Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-27T01:30:24.310Z Has data issue: false hasContentIssue false
  • English
  • Français

In situ characterization of polycrystalline ferroelectrics using x-ray and neutron diffraction

Published online by Cambridge University Press:  03 November 2014

Giovanni Esteves ,
Chris M. Fancher  and
Jacob L. Jones
Giovanni Esteves
Affiliation:
Department of Materials Science and Engineering, North Carolina State University, Raleigh, North Carolina 27695, USA
Chris M. Fancher
Affiliation:
Department of Materials Science and Engineering, North Carolina State University, Raleigh, North Carolina 27695, USA
Jacob L. Jones*
Affiliation:
Department of Materials Science and Engineering, North Carolina State University, Raleigh, North Carolina 27695, USA
*
a)Address all correspondence to this author. e-mail: [email protected]
Get access

Abstract

X-ray and neutron diffraction are particularly useful for characterizing ferroelectric materials in situ, e.g., during application of temperature, pressure, electric field, and stress. In this review, we introduce many experimental approaches for such measurements and highlight important discoveries in ferroelectrics that utilized diffraction. We focus our examples on polycrystalline ferroelectrics, though many of the approaches and analysis methods can also be applied to thin films and single crystals. Methods discussed for characterization of structure include, phase identification, line profile analysis, whole pattern fitting, pair distribution functions, and the x-ray diffraction based three-dimensional microscopy. Further advancement of these and other techniques offers potential for continued important contributions to the fundamental understanding of ferroelectric materials.

Type
Review
Information
Journal of Materials Research , Volume 30 , Issue 3: Focus Issue: In-situ and Operando Characterization of Materials , 14 February 2015 , pp. 340 - 356
Copyright
Copyright © Materials Research Society 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Yashima, M.: In situ observations of phase transition using high-temperature neutron and synchrotron x-ray powder diffractometry. J. Am. Ceram. Soc. 85, 2925 (2004).CrossRefGoogle Scholar
Eckold, G., Schober, H., and Nagler, S.: Studying Kinetics with Neutrons: Prospects for Time-Resolved Neutron Scattering (Springer, New York, NY, 2009).Google Scholar
Nye, J.F.: Physical Properties of Crystals: Their Representation by Tensors and Matrices (Oxford, UK, Clarendon, 1985).Google Scholar
Cohen, R.E.: Origin of ferroelectricity in perovskite oxides. Nature 358, 136 (1992).CrossRefGoogle Scholar
Fang, D., Li, F., Liu, B., Zhang, Y., Hong, J., and Guo, X.: Advances in developing electromechanically coupled computational methods for piezoelectrics/ferroelectrics at multiscale. Appl. Mech. Rev. 65, 060802 (2013).CrossRefGoogle Scholar
Ambika, D.: Deposition of PZT thin films with (001), (110), and (111) crystallographic orientations and their transverse piezoelectric characteristics. Adv. Mater. Lett. 3, 102 (2012).Google Scholar
Goldschmidt, V.M.: Crystal structure and chemical constitution. Trans. Faraday Soc. 25, 253 (1929).CrossRefGoogle Scholar
Jaffe, B.: Piezoelectric properties of lead zirconate-lead titanate solid-solution ceramics. J. Appl. Phys. 25, 809 (1954).CrossRefGoogle Scholar
Jaffe, B. and Cook, W.R.: Piezoelectric Ceramics (Academic Press Limited, New York, NY, 1971).Google Scholar
