Anion-Centered Tetrahedra in Inorganic Compounds - Chemical

Review pubs.acs.org/CR

Anion-Centered Tetrahedra in Inorganic Compounds Sergey V. Krivovichev,*,†,‡ Olivier Mentré,§ Oleg I. Siidra,† Marie Colmont,§ and Stanislav K. Filatov† †

St. Petersburg State University, Department of Crystallography, University Emb. 7/9, 199034 St. Petersburg, Russia Institute of Silicate Chemistry, Russian Academy of Sciences, Makarova Emb. 6, 199034 St. Petersburg, Russia § UCCS, Equipe de Chimie du Solide, UMR CNRS 8181, ENSC LilleUST Lille, BP 90108, 59652 Villeneuve d’Ascq Cedex, France ‡

3.4.4. 2D Units 3.4.5. 3D Units 3.5. O- and N-Centered Tetrahedra in Hg Compounds 3.5.1. General Remarks 3.5.2. 0D Units 3.5.3. 1D Units 3.5.4. 2D Units 3.5.5. 3D Units 3.6. Miscellaneous 3.6.1. Beryllium 3.6.2. Ca, Sr, Ba 3.6.3. Scandium 3.6.4. Actinides 3.6.5. Pd, Pt 3.6.6. Cd, Ni 4. Topological and Geometrical Variations 4.1. Topological Rules 4.2. Bond-Length Variations 4.3. Bond-Angle Variations 4.4. Variations of the A···A Distances 5. Concluding Remarks Author Information Corresponding Author Notes Biographies Acknowledgments References

CONTENTS 1. Introduction 2. Basic Principles 2.1. Anion-Centered Tetrahedra, Structural Anisotropy, and Bond-Length - Bond-Strength Considerations 2.2. Chemistry of Anion-Centered XA4 Tetrahedra 2.2.1. Chemical Nature of Anions X 2.2.2. Chemical Nature of Cations A 2.3. Applicability of the Approach 2.4. Systematics of Tetrahedral Complexes 2.4.1. Basic Parameters 2.4.2. Topological and Geometrical Classification of Tetrahedra 3. Anion-Centered Tetrahedra in Inorganic Compounds: Systematic Description 3.1. OCu4 Tetrahedra in Inorganic Compounds 3.1.1. 0D Units 3.1.2. 1D Units 3.1.3. 2D Units 3.1.4. 3D Units 3.2. OPb4 Tetrahedra in Inorganic Compounds 3.2.1. 0D Units 3.2.2. 1D Units 3.2.3. 2D Units 3.2.4. 3D Units 3.3. Anion-Centered Tetrahedra in Inorganic Lanthanide Compounds 3.3.1. 0D Units 3.3.2. 1D Units 3.3.3. 2D Units 3.3.4. 3D Units 3.4. OBi4 Tetrahedra in Inorganic Compounds 3.4.1. General Remarks 3.4.2. 0D Units 3.4.3. 1D Units © 2013 American Chemical Society

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1. INTRODUCTION It is a common procedure in the description and evaluation of structures of inorganic compounds to consider them in terms of coordination of cations, i.e., as extended arrays of coordination polyhedra with centers occupied by cations and corners occupied by anions. However, there are cases when this kind of structure interpretation does not reflect either basic principles of structural architecture or relationships between different structures and between crystal structure and physical properties. In 1968, Bergerhoff and Paeslack1 considered a series of compounds with the “additional” oxygen atoms, i.e. atoms that do not participate in strongly bonded “acid residue” complexes or ions such as sulfate, silicate, germanate, chloride, fluoride, etc. For instance, they noted that, in the structure of dolerophanite, Cu2O(SO4), there are two types of O atoms:

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of (OPb4) tetrahedra with F− ions in framework cavities; Figure 2d). In the same 1968 year, Caro8 called attention to the fact that (OM4) tetrahedra can be identified in rare earth oxide and oxysalt structures. In particular, he recognized the existence of two different layers of (OM4) tetrahedra in MOCl and A-M2O3 (M = lanthanide, Ln) (Figure 3). In conclusion to his paper,

those that belong to sulfate groups (OS) and those that do not (Oa). The Cu:Oa ratio is equal to 2:1, and the Oa atoms are coordinated solely by the Cu atoms. The coordination number of the Oa atom is four, which means that it can be considered as a central atom for the (OCu4) tetrahedron. The adjacent (OCu4) tetrahedra share edges and corners to produce twodimensional (2D) layers with the composition [OCu2]2+ (Figure 1). These layers can be considered as extended

Figure 3. Layers of OM4 tetrahedra in the structures of MOCl (left) and A-M2O3 (right) (M = rare-earth metal). Reprinted with permission from ref 8. Copyright 1968 Elsevier B. V.

