Due to the presence of superstructure reflections the Bragg peaks of the NBT-0.048BT crystal were indexed using a double cubic perovskite cell with the unit-cell parameter at atmospheric pressure \(a_0=7.7997(4)\). Reconstructed hk0 and hk1 reciprocal-space layers of NBT-0.048BT at selected pressures up to 7.9 GPa are shown in Figs. 1 and 2. As pointed out above, the XDS scattering in the hk0 and hk1 layers is indicative of intermediate-range order of cationic off-center displacements and of octahedral tilts, respectively.Figure 1(hk0) reciprocal space layers of NBT-0.048BT at selected pressures from ambient pressure to 7.9 GPa. The areas marked with a dashed rectangle in (a) are shown enlarged in (b). The reflections are indexed in a doubled cubic perovskite cell. The grey and white arrows mark representative ooe and oee reflections, respectively, while the black arrows point to the satellite reflections visible around {220} reflections in the data measured at ambient pressure in air.Figure 2(hk1) reciprocal space layers of NBT-0.048BT at selected pressures from ambient pressure to 7.9 GPa. The reflections are indexed in a doubled cubic perovskite cell. The black, grey and white arrows mark representative ooo, ooe and oee reflections, respectively.At ambient pressure the XDS around hk0 reflections with \(h, k\ne 0\) has an ellipsoidal shape elongated along \(\langle 110\rangle _\mathrm{{pc}}\) rather than an L-type shape as for pure NBT10, while that around h00 and 0k0 Bragg peaks exhibits a butterfly shape instead of ellipsoidal-like/T-shape along \(\langle 100\rangle _\mathrm{{pc}}\). Thus, at ambient conditions XDS of NBT-0.048BT exhibits the same features as those observed for NBT-0.05BT16 as well as for NBT-0.056BT2, and resembles the XDS typical of Pb-based relaxor ferroelectrics34. This indicates that the presence of Ba with MPB concentrations (\(x\sim 0.05\)) results in nanoregions with cationic polar shifts correlated within \(\{110\}_\mathrm{{pc}}\) planes34, which are surrounded by a pseudocubic polarizable matrix, in contrast to pure NBT, which has small platelets with correlated \(\langle 100\rangle _\mathrm{{pc}}\) A-cation displacements dispersed in a rhombohedral/pseudorhombohedral matrix10,11,35. However, in the vicinity of {220} reflections there are satellite reflections along \(\langle 100\rangle\), which both have a similar intensity and are offset by \(\sim\)0.3 and \(\sim\)0.6 reciprocal lattice units (r.l.u.). Most probably those satellite reflections are due to an incommensurate modulated structure on a length scale of approximately three times the double cubic structure (\(\sim\)24 Å); similar modulated structures with a different periodicity have been also observed for pure NBT and NBT-0.04BT36,37.Upon pressure increase the XDS in the hk0 layer changes, and at moderate pressures between 0.7 and 2.8 GPa it resembles that of pure NBT at atmospheric pressure and room temperature. This shows that external hydrostatic pressure reverses the effect of chemically-induced internal local-stress fields related to the incorporation of large-size Ba\(^{2+}\) at the A site38. The XDS of pure NBT originates from planar nanoregions with correlated \(\langle 100\rangle _\mathrm{{pc}}\) shifts of A-site Na\(^+\) and Bi\(^{3+}\) cations within the pseudorhombohedral matrix, analogous to Guinier-Preston zones10,37. Apparently, moderate external hydrostatic pressure reinforces this structural state also in NBT-0.048BT, overcoming the chemical effect of embedded Ba\(^{2+}\) cations. This suggests how Ba doping modifies the NBT-xBT structure at ambient conditions. Since the applied external pressure is isotropic, it seems unlikely to be able to change the preferred direction of polar cationic shifts within the nanodomains, while at the same time suppressing the polar long-range order in the matrix. A more plausible scenario is that at MPB concentrations barium enters both the pseudorhombohedral matrix and tetragonal nanoregions, disturbing the correlation length of coherent cationic