Keeble, D.S., Barney, E.R., Keen, D.A., Tucker, M.G., Kreisel, J., and Thomas, P.A.: Bifurcated polarization rotation in bismuth-based piezoelectrics. Adv. Funct. Mater. 23, 185 (2013).Google Scholar
Wang, Y.: Diffraction theory of nanotwin superlattices with low symmetry phase: Application to rhombohedral nanotwins and monoclinic MA and MB phases. Phys. Rev. B 76, 024108 (2007).CrossRefGoogle Scholar
Schönau, K.A., Schmitt, L.A., Knapp, M., Fuess, H., Eichel, R-A., Kungl, H., and Hoffmann, M.J.: Nanodomain structure of Pb[Zr1−xTix]O3 at its morphotropic phase boundary: Investigations from local to average structure. Phys. Rev. B 75, 184117 (2007).Google Scholar
Aksel, E., Forrester, J.S., Nino, J.C., Page, K., Shoemaker, D.P., and Jones, J.L.: Local atomic structure deviation from average structure of Na0.5Bi0.5TiO3: Combined x-ray and neutron total scattering study. Phys. Rev. B 87, 104113 (2013).Google Scholar
Levin, I. and Reaney, I.M.: Nano- and mesoscale structure of Na1/2Bi1/2TiO3: A TEM perspective. Adv. Funct. Mater. 22, 3445 (2012).CrossRefGoogle Scholar
Dinnebier, R. and Billinge, S.: Powder Diffraction: Theory and Practice (Royal Society of Chemistry, Cambridge, UK, 2008).Google Scholar
Kocks, U.F., Tomé, C.N., and Wenk, H-R.: Texture and Anisotropy Preferred Orientations in Polycrystals and Their Effect on Materials Properties (Cambridge University Press, New York, NY, 1998), p. 676.Google Scholar
Noheda, B., Cox, D., Shirane, G., Gao, J., and Ye, Z-G.: Phase diagram of the ferroelectric relaxor (1-x)PbMg1/3Nb2/3O3-xPbTiO3. Phys. Rev. B 66, 054104 (2002).CrossRefGoogle Scholar
Chateigner, D., Wenk, H-R., Patel, A., Todd, M., and Barber, D.J.: Analysis of preferred orientations in PST and PZT thin films on various substrates. Integr. Ferroelectr. 19, 121 (1998).CrossRefGoogle Scholar
Rossetti, G.A., Cross, L.E., and Cline, J.P.: Structural aspects of the ferroelectric phase transition in lanthanum-substituted lead titanate. J. Mater. Sci. 30, 24 (1995).CrossRefGoogle Scholar
Bing, Y-H., Bokov, A.A., Ye, Z-G., Noheda, B., and Shirane, G.: Structural phase transition and dielectric relaxation in Pb(Zn1/3Nb2/3)O3 single crystals. J. Phys. Condens. Matter 17, 2493 (2005).CrossRefGoogle Scholar
Chattopadhyay, S., Ayyub, P., Palkar, V., and Multani, M.: Size-induced diffuse phase transition in the nanocrystalline ferroelectric PbTiO3. Phys. Rev. B 52, 13177 (1995).CrossRefGoogle ScholarPubMed
Uchino, K., Sadanaga, E., and Hirose, T.: Dependence of the crystal structure on particle size in barium titanate. J. Am. Ceram. Soc. 72, 1555 (1989).Google Scholar
Johnson-Wilke, R.L., Tinberg, D.S., Yeager, C., Qu, W., Fong, D.D., Fister, T.T., Streiffer, S.K., Han, Y., Reaney, I.M., and Trolier-McKinstry, S.: Coherently strained epitaxial Pb(Zr1−xTix)O3 thin films. J. Appl. Phys. 114, 164104 (2013).Google Scholar
Zhong, W.L., Jiang, B., Zhang, P.L., Ma, J.M., Cheng, H.M., and Yang, Z.H.: Phase transition in PbTiO3 ultrafine particles of different sizes. J. Phys. Condens. Matter 5, 2619 (1993).Google Scholar
Zhou, Z., Obi, O., Nan, T.X., Beguhn, S., Lou, J., Yang, X., Gao, Y., Li, M., Rand, S., Lin, H., Sun, N.X., Esteves, G., Nittala, K., Jones, J.L., Mahalingam, K., Liu, M., and Brown, G.J.: Low-temperature spin spray deposited ferrite/piezoelectric thin film magnetoelectric heterostructures with strong magnetoelectric coupling. J. Mater. Sci. Mater. Electron. 25, 1188 (2014).CrossRefGoogle Scholar