Caro noted that description in terms of oxocentered tetrahedra “...can be considered as simply another way to divide space, but evidence from optical spectra suggests that there is an important covalent contribution to the bonding of the rareearth metal atom, and the persistent appearance of the edgelinked tetrahedron may be a structural consequence of this.”8 From 1968 and till 1984, there were no systematic treatments of structures with oxocentered tetrahedra, though particular researchers described certain crystal structures in terms of anion coordination. For instance, Sleight and Bouchard9 described the structure of Bi3GaSbO11 (= Bi3O2[GaSb2O9]) as consisting of three interpentrating networks: one based upon ((Ga/Sb)O6) octahedra and two based upon (OBi4) tetrahedra (Figure 4). There was a number of other similar observations, which will be mentioned in other parts of this review.

Figure 1. The crystal structure of dolerophanite, Cu2O(SO4), as consisting of the [OCu2]2+ layers of edge- and corner-sharing (OCu4) tetrahedra (lined) and (SO4) tetrahedra (white). Reprinted with permission from ref 1. Copyright 1968 Oldenbourg Verlag.

polycationic structural units; their positive charges are compensated by the tetrahedral (SO4)2− anions. Thus the structure of Cu2O(SO4) was considered as consisting of two basic units: the [OCu2]2+ layers of oxocentered (OCu4) tetrahedra and (SO4)2− tetrahedral oxyanions. Bergerhoff and Paeslack1 included into their scheme some other compounds such as Zn4O(BO2)62 and Be4O(CH3COO)63 (both containing isolated M4O tetrahedra), kyanite, Al2O(SiO4)4 (containing double [OAl2]4+ chains; cf. Figure 2a), Bi2O2(GeO3),5 and

Figure 2. Crystal structures of kyanite, Al2O(SiO4) (a), La2O2S (b), Bi2O2(GeO3) (c), and Pb2OF2 (d) as consisting of polycationic units of OM4 tetrahedra (lined; M = Al, La, Bi, Pb, respectively) and anions. Reprinted with permission from ref 1. Copyright 1968 Oldenbourg Verlag.

Figure 4. The crystal structure of Bi3O2[GaSb2O9] as consisting of three interpenetrating networks. Tetrahedra in the upper part of the figure have Bi atoms at their corners. O atoms are at both ends of the lines connecting the tetrahedra; thus there is an oxygen atom at every face of the tetrahedra. The tetrahedra of one network are shaded with lines and those of the other with dots. The octahedral framework is shown in the lower part of the figure. Reprinted with permission from ref 9. Copyright 1973 American Chemical Society.

La2O2S6 (based upon the layers of edge-sharing (OM4) tetrahedra (M = Bi3+ or La3+); Figure 2, panels b and c, respectively), and Pb2OF27 (containing [OPb2]2+ cristobalite-like framework 6460


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In 1984, Carre and co-workers10 reviewed La oxysulfides containing non-rare-earth metal such as In, Ga, Ge, etc. They noted that many structures of this class contain ribbons of edge-sharing (OLa4) tetrahedra (Figure 5). For instance, the

Figure 7. Different ribbons consisting of the (OLa4) tetrahedra can be produced from the [OLa] layer by shear mechanism. Reprinted with permission from ref 10. Copyright 1984 Elsevier B. V.

