Symmetry Analysis of the Complex Polytypism of Layered Rare-Earth Tellurites and Related Selenites: The Case of Introducing Transition Metals

: Our systematic explorations of the complex rare earth tellurite halide family have added several new [Ln 12 (TeO 3 ) 12 ][M 6 X 24 ] (M = Cd, Mn, Co) representatives containing strongly deficient and disordered metal-halide layers based on transition metal cations. The degree of disorder increases sharply with decrease of M 2+ radius and the size disagreements between the cationic [Ln 12 (TeO 3 ) 12 ] +12 and anionic [M 6 Cl 24 ] − 12 layers. From the crystal chemical viewpoint, this indicates that the families of both rare-earth selenites and tellurites can be further extended; one can expect formation of some more complex structure types, particularly among selenites. Analysis of the polytypism of compounds have been performed using the approach of OD (“order–disorder”) theory. X-ray spectroscopy using a Leo Supra 50 VP electron microscope utilizing 15 kV accelerating voltage and an INCA analyzer. The results indicate that two kinds of crystals were observed in the Eu and Gd-containing samples: those containing only Ln, Te, and Cl, as well as those also containing Co. In the bromide sample, only blue crystals have been studied which were shown to contain La, Co, Te, and Br.

The presence of stacking disorders for the family of compounds containing tetragonal or pseudo-tetragonal [Ln11Mn(ChO3)12] layers have been recently reported based on the TEM images [38]. It was also mentioned that for the accurate description of the polytypes, the corresponding OD analysis is required [38]. Hereby, we report the results of our attempts to prepare such compounds; contrary to the Cd 2+ based prototypes, they exhibit gross disorder in the targeted M 2+ sublattices, which could be plausibly modeled in just a few cases. A new representative was also obtained for the family of Ln-Cd tellurite halides; its structure was refined to quite reasonable values and will be described here as a "best ordered" reference structure. The accurate symmetry analysis for these compounds using the approach of OD theory is given and polytypic relations have been determined.

Synthesis
As in the previous reports [10,[15][16][17], the starting compounds were LnOX, TeO2, and MX2 (M = Mn, Co, Ni). Anhydrous Co and Mn compounds obtained from MnX24H2O and CoX26H2O via dehydration by gentle heating (up to ~100 °C) and subsequent cooling in vacuo (down to ca. 50-70 Pa). Anhydrous nickel halides were prepared in the same way starting from NiX26NH3. The anhydrous halides were pink (MnX2), deep blue (CoCl2), deep green (CoBr2), yellow (NiCl2) and brown (NiBr2). Due to high hygroscopicity of CoX2, all operations with these compounds were conducted in an argon-filled glovebox. The halides of Mn and Ni permit handling in air for a short time. Mixtures of LnOX, MX2, and TeO2 in 1:7:1 ratio were ground, placed in silica capsules, gently heated in a dynamic vacuum until the pressure dropped to ca. 50 Pa, sealed, and annealed according to the following scheme: heating to 600 °C within 12 h, plateau 12 h; heating to 850 °C within 12 h, plateau 120 h; cooling to 650 °C within 120 h. The salt fluxes were dissolved in water (Ni and Mn halides) or 96% ethanol (Co halides). The insoluble residues consisted of small colorless, pinkish (Mn) or deep blue (Co) crystals. Suitable crystals were not produced using NiX2. The novel Ce-Cd-Te oxychloride was obtained as a somewhat unexpected product from a mixture of SrTeO3, CeOCl, TeO2, SrCl2, and CdCl2 (1:1:1:3:4) targeted at a different proposed composition. It is reported here as it belongs to the same structural family.