Daniels, J.E., Jones, J.L., and Finlayson, T.R.: Characterization of domain structures from diffraction profiles in tetragonal ferroelastic ceramics. J. Phys. D. Appl. Phys. 39, 5294 (2006).CrossRefGoogle Scholar
Cullity, B.D. and Stock, S.R.: Elements of X-ray Diffraction 3rd ed. (Prentice Hall, Upper Saddle River, NJ, 2001).Google Scholar
Ueda, R. and Shirane, G.: X-ray study on phase transition of lead zirconate, PbZrO3. J. Phys. Soc. Jpn. 6, 209 (1951).CrossRefGoogle Scholar
Noheda, B., Cox, D.E., Shirane, G., Gonzalo, J.A., Cross, L.E., and Park, S-E.: A monoclinic ferroelectric phase in the Pb(Zr1−xTix)O3 solid solution. Appl. Phys. Lett. 74, 2059 (1999).Google Scholar
Noheda, B., Gonzalo, J., Cross, L., Guo, R., Park, S-E., Cox, D., and Shirane, G.: Tetragonal-to-monoclinic phase transition in a ferroelectric perovskite: The structure of PbZr0.52Ti0.48O3. Phys. Rev. B 61, 8687 (2000).Google Scholar
Zhang, N., Yokota, H., Glazer, A.M., and Thomas, P.A.: Neutron powder diffraction refinement of PbZr(1-x)Ti(x)O3. Acta Crystallogr. B. 67, 386 (2011).Google Scholar
Woodward, D., Knudsen, J., and Reaney, I.: Review of crystal and domain structures in the PbZrxTi1−xO3 solid solution. Phys. Rev. B 72, 104110 (2005).Google Scholar
Noheda, B. and Cox, D.E.: Bridging phases at the morphotropic boundaries of lead oxide solid solutions. Phase Transitions 79, 5 (2006).Google Scholar
Gorfman, S., Keeble, D.S., Glazer, A.M., Long, X., Xie, Y., Ye, Z-G., Collins, S., and Thomas, P.A.: High-resolution x-ray diffraction study of single crystals of lead zirconate titanate. Phys. Rev. B 84, 020102 (2011).Google Scholar
Katrusiak, A.: High-pressure crystallography. Acta Crystallogr. A 64, 135 (2008).Google Scholar
Piermarini, G.: High pressure x-ray crystallography with the diamond cell at NIST/NBS. J. Res. Natl. Inst. Stand. Technol. 106, 889 (2011).Google Scholar
Pecharsky, V. and Zavalij, P.: Fundamentals of Powder Diffraction and Structural Characterization of Materials (Springer, Boston, MA, 2009).Google Scholar
Anzellini, S., Dewaele, A., Mezouar, M., Loubeyre, P., and Morard, G.: Melting of iron at earth’s inner core boundary based on fast x-ray diffraction. Science 340, 464 (2013).CrossRefGoogle ScholarPubMed
Ahart, M., Cohen, R., Struzhkin, V., Gregoryanz, E., Rytz, D., Prosandeev, S., Mao, H., and Hemley, R.: High-pressure Raman scattering and x-ray diffraction of the relaxor ferroelectric 0.96Pb(Zn1∕3Nb2∕3)O3-0.04PbTiO3. Phys. Rev. B 71, 144102 (2005).Google Scholar
Ahart, M., Somayazulu, M., Cohen, R.E., Ganesh, P., Dera, P., Mao, H., Hemley, R.J., Ren, Y., Liermann, P., and Wu, Z.: Origin of morphotropic phase boundaries in ferroelectrics. Nature 451, 545 (2008).Google Scholar
Saito, Y., Takao, H., Tani, T., Nonoyama, T., Takatori, K., Homma, T., Nagaya, T., and Nakamura, M.: Lead-free piezoceramics. Nature 432, 84 (2004).Google Scholar
Daniels, J.E., Jo, W., Rödel, J., Honkimäki, V., and Jones, J.L.: Electric-field-induced phase-change behavior in (Bi0.5Na0.5)TiO3–BaTiO3–(K0.5Na0.5)NbO3: A combinatorial investigation. Acta Mater. 58, 2103 (2010).Google Scholar
Daniels, J.E., Jo, W., Rödel, J., and Jones, J.L.: Electric-field-induced phase transformation at a lead-free morphotropic phase boundary: Case study in a 93%(Bi0.5Na0.5)TiO3–7% BaTiO3 piezoelectric ceramic. Appl. Phys. Lett. 95, 032904 (2009).Google Scholar
Royles, A.J., Bell, A.J., Jephcoat, A.P., Kleppe, A.K., Milne, S.J. and Comyn, T.P.: Electric-field-induced phase switching in the lead free piezoelectric potassium sodium bismuth titanate. Appl. Phys. Lett. 97, 132909 (2010).Google Scholar