Figure 5. Ribbons of (OLa4) tetrahedra in La oxysulfides. Reprinted with permission from ref 10. Copyright 1984 Elsevier B. V.

structure of La4O3(AsS3)211 (Figure 6) can be considered as based upon the [O3La4]6+ ribbons and (AsS3)3− triangular

In 1975−1976, Kamchatka peninsula (Far East, Russia) witnessed one of the largest basalt volcanic eruptions in modern history, which was named a Great fissure Tolbachik eruption (GFTE). The eruption was followed by the extensive posteruption activity, which was accompanied by formation of fumarolic fields. Volcanic gases of the GFTE were enriched in copper, and mineral-formation processes in fumaroles resulted in a unique suite of Cu minerals containing “additional” O atoms. Similar processes, but at a much smaller scale, were detected in other volcanoes such as Vesuvius (Italy) and Isalco (Salvador). Table 1 provides a list of fumarolic mineral species contaning both Cu and “additional” O atoms in their crystal structures. Structural studies demonstrated that, by analogy with dolerophanite, the Oa atoms in the structures of these minerals are tetrahedrally coordinated by Cu (and sometimes by other metals) with a variety of oxocentered tetrahedral complexes. This led Filatov et al.69 to propose that oxocentered (OCu4) tetrahedra may have played the role of carriers of Cu by volcanic gases from a magmatic chamber to the surface of the Earth. This proposal was later confirmed by a series of modeling experiments, where mineral analogues have been prepared in the course of chemical transport reactions.70 Further development of these works in both theoretical and experimental directions was summarized in the review71 and in the book72 published in 2001 in Russian. Inspired by these studies, Magarill et al.73 applied this approach to Hg oxysalts with “additional” O atoms and constructed a hierarchy of structures based upon units consisting of polymerized (OHg4) tetrahedra. Extensive studies of Pb mineral assemblages from oxidation zones of polymetallic mineral deposits revealed a group of Pb oxysalt minerals consisting of different units of polymerized (OPb4) tetrahedra,74−83 which prompted both experimental and theoretical works.84−87,89−94 Independently of the St. Petersburg school of structural mineralogy and crystal chemistry, the theory of oxocentered tetrahedra was developed by the group of solidstate chemistry of Lille, which applied the approach to the description and rational design of novel structural architectures in the Bi-M oxophosphates and oxoarsenates (M = transitional metal).95−110 This led to the sufficient extension of the knowledge on structural diversity and complexity of inorganic compounds based upon anioncentered tetrahedra.

Figure 6. Crystal structure of La4O3(AsS3)2 projected along the c axis. Reprinted with permission from ref 10. Copyright 1984 Elsevier B. V.

pyramids. Carre et al.10 suggested to consider the ribbons of oxocentered tetrahedra as generated from the [LaO]+ layer by shear mechanisms (Figure 7). A number of structures containing various units of (OPb4) tetrahedra have been reported by Keller and co-workers.12−15 It was suggested that different types of oxo- and hydroxo-centered Pb units exist in noncrystalline state and may be considered as precursors to the (OPb4) tetrahedral units in crystals.16,17 Effenberger18 reported on the structure refinement of dolerophanite, Cu2O(SO4), and provided a brief review of (OCu(II)4) tetrahedra in inorganic compounds. She noticed that the Cu−Oa bonds are usually shorter and therefore stronger than other Cu−O bonds in the crystal structures, which suggested that consideration in terms of oxocentered tetrahedra is not “simply another way to divide space”, but may also have important influences upon distribution of chemical bond strength and, as a consequence, upon certain physical properties. Important contributions toward understanding structural diversity and complexity of lanthanide compounds containing (XM4) tetrahedra (X = O2−, N3−; M = Ln) have been made by Schleid and co-workers (see reviews19,20 and description of structures in the section 3.3 of this review). 6461


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Table 1. Cu(II) Oxysalt Minerals of Fumarolic Origin Containing “Additional” O Atomsa ref mineral name allochalcoselite alumoklyuchevskite atlasovite averievite burnsite chloromenite coparsite cupromolybdite dolerophanite euchlorine fedotovite fingerite georgbokiite ilinskite kamchatkite klyuchevskite melanothallite nabokoite parageorgbokiite piypite ponomarevite prewittite starovaite stoiberite vergasovaite a

chemical formula +

2+

PbCu Cu 5O2(SeO3)2Cl5 K3Cu3FeO2(SO4)4 KFe3+Cu6BiO4(SO4)5Cl Cu5O2(VO4)2(CuCl) KCdCu7O2(SeO3)2Cl9 Cu9O2(SeO3)4Cl6 Cu4O2[(As,V)O4]Cl Cu3O(MoO4)2 Cu2O(SO4) NaKCu3O(SO4)3 K2Cu3O(SO4)3 Cu11O2(VO4)6 α-Cu5O2(SeO3)2Cl2 NaCu5O2(SeO3)2Cl3 KCu3O(SO4)2Cl K3Cu3FeO2(SO4)4 Cu2OCl2 Cu7TeO4(SO4)5Cl β-Cu5O2(SeO3)2Cl2 K4Cu4O2(SO4)4(Cu0.5Cl) K4Cu4OCl10 KPb1.5ZnCu6O2(SeO3)2Cl10 KCu5O(VO4)3 Cu5O2(VO4)2 Cu3O(MoO4)(SO4)

locality

M.D.

