Hierarchical domain structure of lead-free piezoelectric (Na_1/2 Bi_1/2)TiO₃-(K_1/2 Bi_1/2)TiO₃ single crystals

(Na_0.5Bi_0.5)TiO₃ (NBT) based single crystals and ceramics are promising candidate lead-free piezoelectric materials to replace the dominating Pb-based Pb(Zr,Ti)O₃ perovskite, as there are environmental concerns over the toxicity of Pb.^1–8 The common key to enhanced performance is the presence of a morphotropic phase boundary (MPB) around which the piezoelectric constant and electromechanical coupling coefficient are maximum.^2–8 Near the MPB in Pb-based single crystals, such as Pb(Mg_1/3Nb_2/3)O₃-xat. %PbTiO₃ (PMN-xPT) (31 ≤ x ≤ 37) and Pb(Zn_1/3Nb_2/3)O-xat. %PbTiO₃ (PZN-xPT) (8 ≤ x ≤ 11), various structurally bridging monoclinic (M) phases are known to exist,⁹ which enables polarization rotation with significantly reduced hysteretic losses within a domain engineered state¹⁰ between ferroelectric rhombohedral (R) and tetragonal (T) phases.

Following the successful development of MPB compositions of PMN-xPT and PZN-xPT single crystals with high piezoelectric properties,¹¹ investigations of next-generation Pb-free piezoelectrics have focused on NBT-based perovskites due to the presence of a similar MPB in its phase diagram between R (R3c) and T (P4bm) phases. And there are two main solid solution systems within them, that is, NBT-xat. %BaTiO₃ (NBT-xBT) and NBT-xat. %(K_1/2 Bi_1/2)TiO₃ (NBT-xKBT), which had been earlier reported by Takenaka and Nagata⁴ and Sasaki et al.,¹² respectively. Generally, the performances of single crystals are better than ceramics, and their growth methods also greatly affect the properties. In this paper, NBT-xKBT single crystals were grown by a top-seed solution growth (TSSG) method. Obtained by the same TSSG method, NBT-xBT is reported to have a MPB near x = 5,¹³ and to have the peak piezoelectric property of d₃₃ = 423 pC/N.¹⁴ Other growth methods include the slow-cooling method used by Chiang et al., and their NBT-5.5%BT had a peak value of d₃₃ = 450 pC/N.¹⁵ However, these enhancements have not yet been found to be as large as those of Pb-based ones (d₃₃ ≈ 2500 pC/N (Ref. 11)). The reasons for the lower maximum properties in the Pb-free, versus Pb-based, single crystals are not yet known.

It is widely believed that polar nano-domains (PNDs) play an important role in the MPB systems of both Pb-based and Pb-free piezoelectrics.^16,17 In PMN-xPT, the presence of PNDs that self-assemble into hierarchical domains over various length scales has been reported,¹⁸ which results in the achievement of the compatibility conditions of the elastically relaxed state.¹⁸ In this case, the adaptive phase theory¹⁹ predicts that the structurally bridging M phases are in fact composed of nano-domains of R and T phases, and that the high piezoelectric properties result from a redistribution of the PNDs under field. In NBT, hierarchical domains have also been reported where a high-temperature ferroelastic T domain structure is elastically inherited into the R ferroelectric phase field, and where polar domains of about micron-size form within this geometrical constraint.²⁰ With increasing BT content, as the MPB of NBT-xBT was approached, the size of the polar domains was reported to be refined and the degree of self-organization in the domain hierarchy enhanced.^17,20 Furthermore, high-resolution transmission electron microscopy (HRTEM) images have shown the presence of multiple oxygen octahedral tilt domains, of a few nanometers in size, within the lamellar domains.²¹ Both kinds of superlattice reflections, in-phase tilt $12$(ooe) and anti-phase tilt $12$(ooo) (where o designates odd values of the Millers indices, and e even), were reported in NBT-5.5%BT.¹⁷ These reflections are believed to, respectively, originate from a T (P4bm) structure with an a⁰a⁰c⁺ tilt system and a R (R3c) structure with an a^–a^–a^– tilt system (Glazer notation²²). With increasing BT content (approaching the MPB), the intensity of the $12$(ooe) reflections and the volume fraction of the in-phase tilt domains were found to increase.¹⁷ Both types of tilt domains were also found to be present over a large temperature range, with their respective volume fractions changing gradually with temperature.²³ These results indicate the presence of PNDs with a structural frustration on the nm-scale between tilt clusters, which gradually evolve with temperature and composition.

