Structural studies of CaAl₁₂O₁₉, SrAl₁₂O₁₉, La_2/3+δ Al_12–δO₁₉, and CaAl₁₀NiTiO₁₉ with the hibonite structure; indications of an unusual type of ferroelectricity

3.1 CaAl₁₂O₁₉

The structure of CaAl₁₂O₁₉ was refined from neutron diffraction data obtained at 11 K and 298 K. Three different structures were considered: paraelectric in space group P6₃/mmc with disordered dipoles (Fig. 1a), ferroelectric in space group P6₃mc (Fig. 1b), and antiferroelectric in space group P3̅m1 (Fig. 1c). Good Rietveld fits (Fig. S1–S5; Supporting Information online) at both temperatures were obtained regardless of the space group assumed. No new peaks were observed in the low temperature diffraction pattern. For space groups P6₃/mmc and P6₃mc the only systematic absence is for hhl reflections when l is odd. There are no systematic absences in space group P3̅m1, but intensities calculated for hhl relections with l odd are so weak (<0.1 % relative to the strongest peak) that they would not be observed even if present. The refinement in space group P6₃mc did not converge due to correlations between atomic positions caused by the increased number of variables in the lower symmetry space group. The refinement converged in space group P3̅m1. However, the fit did not improve significantly despite the six additional positional parameters. The structure was essentially unchanged except that now Al2 cations are ordered; there are no partially occupied sites. There was no improvement in the BVS values relative to the refinement in P6₃/mmc. Thus, we conclude that the structure is best described in P6₃/mmc at 298 and 11 K (Table 1). Therefore, the dipoles are disordered at both 11 and 298 K. This does not preclude a model with considerable dipole ordering in chains along the c axis, but with a random polarity between adjacent chains. The lack of a second harmonic generation signal (SHG) at room temperature for CaAl₁₂O₁₉, SrAl₁₂O₁₉, and PbAl₁₂O₁₉ indicates all are centric at room temperature. This rules out ferroelectric ordering at room temperature but does not rule out antiferroelectric ordering. Our room temperature relative-permittivity data on pellets of these three compounds do not suggest enhanced polarizability (Table S1; Supporting Information online), but the concentration of dipoles is very low and they are only expected to be active in one direction.

Bond valence sum calculations for the refinement in space group P6₃/mmc have shown low BVS values for Al3 in tetrahedral coordination and for Ca. These atoms would then be loosely bound and would be expected to show larger displacement parameters than the atoms showing BVS values close to those expected. The U value for Ca is much higher than the values obtained for Al or O (Table 1). However, high displacement values for Al3 were not observed when using harmonic terms only. This is not surprising because an ellipsoid is not an appropriate shape for displacements of an atom at a tetrahedral site. Figure 2 shows the result of refining displacement factors incorporating anharmonic terms for Al3 and Al4. The site symmetry is the same for Al3 and Al4, but Al4 is not at a tetrahedral site. We see that in fact the shape obtained for Al3 is very anharmonic. The Zn atom in hexagonal ZnO is in the same type of site as Al3 in CaAl₁₂O₁₉. But in ZnO the BVS for Zn and O are normal, and applying anharmonic terms shown that an isotropic description of displacement factors is adequate [26].

Fig. 2:

Shapes of anharmonic displacements for Al at (a) the Al3 site and (b) the Al4 site, both in 4f 3m. For the Al3 site there is major anharmonicity along the c axis, and minor anharmonicity perpendicular to c. For the Al4 site there is minor anharmonicity along c with more significant anharmonicity perpendicular to c.

3.2 SrAl₁₂O₁₉

Our neutron diffraction pattern for SrAl₁₂O₁₉ showed high angle shoulders for some, but not all, peaks (Fig. 3). Such shoulders can in some cases be modeled as anisotropic strain resulting from a sample with inhomogeneous composition. However, the shape of the peaks with shoulders in this case required a two-phase refinement. The cell dimensions of the main hexagonal phase and the minor hexagonal phase are a = 5.5766, c = 22.143 Å and a = 5.5718, c = 22.012 Å, respectively. The ratio of the two phases was about 4:1. The minor phase is contracted relative to the major phase by 0.6 % along c and only 0.09 % along a. Thus, the peak shoulders are caused almost exclusively by the contraction along c. Refinement of the primary phase indicated the presence SrAl₁₂O₁₉ with the hibonite structure (Table 2). Possibilities for the minor phase are suggested by findings in the Sr–Al–Mg–O system [27]. Single crystal studies in this system established both a β-alumina structure and a structure based on alternating layers of β-alumina and hibonite structures with ideal formulas of SrMgAl₁₀O₁₇ and Sr₂MgAl₂₂O₃₆, respectively. Without Mg and compensation with Sr vacancies, these formulae become Sr_0.5Al₁₁O₁₇ and Sr_1.5Al₂₃O₃₆. Both of these were evaluated as possible minor phases in our sample with the conclusion being that both structures gave an equivalently good result.