shifts in both the pseudorhombohedral matrix and tetragonal-type platelet zones. This results in a pseudocubic matrix of uncorrelated polar distortions, which can mutually align under an externally applied electric field37,39 , i.e. at the MPB the matrix is polarizable, as in the case of Pb-based relaxor ferroelectrics40,41,42. Remnants of pseudorhombohedral regions, stemming from the matrix, are still preserved, which give rise to the \(\langle 110\rangle _\mathrm{{pc}}\) oval-shape XDS. Due to the shrinking volume, external pressure overcomes the internal local elastic stresses in the vicinity of the A-site Ba\(^{2+}\), leading to an increase in the correlation length between tetragonal-type off-center shifts as well as between local distortions of pseudorhombohedral type, which is shown by the increasing intensity and sharpness of the diffuse scattering (Figs. 1 and 2).The satellite reflections arising from modulated structures are not observed at elevated pressures. Unfortunately it is unclear whether they are suppressed by pressure or they are just too weak to be measured inside a DAC.At 3.4-4.4 GPa the diffuse scattering streaks in the hk0 layers of NBT-0.048BT have reached their maximum length and strong but still diffuse scattering appears between adjacent ee0 Bragg reflections (see white arrows in Fig. 1a and b), which is a precursor of new oee Bragg reflections that appear above 5 GPa. At 5.5 GPa the XDS is strongly reduced. However, there are still remnants of the \(\langle 100\rangle _\text {pc}\) streaks, indicating that on a mesoscopic scale there is still a small fraction of tetragonal-type nanoregions that differ from the average high-pressure phase. The broad diffuse scattering at the lower-\(\theta\)-angle side of eee reflections (see e.g. 040 in Fig. 1), which results from the unequal scattering power of chemically disordered A-site Bi\(^{3+}\) and Na\(^{1+}\) cations10,14,15, is better seen at high pressures due to the suppression of the L-shaped XDS; this type of XDS persists at all pressures due to its chemical origin.The pressure dependence of the superstructure reflections gives information on the evolution of the octahedral tilt pattern. The R-point reflections (ooo) are systematically stronger than the M-point reflections (ooe); they appear clear and sharp, and increase in intensity in the whole pressure range measured (Fig. 3a). In contrast, the M-point reflections appear as diffuse short streaks that are elongated in \(\langle 100\rangle\) directions and have a very low intensity up to 3.4 GPa, just above 3\(\sigma (I)\), where \(\sigma (I)\) is the estimated uncertainty of the integrated intensity. Only above 4.4 GPa does the intensity of the diffraction around the M-point increase strongly in intensity (Fig. 3b). These observations unambiguously confirm the dominance of the anti-phase \(a^-a^-a^-\) octahedral tilt pattern (Fig. 3d) over in-phase \(a^0a^0c^+\) tilting (Fig. 3e) at ambient and low pressure, which above 4 GPa evolves into a pattern of unequal BO\(_{6}\) tilts, as suggested on the basis of Raman scattering analyses28. Precursor oee signals are observed already above 2.8 GPa, but they evolve into strong and sharp Bragg diffraction peaks only at 5.5 GPa (Fig. 3c). Bragg reflections of oee type are characteristic of distortions triggered by X-point phonons of the primitive cubic cell. The oee Bragg-diffraction maxima are significantly stronger than the ooe peaks, indicating that the X-point distortion involves A-site cationic off-centered displacements19,43. Hence, the co-appearance of M- and X-point reflections, along with the pre-existing R-point reflections, reveals a change in the octahedral tilt pattern from anti-phase to mixed (Fig. 3d,f), accompanied by the development of antipolar long-range order of A-cation shifts (Fig. 3g)19,43.Figure 3Pressure dependence of the integrated intensities of representative ooo (a), ooe (b) and oee (c) reflections. The intensities are averaged over all peaks, which are symmetry-equivalent with the Miller