International
Tables for
Crystallography
Volume H
Powder diffraction
Edited by C. J. Gilmore, J. A. Kaduk and H. Schenk

International Tables for Crystallography (2018). Vol. H, ch. 2.8, pp. 177-181

Section 2.8.3.1. In situ studies of ferroelectrics in an external electric field

H. Ehrenberg,a* M. Hinterstein,a A. Senyshynb and H. Fuessc

aInstitut für Angewandte Materialien (IAM-ESS), Karlsruhe Institut für Technologie (KIT), Eggenstein-Leopoldshafen, Germany,bTechnische Universität München, Garching b. München, Germany, and cTechnische Universität Darmstadt, Darmstadt, Germany
Correspondence e-mail:  helmut.ehrenberg@kit.edu

2.8.3.1. In situ studies of ferroelectrics in an external electric field

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The function of ferroelectrics as stress sensors, high-frequency microphones, medical injectors or large strain actuators is based on electric poling. A polycrystalline material exhibits a zero net polarization. When an electric field is applied to the sample, the spontaneous electric polarization of the ferroelectric material is reoriented along the electric field vector. This occurs by a reorientation of domains. Additional polarization is obtained by an increase of the spontaneous polarization induced by the applied electric field. With in situ experiments, the field-induced changes in the powder diffraction reflections are measured. Fig. 2.8.1[link] is a schematic representation of some in situ sample geometries. The electric field is applied via electrodes on the sample surface.

[Figure 2.8.1]

Figure 2.8.1 | top | pdf |

Sample geometries for in situ experiments with an applied electric field. Samples are poled via an applied voltage (U) at the sample electrodes (grey). Different sample geometries are necessary to account for different beam sizes, absorption and detector concepts. Yellow indicates the irradiated sample volume. (a) Flat-plate samples for X-ray experiments with strip detectors, limiting photon energies to around 30 keV. (b) Bar-shaped samples for high-intensity neutron powder diffraction (NPD) or high-energy X-ray diffraction (XRD). (c) Cylinder-shaped samples for high-resolution neutron diffraction with fixed detector collimators.

Many of these ferroelectric materials crystallize in a structure derived from the cubic perovskite type, but in a crystal system with lower symmetry and with a non-centrosymmetric space group. The most widely used material is lead zirconate-titanate (PbZr1−xTixO3, PZT), which exhibits the highest strain response at the so-called morphotropic phase boundary with a composition of about 50% for Ti and Zr. It is generally accepted that the phase on the Ti-rich side of the PZT phase diagram has a tetragonal structure with space group P4mm. On the rhombohedral Zr-rich side, two ferroelectric phases can be identified, with space groups R3m for high and R3c for low temperatures. A considerable amount of work has been devoted to the elucidation of the crystal structure of the material close to the morphotropic phase boundary. Neutron and synchrotron diffraction detected monoclinic symmetry at low temperatures and nanometre-sized regions (the so-called polar nanoregions) were inferred from diffuse scattering (Noheda et al., 2000[link]; Hirota et al., 2006[link]). Alternative interpretations explained the new reflection found in the pattern between the 111C and 200C reflections (where the subscript `C' corresponds to the cubic archetype structure) as diffuse scattering from diffuse incoherent scattering by small domains (Jin et al., 2003[link]).

Unique information on structural changes during poling is obtained from in situ studies in applied external electric fields (Hoffmann et al., 2001[link]). Fig. 2.8.2[link] displays two groups of powder reflections (Schönau, Schmitt et al., 2007[link]) observed by synchrotron X-ray diffraction. They are directly compared with the domain structure from TEM observations (Schmitt et al., 2007[link]) for a range of compositions near the morphotropic phase boundary. One group of reflections is derived from the cubic 111C reflection, the other from the archetype 200C reflection. The transition from the rhombohedral splitting to the tetragonal one with increasing Zr content is correlated with the forms of ferroelectric domains in TEM. Close to the morphotropic phase boundary, nanodomains (ranging in width from 20 to 200 nm) are observed in addition to the well known microdomains. The nanodomains react immediately under the influence of an electric field to become microdomains. Fig. 2.8.3[link] shows the intensity changes observed for the 110C group of reflections. The changes under an electric field are pronounced and depend on the c/a ratio (Schönau, Knapp et al., 2007[link]), the formation and disappearance of nanodomains, and the local symmetry of these domains.