Fig. 3:

A section of the neutron diffraction pattern for SrAl₁₂O_19. High angle shoulders occur on some, but not all, peaks. These shoulders are caused by a second hexagonal phase that is structurally related to that of hibonite. These shoulders are mainly caused by shortening of the c cell edge in the minor hexagonal phase. (a) Without the second hexagonal phase; (b) with the second hexagonal phase. Red markers for primary phase; black markers for minor phase.

3.3 La_2/3+δAl_12–δO₁₉

Refinement of our neutron diffraction data on the hibonite structure in the La/Al/O system gave results (Tables 3 and 4) similar to those obtained from two different single crystal XRD studies reported in 1984 [13, 14]. The approximate formula can be represented as La_2/3+δAl_12–δO₁₉ with the Al vacancies confined to Al sites in the edge sharing sheets. Based on the refined La content, the values of δ obtained from the two XRD single crystal studies are 0.16 and 0.18. Our refinement gives a δ value of 0.25. One can expect the value of δ to vary with synthesis conditions, which were different. The single crystals were prepared from the melt at temperatures higher than 1700 °C. Our polycrystalline powders were prepared at 1500 °C. The vacancies on La and Al5 sites cause general disorder in the structure, which impedes an accurate description of the structure. The disorder in the planes at the z = ¼ and ¾ includes disorder within the plane for La, disorder of Al2 displaced from the plane, and a partial occupancy for O3. In addition, our difference Fourier map shows a peak just above and below the planes at x = 0.18, y = 0.36 with an intensity of about 6 % of an O atom. The disorder caused by the Al vacancies in the Al5 layer also causes apparent O vacancies at the O4 position, which is bonded to two Al5 atoms. Peaks in our difference Fourier map near the plane of Al5 atoms can also be attributed to the disorder at and near the Al5 plane. The refined composition yields a positive charge about 1 % too high for charge balance, but this is as close as could be expected based on the uncertainties of the occupation factors for several cation and anion sites.

Our results are compared to those of the two previous studies in Table 4. Due to common systematic errors, the c/a ratio is more reliable than the values of a and c themselves. This ratio is essentially the same for the two XRD studies, consistent with the fact that their value of δ is nearly the same. The c/a ratio for our sample is significantly smaller (Table 4), consistent with our higher La content. All three studies have found that an atomic fraction of 30–40 % of the La is displaced about 0.5 Å from the ideal site. We did not observe such displacements of La for LaAl₁₁NiO₁₉ hibonite where there are no La vacancies. We conclude that the displacement of some La atoms from the ideal site is caused by adjacent La site vacancies.

3.4 CaAl₁₀NiTiO₁₉

We have prepared and structurally characterized many hibonite phases where Al has been partially substituted by various 3d transition elements. Most of this work is reported in a separate paper that focuses on the optical properties of these phases, which show promise as pigments. Here we present our structural results on one such substitution, CaAl₁₀NiTiO₁₉. Determination of the distribution of Ni and Ti on the five different Al sites is challenging because one cannot refine the occupancies of Al, Ni, and Ti on one site even if one constrains the total site occupancies to be 100 % and constrains the overall stoichiometry of the compound. An unconstrained refinement of the three elements would require additional information, such as XRD data. One can, however, take advantage of the fact that whereas the scattering lengths for Al and Ni are positive with a much higher value for Ni, the scattering length of Ti is negative. Our strategy was to first refine the structure of a CaAl₁₀NiTiO₁₉ composition using 100 % Al in all five Al sites. Assuming that the Ca and O sites are essentially fully occupied, the scale factor would be set and the total scattering powers at the five Al sites would be determined. If the refined Al occupancy at a given site decreased, there must be Ti on that site with this assumption. If the refined Al occupancy on a given site increased above 100 %, there must be Ni on that site. The possibility that some Ni and Ti are both substituting on the same site is at first ignored except in the case of the TBP site where we fixed the Ni occupancy to the value we found for LaAl₁₁NiO₁₉ and Ca_0.5La_0.5Al_11.5Ni_0.5O₁₉. Next the sites with decreased scattering power were refined as a mixture of Al and Ti, and the sites with increased scattering power are refined as a mixture Al and Ni. The results of this refinement are presented in Table 5. The composition obtained from this refinement is CaAl_10.02Ni_0.98Ti_1.00O₁₉, which is very close to a nominal CaAl₁₀NiTiO₁₉ composition. We see that Ni is showing a strong preference for the tetrahedral site (Al3), and that Ti is showing a strong preference for the site with face-sharing octahedra (Al4). Significant Ti substitution also occurs at the Al2 (TBP) site. The results indicate some Ni on the Al1 and Al5 sites, and there could possibly be a very small amount of Ni on the Al4 site that is dominated by Ti substitution.

