Unprecedented lattice volume expansion on doping stereochemically active Pb²⁺ into uniaxially strained structure of CaBa_1−xPb_xZn₂Ga₂O₇

Abstract

Lone pair cations like Pb²⁺ are extensively utilized to modify and tune physical properties, such as nonlinear optical property and ferroelectricity, of some specific structures owing to their preference to adopt a local distorted coordination environment. Here we report that the incorporation of Pb²⁺ into the polar “114”-type structure of CaBaZn₂Ga₂O₇ leads to an unexpected cell volume expansion of CaBa_1-xPb_xZn₂Ga₂O₇ (0 ≤ x ≤ 1), which is a unique structural phenomenon in solid state chemistry. Structure refinements against neutron diffraction and total scattering data and theoretical calculations demonstrate that the unusual evolution of the unit cell for CaBa_1-xPb_xZn₂Ga₂O₇ is due to the combination of the high stereochemical activity of Pb²⁺ with the extremely strained [Zn₂Ga₂O₇]⁴⁻ framework along the c-axis. The unprecedented cell volume expansion of the CaBa_1−xPb_xZn₂Ga₂O₇ solid solution in fact is a macroscopic performance of the release of uniaxial strain along c-axis when Ba²⁺ is replaced with smaller Pb²⁺.

Introduction

Lone pair (LP) cations (Tl⁺, Pb²⁺, Bi³⁺, Te⁴⁺, Sb³⁺, I⁵⁺, etc.) with (n−1)d¹⁰ns² electronic configurations are prone to adopt an asymmetric coordination environment and thus form a locally distorted structural unit possessing a dipolar moment. A long-range ordered alignment of such asymmetric units may break the inversion symmetry of the structure, possibly leading to a polar structure with intriguing properties. The strategy of using asymmetric units with LP cations is extensively utilized to design and synthesize noncentrosymmetric structures with enhanced nonlinear optical properties^{1,2,3,4,5,6,7}. Moreover, LP cations in polar structures may lead to spontaneous electric polarizations and form ferroelectric structure, e.g., BiFeO₃⁸. In some cases, such LP cations-induced ferroelectricity can also trigger large negative thermal expansion (NTE) upon warming, which has also been extensively investigated in PbTiO₃-based perovskites^{9,10,11,12,13}.

Recently, the stereochemical activity owing to the LP electrons of Sn²⁺ in CsSnBr₃¹⁴, and Pb²⁺ and Sn²⁺ in rock-salt chalcogenides PbS¹⁵, PbTe¹⁵, and SnTe¹⁶, is shown to cause a local symmetry lowering in a limited temperature range upon warming. This phenomenon is unique because it is an opposite behavior to that of most crystals showing symmetry lowering on cooling. X-ray and neutron total scattering experiments revealed that the progressively local distortion state in these compounds stems from the lattice expansion-induced dynamic off-center displacement of LP cations upon warming^14,15.

As described above, the incorporation of the stereochemically active LP cations into some structures brings not only intriguing physical properties but also some uncommon phenomena. In this work, we report another unprecedented phenomenon based on stereochemical activity of LP cations, i.e., cell volume expansion in solid solutions of CaBa_1−xPb_xZn₂Ga₂O₇ (0 ≤ x ≤ 1) when substituting Ba²⁺ (r = 1.61 Å in 12-fold coordination) with smaller Pb²⁺ (r = 1.49 Å in 12-fold coordination)¹⁷. Ostensibly, the abnormal cell volume expansion in CaBa_1−xPb_xZn₂Ga₂O₇ is ascribed to the fact that the expansion of the c axis (0.11 Å) is much larger than the contraction of the a axis length (0.011 Å) in the space group P6₃mc. Neutron pair distribution function (nPDF) data analyses confirm that CaBa_1−xPb_xZn₂Ga₂O₇ locally adopt a distorted orthorhombic structure (Pna2₁); however, this local distortion is not responsible for the abnormal cell volume expansion, as suggested by the Rietveld refinements based on high-resolution X-ray and neutron diffraction (ND) data. Density functional theory (DFT) calculations reveal that Pb²⁺ 6s6p orbitals are highly hybridized with O²⁻ 2p orbitals, which leads to the formation of a strong covalent bond and the resulting structural strain of the original [Zn₂Ga₂O₇]⁴⁻ framework is released by significantly elongating the c axis length.