Tolbachik, Russia Tolbachik, Russia Tolbachik, Russia Tolbachik, Russia Tolbachik, Russia Tolbachik, Russia Tolbachik, Russia Tolbachik, Russia Vesuvius, Italy; Tolbachik, Russia Tolbachik, Russia; Vesuvius, Italy Tolbachik, Russia Isalco, Salvador Tolbachik, Russia Tolbachik, Russia Tolbachik, Russia Tolbachik, Russia Vesuvius, Italy; Tolbachik, Russia Tolbachik, Russia Tolbachik, Russia Tolbachik, Russia; Vesuvius, Italy Tolbachik, Russia Tolbachik, Russia Tolbachik, Russia Isalco, Salvador Tolbachik, Russia

21 23 25 26 28 30 32 34 35 36 38 40 42 44 46 48 50, 51 25 55 57, 58 60 63 64 65 67

S.R. 22 24 27 29 31 33 34 18 37 39 41 43 45 47 49 52, 53 54 56 59 61, 62 63 64 66 68

M.D. = mineral description; S.R. = structure report.

Recent papers111−118 testify increasing attention to the inorganic compounds consisting of anion-centered tetrahedra, and the goal of this review is to present a comprehensive account of the theory and review of experimental data accumulated on these materials over the last 50 years.

which, along with the TOk units, constitute the basis of the crystal structures. The structure of georgbokiite, Cu5O2(SeO3)2Cl2,43,140 can be considered from two different points of view. There are three symmetrically independent Cu sites in the structure: the Cu(1) site is in trigonal bipyramidal coordination to three O and two Cl atoms, whereas the Cu(2) and Cu(3) atoms are at the centers of the [Cu(2)O4Cl2] and [Cu(3)O5Cl] octahedra, respectively. The octahedra are strongly distorted owing to the Jahn−Teller effect141 with four short equatorial Cu−O bonds and two longer apical Cu-φ bonds (φ = O, Cl). The [Cu(3)O4] squares formed by four short Cu(3)-O bonds link by sharing edges to form chains running in the structure along the a axis. From the viewpoint of cation coordination, these chains have to be the strongest structural units, which determine an anisotropic character of the crystal structure. However, a hightemperature X-ray diffraction study142 indicated that thermal expansion is maximal along b and minimal along the c axis, whereas thermal expansion along the a axis is intermediate in value. However, in the structure of georgbokiite, there is a tetrahedrally coordinated “additional” Oa atom. The (OCu4) tetrahedra formed by this atom share common Cu corners and Cu···Cu edges in alternate to form the [O2Cu5] chains extended along the c axis. Since the Cu−Oa bonds in georgbokiite are the shortest among the Cu−O bonds in the structure, the [O2Cu5] chains should be described as the strongest structural units that determine anisotropy of the network of the chemical bonds (Figure 8). Indeed, anisotropy of thermal expansion can better be described in terms of anioncentered tetrahedra than in terms of different cation-centered polyhedra. It should also be noted that the anion-centered description in the case of georgbokiite appears to be more

2. BASIC PRINCIPLES 2.1. Anion-Centered Tetrahedra, Structural Anisotropy, and Bond-Length - Bond-Strength Considerations

It is sometimes assumed that the description in terms of coordination polyhedra of anions is a merely geometrical approach that helps to explain particular complex structural architectures in terms of cation arrangements with anions in interstitial sites.119−121 Undoubtedly, the fact that the same atomic arrangements are repeated from structure to structure may serve as an additional argument for their strength and stability. However, in this review we consider only those structures, where anion-centered tetrahedral complexes are indeed one of the most robust structural units. Table 2 provides average bond-lengths in selected oxo-compounds with two types of O atoms: those bonded to high-valent cations Tm+ such as S6+, Si4+, Se4+, Mo6+, V5+, P5+, As5+, Cr6+, etc. (the OT atoms), and additional Oa atoms, which are bonded only to the An+ cations such as Cu2+, Pb2+, and Ln3+. In all of the compounds listed in Table 2, coordination of the Oa atoms is invariably tetrahedral. It can be seen that the An+−Oa bonds are in general shorter (and therefore stronger) than the An+−OT bonds; i.e., they are the strongest cation−anion bonds formed by the An+ cations in the structure. This shows that (OaA4) tetrahedra can be considered as independent structural subunits, whose linkage results in formation of strong polycationic moieties, 6462