4.1 Ferroelectric/multiferroic considerations

The situation in magnetoplumbites is the same as in hibonite compounds. Table 8 gives the displacements of the “TBP cations” from the ideal value of 0 0 ¼ in the center of the O triangle. The situation for hibonite/magnetoplumbite compounds is very much like the situation in LiNbO₃ and LiTaO₃. Switching polarity in an electric field causes in both cases a cation to move through the center of a triangle of O atoms. The displacements from the ideal paraelectric position are much greater for Li (~0.65 Å) than for the TBP cations in the hibonite/magnetoplumbite compounds. However, if net polarization for the dipoles is calculated based on formal charges, as is frequently practiced, the net polarization caused by the large displacements of Li and the smaller displacements for TBP cations is about the same. It is generally accepted that Li in the paraelectric states of LiNbO₃ and LiTaO₃ does not reside in the center of the O triangle, but is instead randomly distributed above and below this triangle [29]. The same situation apparently pertains to the “TBP cation” in hibonite/magnetoplumbite compounds.

Table 8 also gives the bond valence sum for the TBP cation (M2) at various sites along the c axis. The first BVS value is for this cation placed at the ideal site (z = ¼). The second BVS value pertains to this cation placed according to the reported structure refinement. The final BVS value pushes this cation even further from the ideal site to a position where one of the apical distances is now equal to the three equatorial distances, a tetrahedral situation but with only one 3-fold axis. Note first that the BVS values are always much lower than the expected value of 3.0. Also note that the BVS does not change significantly as the TBP cation moves from the ideal TBP symmetry to a position where there would be four equal distances for tetrahedral coordination. We conclude from this that the TBP cation is loosely bound and that any barrier preventing its movement through the O triangle of the TBP unit is very small.

In situations where dipoles orient along a particular direction, simple electrostatic considerations favor ferroelectric chains as in Fig. 1b. This occurs in tetragonal BaTiO₃ and hexagonal LiNbO₃ where all the chains along the c axis are polarized in the same direction. However, simple electrostatic considerations would have half the chain dipoles ordered in one direction and half in another direction, as occurs in PbZrO₃ [32]. The triangular orientation of the chains in YInO₃ type structures causes a frustration, the result of which is that 1/3 of the chains are polarized up and 2/3 down. In some cases it has been demonstrated that the application of an electric field can cause such antiferroelectric or ferrielectric structures to become ferroelectric [33]. Thus even if the stable form of hibonite were antiferroelectric or ferrielectric, it would likely exhibit ferroelectric behavior when an electric field is applied along the c axis.

A very unusual aspect of the hibonite structure is the dilution of the dipoles. Only 1 out of 12 Al atoms participates, and the distance between such atoms is about 5.5 Å in the ab plane. The more important direction for dipole ordering is along the c axis where the distance between dipoles is about 11 Å. There are no O atoms that link the TBP units together. Ferroelectricity is well established in the hexagonal (again P6₃/mmc) oxides such as YInO₃, where also again there are no empty d levels close to the Fermi level, a condition frequently regarded as essential for ferroelectricity in oxides [34]. The dipoles in this YInO₃ structure are separated by only somewhat more than 3 Å, and they remain ordered up to very high temperatures (~1000 °C).

Mössbauer spectroscopic studies of ⁵⁷Fe in BaFe₁₂O₁₉ confirm that Fe at the TBP site is actually in tetrahedral coordination [18]. At higher temperatures it is jumping back and forth between sites on either side of the triangle of the TBP site. At temperatures well below room temperature the Fe atoms become trapped on one side of the triangle. The behavior of Al in hibonites is likely very much the same as that of Fe in BaFe₁₂O₁₉. The trapping of Fe at low temperatures does not infer that these displacements will necessarily produce an ordered arrangement of the dipoles.

The lack of dipole ordering in hibonite phases cannot be taken as evidence that they are not ferroelectrics. Amorphous materials with dipoles can develop ferroelectric properties by ordering of the dipoles in the presence of an electric field [35, 36]. The expected ferroelectric moment in hibonites is low due to the low concentration of dipoles and because the dipoles only occur along the c axis. However, in a dipole ordered structure, displacements of the loosely bound M3 cations can be expected to occur and contribute to the moment. Enhancement of a ferroelectric moment might also occur in PbAl₁₂O₁₉ due to the high polarizability of Pb²⁺.