Results

Unexpected cell volume expansion for CaBa_{1− x}Pb_xZn₂Ga₂O₇

CaBa_1−xPb_xZn₂Ga₂O₇ crystallize in the so-called “114”-type oxide structure, where the [BaO₃] and [O₄] layers form a mixed cubic and hexagonal closed-packing ionic structure with the stacking sequence of -CBABC-, leaving the octahedral and tetrahedral cavities partially occupied by Ca²⁺ and Zn²⁺/Ga³⁺ cations, respectively¹⁸. This structure is more commonly viewed as a layered structure with alternating stacking of triangular and Kagome layers along the polar axis. Up to now, nitrogen ions and various metal cations could be incorporated into this structure^{19,20,21,22,23}. This work is the report of Pb²⁺ doping.

Powder X-ray diffraction (XRD) patterns for CaBa_1−xPb_xZn₂Ga₂O₇ (Supplementary Fig. 1) indicate the phase purity as well as the high crystallinity of the samples. The anisotropic change of the lattice parameters can be readily visualized from XRD, as the position for the (004) reflection evolves to lower angles, whereas the position for the (200) reflection shifts to higher angles on the Pb²⁺-to-Ba²⁺ substitutions. It is firmly corroborated by plotting the lattice parameters against the Pb²⁺ content (Fig. 1), where the unit cell lattice contracts and expands along the a and c-axes, respectively. Such an anisotropic change leads to an overall expansion of the unit cell volume for CaBa_1−xPb_xZn₂Ga₂O₇ up to x = 0.7 and saturates thereafter. As discussed above, given the smaller ionic radius of Pb²⁺ compared with that of Ba²⁺, this is an unexpected and unique structural phenomenon in solid state chemistry. One might argue that the simple comparison of the cationic radii for Ba²⁺ and Pb²⁺ is not sufficient because the ionic size for LP cation-like Pb²⁺ is not well defined owing to their typical distorted coordination environment. Therefore, a series of Ba²⁺- and Pb²⁺-containing compounds with identical structure types were compared in terms of their cell volumes per formula, as summarized in Supplementary Table 1. It is obvious that all the Pb²⁺-containing compounds possess smaller volumes in comparison with those of Ba²⁺-containing compounds, which confirms that the observed cell volume expansion in CaBa_1−xPb_xZn₂Ga₂O₇ is unprecedented.

Fig. 1: Lattice parameters.

Plots of the average A-site size and refined lattice parameters for CaBa_1−xPb_xZn₂Ga₂O₇ along with the increasing Pb content. The average radius of A-site cation is calculated according to the equation: r(A²⁺) = (1−x) r(Ba²⁺) + x r(Pb²⁺). Source data are provided as a Source Data file.

Furthermore, we synthesized CaBa_0.5Sr_0.5Zn₂Ga₂O₇ for comparison, because Sr²⁺ (r = 1.44 Å) has a comparable cationic radius with Pb²⁺¹⁷, however, the Sr²⁺-to-Ba²⁺ substitution led to a significant cell volume contraction, i.e., V = 351.55 ų for CaBa_0.5Sr_0.5Zn₂Ga₂O₇ and 356.73 ų for CaBaZn₂Ga₂O₇. Accordingly, we conclude that it is not the cationic size that governs the lattice expansion in CaBa_1−xPb_xZn₂Ga₂O₇, instead, it strongly points to the special characteristics of Pb²⁺ (6 s² LP electrons).