indices referring to the doubled pseudocubic unit cell.The octahedral tilting patterns relevant for NBT-0.048BT are shown in (d–f): pure anti-phase BO\(_6\) tilting (\(a^{-}a^{-}a^{-}\)), in-phase tilting around one axis (\(a^{0}a^{0}c^{+}\)) and mixed tilting (\(a^{-}a^{-}c^{+}\)); right-hand-side plots are viewed along \([001]_\mathrm{{pc}}\). A sketch of anti-polar A-cation displacements is shown in (g); for the sake of clarity the magnitude of the displacements is exaggerated. Figures (d–g) were prepared using VESTA45.Even though no splitting of any of the cubic Bragg peaks is observed, the additional reflections and the disappearance of most of the diffuse scattering at 5.5 GPa clearly show that a phase transition has taken place. The set of data collected in He (at 5.0, 8.1 and 12.3 GPa) indicates that at 5.0 GPa the phase transition has already occurred, and there are no further phase transitions detected up to 12.3 GPa, as no additional peaks appear at 8.1 and 12.3 GPa (see Supplementary Fig. S3 online). However, due to smaller crystal size and different experimental conditions the integrated intensities of the He data set are not included in Fig. 3.Structure refinements of the high-pressure phase are consistent with the orthorhombic space group Pnma (see Fig. 4), which was also found to be the symmetry to develop in pure NBT above \(\sim\)2 GPa27. The intensities used for the refinements with Jana200633 were integrated with CrysAlisPro32 using the doubled cubic unit cell, since the orthorhombic distortion of the crystal is very small. A detailed description of the refinement details is given in the supplementary material. The unit cell and refinement parameters of NBT-0.048T at 4.4-8.1 GPa are listed in Supplementary Table S3 online. At 12.3 GPa no successful structure refinement could be achieved due to poor data quality. However, the reconstructed hkl layers indicate that the symmetry should still be the same (see Supplementary Fig. S3 online). The higher R-value (\(R>5\%\)) and goodness of fit (GoF = 1.26) for the refinements at 4.4 GPa show that the structure has not fully adopted the Pnma symmetry yet. This is also seen in the high \(U_\text {eq}\) values of Bi/Na and O1 atoms, which indicate that the symmetry imposed during refinement prevents the atomic positions from being determined correctly. Also the presence of strong diffuse scattering in the reconstructed layers of the reciprocal space at 4.4 GPa (see Figs. 1 and 2) shows that the phase transition has not been completed yet. The same is seen when considering the pressure dependence of the integrated intensities (Fig. 3a–c), which shows an abrupt increase in intensity between 4.4 and 5.5 GPa. The structure refinements in Pnma for the data sets collected below 4.4 GPa only yielded unsatisfactory R-values. Hence, the low-pressure phase is pseudocubic although its structural features include octahedral tilts and A-cation polar shifts correlated at the mesoscopic scale. The unit cell parameters of the low pressure data are reported in Supplementary Table S2 online.Figure 4The high-pressure structure of NBT-0.048BT at 7.9 GPa refined in orthorhombic space group Pnma. AO\(_{12}\) polyhedra are shown in blue, BO\(_6\) octahedra in brown and oxygen atoms in white. All atoms are displayed as displacement ellipsoids. The corresponding refinement results are listed in Supplementary Tables S3–S5 online. This figure was prepared using VESTA45.Figure 5a shows the pressure dependence of the off-centering of the AO\(_{12}\) polyhedra, calculated as the difference between the cation coordinates and the averaged oxygen coordinates \(\mathbf {\overrightarrow\delta }_{A}=\overrightarrow{r}_{A}-\frac{1}{12}\times \sum _{i=1}^{12}\overrightarrow{r}_{iO}\)44, where \( \overrightarrow{r}\) refers to the corresponding position vector. In the Pnma phase the A-cations are only allowed to be off-set along a and c and the results show that above the phase-transition pressure the A-cation off-centering along the a axis significantly exceeds