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Table 2. Average ⟨A−Oa⟩and ⟨A−OT⟩ Bond Lengths and Their Variations (in Square Brackets) in the Crystal Structures of Inorganic Oxysalts with the “Additional” Oa Atoms and the OT Atoms bonded to High-Valent T Cations (T = Se, S, P, V, As, Cr, Re, Mo)a chemical formula Cu5O2(SeO3)2Cl2 KCu3OCl(SO4)2 Cu2O(SO4) NaKCu3O(SO4)3 K2Cu3O(SO4)3 Na2Cu4O(PO4)2Cl Cu4O(PO4)2 Cu2O(SeO3) P21/n Cu2O(SeO3) P213 Cu5O2(VO4)2 Cu5O2(PO4)2 Cu4O(AsO4)2 P1̅ Pb2O(CrO4) Pb2O(SO4) Pb3O2(SO4) P21/m Pb3O2(SO4) Cmcm Pb3O2(SO4) P1 Pb19(VO4)2O9Cl4 Pb5O3(GeO4) Pb3O2(CO3) Pb8Cu(AsO3)2O3Cl5 La3O2(ReO6) P21/m La4O2(Re2O8) La3O2(ReO6) C2 La2[La2O](Mo2O10) a

⟨A−Oa⟩ (Å) 1.95 1.92 1.92 1.93 1.93 1.88 1.91 1.96 1.94 1.94 1.93 1.91 2.30 2.30 2.32 2.36 2.32 2.32 2.32 2.29 2.40 2.38 2.41 2.39 2.40

⟨A−OT⟩ (Å)

[1.93−1.98] [1.86−1.98] [1.88−2.00] [1.91−1.94] [1.92−1.96] [1.85−1.91] [1.90−1.92] [1.93−1.97] [1.92−1.97] [1.90−2.10] [1.91−1.94] [1.90−1.93] [2.28−2.31] [2.27−2.33] [2.18−2.43] [2.32−2.39] [2.12−2.49] [2.18−2.59] [2.19−2.68] [2.20−2.39] [2.18−2.57] [2.32−2.45] [2.41] [2.32−2.50] [2.39−2.41]

2.00 2.01 1.99 1.97 1.97 2.00 1.98 1.97 2.02 1.98 1.96 1.97 2.78 2.66 2.80 2.62 2.76 2.77 2.54 2.95 2.57 2.60 2.57 2.60 2.56

[1.94−2.05] [1.93−2.08] [1.91−2.07] [1.92−2.03] [1.93−2.03] [1.92−2.03] [1.92−2.09] [1.93−2.02] [1.98−2.08] [1.89−2.05] [1.90−2.06] [1.93−2.02] [2.46−2.93] [2.46−2.85] [2.69−2.95] [2.55−2.70] [2.55−2.97] [2.36−3.10] [2.14−2.92] [2.54−3.27] [2.34−2.89] [2.42−2.86] [2.54−2.60] [2.24−3.00] [2.37−2.90]

ref 43 47 18 37 39 122 123 124 124 66 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139

For compounds with different polymorphs, space group is given in order to identify the phase.

