In contrast to XRD patterns displayed in Figure 5.32, a monochromator was employed to filter Cu Kα2 radiation in order to allow a better distinction of reflection splitting due to lattice distortions.
The high angle reflections of the calcined powder indicates peak splitting, as visible in the magnified view of Figure 5.33 in the (222)pc reflection. The high angle peak splitting can be
attributed to the diffraction of a heterogeneous material with the presence of two perovskite phases with different lattice parameters based on the results from the previous section, as well as the negligible non-cubic distortions of BNT-0.25ST reported in the literature.248,356 Moreover, in agreement with literature248,356, the sintered sample features sharp and narrow peaks ascribed to a pseudocubic perovskite structure with no obvious splitting in either the (111)pc, (222)pc, (100)pc, or
(200)pc reflections. It should be noted that small FD distortions are a common feature of several
BNT-based lead-free materials.141 In general, this is due to competing FD and AFD instabilities.367 In order to corroborate the existence of AFD instabilities leading to octahedral tilting, neutron
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diffraction was performed because this technique is sensitive to the position of all O2- isotopes due to their relatively large neutron scattering length.420 In situ electric field and orientation-dependent neutron diffraction patterns are displayed in Figure 5.34 in the most relevant 2𝜃 angular range to investigate the presence and the changes under electric field of ½(311)pc, (111)pc, and (200)pc
reflections. It is noted that no presence of ½(310)pc corresponding to a 𝑃4𝑏𝑚 symmetry was
observed, thus the angle corresponding to this reflection is omitted. Figure 5.34 (a) provides the pattern under electric field and in the remanent state for the sample with an orientation angle 𝜔 = 33°, whereas (b) introduces the pattern under electric field and in the remanent state for the sample with 𝜔 = -57°. The virgin state almost perfectly mimics the remanent state and is not displayed. Since a diffraction pattern in polycrystalline materials is composed of intensities of randomly oriented diffracting grains in space that fulfill the Bragg condition379, grains leading to ½(311)pc, (111)pc, and (200)pc reflections do not necessarily coincide. The diffraction patterns
presented in Figure 5.34 indicate the two extreme cases where the scattering vectors 𝑘ℎ𝑘𝑙 are
parallel (𝜔 = 33°) or orthogonal (𝜔 = -57°) to the applied electric field, respectively. From now the scattering vectors are referred to as 𝑘, since the spatial grain orientation for the analyzed cases compensates the spatial orientation of 𝑘.
Figure 5.34: Selected angular range of in situ neutron diffraction pattern depicting the
most relevant reflections for (a) 𝝎 = 33° and (b) 𝝎 = -57°.
In the remanent state, the (111)pc and (200)pc display features corresponding to a material with
small non-cubic distortions. This result is in agreement with the high resolution XRD results from sintered samples (Figure 5.33). Even though patterns of Figure 5.34 are plotted in a logarithmic scale, the ½(311)pc SSR cannot be distinguished from the background indicating a commensurate
phase. Upon the application of an electric field of 3 kV/mm, the ½(311)pc, (111)pc, and (200)pc
reflection positions and intensities vary significantly from the remanent state and with sample orientation. For the case of 𝐸∥𝑘 (Figure 5.34 (a)), the maximized shift in position of the main reflections indicates a strong electric field induced lattice strain. Apart from lattice strain, the considerable shift of the (200)pc and the apparent asymmetry of the reflection indicates peak
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splitting ascribed to texturing as indicated by the indexing performed for a T material with reflections corresponding to the (002)T and (020)T/(200)T lattice planes. The pronounced splitting of
the (200)pc indicates the presence of a T phase. It is noted that the absence of ½(311)pc SSR
indicates that the 𝑅3𝑐 symmetry previously observed in the BNT-ST with low ST content366 is not favored for this orientation and the electric field induced phase is commensurate. Moreover, since the ½(310)pc was not visible neither with nor without applied electric field, the most probable