that along the c axis (Fig. 5a). The pressure dependence of the squared octahedral tilting angles \(\varphi ^2 =[(180 -\angle B’-O-B”)/2]^2\) calculated from the refined atomic structures above 4 GPa is shown in Fig. 5b . A simplified model using a Boltzmann growth function to fit the \(\overrightarrow {\delta }_{A}(p)\) and \(\varphi ^2(p)\) data points reveals an inflection point of 4.6(1) GPa, suggesting that this is the phase transition pressure (\(p_c\)). However the subtle but steady increase of \(\overrightarrow {\delta }_{A}\) and \(\varphi ^2\) above \(\sim\)5.0 GPa indicates that pressure continues to enhance the tilting of BO\(_6\) octahedra and off-centering of A-cations. It should be noted that in Pnma the Ti\(^{4+}\) cations are constrained to the centre of BO\(_6\) octahedra. On the other hand, the Raman scattering analysis of NBT-0.048BT indicates that the B-site off-centered shifts, although reduced, persist up to \(\sim\)9 GPa28. Therefore, the high-pressure phase of NBT-0.048BT should still comprise Ti\(^{4+}\) polar displacements, which however are uncorrelated and therefore, undetectable by XRD.Figure 5A-cation off-centering displacements \(\overrightarrow {\delta }_{A}\) (a) and squared octahedral tilting angles \(\varphi ^2\) (b). Filled symbols represent data on NBT-0.048BT from this study, assuming cubic structure below 4.4 GPa; lines are Boltzmann growth-function fits to the data points. Open symbols represent data derived from structure refinements on pure NBT by Thomas et al. 200527.On decompression the pressure-induced structural changes in NBT-0.048BT reverse, but the XRD pattern typical of the NBT-\(x_\mathrm{{MPB}}\)BT structural state at ambient conditions was reestablished only after a prolonged period of time (at least a few hours ). Given that the in situ high-pressure Raman-scattering experiments indicate that the local-scale structure recovers immediately28, this suggests that the dominant phase-transition mechanism is order-disorder rather than displacive, as the system needs a prolonged relaxation time to reach a thermodynamic equilibrium after the pressure release, with a structural state comprising abundant uncorrelated local ferroic distortions.Structure data for the high-pressure phase of pure NBT at 4.0-9.7 GPa have been published by Thomas et al. 200527. Within uncertainties, there is no clear difference between the calculated \(\overrightarrow {\delta }_{A}\) for the high-pressure phase of NBT and NBT-0.048BT (Fig. 5a). The equivalent isotropic atomic displacement parameters (\(U_{\text {eq}}\)) of the Bi/Na-atoms for pure NBT are lower at all reported pressures than those we obtained from our structure refinements for NBT-0.048BT (0.019(1)-0.010(1) \(\text{\AA}^{2}\) vs. 0.032(1)-0.026(1) \(\text{\AA}^{2}\)) (see Supplementary Table S4 online). The \(U_{\text {eq}}\) parameters of Ti are in the same order of magnitude (0.006(1)-0.015(1) for \(x=0\) vs. 0.012(3)-0.013(4) \(\text{\AA}^{2}\) for \(x=0.048\)), indicating that the different A-cation \(U_{\text {eq}}\) should not be due to different experimental conditions. The increased A-cation \(U_{\text {eq}}\) in NBT-0.048BT can be explained by substitutional disorder induced by Ba\(^{2+}\) cations, which have a larger ionic radius than Bi\(^{3+}\) and Na\(^+\) cations (1.61 Å vs. 1.36 and 1.39 Å). In addition, the larger \(U_{\text {eq}}\) may imply that not only the fraction of off-centered A-cations is increased in the Ba-doped compound (as indicated by Raman spectroscopy28), but also the dynamical disorder, i.e. the amplitude of atomic vector displacements of the off-centered A-site cations is higher compared to pure NBT. The octahedral tilt angle \(\varphi\) of the high-pressure phase of pure NBT27 tends to be higher than that of NBT-0.048BT (Fig. 5b). This indicates that the presence of large-sized Ba cations restrains the tilting of BO\(_6\) octahedra not only in terms of the correlation length as at low pressure, but also in terms of the degree of tilting in the high-pressure phase.
