975-985.

    [182] PAGE K, HOOD T C, PROFFEN T, et al. Building and refining complete nanoparticle structures with total scattering data[J]. J Appl Cryst, 2011, 44(2): 327-336.

    [183] NEDER R B, PROFFEN T. Diffuse scattering and defect structure simulations: A cook book using the program DISCUS[M]. Oxford: Oxford University Press, 2008.

    [184] MURTY M V R, STREIFFER S K, STEPHENSON G B, et al. In situ X-ray scattering study of PbTiO3 chemical-vapor deposition[J]. Appl Phys Lett, 2002, 80(10): 1809-1811.

    [185] DIPPEL A-C, ROELSGAARD M, BOETTGER U, et al. Local atomic structure of thin and ultrathin films via rapid high-energy X-ray total scattering at grazing incidence[J]. IUCrJ, 2019, 6(2): 290-298.

    [186] HIGHLAND M J, FISTER T T, RICHARD M I, et al. Polarization switching without domain formation at the intrinsic coercive field in ultrathin ferroelectric PbTiO3[J]. Phys Rev Lett, 2010, 105(16): 167601.

    [187] JUNQUERA J, GHOSEZ P. Critical thickness for ferroelectricity in perovskite ultrathin films[J]. Nature, 2003, 422(6931): 506-509.

    [188] JIANG B, PENG J L, BURSILL L A, et al. Size effects on ferroelectricity of ultrafine particles of PbTiO3[J]. J Appl Phys, 2000, 87(7): 3462-3467.

    [189] FONG D D, STEPHENSON G B, STREIFFER S K, et al. Ferroelectricity in ultrathin perovskite films[J]. Science, 2004, 304(5677): 1650-1653.

    [190] PAGE K, PROFFEN T, NIEDERBERGER M, et al. Probing local dipoles and ligand structure in BaTiO3 nanoparticles[J]. Chem Mater, 2010, 22(15): 4386-4391.

    [191] RABUFFETTI F A, BRUTCHEY R L. Structural evolution of BaTiO3 nanocrystals synthesized at room temperature[J]. J Am Chem Soc, 2012, 134(22): 9475-9487.

    [192] HAO Y, FENG Z, BANERJEE S, et al. Ferroelectric state and polarization switching behaviour of ultrafine BaTiO3 nanoparticles with large-scale size uniformity[J]. J Mater Chem C, 2021, 9(15): 5267-5276.

    [193] RABUFFETTI F A, BRUTCHEY R L. Local structure of Ba1-xSrxTiO3 and BaTi1-yZryO3 nanocrystals probed by X-ray absorption and X-ray total scattering[J]. ACS Nano, 2013, 7(12): 11435-11444.

    [194] WHITFIELD R E, GOOSSENS D J, WELBERRY T R. Total scattering and pair distribution function analysis in modelling disorder in PZN (PbZn1/3Nb2/3O3)[J]. IUCrJ, 2016, 3: 20-31.

    [195] WEBER T, SIMONOV A. The three-dimensional pair distribution function analysis of disordered single crystals: basic concepts[J]. Z Krist, 2012, 227(5): 238-247.

    [196] SIMONOV A, BAERDEMAEKER T de, BOSTRM H L B, et al. Hidden diversity of vacancy networks in Prussian blue analogues[J]. Nature, 2020, 578(7794): 256-260.

    AN Zheyi, ZHANG Nan. Scattering Techniques and Local Structures of Ferroelectric Perovskites[J]. Journal of the Chinese Ceramic Society, 2022, 50(3): 661
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