Dutta, I. and Singh, R.N.: Dynamic in situ x-ray diffraction study of antiferroelectric–ferroelectric phase transition in strontium-modified lead zirconate titanate ceramics. Integr. Ferroelectr. 131, 153 (2011).Google Scholar
Hinterstein, M., Rouquette, J., Haines, J., Papet, P., Knapp, M., Glaum, J., and Fuess, H.: Structural description of the macroscopic piezo- and ferroelectric properties of lead zirconate titanate. Phys. Rev. Lett. 107, 077602 (2011).CrossRefGoogle ScholarPubMed
Jones, J.L., Aksel, E., Tutuncu, G., Usher, T-M., Chen, J., Xing, X., and Studer, A.J.: Domain wall and interphase boundary motion in a two-phase morphotropic phase boundary ferroelectric: Frequency dispersion and contribution to piezoelectric and dielectric properties. Phys. Rev. B 86, 024104 (2012).CrossRefGoogle Scholar
Simons, H., Daniels, J.E., Studer, A.J., Jones, J.L., and Hoffman, M.: Measurement and analysis of field-induced crystallographic texture using curved position-sensitive diffraction detectors. J. Electroceramics 32, 283 (2014).Google Scholar
Rietveld, H.M.: A profile refinement method for nuclear and magnetic structures. J. Appl. Crystallogr. 2, 65 (1969).Google Scholar
McCusker, L.B., Von Dreele, R.B., Cox, D.E., Louër, D., and Scardi, P.: Rietveld refinement guidelines. J. Appl. Crystallogr. 32, 36 (1999).Google Scholar
Young, R.A.: The Rietveld Method (Oxford University Press, Oxford, UK, 1995).Google Scholar
Toby, B.H.: EXPGUI, a graphical user interface for GSAS. J. Appl. Crystallogr. 34, 210 (2001).Google Scholar
Larzon, A.C. and Von Dreele, R.B.: GSAS (General Structure Analysis System). LANSCE, MS-H805; Los Alamos, NM, 1994.Google Scholar
Rodríguez-Carvajal, J.: Recent advances in magnetic structure determination by neutron powder diffraction. Phys. B Condens. Matter 192, 55 (1993).Google Scholar
Božin, E.S., Malliakas, C.D., Souvatzis, P., Proffen, T., Spaldin, N.A., Kanatzidis, M.G., and Billinge, S.J.L.: Entropically stabilized local dipole formation in lead chalcogenides. Science 330, 1660 (2010).Google Scholar
Zhang, Y., Ke, X., Kent, P.R.C., Yang, J., and Chen, C.: Anomalous lattice dynamics near the ferroelectric instability in PbTe. Phys. Rev. Lett. 107, 175503 (2011).Google Scholar
Axe, J.: Apparent ionic charges and vibrational eigenmodes of BaTiO3 and other perovskites. Phys. Rev. 157, 429 (1967).Google Scholar
Shimakawa, Y., Kubo, Y., Nakagawa, Y., Goto, S., Kamiyama, T., Asano, H., and Izumi, F.: Crystal structure and ferroelectric properties of ABi2Ta2O9 (A=Ca, Sr, and Ba). Phys. Rev. B 61, 6559 (2000).Google Scholar
Megaw, H.D. and Darlington, C.N.W.: Geometrical and structural relations in the rhombohedral perovskites. Acta Crystallogr. Sect. A 31, 161 (1975).CrossRefGoogle Scholar
Pandey, D., Singh, A.K., and Baik, S.: Stability of ferroic phases in the highly piezoelectric Pb(ZrxTi1-x)O3 ceramics. Acta Crystallogr. A 64, 192 (2008).CrossRefGoogle Scholar
Forrester, J.S., Kisi, E.H., Knight, K.S., and Howard, C.J.: Rhombohedral to cubic phase transition in the relaxor ferroelectric PZN. J. Phys. Condens. Matter 18, L233 (2006).Google Scholar
Corker, D.L., Glazer, A.M., Whatmore, R.W., Stallard, A., and Fauth, F.: A neutron diffraction investigation into the rhombohedral phases of the perovskite series. J. Phys. Condens. Matter 10, 6251 (1998).Google Scholar
Glazer, A.M. and Mabud, S.A.: Powder profile refinement of lead zirconate titanate at several temperatures. II. Pure PbTiO3. Acta Crystallogr. Sect. B Struct. Crystallogr. Cryst. Chem. 34, 1065 (1978).Google Scholar