Diagnostics
Single crystals of the Co compounds were characterized by energy-dispersive X-ray spectroscopy using a Leo Supra 50 VP electron microscope utilizing 15 kV accelerating voltage and an INCA analyzer. The results indicate that two kinds of crystals were observed in the Eu and Gd-containing samples: those containing only Ln, Te, and Cl, as well as those also containing Co. In the bromide sample, only blue crystals have been studied which were shown to contain La, Co, Te, and Br.
The observed single-crystal diffraction patterns indicated the bad quality of studied crystals which was typically manifested by essential streaking (indicating stacking disorder) and poorly resolved reflections. In accordance with the analysis of systematic absence of reflections, the space group P4/nbm (No. 125) for all compounds was chosen. The experimental details of the data collection and refinement results are also listed in Table 1. Structure models were determined by the "charge flipping" method using the SU-PERFLIP computer program [42] and were refined using the JANA2006 computer program [43]. Illustrations were produced with the JANA2006 program package in combination with the DIAMOND program [44]. Atomic scattering factors for neutral atoms together with anomalous dispersion corrections were taken from International Tables for Crystallography [45]. These essential values of Δρmin and Δρmax are most likely the result of stacking faults common for the layered structures and indicating their possible OD character that was also manifested by streaks in the diffraction patterns. Similar problems, though slightly less pronounced, were encountered in some previous studies [15][16][17]. Attempts to split the corresponding sites were not successful, leading mostly to non-positive definite sites, and were finally abandoned. Tables S1 list fractional site coordinates and equivalent displacement parameters for 1 to 5. Selected bond distances are given in Table  S2. CCDC 1939965, 1939966, 1974365, 2202775, 2202776 contain the supplementary crystallographic data for these compounds. The data can be obtained free of charge from The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/structures.

Crystal Structure Description
The crystal structures of the studied compounds 1-5 are similar to the previously studied ones with the space group P4/nbm ( Figure 1d) Their crystal structures contain two blocks which alternate along c parameter. The first block is represented by a complex slab formed by edge-shared Lnφn-polyhedra (n = 8-12) with the general formula [Ln12(TeO3)12] (type B slab [17]) (Figure 2), where Ln = La, Ce, Nd, Eu, and Gd. The second slab is represented by three-layered close-packing formed by the halide X − anions (X = Cl or Br) with octahedral sites occupied by the M 2+ cations (M = Mn, Co, Cd).
In the crystal structures of compounds 1-5, the [Ln12-x(TeO3)12] type B slabs are nearly identical, with differences in bond lengths due to the varied size of Ln 3+ cations. In the [M II 6+yX24] blocks, the M 2+ cations fill the octahedral voids; however, refinement of the corresponding site occupancies and analysis of the electron density maps for 1-3 indicate presence of maxima which we interpret as the additional weakly occupied M sites (close to the main ones) (Figure 3a). The statistical distributions of M 2+ cations within the octahedral cavities lead to the formation of two types of the layers characterized by the different orientations of octahedra (Figure 3b,c).
The final refinement cycles converged to reasonable values for 1 and 2; however, an ordered model could be refined only for 1. In the structure of 2 and particularly of 3-5, occupancies of octahedrally coordinated M 2+ positions (M 2+ = Mn, Co) were evidently below unity; in addition, relatively high electron density peaks were found in different Fourier maps. Some of these could be tentatively assigned to additional weakly occupied M 2+ sites. This is another clear manifestation of the OD character of the structures.