Reciprocal space structure refinements

Crystal structures for all solid solutions were investigated by Rietveld refinements using XRD data so as to reveal the origin of this unexpected cell volume expansion. CaBaZn₂Ga₂O₇ was used as the starting structural model (P6₃mc) for structure refinements. Zn²⁺ and Ga³⁺ could not be distinguished by X-ray scattering owing to their similar atomic form factors, thus Zn²⁺ and Ga³⁺ were treated as the same cation during the Rietveld refinements on XRD. As all the samples were found phase pure and metal disorder between (Ba, Pb) and (Ga, Zn) sites is implausible due to very large difference in size (>220%), the occupancy factors for Ba²⁺ and Pb²⁺ were fixed to the nominal values. Finally, a model with anisotropic atomic displacements (ADPs) was used to account for the local displacement disorder Ba²⁺/Pb²⁺ cations in CaBa_1−xPb_xZn₂Ga₂O₇ (0 < x < 1) (see more detail in Supplementary Note 2). The ADPs for the (Ba/Pb) site were found elongated along the c axis (Supplementary Table 2), which is consistent with the LP effect of Pb²⁺. Moreover, the U₃₃/U₁₁ ratio evolution with x proved a good indicator of the structural strain being relieved with increasing content of Pb²⁺. At low doping levels, where the geometry of the crystal structure is determined mostly by Ba²⁺, the local displacements mimicked by the ADPs are the largest (Supplementary Fig. 2). Further increasing content of Pb²⁺ relieves the strain by stretching the c axis and the ADPs become progressively isotropic. In the composition with the highest x, it is Pb²⁺ that controls the crystal structure geometry and c axis becomes too long for Ba²⁺ and ADP becomes a flattened ellipsoid within the ab-plane, so CaPbZn₂Ga₂O₇ was described with a site splitting model. The refinements converged rapidly to give stable structures with reasonable crystallographic parameters and advantageous agreement factors for the solid solutions. The final Rietveld refinement patterns for solid solutions are presented in Supplementary Fig. 3. The resultant crystallographic data are summarized in Supplementary Tables 2 and 3.

To determine the crystal structure accurately, high-resolution constant wavelength ND data and Cu Kα1 data for representative compositions CaBa_1−xPb_xZn₂Ga₂O₇ (x = 0, 0.5, and 1) were collected. By ND, the occupancy factors of Ga³⁺ and Zn²⁺ at T sites could be determined, because there is a large contrast in neutron scattering length between Zn²⁺ (5.68 fm) and Ga³⁺ (7.29 fm). Combined Rietveld refinements against both the ND and XRD data revealed that the occupancy factor for Zn²⁺ at T1 site converged to ~ 0.21 for all compositions, which confirms that the evolution of cell parameters and cell volume as a function of x is driven by Pb²⁺ content, and not by Zn/Ga distribution, which remains constant across the series.

It is noteworthy that the local displacement of Pb²⁺ does not cause any average structure symmetry lowering and the CaBa_1−xPb_xZn₂Ga₂O₇ samples can be well described using P6₃mc. All these observations in CaBa_1−xPb_xZn₂Ga₂O₇ are thus different from other isostructural oxides without stereochemically active cations, e.g., MAZn₂Ga₂O₇ (M = Ca²⁺, Sr²⁺; A = Ba²⁺, Sr²⁺), where successive symmetry lowering and cation disorder-order transitions were observed¹⁸. Such symmetry and cation disorder-order transitions might be observed for CaBa_1−xPb_xZn₂Ga₂O₇ at lower temperatures. The plots of combined Rietveld refinements are presented in Fig. 2 and Supplementary Fig. 4. The final crystallographic data and selected interatomic distances are summarized in Supplementary Tables 4 and 5.

Fig. 2: Reciprocal space structure refinements.

Combined Rietveld refinement plots of Cu Kα₁ XRD and constant wavelength ND data for CaPbZn₂Ga₂O₇ refined with the P6₃mc model. The overall reliability factors for combined Rietveld refinements are R_wp = 6.44%, R_p = 4.77%. Source data are provided as a Source Data file.

Real space structure refinements

Combined Rietveld refinements using both XRD and ND data are powerful to analyze the average structure. On the other hand, the total scattering technology allows both the coherent and diffuse components of the XRD/ND pattern to be properly accounted for when modeling a crystal structure. We utilized nPDF analyses to reveal the evolution of local structural distortions and cationic ordering, which helps understand the unique cell volume expansion phenomenon in CaBa_1−xPb_xZn₂Ga₂O₇.

The normalized structure functions and nPDFs for CaBa_1−xPb_xZn₂Ga₂O₇ (x = 0, 0.5, and 1) are presented in Supplementary Fig. 5. Apparent shift of the positions of Pb/Ba−O and Zn/Ga−Zn/Ga pairs are observed for the nPDFs (Supplementary Fig. 5b), which is in line with the results deduced from XRD and ND. The peak for nearest Zn/Ga−O pairs is almost symmetric although the cationic size difference for Zn²⁺ and Ga³⁺ is large. Moreover, owing to the overlap of the positions between Zn/Ga−Zn/Ga and Pb/Ba−O pairs, the local Zn/Ga ordering cannot be visually observed. Apart from the change of peak positions, another noteworthy feature is the obvious decrease or increase in the magnitude of the atomic pairs with increasing Pb²⁺ content, i.e., Zn/Ga−O and Ca−O pairs, indicating a wide range of atomic distributions. This observation suggests the Pb²⁺ doping may lead to a local structure distortion.