Kornev, I.A., Bellaiche, L., Janolin, P-E., Dkhil, B. and Suard, E.: Phase diagram of Pb(Zr,Ti)O3 solid solutions from first principles. Phys. Rev. Lett. 97, 157601 (2006).CrossRefGoogle ScholarPubMed
Hill, R.J. and Howard, C.J.: Quantitative phase analysis from neutron powder diffraction data using the Rietveld method. J. Appl. Crystallogr. 20, 467 (1987).CrossRefGoogle Scholar
Jones, G.O. and Thomas, P.A.: Investigation of the structure and phase transitions in the novel A-site substituted distorted perovskite compound Na0.5Bi0.5TiO3. Acta Crystallogr. Sect. B Struct. Sci. 58, 168 (2002).CrossRefGoogle Scholar
Aksel, E., Forrester, J.S., Kowalski, B., Jones, J.L., and Thomas, P.A.: Phase transition sequence in sodium bismuth titanate observed using high-resolution x-ray diffraction. Appl. Phys. Lett. 99, 222901 (2011).Google Scholar
Hiruma, Y., Nagata, H., and Takenaka, T.: Thermal depoling process and piezoelectric properties of bismuth sodium titanate ceramics. J. Appl. Phys. 105, 084112 (2009).Google Scholar
Aksel, E., Forrester, J.S., Foronda, H.M., Dittmer, R., Damjanovic, D., and Jones, J.L.: Structure and properties of La-modified Na0.5Bi0.5TiO3 at ambient and elevated temperatures. J. Appl. Phys. 112, 054111 (2012).Google Scholar
Aksel, E., Forrester, J.S., Kowalski, B., Deluca, M., Damjanovic, D., and Jones, J.L.: Structure and properties of Fe-modified Na0.5Bi0.5TiO3 at ambient and elevated temperature. Phys. Rev. B 85, 024121 (2012).Google Scholar
Sani, A., Hanfland, M., and Levy, D.: Pressure and temperature dependence of the ferroelectric–paraelectric phase transition in PbTiO3. J. Solid State Chem. 167, 446 (2002).Google Scholar
Thomas, P.A., Kreisel, J., Glazer, A.M., Bouvier, P., Jiang, Q., and Smith, R.: The high-pressure structural phase transitions of sodium bismuth titanate. Zeitschrift für Krist. 220, 717 (2005).Google Scholar
Pramanick, A., Damjanovic, D., Daniels, J.E., Nino, J.C., and Jones, J.L.: Origins of electro-mechanical coupling in polycrystalline ferroelectrics during subcoercive electrical loading. J. Am. Ceram. Soc. 94, 293 (2011).Google Scholar
Tutuncu, G., Fan, L., Chen, J., Xing, X., and Jones, J.L.: Extensive domain wall motion and deaging resistance in morphotropic 0.55Bi(Ni1/2Ti1/2)O3–0.45PbTiO3 polycrystalline ferroelectrics. Appl. Phys. Lett. 104, 132907 (2014).Google Scholar
Jones, J.L., Slamovich, E.B., and Bowman, K.J.: Domain texture distributions in tetragonal lead zirconate titanate by x-ray and neutron diffraction. J. Appl. Phys. 97, 034113 (2005).Google Scholar
Tutuncu, G., Li, B., Bowman, K., and Jones, J.L.: Domain wall motion and electromechanical strain in lead-free piezoelectrics: Insight from the model system (1−x)Ba(Zr0.2Ti0.8)O3–(Ba0.7Ca0.3)TiO3 using in situ high-energy x-ray diffraction during application of electric fields. J. Appl. Phys. 115, 144104 (2014).Google Scholar
Grigoriev, A., Do, D-H., Kim, D., Eom, C-B., Adams, B., Dufresne, E., and Evans, P.: Nanosecond domain wall dynamics in ferroelectric Pb(Zr,Ti)O3 thin films. Phys. Rev. Lett. 96, 187601 (2006).Google Scholar
Genenko, Y.A., Zhukov, S., Yampolskii, S.V., Schütrumpf, J., Dittmer, R., Jo, W., Kungl, H., Hoffmann, M.J., and von Seggern, H.: Universal polarization switching behavior of disordered ferroelectrics. Adv. Funct. Mater. 22, 2058 (2012).Google Scholar
Daniels, J.E., Cozzan, C., Ukritnukun, S., Tutuncu, G., Andrieux, J., Glaum, J., Dosch, C., Jo, W., and Jones, J.L.: Two-step polarization reversal in biased ferroelectrics. J. Appl. Phys. 115, 224104 (2014).CrossRefGoogle Scholar