Polytypism of Tetragonal Halides Containing the [Ln12(TO3)12] Slabs
The diffraction patterns of tetragonal layered rare-earth tellurite halogenides [16,17] are typically characterized by a remarkably low quality of the single crystal X-ray diffraction data which indicates the presence of various stacking faults and possibly some other 2D defects such as single halide sheets. Within the family of related compounds ( Taking into account the layered type of the structures as well as different possible ways of their linkage, the observed structural variants can be considered as polytypes [18,46]. The presence of the twinning indicates the possible stacking disorder and OD ("order-disorder") [47,48] [15] can be described using the same OD groupoid family, more precisely, a family of OD structures built up by two kinds of non-polar layers (category IV) [49]. The layers are the following (Figure 4a,b): (i) L2n type with layer symmetry p4/nmm [or P(4/n)mm in the terms of OD notation] is formed by [M6X24], [M6X16] or [X8] layer (Figure 4b). (ii) L2n+1 type with layer symmetry p4/nbm11[or P(4/n)bm in terms of the OD notation, where braces in the third position indicate the direction of missing periodicity [50]] is formed by a [Ln12(TeO3)12] type B slab (Figure 4a).
The layers of both types (L2n and L2n+1) alternate along the c direction and have common translation vectors a and b, with c0, the distance between the two nearest equivalent layers, corresponding to (c/2)~6.6 Å. The ordered or disordered alternation of the two kinds of layers gives rise to a whole family of ordered polytypes or disordered sequences, which can be obtained through the action of the following symmetry operators that may be active in the L2n-type of layer: the 2 and 21 axes parallel to a ([2 1 1] where the first line contains the layer-group symbols of the two constituting layers, while the second line indicates the positional relations between the adjacent layers [51]. In all the polytypes, as well as in the disordered sequences, pairs of adjacent layers are geometrically equivalent (according to the general principle of OD structures). Polytypes presenting the smallest possible number of different triples of layers are called MDO (Maximum Degree of Order) polytypes (the principle of MDO structures). The first MDO structure (MDO1-polytype) can be obtained when the 2x and 2y axes are active in the L2ntype layers (Figure 4c), giving the tetragonal structure with a~16.0 Å, c~13.2 Å and the space group P4/nbm. The second MDO structure (MDO2-polytype) can be obtained when the 21x and 21y axes are active in the L2n-type layers: a~16.0 Å, c~25.5 Å and the space group I4/mcm.
The similar stacking disorder with the formation of different types of polytypes have been also previously observed for the related rare-earth selenites [12,13,38,[52][53][54][55] [55] are crystal chemical isotypical and represent the third type of MDO structure (MDO3-polytype). This polytype can be obtained when the 21x and 2y axes are active in the L2n-type layers (Figure 5a) giving the orthorhombic (pseudo-tetragonal) structure with a~15.7 Å, a~15.7 Å c~17.9 Å and the space group Bbab (non-standard setting of the space group Ccca).
Compounds  [38] are characterized by another MDO structure (MDO4-polytype) which can be obtained when the 2y axes are active in the L2n-type layers (Figure 5b) giving the orthorhombic (pseudo-tetragonal) structure with a~15.7 Å, a~15.7 Å c~17.9 Å and the space group Pnan. For the compound [Nd11(SeO3)12][Cs7Cl16] [38], symmetry lowering was confirmed by a second harmonic generation test, and the space group Pna21 (which is a subgroup of the space group Pnan) was established. It needs be noted that among selenites, one site in the type B layer is mostly empty while on the CsCl layer, one additional cubic void is occupied instead by a voluminous alkali cation.  [38] show the regular stacking disorder and different kinds of symmetrical operation active in L2n-type layers.
Except for different MDO and non-MDO structures, the modular structures can also be formed when the different types of the interstitial block between adjacent [Ln12 (TeO3)12] type B slab are present. As a result, the different types of alternation can form a merotypic modular series [18,33,46,[57][58][59] [11]. Such mixed-layer structures are as yet observed only for selenites; note the compositional shift of the CsCl slabs from [M I 7Cl16] −9 in "bilayer" structures ( Figure 1b) to [M I 6X16] −10 in their mixed-layer derivatives [11,53]. In the structures of tellurites, simple "bi-layer" sequences are charge balanced  Table 2. Other polytypes can be easily obtained using the different combinations of the symmetry operations active in L2n layer.
21x, 2y * The initial unit cell parameters and the space groups have been transformed to preserve the orientation and stacking direction of the OD layers and modules; n.d., no data.