Recently, solid solutions of NBT-xKBT in single crystalline form were found to achieve promising performances.^24–28 Table I summarizes the dielectric and piezoelectric properties of such NBT-xKBT crystals, grown by a top-seed solution growth (TSSG) method, as previously reported.^24,29,30 The value of d₃₃ is enhanced, while the remnant polarization (P_r) is suppressed in the vicinity of the MPB.²⁴ In particular, this material has a high depolarization temperature and a large kt/kp ratio (thickness to planar coupling coefficient),²⁴ both of which have been critically limiting issues in PMN-xPT and PZN-xPT.³¹ The characteristics of the NBT-xKBT solid solutions are thus promising for applications. However, the structure and domain structure of NBT-xKBT are not yet fully understood. Sasaki et al.¹² were the first to report the presence of a MPB between R and T phases in NBT-xKBT in the compositional range of x = 0.16–0.20, which was inferred using NBT-xKBT ceramics by the maximum in the piezoelectric properties. Although the general location of the MPB is widely agreed upon,⁸ variations in the phase diagrams are known due to different single crystal/ceramic growth methods and conditions.³² 

Here, we present the results of an investigation of the domain hierarchy of NBT-xKBT single crystals for x = 0.05 and 0.08. The domain structures have been studied by transmission electron microscopy (TEM) in the bright field (BF) mode, selected area electron diffraction (SAED), and dark field (DF) imaging. In addition to the similar polar domain structure previously reported in NBT,³³ an even finer nano-sized sub-domain structure was observed by HRTEM that self-assembled into a quadrant-like configuration. The density of such sub-domains was found to decrease with increasing KBT content, while the SAED patterns revealed that the octahedral tilt regions and phase coexistence did not change notably.

NBT-xKBT (x = 0.05 and 0.08) single crystals were grown using a top-seed solution growth (TSSG) method at the Shanghai Institute of Ceramics. The details of NBT-xKBT growth experiment are very similar to each other and are already reported by Sun et al.³⁴ and Zhang et al.³⁵ The concentration of K+ ions in the as-grown single crystals was determined by inductive coupled plasma atomic emission spectrometry (ICP-AES). All TEM experiments were made at the Virginia Tech Institute for Critical Technology and Applied Science (ICTAS), the Nanoscale Characterization and Fabrication Laboratory (NCFL). Samples for TEM were prepared by mechanical polishing, followed by a dimple grinder thinning process, and finally by argon ion milling. Electron diffraction and low magnification imaging were first performed using a Philips EM 420 electron microscope working at 120 kV, with a double-tilt sample holder to enable access to the various zone axes. The Bragg peaks were labeled in a pseudo-cubic lattice index. High-resolution TEM images were obtained using JEOL TEM working at 200 kV, which elucidated nm-scale features.

In Figure 1, bright field images are shown for NBT-5%KBT, taken along [001] orientation. Parts (a) through (d) show increasingly higher resolution images, revealing the presence of hierarchical domains. The images with lower magnification (see Figs. 1(a) and 1(b), taken using EM 420) show a quadrant-like (i.e., square) domain morphology, with a domain width/length on the order of about 35 nm. These quadrant domains had {110} type orientations, and were stacked together along the same family of directions. This imparted a 4-fold texture symmetry to the domain morphology at length scales above 500 nm; however, at finer length scales this pattern was lost. With increasing magnification (see Figs. 1(c) and 1(d), taken using JEOL), each quadrant-like domain was found to have a sub-domain structure that consisted of about four to six very fine polar lamellar domains, which were about 8 ∼ 20 nm in width and which were stacked along the same [100] and [010] directions. The sub-domain width varies in different areas but is almost the same in a single quadrant domain. Figures 1(e) and 1(f) illustrate, with lines to guide the eyes, how the domains and sub-domains are stack together, establishing the domain hierarchy.

Figure 2 shows that NBT-8%KBT has a similar hierarchical domain structure as that found in NBT-5%KBT. The nature of the self-assembly remains unchanged with KBT content. The width and density changes in the average quadrant domain and in the average sub-domain (lamellar) are given in Table II. Generally, the quadrant domains are relatively unchanged compared with the lamellar sub-domains. The lamellar sub-domains in NBT-8%KBT have a slightly bigger size but much weaker domain wall contrast, which results in fewer sub-domains within a single quadrant domain. A schematic summarizing the hierarchical domain structure is shown in Figure 3. This schematic illustrates how multiple lamellar sub-domains having the same orientation and size stack together to form a quadrant-like domain, and how the orientation of the lamellar domains within neighboring quadrant changes. Both domain and sub-domain are stacking along [100]/[010] directions, and this pattern then self-assembles into macro-domain plates that fill the entire volume of the low temperature transformed phase.