Gorfman, S., Schmidt, O., Pietsch, U., Becker, P., and Bohatý, L.: X-ray diffraction study of the piezoelectric properties of BiB3O6 single crystals. Zeitschrift für Krist. 222, 396 (2007).Google Scholar
Fertey, P., Alle, P., Wenger, E., Dinkespiler, B., Cambon, O., Haines, J., Hustache, S., Medjoubi, K., Picca, F., Dawiec, A., Breugnon, P., Delpierre, P., Mazzoli, C., and Lecomte, C.: Diffraction studies under in situ electric field using a large-area hybrid pixel XPAD detector. J. Appl. Crystallogr. 46, 1151 (2013).Google Scholar
Gorfman, S., Tsirelson, V., Pucher, A., Morgenroth, W., and Pietsch, U.: X-ray diffraction by a crystal in a permanent external electric field: Electric-field-induced structural response in alpha-GaPO4. Acta Crystallogr. A 62, 1 (2006).Google Scholar
Gorfman, S., Schmidt, O., Tsirelson, V., Ziolkowski, M., and Pietsch, U.: Crystallography under external electric field. Zeitschrift für Anorg. und Allg. Chemie 639, 1953 (2013).Google Scholar
Ghosh, D., Sakata, A., Carter, J., Thomas, P.A., Han, H., Nino, J.C., and Jones, J.L.: Domain wall displacement is the origin of superior permittivity and piezoelectricity in BaTiO3 at intermediate grain sizes. Adv. Funct. Mater. 24, 885 (2014).Google Scholar
Evans, J.D.S., Oliver, E.C., Withers, P.J., Mori, T. and Hall, D.A.: In situ neutron diffraction study of the rhombohedral to orthorhombic phase transformation in lead zirconate titanate ceramics produced by uniaxial compression. Philos. Mag. Lett. 87, 41 (2007).Google Scholar
Forrester, J.S., Kisi, E.H., and Studer, A.J.: Direct observation of ferroelastic domain switching in polycrystalline BaTiO3 using in situ neutron diffraction. J. Eur. Ceram. Soc. 25, 447 (2005).Google Scholar
Tutuncu, G., Motahari, M., Bernier, J., Varlioglu, M., Jones, J.L., and Ustundag, E.: Strain evolution of highly asymmetric polycrystalline ferroelectric ceramics via a self-consistent model and in situ x-ray diffraction. J. Am. Ceram. Soc. 95, 3947 (2012).Google Scholar
Webber, K.G., Zhang, Y., Jo, W., Daniels, J.E. and Rödel, J.: High temperature stress-induced “double loop-like” phase transitions in Bi-based perovskites. J. Appl. Phys. 108, 014101 (2010).Google Scholar
Jones, J.L., Motahari, S.M., Varlioglu, M., Lienert, U., Bernier, J.V., Hoffman, M., and Üstündag, E.: Crack tip process zone domain switching in a soft lead zirconate titanate ceramic. Acta Mater. 55, 5538 (2007).Google Scholar
Pojprapai(Imlao), S., Luo, Z., Clausen, B., Vogel, S.C., Brown, D.W., Russel, J., and Hoffman, M.: Dynamic processes of domain switching in lead zirconate titanate under cyclic mechanical loading by in situ neutron diffraction. Acta Mater. 58, 1897 (2010).Google Scholar
Rogan, R.C., Üstündag, E., Clausen, B., and Daymond, M.R.: Texture and strain analysis of the ferroelastic behavior of Pb(Zr,Ti)O3 by in situ neutron diffraction. J. Appl. Phys. 93, 4104 (2003).CrossRefGoogle Scholar
Marsilius, M., Granzow, T., and Jones, J.L.: Quantitative comparison between the degree of domain orientation and nonlinear properties of a PZT ceramic during electrical and mechanical loading. J. Mater. Res. 26, 1126 (2011).Google Scholar
Jo, W., Daniels, J.E., Jones, J.L., Tan, X., Thomas, P.A., Damjanovic, D., and Rödel, J.: Evolving morphotropic phase boundary in lead-free (Bi1/2Na1/2)TiO3–BaTiO3 piezoceramics. J. Appl. Phys. 109, 014110 (2011).Google Scholar