Then real space refinements were performed against the neutron PDF data with the average structure model (P6₃mc) obtained from the combined refinement. However, this model does not reproduce well the peak at ~ 2.3 Å, which is corresponding to the Ca−O pairs (Fig. 3 and Supplementary Fig. 6). Moreover, this structure model also overestimates the Zn/Ga−O distances (at ~ 4.8 and 6.3 Å) by ~ 0.08 Å. These observations suggest that neither the CaO₆ nor (Zn/Ga)O₄ polyhedra extracted from the neutron PDF data can be well described by the average structure model, especially in the low r range. This is a strong indication of the local structural distortion in CaBa_1−xPb_xZn₂Ga₂O₇. To gain an accurate picture of the local structure, structure models in the space group P31c and Pna2₁, which allow the free distortion of (Zn/Ga)O₄ tetrahedra, were employed. As shown in Fig. 3 and Supplementary Fig. 6, the refinement using the P31c model gives agreement similar to that of the P6₃mc model, whereas the refinements using the Pna2₁ model provides an excellent fit for both peaks of Ca−O and Zn/Ga−O pairs. Therefore, the local structure for CaBa_1−xPb_xZn₂Ga₂O₇ exhibits a lower symmetry, Pna2₁. Because both Pb²⁺-containing and -free compounds are locally distorted, such a local structure distortion unambiguously ascribes to Zn²⁺/Ga³⁺ disordering, rather than the Pb²⁺-to-Ba²⁺ substitutions. It was recently reported that a similar cation inversion disordering induced a local structure distortion in spinel Mg_1−xNi_xAl₂O₄ and CuMn₂O₄^24,25, which were also probed by the neutron total scattering technique. Here, the refined nanoscale structures for CaBa_1−xPb_xZn₂Ga₂O₇ (x = 0 and 1) (Supplementary Fig. 7) demonstrate that the local orthorhombic distortion is not significant, further indicating the distortion on the long range would be also insignificant. The lattice parameters extracted from neutron PDF analyses also exhibit an anisotropic shrinkage and expansion within the ab-plane and along the c axis (Supplementary Fig. 8), respectively, which results in the increase of the unit cell volume with the increasing Pb²⁺ content.

Fig. 3: Real space structure refinements.

Real space Rietveld refinements of neutron PDF data for CaBaZn₂Ga₂O₇ and CaPbZn₂Ga₂O₇ with P6₃mc, P31c, and Pna2₁ models. Source data are provided as a Source Data file.

Combined reciprocal and real space Rietveld refinements against ND and PDF data were further performed to reveal the long-range structure symmetry. In the long range, only the P6₃mc and P31c models were considered because the reflection conditions for the Pna2₁ model are not consistent with the ND data. As shown Supplementary Figs. 9–11, all the PDF peaks for CaBa_1−xPb_xZn₂Ga₂O₇ (x = 0, 0.5, 1) in long range (30–50 Å) can be well produced by the P6₃mc model with reliable factors comparable with or even better than that of the low symmetry P31c model, demonstrating the long-range structure symmetry for CaBa_1−xPb_xZn₂Ga₂O₇ is P6₃mc, which is in good agreement with the combined Rietveld analysis of XRD and ND data.

Structure evolution

Figure 4 and Supplementary Fig. 12 give the comparison crystal structures for CaBa_1−xPb_xZn₂Ga₂O₇ (x = 0 and 1) and CaBa_0.5Sr_0.5Zn₂Ga₂O₇. Apparently, Ba²⁺/Sr²⁺ in CaBaZn₂Ga₂O₇ and CaBa_0.5Sr_0.5Zn₂Ga₂O₇ are located in the same ab-plane defined by O3 anions. In contrast, the Pb²⁺ cations in CaPbZn₂Ga₂O₇ show stereochemical activity with a significant displacement along the polar c axis, which can be also deduced from the change of Ba²⁺/Pb²⁺−O interatomic distances in CaBa_1−xPb_xZn₂Ga₂O₇ (0 ≤ x ≤ 1). As shown in Fig. 5a, the difference between the group of Ba²⁺/Pb²⁺−O1 bond lengths becomes larger when increasing the Pb²⁺-content. The Ba²⁺/Pb²⁺−O3 bond also exhibits an increasing trend (Fig. 5b). Such evolution of Ba²⁺/Pb²⁺−O bond lengths indicates that the Pb²⁺ cation displaces from the center of the [Ba/PbO₁₂] dodecahedron rather than merely attracts the apical oxygen atom closer as in the case of CaBa_0.5Sr_0.5Zn₂Ga₂O₇ (Supplementary Table 3).