Similar square-like domains have previously been reported in NBT,^20,33,36 where small rhombohedral polar domains with a square-like morphology were found to nucleate on cooling within the geometrical constraints imposed by a tetragonal ferroelastic macro-domain structure inherited from high temperatures.³⁶ However, previous studies have not reported the presence of small lamellar sub-domains within the quadrant-like ones. This is the first report that demonstrates a high density of polar nano-twins in NBT-derived materials that results in a hierarchical domain structure near the MPB.

It is relevant to note that geometrically arranged and stacked PNDs having a lamellar morphology have previously been reported within the macro-domain platelets for PMN-xPT³⁷ in the vicinity of its MPB. These lamellar domains were oriented along [110] and were much longer than those observed here for NBT-xKBT, but they did not assemble into a quadrant-like pattern at intermediate length scales. The domain self-assembly in PMN-xPT is driven by geometrical invariant conditions that achieve the elastic compatibility conditions.³⁷ Investigations of the hierarchical domains in PMN-xPT under dc electric bias E_DC have shown a redistribution of the PNDs, which, following the adaptive phase theory, can be used to account for its exceptionally high piezoelectric properties near its MPB.

On the other hand, similar quadrant-like morphologies have previously been reported in ferroelectric vortices.³⁸ Thermodynamically, true quadrant domains form with large declination stresses, and would become unstable for sizes above a few nanometers. However, partial stress relaxation has been reported to be achieved by the formation of internal stripe-like domains.³⁹ Such quadrant like morphologies are favored by large domain wall energies (γ) and low spontaneous elastic strains (ε).^40,41 Interestingly, even though the domain wall energy of MPB solid solutions is low,³² the domains in the NBT-derived systems do not self-assemble into an elastically relaxed condition, preferring the quadrant-like structure over the adaptive state. This presents a paradox for understanding the origins of the quadrant-like morphology in NBT-xKBT. Other factors could complicate this self-assembly, such as, but not limited to, multiple competing order parameters, i.e., frustration.

Figure 4 shows SAED patterns for both NBT-5%KBT (Parts (a) and (b)) and NBT-8%KBT (Parts (c) and (d)). These patterns were collected using the EM420 TEM, focusing on [11–2] (Parts (a) and (c)) and [001] (Parts (b) and (d)) zone axes. The SAED patterns from the two compositions were not noticeably different. The $12$(ooe) and $12$(ooo) superlattice reflections are identified in the patterns as open circles and squares, respectively. For both NBT-5%KBT and NBT-8%KBT, the most intense superlattice reflection was the $12$(ooo) corresponding to the anti-phase tilting, which is similar to previous reports for NBT-xBT.¹⁷ These results show that the dominant phase on a local scale for both compositions has the R structure, consistent with the left side of the MPB in the phase diagram of NBT-xKBT; however, there was clear evidence of the coexistence of the T structure on a local scale. These findings are consistent with the SAED investigations in solid state grown NBT-xKBT,⁴² and in contrast, those NBT-xKBT grown via slow-cooling method showed no phase coexistence.³² 

Recent X-ray diffraction (XRD) diffuse scattering analysis has also proved phase coexistence in the NBT-xBT solution. On the R-phase side of the MPB, PNDs stacked along (001) and a related L-shape diffuse scattering has been reported.⁴³ Close to the MPB, as the stability of the T-phase is increased, oval-shaped diffuse scattering replaced the L-shaped one and PNDs correspondingly re-stack along (110).⁴³ In order to confirm whether, or not, similar changes in PND distribution occur for NBT-xKBT, Figure 5 is given to illustrate the different orientations of the hierarchical domain structure. The insets in the top-left of this figure are SAED patterns where the selected reflections are marked by dashed squares. Figure 5(a) shows a dark field (DF) image taken along the [001] zone axis with filters selected to allow (110) contributions only. Large quadrant-like domain contours were found in the DF image and had weak contrast, where dashed lines are used in the figure to help better illustrate the contours. Figure 5(b) shows the corresponding bright field image taken from the same zone axis and same sample area. Here, the quadrant-like domain contours are no longer visible and instead the lamellar sub-domain structures appear. Clearly, the quadrant-like domains are oriented along (110), whereas the lamellar sub-domains are oriented along (001). Thus, it can be confirmed that the quadrant-like domains have elastic invariant conditions inherited from the T-phase, whereas the lamellar sub-domains represent those of the average structure of the polar R-phase. Thus, a similar PNDs model can be used in NBT-xKBT, and the decreasing domain wall density shown in Table II also supports the adaptive phase theory applied to NBT-xBT.