symmetry for the T phase is 𝑃4𝑚𝑚 with polarization along [001]. Although a certain small amount of asymmetry becomes apparent in the (111)pc is not as clear as in (200)pc. For the case of 𝐸⊥𝑘
(Figure 5.34 (b)), main reflections are only slightly shifted from their positions. A considerable change of the (111)pc reflection is discerned for this sample orientation suggesting texturing. The
two (111)R peaks resulting from the texturing effect under electric field are marked. The presence
of the ½(311)pc SSR with a non-zero intensity indicates that an incommensurate phase was
nucleated with electric field. The ½(311)pc SSR are a result of either an increase in the correlation
length of the octahedral tilting with respect to the virgin/remanent state that was formerly below the detection limit of the measurement or to a non-zero (𝑎−𝑎−𝑎−) octahedral tilt angle.366 In either case, the results suggest the presence of a R phase with 𝑅3𝑐 symmetry and polarization along [111]. Therefore, the results indicate a selective orientation-dependent electric field induced phase transformation to either R or T phase. Moreover, the features of the ½(311)pc, (111)pc, and
(200)pc reflections indicating a pseudocubic structure in the remanent state suggest that the
electric field induced processes described are almost entirely reversible. In order to give further insight into the orientation-dependent phase transition, Figure 5.35 provides a contour plot of the ½(311)pc, (111)pc, and (200)pc reflection intensities as a function of sample orientation 𝜔 and 2𝜃
angular range. The cases previously analyzed for 𝐸∥𝑘 and 𝐸⊥𝑘 are marked by a white line. Note that the lines indicating each orientation with respect to the applied electric field have a non-zero slope since 𝜔 = 90° represents the electric field vector parallel to the incident beam. The contour plot in the remanent state (Figure 5.35 (a)) displays orientation independent intensities and positions corroborating the reversibility of the phase transition. In contrast, application of an electric field leads to a maximized shift in the peak position observed for 𝐸∥𝑘, although considerable peak shift is featured in a relatively broad 𝜔 range of 60° around the 33° sample orientation (Figure 5.35 (b)). This angular range indicates negligible intensity of the ½(311)pc SSR,
similar to the virgin and remanent states. Note that the negligible intensity of the ½(311)pc SSR
cannot be assigned to texturing, since this reflection does not admit splitting. Vanishing of the ½(311)pc SSR intensity may be explained by considering that this reflection is closer to 〈00𝑙〉 family
of directions, than to the 〈ℎℎℎ〉 ones. Therefore, the pseudocubic phase seems to transform preferentially under electric field to the T phase for the grains satisfying the Bragg condition oriented along the ½(311)pc. For the 𝜔 range near 𝐸⊥𝑘, the main reflections are slightly shifted to
higher diffraction angles indicating macroscopic shrinking perpendicular to the electric field direction. Meanwhile, the ½(311)pc SSR display a non-zero intensity in a considerably broad 𝜔
range. Therefore, it can be concluded that an orientation-dependent reversible phase transformation from a commensurate virgin state to an incommensurate state under electric field is observed, with the exception of grains satisfying the diffraction condition of the ½(311)pc for 𝐸∥𝑘
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Figure 5.35: In situ neutron diffraction patterns of the remanent state at 0 kV/mm and
applied electric field at 3 kV/mm for different sample orientation angles. The cases
corresponding to 𝑬∥𝒌 (𝝎 = 33°) and 𝑬⊥𝒌 (𝝎 = -57°) are marked. The resolution of the
contour plot in the 𝝎-𝜽 space is indicated by 274 x 12 experimental data points.
5.2.3
Microstructure Characterization
The heterogeneity of BNT-0.25ST discussed in Sections 5.2.1 and 5.2.2 is revealed by BF TEM of calcined powders in Figure 5.36 (a), which was taken along <112>pc zone axis. Figure 5.36 (b)
introduces a DF micrograph obtained using the R ½{ooo} SSR. The difference in contrast in both images is ascribed to different crystallographic orientations of the core and shell suggesting the presence of an incoherent interface. This result is in agreement with the XRD results of calcined powders (Figure 5.33).