[Figure 2.8.2]

Figure 2.8.2 | top | pdf |

(a), (b) High-resolution synchrotron X-ray powder diffraction patterns and TEM imaging of PZT with a varying Zr/Ti ratio. An increase in broadening is seen in changes in shape and width of the 002T reflection between the samples PZT 45/55, 52.5/47.5 and 54/46. The asymmetry and width of the tetragonal 101T reflection not only change, but also evolve into a new peak between 101T and 110T in sample PZT 54/46, which gains in intensity towards PZT 57.5/42.5. This rise is accompanied by a decrease in intensity of the visible 110T reflection, which then seems to be absent or overlapped in sample PZT 56/44. The domain structure changes from a lamellar tetragonal configuration via nanodomains to a rhombohedral herringbone structure. Reproduced with permission from Schönau, Schmitt et al. (2007) [link]. Copyright (2007) by the American Physical Society.

[Figure 2.8.3]

Figure 2.8.3 | top | pdf |

Diffraction patterns of the tetragonal 101T /110T reflection pairs of PZT 52/48, PZT 53/47, PZT 54/46, PZT 55/45 and PZT 56/44 recorded in situ under an electric field for the first poling cycle of up to 4 kV mm−1. Reproduced with permission from Schönau, Knapp et al. (2007) [link]. Copyright (2007) by the American Physical Society.

The different poling mechanisms can be studied in transmission geometry, which allows variation of the angle between the electric field vector E and the direction of the incident X-ray beam k from 0° to about 45° (Fig. 2.8.4[link]) (Hinterstein et al., 2011[link]). Two sputtered electrodes (Ag, Pt) were used for polarization.

[Figure 2.8.4]

Figure 2.8.4 | top | pdf |

In situ transmission geometry developed by Schönau, Schmitt et al. (2007[link]) with the electric field vector perpendicular to the flat-plate sample surface. The electric field results from an applied voltage U between two opposing sputtered electrodes (Ag, Pt) with a thickness of about 15 nm. (a) ω = 0° and (b) ω = 45°.

An extensive study under an electric field has been carried out on the commercially available sintered PZT material named PIC, in which Ti is partially replaced by Ni and Sb [Pb0.99Zr0.45Ti0.47(Ni0.33Sb0.67)0.08O3], in transmission geometry. The angle between the electric field perpendicular to the flat sample surface and the incident beam was varied between 0 and 45°. The effect of domain switching in tetragonal symmetry mainly affects the {h00}C reflections, whereas the piezoelectric effect predominantly influences the {hhh}C reflections. Thus, the reflection pair 111C and 200C are the only reflections analysed in most studies. Fig. 2.8.5[link] displays just these reflections, with 200C split into 002T and 200T, where the subscript `T' refers to the tetragonal distorted cell, which is translationengleich to the cubic one (i.e. they have the same group of translations). The shift to higher angles of 111C under an applied field indicates a decrease in volume. This is explained by the large angle between the electric field vector and the vector of spontaneous polarization for the unit cells contributing to 111C. This induced compression remains in the remanent state.

[Figure 2.8.5]

Figure 2.8.5 | top | pdf |

111C and 200C reflections of the unpoled, remanent and applied field state of PIC 151 at ω = 0°. Owing to the piezoelectric effect, the 111C reflection is shifted. The preferred orientation of the 200C reflection indicates tetragonal 90° domain switching.

While analysis of single reflections or orientations can yield valuable information on textured functional materials, a more sophisticated approach involves coupling the Eulerian angles to the diffraction patterns and modelling all observable mechanisms within a single refinement. By applying this method to a technically applied actuator material, Hinterstein, Hoelzel et al. (2015[link]) could quantify all strain mechanisms and calculate the macroscopic response to an applied electric field with a structure model at the atomic scale.