Synthesis
In line with our expectations, the family of layered rare-earth chalcogenite halides could be more or less successfully extended into the realm of transition-metal compounds. As yet, the generally employed self-flux synthetic pathway (the use of metal halides as both reactants and fluxing agents) is quite effective in producing single crystals of selenites but essentially less so in the case of tellurites; we estimate the probability of preparing suitable single crystals from a single synthetic run to be as low as 20-30%. The possible explanation is that the targeted tellurites are less soluble in the molten fluxes compared to the selenites. The quality of the produced tellurite crystals is also essentially lower in contrast to selenites. This is the reason why most isostructural series are only sparsely characterized, i.e., structures have been determined for certain members only. This approach also does not provide phase-pure samples. The most common byproduct is microcrystalline TeO2 which, in the case of alkali fluxes, is generated due to a side reaction yielding hexahalotellurites and their subsequent hydrolysis upon flux leaching. An alternative chemical vapor approach, which works well for structurally related bismuth selenite halides [61], does not work for rare earths due to much lower volatility of their compounds. Yet, the use of reactive MnX2 and CoX2 fluxes permitted to prepare the first representatives of two new series of rare-earth-manganese and cobalt tellurite halides.
The structure of the metal-tellurite [Ln12(TeO3)12] 12+ slabs remains nearly the same in all structures reported herein and in [10][11][12][13][14][15][16][17] and are composed by three types of the sheets: the LnO8 and LnO10 polyhedra share edges and vertices to form an "inner" metal-oxide sheet decorated by the TeO3 squashed tetrahedra and LnO4X4 tetragonal antiprisms ("outer" sheet; Figure 2). Refinement of these parts of the structures proceeds relatively smoothly; they exhibit the best ordering and can be considered structure-directing. The structure of 1 is analogous to those of the other early rare-earth-cadmium compounds and adopts the same P4/nbm space group with c~13 Å and one cationic and one anionic slab per unit cell ( Figure 1d). As we noted earlier in [16], there exists a considerable mismatch between the size of the layer comprised from regular CdCl6 octahedra (estimated subcell parameter of ~3.75 Å) and the cerium-tellurite slab (a/4 = 4.08Å), which can somewhat be compensated by deformations of the octahedral layer; yet some disorder is already invoked. This discrepancy increases sharply when passing from Cd 2+ ( [6] r = 0.95 Å) to Mn 2+ ( [6] r = 0.83 Å) and further to Co 2+ ( [6] r = 0.75 Å) [67]. In these cases, the distortions are already unable to compensate the adjustment of the metal-halide to the metal-oxide slab. Local deviations from the ideal structure which permit either to preserve the acceptable M-X distances or to adapt some M 2+ cations in tetrahedral coordination are very likely to be present. Unfortunately, only an averaged and statistical picture can be extracted from the single-crystal X-ray data; the observed disorder can otherwise reflect just the overlapping contributions from various "islands" with different M-X arrangements. One may suggest that these discrepancies might decrease when passing from MCl6 to larger MBr6 octahedra; however, it is likely to be overruled by the swelling of the unit cell in the ab plane. It is also worth noting that while a polytypic-like transition from P4/nbm to I4/mcm occurs in the [Ln12(TeO3)12][Cd6Cl24] series with the borderline between Eu and Gd compounds, no such transition occurs between 4 and 5. It is, therefore, possible that among compounds of Mn and Co, this transition occurs smoothly and the OD character of the structure is represented by more or less thick lamellae of both P4/nbm and I4/mcm layer sequences. It is also rather likely that the compound mentioned in [11] as [La11(SeO3)12][Co7.5Cl24] also exhibited strong disorder in the metal-halide part of the structure, which could not be plausibly modeled and was thus abandoned. Overall, it should be noted that while metalhalide layers containing magnetically active transition metal cations can indeed be incorporated into the structures of layered rare-earth chalcogenite halides, they form strongly disordered sublattices which are unlikely to result in magnetic ordering.
We also note that by now, the [Ln12(TeO3)12][M6X24] compounds have been obtained for the M 2+ cations characterized by zero (Mn 2+ , Cd 2+ ) or relatively low (Co 2+ ) values of crystal field stabilization energy (CFSE) which permit essential distortions of their octahedral environment. One can suggest that it is also possible to introduce non-magnetic Mg 2+ , of the size similar to Co 2+ ( [6] r = 0.72 Å [67]) also characterized by CFSE = 0 (as there are no d orbitals), into the structures reported here.

Conclusions
To summarize, we succeeded in further developing the layered rare-earth telluritehalide family by introducing, for the first time, magnetically active transition metal cations into the halide blocks. Despite essential variation of their size, these cations tend to keep the octahedral environment of halide anions; the geometrical mismatch between the cationic and anionic layer can be, more or less effectively, compensated by the increasing degree of disorder in the transition metal sublattice. This disorder increases essentially also when passing from chlorides to bromides, which is in line with the fact that no tellurite iodide featuring the [(M,Ln)11(TeO3)12] layers has been reported so far. It is more or less evident from this study that further directions of developing this family are possible; however, there is yet little hope in the pursuit of magnetic properties. Other properties related to the type of polytypic structures, including ionic exchange and trapping or soft-chemistry transformations (under mild conditions), might, however, be of interest.

Conflicts of Interest:
The authors declare no conflict of interest.