reproduced under laboratory conditions.144 In order to investigate structural anisotropy, synthetic analogue of francisite was prepared by chemical transport reactions and studied using high-temperature X-ray diffraction.145 It was shown that thermal expansion of francisite has an anisotropic character with the following main thermal expansion coefficients αa = 9.0 × 10−6 K−1, αb = 4.7 × 10−6 K−1, αc = 17.0 × 10−6 K−1. This means that thermal expansion is maximal along the c axis, whereas it is two times less intensive along a and four times less intensive along the b axis. In the original report,143 the structure of francisite was described as a three-dimensional (3D) framework formed by [CuO4] squares, (SeO3) pyramids and (BiO8) coordination polyhedra (Figure 9a). This description does not provide any obvious idea to explain the observed anisotropy of thermal expansion. In contrast, description in terms of oxocentered tetrahedra allows to view the structure as based upon the [O2Cu3Bi]5+ layers formed by edge- and corner-sharing of (OCu3Bi) tetrahedra (Figures 9a and 10). The layers are parallel to (001), which explains the largest thermal expansion along the c axis. The expansion within the layers appears to be anisotropic as well: it is two times more intensive along a than along b axis (Figure 10a). This can readily be explained by analyzing the topology of linkage of oxocentered tetrahedra in the layer. The (OCu3Bi) tetrahedra are linked by edge-sharing along the b axis (smallest thermal expansion coefficient) and by corner-sharing along the a axis (intermediate thermal expansion coefficient). As in the case of georgbokiite, thermal expansion of the structure of francisite is better understood if viewed in terms of anion-centered tetrahedra than using traditional cation-centered approach.

Figure 8. The structure of georgbokiite, [Cu5O2](SeO3)2Cl2, shown as based upon chains of edge-and corner-sharing (OCu4)6+ tetrahedra running parallel to the c axis. Thermal expansion coefficient figure is shown to demonstrate that thermal expansion is minimal parallel to the chain extension. See text for details.

simple and more elegant, which additionally emphasizes its relevance to the description of structural organization. Francisite, Cu3BiO2(SeO3)2Cl, was first described as a natural mineral from Iron Monarch, South Australia,143 and later was 6463


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The structure of BiMg2O2(VO4) contains 5-coordinated Mg2+ cations and (VO4) tetrahedra.147 In terms of coordination of the Oa atoms, it consists of (OBi2Mg2) tetrahedra linked by edge sharing into the [O2BiMg2] double chains. The polyhedral volume expansion (αV) values for the (MgO5), (VO4), and (OBi2Mg2) polyhedra are 67 × 10−6 °C, 28 × 10−6 °C, and 19 × 10−6 °C, respectively. Therefore, the relative strength of the coordination polyhedra can be described as follows: (OBi2Mg2) > (VO4) ≫ (MgO5). In this case, anion-centered tetrahedra appear to be among the most strongest subunits in the crystal structure. For braunite, Mn7O8(SiO4),148 the polyhedral volume compressibilities (βV) for the (SiO4), (MnO8), (MnO6), and (OMn4) polyhedra are equal to ∼0, 5.2, 6.5, and 4.3−4.5 × 10−6 bar−1, respectively. The (SiO4) tetrahedra are the strongest structural subunits, followed by the (OMn4) tetrahedra, and then by the Mn-centered polyhedra. It is noteworthy that the compressibilities for the oxocentered tetrahedra are only slightly lower than those for the Mncentered polyhedra, which means that, in this case, description in terms of (OMn4) tetrahedra has less physical sense than for georgbokiite and francisite. In kyanite, Al2O(SiO4),149 the following coordination polyhedra may be considered: (AlO6) octahedra, (SiO4) tetrahedra, and (OAl4) tetrahedra formed by the “additional” Oa atoms. The polyhedral volume expansivities (αV) for these polyhedra are equal to 25−32, 10, and 27−28 × 10−6 °C, respectively. Again, oxocentered tetrahedra do not play a crucial role in determining structural anisotropy of the mineral; their use in structural description is more of a kind of geometrical exercise than a kind of physical interpretation. The last two examples indicate that the anion-centered approach is not equally applicable to all structures with “additional” O atoms. The problem of applicability of structural description from the viewpoint of anion coordination is further discussed in section 2.3.

Figure 9. Crystal structure of francisite, [Cu3BiO2](SeO3)2Cl, shown in terms of cation-centered polyhedra (a), and as consisting of the [O2BiCu3]5+ layer parallel to (001), (SeO3) groups and Cl− anions (b). Thermal expansion coefficient figure is shown. Reprinted with permission from ref 145. Copyright 2000 Springer Verlag.