The function of piezoceramics is related to periodic cycling of the polarization, accompanied by periodic changes of macroscopic strain. Fatigue in piezoceramic materials means that this strain is reduced as a result of the cycling; this has been studied with respect to the underlying structural changes (Hinterstein et al., 2011[link], 2014[link]).

Whereas strain is related to texturing, no preferred orientation is observed in fatigued samples. The orientation of nanodomains is demonstrated in different patterns: in Fig. 2.8.6[link] the two reflections are shown for the remanent state (0 kV mm−1) at different diffraction angles and in Fig. 2.8.7[link] for values of the external field ranging from 0 to 2 kV mm−1.

[Figure 2.8.6]

Figure 2.8.6 | top | pdf |

111C and 200C reflections of bipolar fatigued PIC 151 (50 Hz, 107 cycles) in the remanent state (0 kV mm−1 at ω = 0°, 15°, 30° and 45°).

[Figure 2.8.7]

Figure 2.8.7 | top | pdf |

111C and 200C reflections of bipolar fatigued PIC 151 (50 Hz, 107 cycles) at ω = 45° with 0.0, 0.72, 1.41 and 2.0 kV mm−1.

The diffuse scattering between the split 200C reflections in the fatigued sample is reduced and the texturing increases after static poling for a few seconds. Thus, the fatigued samples show a more tetragonal appearance after cycling. The energy of the electric field induces a transition of well oriented nanodomains with preferred orientation along the field vector, leading to texturing for ω = 0°. At a certain point the system will no longer respond to the electric field because of crack formation and a decrease in the volume of switchable nanodomains. From that point, the diffraction pattern recorded under a field is no different to the diffraction pattern recorded without a field.

Cyclic loading with high frequencies is required in real applications of ferroelectric ceramics. Exposure times in the range of seconds are necessary to ensure sufficient statistics for single diffraction experiments in the subsecond regime. Stroboscopic measurements can be used to achieve this.

Absolutely reversible processes are necessary for a successful stroboscopic analysis. The stability of the system is achieved by pre-cycling circa 105 times. Time resolutions in the range of several tens of milliseconds are possible with modern X-ray detectors. By repeating the excitation and summing the intensities, proper statistics can be achieved (Choe et al., 2015[link]; Hinterstein et al., 2014[link]).

The use of the stroboscopic data-collection technique and cyclic fields in neutron diffraction experiments enabled a direct measurement of non-180° domain wall motion during the application of subcoercive cyclic electric fields (Fig. 2.8.8[link]) (Jones et al., 2006[link], 2007[link]; Jones, 2007[link]; Daniels et al., 2007[link]). It was shown that the non-180° domain switching contributes 34% of the macroscopically measured strain during cycling with half of the coercive field.

[Figure 2.8.8]

Figure 2.8.8 | top | pdf |

Diffracted intensities of the pseudo-cubic 002 reflections as a function of 2θ and time during application of a square, bipolar electric field waveform of frequency 1 Hz and amplitude of plus or minus half the coercive field. The timescale is described using eight steps. The positive (P) state of the electric field is applied between 0.25 and 0.75 s, which is bounded on either side by the negative (N) field state. The diffraction vectors 002 and 200 are parallel to the applied electric field. Reproduced with permission from Jones et al. (2006[link]). Copyright (2006) AIP Publishing.

The highest time resolutions are obtained in a pump–probe setup. Under the influence of an electric field of 2 kV mm−1, the switching kinetics can be investigated directly. With a time resolution of 1 ms only one intermediate step is observed (Fig. 2.8.9[link]a). With a time resolution of 250 µs a significant number of intermediate steps can be studied (Fig. 2.8.9[link]b). The commercially available soft-doped PZT material EC-65 has also been observed under the application of an electric field and mechanical stress. Lattice strains were measured under cyclic electric fields at times as short as 30 µs (Pramanick et al., 2010[link]).

[Figure 2.8.9]

Figure 2.8.9 | top | pdf |

Pump–probe measurements of the 200C reflection at ω = 45°. Cycling switching between the remanent and the applied field state at 2 kV mm−1 with 50 Hz and a time resolution of (a) 1 ms and (b) 250 µs. Only a time resolution of 250 µs results in sufficient intermediate steps between the remanent and the poled state to study the processes during poling.