Eckold, G., Gibhardt, H., Caspary, D., Elter, P., and Elisbihani, K.: Stroboscopic neutron diffraction from spatially modulated systems. Zeitschrift für Krist. 218, 144 (2003).Google Scholar
Eckold, G., Hagen, M., and Steigenberger, U.: Kinetics of phase transitions in modulated ferroelectrics: Time-resolved neutron diffraction from Rb2ZnCl4. Phase Transitions 67, 219 (1998).Google Scholar
Huang, Z., Zhang, Q., and Whatmore, R.: The role of an intermetallic phase on the crystallization of lead zirconate titanate in sol–gel process. J. Mater. Sci. Lett. 17, 1157 (1998).CrossRefGoogle Scholar
Nittala, K., Mhin, S., Dunnigan, K.M., Robinson, D.S., Ihlefeld, J.F., Kotula, P.G., Brennecka, G.L., and Jones, J.L.: Phase and texture evolution in solution deposited lead zirconate titanate thin films: Formation and role of the Pt3Pb intermetallic phase. J. Appl. Phys. 113, 244101 (2013).Google Scholar
Tutuncu, G., Chang, Y., Poterala, S., Messing, G.L., and Jones, J.L.: In situ observations of templated grain growth in (Na0.5K0.5)0.98Li0.02NbO3 piezoceramics: Texture development and template-matrix interactions. J. Am. Ceram. Soc. 95, 2653 (2012).Google Scholar
Egami, T. and Billinge, S.J.L.: Underneath the Bragg Peaks: Structural Analysis of Complex Materials (Elsevier, Oxford, UK, 2003).Google Scholar
Jeong, I-K. and Lee, J.K.: Local structure and medium-range ordering in relaxor ferroelectric Pb(Zn1∕3Nb2∕3)O3 studied using neutron pair distribution function analysis. Appl. Phys. Lett. 88, 262905 (2006).Google Scholar
Jeong, I-K., Lee, J.K., and Heffner, R.H.: Local structural view on the polarization rotation in relaxor ferroelectric (1−x)Pb(Zn1∕3Nb2∕3)O3–xPbTiO3. Appl. Phys. Lett. 92, 172911 (2008).Google Scholar
Jeong, I-K., Darling, T., Lee, J., Proffen, T., Heffner, R., Park, J., Hong, K., Dmowski, W., and Egami, T.: Direct observation of the formation of polar nanoregions in Pb(Mg1/3Nb2/3)O3 using neutron pair distribution function analysis. Phys. Rev. Lett. 94, 147602 (2005).Google Scholar
Grinberg, I. and Rappe, A.: Local structure and macroscopic properties in PbMg1∕3Nb2∕3O3-PbTiO3 and PbZn1∕3Nb2∕3O3-PbTiO3 solid solutions. Phys. Rev. B 70, 220101 (2004).Google Scholar
Egami, T., Dmowski, W., Akbas, M., and Davies, P.K.: Local structure and polarization in Pb containing ferroelectric oxides. AIP Conf. Proc. 436, 1 (1998).Google Scholar
Chapman, K.W., Chupas, P.J., Halder, G.J., Hriljac, J.A., Kurtz, C., Greve, B.K., Ruschman, C.J., and Wilkinson, A.P.: Optimizing high-pressure pair distribution function measurements in diamond anvil cells. J. Appl. Crystallogr. 43, 297 (2010).Google Scholar
Poulsen, H.: Three-Dimensional X-Ray Diffraction Microscopy (Springer, Berlin Heidelberg, 2004), p. 205.Google Scholar
Jensen, D.J. and Poulsen, H.F.: The three dimensional x-ray diffraction technique. Mater. Charact. 72, 1 (2012).CrossRefGoogle Scholar
Schmidt, S.: GrainSpotter: A fast and robust polycrystalline indexing algorithm. J. Appl. Crystallogr. 47, 276 (2014).Google Scholar
Lauridsen, E.M., Schmidt, S., Suter, R.M., and Poulsen, H.F.: Tracking: A method for structural characterization of grains in powders or polycrystals. J. Appl. Crystallogr. 34, 744 (2001).Google Scholar
Schmidt, S.: GrainSweeper Program. <http://fable.wiki.sourceforge.net/GrainSweeper>..>Google Scholar
Varlioglu, M., Lienert, U., Park, J-S., Jones, J.L., and Üstündag, E.: Thermal and electric field-dependent evolution of domain structures in polycrystalline BaTiO3 using the 3D-XRD technique. Texture, Stress. Microstruct. 2010, 1 (2010).Google Scholar