Fig. 4: Crystal structures for CaBaZn₂Ga2O₇ and CaPbZn₂Ga₂O₇.

Crystal structures were obtained from the combined Rietveld refinements on ND and XRD data with the P6₃mc model. In both structures T1 and T2 sites are co-occupied by Ga³⁺ and Zn²⁺ but with different occupancies, where T1 site is dominated by Ga³⁺ with an occupancy factor of 0.79(3), accordingly T2 site is mainly occupied by Zn²⁺ with an occupancy factor of 0.60(2). The black arrows represent the shift direction of oxygen atoms.

Fig. 5: Evolution of Ba/Pb−O bond lengths and Ba/Pb displacements.

Plots of Pb²⁺/Ba²⁺−O1 bond lengths a, Pb²⁺/Ba²⁺−O3 and average < Pb²⁺/Ba²⁺−O > bond lengths b, and average Pb²⁺/Ba²⁺ displacement distance c against the Pb content in CaBa_1−xPb_xZn₂Ga₂O₇. The inset shows the coordination environment of Ba²⁺/Pb²⁺ in CaBa_1−xPb_xZn₂Ga₂O₇ (0 < x < 1) obtained from Rietveld refinements against XRD data with the P6₃mc model, where a highly anisotropic thermal motion along c axis can be visually observed. For x = 0, 0.5, and 1, the parameters are obtained from combined Rietveld refinement against both XRD and ND data. Source data are provided as a Source Data file.

The calculated average deviation distance (D) for Ba²⁺/Pb²⁺ continuously increases along with the increase of the Pb²⁺ content (Fig. 5c). The largest D value ~ 0.5 Å is observed in CaPbZn₂Ga₂O₇. Such a significant deviation of Pb²⁺ from the O3-plane towards to O1 results in a very irregular coordination environment for Pb²⁺. The shortest Pb−O bond length (2.337 Å) in CaPbZn₂Ga₂O₇ is comparable with the values in Ca₂PbGa₈O₁₅ (2.29 Å)²⁶, PbTiO₃ (2.51 Å)²⁷, and PbRuO₃ (2.50 Å)²⁸, where the Pb 6s6p orbitals are all strongly hybridized with O 2p orbitals. So it is expected that the Pb²⁺ 6s6p orbitals in CaPbZn₂Ga₂O₇ are also strongly hybridized with O 2p orbitals, which is further corroborated by DFT calculations. For example, the density of states analyses for CaPbZn₂Ga₂O₇ (Supplementary Fig. 13) indicate that both the bottom of the conduction band and the top of the valence band comprise the Pb²⁺ 6s6p states, which is a solid evidence of the hybridization between Pb 6s6p and O 2p orbitals.

Discussion

As discussed above, both real space and reciprocal data analysis decipher that the unprecedented cell volume expansion for CaBa_1−xPb_xZn₂Ga₂O₇ (0 ≤ x ≤ 1) from nanoscale to a long-range scale is ascribed neither to the local structure distortion nor the cationic ordering. All these results deduced from the structure refinements point to the stereochemical activity of Pb²⁺. LP induced displacement along a polar axis is commonly observed for many Bi³⁺ and Pb²⁺-containing perovskites, i.e., BiMO₃^29,30,31 and PbMO₃ (M = transition metals)^32,33, which always results in a large tetragonality with c/a > 1.0. This enhanced tetragonality is closely related to the highly hybridization between Pb²⁺ 6 s² and O²⁻ 2p orbitals, which is indeed observed in (x)BiFeO₃-(1−x)PbTiO₃³⁴ and Pb_0.8-xLa_xBi_0.2VO₃¹² solid solutions. Here in CaBa_1−xPb_xZn₂Ga₂O₇, the enhancement of c/a values is also accompanied with the increase of the stereochemical activity of Ba/Pb²⁺ cations (or enhancement of Ba²⁺/Pb²⁺−O covalency) (Fig. 6a). This observation corroborates that the structural anisotropy as well as the cell volume expansion for CaBa_1−xPb_xZn₂Ga₂O₇ is dominated by the stereochemically active LP electrons of Pb²⁺. Moreover, the c/a value for CaPbZn₂Ga₂O₇ can be reduced upon heating (Supplementary Fig. 14), which is similar to the PbTiO₃-based ferroelectricity-NTE materials^9,10. This observation further reinforces the hypothesis that the stereochemical activity of Pb²⁺ is responsible for the anisotropic lattice expansion. However, NTE is not realized for CaPbZn₂Ga₂O₇ and an expansion of the c axis rather than contraction was observed, suggesting the unique structure for “114” oxides should be also responsible for the lattice volume expansion.