The use of lead-containing materials may in the future be banned because of environmental concerns, hence considerable efforts are being made to find materials with properties similar to PZT. Only a few elements (Ba, Bi, Na, K, Nb, Ti) seem to be suitable. Nevertheless, a combination of the relevant oxides of these leads to a large variety of potential materials. (Bi0.5Na0.5)­TiO3–BaTiO3 (BNT–BT) (Hinterstein, Schmitt et al., 2015[link]), (Bi0.5Na0.5)TiO3–(Bi0.5K0.5)TiO3 (BNT–BKT) (Levin et al., 2013[link]), BNT–BT–K0.5Na0.5NbO3 (BNT–BT–KNN) (Schmitt et al., 2010[link]), BNT–BKT–KNN (Anton et al., 2012[link]) and BNT–KNN (Liu et al., 2017[link]) are the focus of most attention. The materials in the (1 − x − y)BNT–xBT–yKNN system exhibit remarkable piezoelectric properties over a narrow composition range 0.05 ≤ x ≤ 0.07 and 0.01 ≤ y ≤ 0.03 (Zhang et al., 2007[link]). Daniels et al. (2010[link]) proposed a combinatorial approach to studying a range of compositions in a single sample, where different stoichiometries created a compositional gradient in the sample. A limited number of bulk homogeneous samples were prepared for comparison. Microfocus X-ray beams from a synchrotron allowed investigation of the gradient material under a field.

Fig. 2.8.10[link] displays the diffraction patterns under an external electric field up to 5.5 kV mm−1. Data analysis was performed by fitting the data of the pseudo-cubic 002 reflection to distorted pseudo-cubic and tetragonal symmetry for each composition and electric field. Whereas in the 0.86BNT–0.14KNN composition only a distorted pseudo-cubic behaviour is observed above a threshold of 0.5 kV mm−1, a very pronounced distortion is observed for 0.93BNT–0.07BT, which eventually above 2 kV mm−1 develops into a tetragonal structure. In addition to the combination of various compositions, the authors simultaneously measured the X-ray fluorescence spectra, thus confirming the actual composition.

[Figure 2.8.10]

Figure 2.8.10 | top | pdf |

The pseudo-cubic 002 reflection of (a) 0.93BNT–0.07BT end member, (b) 0.938BNT–0.053BT–0.009KNN, (c) 0.932BNT–0.045BT–0.023KNN and (d) 0.86BNT–0.14KNN end member as a function of electric field from the initial zero-field state (top) to an applied field of 5.5 kV mm−1 (bottom). The sample orientation is such that the scattering vector is parallel to the electric field. Reproduced with permission from Daniels et al. (2010[link]). Copyright (2010) Elsevier.

Fig. 2.8.11[link] depicts a Rietveld refinement of a lead-free ferroelectric material with the composition 0.92Ba0.5Na0.5TiO3–0.06BaTiO3–0.02K0.5Na0.5NbO3. New superstructure ref­lections (Fig. 2.8.11[link]b, arrows) and a lattice distortion (Fig. 2.8.11[link]b, circled) were observed due to a transition from space group P4bm to R3c (Hinterstein et al., 2010[link]).

[Figure 2.8.11]

Figure 2.8.11 | top | pdf |

Rietveld refinement based on different patterns of 0.92Bi0.5Na0.5TiO3–0.06BaTiO3–0.02K0.5NbO3 (a) in the unpoled and (b) in the applied field state at 6 kV mm−1. Experimental data are shown by grey crosses, black lines denote calculated profiles, and the lower plot shows their difference. Calculated positions of Bragg reflections are shown by vertical tick marks, where the different rows correspond to the initial tetragonal phase with space group P4bm (1) and the field-induced rhombohedral phase with space group R3c (2). Arrows mark superlattice reflections of type ½{ooe} and the circle highlights the rhombohedral split 331C reflection.

In an overview, Jones summarized the use of diffraction techniques. Along with the importance of microdiffraction, diffuse scattering and texture effects, the importance of time-resolved studies including stroboscopy was acknowledged (Jones, 2007[link]).

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