There are many reports of multiferroic behavior in magnetoplumbite phases [36–54]. The electrical conductivity, attributed to very small amounts of Fe²⁺ in such ferrites, is generally too high at room temperature to support ferroelectric behavior. However, the conductivity decreases with decreasing temperature allowing multiferroic behavior to be observed below room temperature. Some reports of multiferroic behavior at room temperature and above are most likely due to space charge polarization owing to electrical conductivity rather than actual ferroelectricity [55]. The polarization observed for the confirmed multiferroic magnetoplumbites is perpendicular to the c axis and thus cannot be related to the dipoles shown in Fig. 1. The observed polarization is instead attributed to mutually canted interacting spins producing the local electric polarization by a spin-orbit interaction [48]. It could be that spin-orbit interactions dominate for all the magnetoplumbite phases. Further studies on insulating single crystals are required to fully understand how the dipoles at the TBP sites in magnetoplumbites have an impact on their properties.

4.2 CaAl₁₀NiTiO₁₉

A very recent study described neutron diffraction refinements of CaAl₁₂O₁₉ samples with substitutions of Ti and Mg for Al [56]. Most of the compositions were purposely prepared under reducing conditions to produce some Ti³⁺, but one composition, CaAl_9.96Mg_0.98Ti_0.98O₁₉, contained only Ti⁴⁺ and can thus be considered for comparison to our results for CaAl₁₀NiTiO₁₉ (Tables 5 and 9). These studies show a strong preference of Mg and Ni for the tetrahedral site. This might be expected considering that Mg and Ni also prefer the tetrahedral sites in the spinels MgAl₂O₄ and NiAl₂O₄. Both studies also show a strong preference of Ti for the face sharing octahedral units, and both studies found about the same amount of Ti on the TBP M2 site. The two studies, however, differ with respect to the octahedral M1 and M5 sites. No substitution is reported for Al1 and Al5 in the study of CaAl_9.96Mg_0.98Ti_0.98O₁₉, but we find small but significant amounts of Ni on these two sites (Table 5). The very high scattering length of Ni (10.3 fm) vs. Al (3.449 fm), Mg (5.38 fm), and Ti (–3.438 fm) provides high accuracy for the amount of Ni on the M1 and M5 sites. A rather dramatic increase of the M2 cation distance from the triangle of the TBP unit has occurred with Ni and Mg substitution. This displacement, which was 0.17 Å in CaAl₁₂O₁₉, has become 0.31 Å in CaAl₁₀MgTiO₁₉ and 0.35 Å in CaAl₁₀NiTiO₁₉. Since Mg²⁺, Ni³⁺, and Ti⁴⁺ are all significantly larger than Al³⁺, one might expect that bonding distances would increase as any of these cations replaces Al³⁺. In fact, such increases are observed for all five Al sites in the case of CaAl₁₀NiTiO₁₉ (Table 5). In the case of CaAl₁₀MgTiO₁₉, the M–O distance at the M1 site has not increased significantly indicating any Mg substitution at that site is very small, in agreement with the report on CaAl₁₀MgTiO₁₉ [56]. However, in CaAl₁₀MgTiO₁₉ there is a significant increase in the average M5–O distance suggesting some Mg at this site, which was not reported [56]. It is not surprising that little or no Ti occupies the tetrahedral site because this is a rare site for Ti. Both studies have indicated that Ti also avoids the M1 octahedral site. Possibly, this is due to the overbonded situation at this site, which would worsen if Ti were introduced. Some Ti is expected to enter the M2 site because Ti⁴⁺ readily accepts TBP symmetry. There are strong cation-cation repulsive interactions across the edge-sharing octahedra in the case of the M5 cation and across face-sharing octahedra in the case of the M4 cations. One might then expect that the higher charge of Ti⁴⁺ would inhibit its substitution into the M4 and M5 sites. But in fact, Ti strongly prefers the M4 site to all other sites. Relative to the M5 site, there are two important factors. One is that the M4–M4 distance across the shared face is relatively free to increase as the Al–Ti interactions are introduced (Table 5). This distance actually increases to about the same value as found for the edge-sharing case of M5 cations. The other relevant factor is that a M5 cation shares edges with four other M5 cations whereas the M4 cation shares a face with only one M4 cation. Thus, cation-cation repulsion consideration is far more important for the M5 site relative to the M4 site. The Ti concentration at the M4 site does not exceed 50 %; thus, it is likely that Ti–Ti interactions do not occur at this site, and this may be a factor that limits the Ti substitution into CaAl₁₂O₁₉.