Fig. 6: Evolution of c/a values.

Plots of c/a values against a the doping Pb content and b the stereochemical lone pair activity (average displacements for Ba²⁺/Pb²⁺ cations) in CaBa_1−xPb_xZn₂Ga₂O₇. For x = 0, 0.5, and 1, the parameters are obtained from combined Rietveld refinement against both XRD and ND data. Source data are provided as a Source Data file.

To further elucidate this conjecture, we also prepared the solid solutions of Ba_1−yPb_yTiO₃ (y = 0, 0.5, and 1). Pb²⁺-to-Ba²⁺ substitutions in Ba_1−yPb_yTiO₃ also lead to an anisotropic change of the cell dimensions as expected, however the cell volume shrinks (Supplementary Figs. 15 and 16). For Ba_1−yPb_yTiO₃, the enhancement of A-site stereochemical activity also leads to an obvious off-center shift of Ti⁴⁺ along the c axis, which in turn results in a significant contraction of the a axis, which compensates c axis elongation, so that the overall cell volume decreases. In contrast, the crystal structure for “114” oxides is highly strained in comparison with the flexible framework of perovskite, which can be deduced by the c/a value and bond valence sum (BVS) calculations^35,36. The c/a value for CaBaZn₂Ga₂O₇ (~ 1.605) is much smaller than the ideal closed-packing value (c/a_ideal = 1.633) and the BVS for Ca²⁺ in CaBaZn₂Ga₂O₇ is estimated to be 2.48(1). All that suggests the fact that [Zn₂Ga₂O₇]⁴⁻ anionic framework is highly strained along the c axis (or c axis is over-compressed), especially for the triangular layers because Ca²⁺ is seriously over-bonded (Fig. 4).

Structure strain is usually released through structure symmetry lowering and polyhedral distortion/rotation, which was observed indeed in numerous “114” oxides such as LnBaFe₄O₇ (Ln = Y, Dy–Lu)^23,37, LnBaCo₄O₇ (Ln = Ca, Y, Tb–Lu)^38,39,40, and MAZn₂Ga₂O₇ (M = Ca²⁺, Sr²⁺; A = Sr²⁺, Ba²⁺)¹⁸. Herein, the structure strain of CaBa_1−xPb_xZn₂Ga₂O₇ is released without a significant distortion of the [Zn₂Ga₂O₇]⁴⁻ framework, that is, the stereochemically active LP effect of Pb²⁺ helps the release of the structure strain. In detail, the LP active Pb²⁺ displaces from the center of the [Ba/PbO₁₂] dodecahedron to form strong covalency bonds with O1, which attenuates the covalency of [Zn₂Ga₂O₇]⁴⁻ anionic framework and drives displacement of O1 and O2 downwards along the c axis (Fig. 4b), resulting in a relief of uniaxial structure strain through a significant expansion of the c axis. Such a significant expansion for c axis further leads to an enhancement of the c/a value to 1.626 for CaPbZn₂Ga₂O₇ and improvement of BVS value for Ca²⁺ in CaPbZn₂Ga₂O₇ to 2.31(4), suggesting the anisotropic lattice-change and cell volume expansion is cooperative with the release of uniaxial structure strain along the c axis in CaBa_1−xPb_xZn₂Ga₂O₇. Thus, the expansion of polar c axis for CaPbZn₂Ga₂O₇ upon heating, which is different from the behavior of NTE materials, is also understandable. Finally, we can conclude that both the anisotropic chemical pressure induced by the highly stereochemical active LP electrons of Pb²⁺ and the uniaxial structure strain along c axis are responsible to the unprecedented cell volume expansion in CaBa_1−xPb_xZn₂Ga₂O₇ solid solutions. In summary, substitution of Ba²⁺ in CaBaZn₂Ga₂O₇ with the smaller but stereochemically active Pb²⁺ results in an unprecedented lattice volume expansion, which has not been observed in solid state chemistry to the best of our knowledge. Both reciprocal and direct space XRD and ND data analysis were utilized to decipher the origin of this unique phenomenon on the scale of both local and average structure of CaBa_1−xPb_xZn₂Ga₂O₇. The results revealed that the LP electrons of Pb²⁺ are highly stereochemically active in this uniaxial greatly strained framework. Further DFT calculations revealed that the Pb²⁺ 6s6p orbitals are highly hybridized with O²⁻ 2p orbitals. The combined effect of these factors is the displacement of Pb²⁺ along the c axis, resulting in the release of structure strain associated with the axial cell expansion that is not compensated by contraction of the ab-plane and in turn produces the overall cell volume expansion of CaBa_1−xPb_xZn₂Ga₂O₇. In general, our findings open new opportunities to use stereochemically active cations (Pb²⁺, Sn²⁺, Bi³⁺, etc.) to tune crystal structural strain, which has important role in ferroic materials.