There are various versions of the phase diagram for the NBT-xKBT solid solution.³² However, most authors agree that the MPB region between the R phase of NBT and T phase of KBT is near 0.15 < x < 0.20. Difference in the location of the MPB and details of the phase diagram are attributed to variations in single crystal growth methods. In this study, as mentioned earlier, the TSSG method was used. Structural and electrical properties of similar TSSG crystals have previously been published.²⁴ It is relevant to note the significant P_r decrease with changing composition from the R side to the T side of the phase diagram that has been reported for NBT-xBT,¹³ suggesting similar structure–property relations. We believe that the variations in the MPB location can be understood by changes in the hierarchical domain distributions that appear to have coexisting T and R geometrical invariant conditions over a wide length scale, in addition to having coexisting R (⁠$12$(ooo)) and T (⁠$12$(ooe)) tilt domains of about several nm in size.

Considering the similarities between structure and properties, R-T phase diagrams, and mixed A-site cation natures, a generic description of PNDs can be used to describe both NBT-xBT and NBT-xKBT. In the vicinity of the MPB, the polar lamellar orientation (and twin stacking) changes from the R phase (001) direction to the T phase (110) one; correspondingly, contrast features of the R phase lamellar sub-domains are weakened. Meanwhile, the change of quadrant domains is not that obvious. These observations support the conclusions that the polar hierarchical, or quadrant-like, domain structure is not sensitive to the domain distribution that achieves a lower elastic free energy, as characterized by the compatibility conditions. We believe that this is due to the presence of competing domain structures with different order parameters. The interlocking of the tilted oxygen octahedra, internally within the polar lamellar domains, makes it difficult to realize the fully relaxed elastic state. In these regards, the Pb-free NBT-derived systems are notably different than the Pb-based ones typified by PMN-xPT. Furthermore, the interlocking tilted octahedra make it difficult for the small polar lamellar domains to be redistributed under an applied E electric field in NBT-derived systems. Accordingly, the domain contribution to the piezoelectric properties may come dominantly from a polarization extensional mode,⁴⁴ rather than a rotational one of either the adaptive³⁷ or homogenous M phases.⁴⁵ The residual elastic energy locked within the domain structure of NBT-derived systems, typified by the quadrant-like morphologies, may significantly reduce the piezoelectric properties. Accordingly, to enhance the piezoelectricity of Pb-free systems, future efforts may need to focus on de-slaving the polar order parameter from the octahedral rotation order parameter, for compositions near the MPB.

The ferroelectric domain and local structures of NBT-xKBT single crystals have been investigated by various TEM methods. We find the presence of a unique hierarchical domain structure. Small polar lamellar sub-domains exist that are oriented/stacked along (001) and that corresponded to the R (R3c) phase. These fine lamellar sub-domains self-assembled into a quadrant-like morphology oriented along (110) that corresponded to the T (P4bm) phase. Furthermore, the fine lamellar (polar) domains contained many nm-sized oxygen tilt (nonpolar) domains, where both in-phase (P4bm) and anti-phase (R3c) tilt regions coexisted, as shown by the SAED patterns. The main change in the domain hierarchy with KBT content was a slightly larger size of the subdomains with increasing x, which resulted in fewer subdomains per quadrant. A comparison of dark field and bright field images revealed that these domain changes corresponded to a gradual PND evolution from average R3c to P4bm phases.

Similar to NBT-xBT, the NBT-xKBT system has a polar order parameter with a coherence length on the orders of 10–100 nm, and also has both R- and M-type nonpolar rotational order parameters with a coherence length of a few nanometers. These ferroelectric polarization and oxygen rotational order parameters are known to be coupled through rotostriction.⁴⁶ Thus, domain frustration over multi-scales plays an important role in the hierarchical arrangement, resulting in similar quadrant-like domains. In turn, following the adaptive phase theory,³² this may restrict the piezoelectricity in NBT-derived systems, due to an increased difficulty in redistributing the domain distribution under electric field.

Authors C.L., D.V., and O.D. would like to thank the ONRL-GO program for support of this work, and Y.W. and J.F.L. would like to thank the Office of Naval Research for support of this work (N00014-13-1-0049). The authors also thank Dr. C. Winkler for useful discussion and the Nanoscale Characterization and Fabrication Laboratory in Virginia Tech for the instrumentation support and training. O.D. acknowledges funding from the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the U.S. DOE.