Methods

Sample preparation

Polycrystalline samples of CaBa_1−xPb_xZn₂Ga₂O₇ (0 ≤ x ≤ 1) and CaSr_0.5Ba_0.5Zn₂Ga₂O₇ were prepared by conventional high temperature solid state reactions. Calcium carbonate (CaCO₃, 99.99%), barium carbonate (BaCO₃, 99.99%), strontium carbonate (SrCO₃, 99.99%), lead oxide (PbO, 99.9%), zinc oxide (ZnO, 99.99%) and gallium oxide (Ga₂O₃, 99.99%) were used as starting materials. All the raw materials except for PbO were heated at 500 °C for 10 h before being weighted, in order to remove any adsorbed moisture. Stoichiometric raw materials were mixed and ground in an agate mortar and pre-heated at 800 °C for 10 h to decompose the carbonate. After this initial calcination, the resultant powder samples were re-ground thoroughly by hands and pressed into a pellet (φ = 13 mm). With increasing the doping content of Pb²⁺, the synthetic temperatures of CaBa_1−xPb_xZn₂Ga₂O₇ decrease owing to the relative low melting point of PbO. The pellets were heated in the range of 860–1100 °C for 60 h with intermediate re-grindings. Moreover, for the preparation of CaBa_1−xPb_xZn₂Ga₂O₇ (0.7 ≤ x ≤ 1), additional 10 mg PbO should be added to compensation the volatilization of PbO after every cycle of calcination. CaSr_0.5Ba_0.5Zn₂Ga₂O₇ was prepared by heating raw materials at 1100 °C for 45 h with intermediate re-grindings.

Structure characterizations

The phase purity of the samples can be ensured by powder XRD. XRD was performed on a PANalytical Empyrean powder diffractometer equipped with a PXIcel 1D detector. Room temperature constant ND data for CaBa_1−xPb_xZn₂Ga₂O₇ (x = 0 and 0.5) (λ = 2.0775 Å) and CaPbZn₂Ga₂O₇ (λ = 1.6215 Å) were collected at the BT-1 high-resolution ND diffractometer at the NIST Center for Neutron Research (NCNR) and ECHIDNA high-resolution powder diffractometer at the OPAL research facility (Lucas Heights, Australia)⁴¹, respectively. Combined Rietveld refinements on ND and X-ray data were performed using the TOPAS-Academic V6 software⁴².

Neutron total scattering experiments were performed at room temperature utilizing the nanoscale ordered materials diffractometer (NOMAD) at the spallation neutron source located at Oka Ridge National Laboratory. About 150 mg of each sample were loaded into a 2 mm diameter quartz capillary for measurements at room temperature with a collection time of ~ 2 h per sample. The PDF, G(r), was obtained through the Fourier transformation of S(Q) with Q value between 0.1 and 31.4 Å.

DFT calculations

Theoretical study of CaPbZn₂Ga₂O₇ was carried out using Vienna ab-initio simulation package (VASP)⁴³. The projector augmented-wave method implemented in the VASP code was utilized to describe the interaction between the ionic cores and the valence electrons⁴⁴. The generalized gradient approximation parameterized by Perdew, Burke, and Ernzerhof was employed to describe the exchange-correlation potential in the standard DFT calculations⁴⁵. For single point energy and density of states, a cutoff energy of 500 eV for the plane-wave basis and 13 × 13 × 7 Monkhorst-Pack G-centered k-point meshes were employed.