2.2. Chemistry of Anion-Centered XA4 Tetrahedra

2.2.1. Chemical Nature of Anions X. A number of experimental and theoretical works reviewed in the section 1 indicate that most common X anions that form anion-centered XA4 tetrahedra are O2− and N3−. Other anions such as halogens occur in tetrahedral coordination much more rarely. In Clbearing sodalite structures, the existence of (ClA4) tetrahedra was pointed out by Schnick and Luecke150 and Stock et al.151 Qi and Corbett 1 5 2 reported on the structures of (A4Br)2Zr6Br18X′ (A = Na, K, Rb, Cs; X′ = H, Be, B, Mn) as containing isolated bromine-centered (BrA4)3+ tetrahedra (Figure 11). Iodine-centered (IK4)3+ tetrahedra were described in the structure of β-K4La6I14Os (Figure 12).153 The I−K bond lengths in these tetrahedra are equal to 3.37 Å, whereas the K···K contacts are equal to ca. 5.5 Å. These structure types should be considered as rather exotic singular examples of halogen-centered alkali metal tetrahedra. The S2−-centered metal tetrahedra are more common; the classical example is the structure of Pb5S2I6,154 which contains georgbokiite-type [S2Pb6]6+ polycationic chains of edge- and corner-sharing (SPb4)6+ tetrahedra. Schleid and coauthors155−161 provided several examples of lanthanide sulfides based upon S-centered (SLn4) tetrahedra. In particular, the structure of LaSCl155 can be described as based upon dense layers of (SLa4) tetrahedra (Figure 13), whereas the structure of Sm2SCl4156 features chains of trans-edge-sharing (SSm4) tetrahedra (Figure 14).

Figure 10. The crystal structure of francisite projected along the c axis (a) and the structure of the [OBiCu3]5+ layer of edge- and cornersharing (OCu3Bi)7+ tetrahedra (b). Reprinted with permission from ref 145. Copyright 2000 Springer Verlag.

Polyhedral volume expansion (αV) and polyhedral volume compressibility (βV) are two useful measures to estimate relative strength of chemical bonds within particular coordination polyhedra.146 Comparison of these parameters for anionand cation-centered polyhedra in the same structure allows determination of their relative strength and to provide a strong qualitative physical basis for more effective structure interpretation. Unfortunately, there are very few data available on high-temperature and high-pressure behavior of compounds with “additional” O atoms. As to our knowledge, the respective studies were performed for BiMg2O2(VO4) (structure refinements at different temperatures),147 braunite, Mn7O8(SiO4) (high-pressure experiments),148 and kyanite, Al2O(SiO4) (high-pressure experiments).149 6464


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Figure 14. The [SSm2]4+ chain of edge-sharing (SSm4)10+ tetrahedra (a) and its surrounding by the Cl− anions (b) in the structure of [Sm2S]Cl4. Reprinted with permission from ref 156. Copyright 1998 Wiley-VCH Verlag GmbH & Co KGaA.

Figure 11. The (BrK 4 ) 3+ tetrahedron in the structure of (K4Br)2ZrBr18B. Reprinted with permission from ref 152. Copyright 1997 American Chemical Society.

In order to explain why the O2− and N3− anions frequently form anion-centered tetrahedra, one has to examine electronegativities and hardnesses of the respective atoms. According to the density functional theory (DFT),168,169 electronegativity, χ, is the first derivative of energy E relative to the total number of electrons N: −χ = [∂E /∂N ]V = const

where V = const indicates a constancy of the external potential. In other words, following Pauling’s definition, electronegativity is the ability of atoms to attract electrons in a molecule. Resistivity of atoms to the transfer of electrons is measured by the hardness η, which is defined as the second derivative of E relative to N: η = [∂ 2E /(∂N )2 ]V = const

The hardness is inversely proportional to α1/3, where α is polarizability: the harder the atom, the less polarizable it is. According to the different electronegativity scales,170−173 the highest χ values are possessed by F, O, N, and Cl. Among these elements, N, O, and F have the highest atomic hardnesses (7.23, 6.08, and 6.08, respectively).172 The Cl− ion has a high electronegativity, but it is soft and has a low charge. The F− ion is both highly electronegative and hard, but its charge is quite low. Thus, the O2− and N3− anions possess all properties necessary to act as central ions in the (XA4) tetrahedra: high electronegativity, high hardness, and relatively high charge. This explains the comparatively frequent occurrence of the (OA4) and (NA4) tetrahedra in crystal structures of inorganic compounds. Technically speaking, both hydronium, H3O+, and ammonium, NH4+, ions can be considered as O2−- and N3−-centered atomic moieties, respectively, if H+ is considered as a cation species. It is worthy to note that tetrahedral coordination of the O2−- and N3− anions in the structures considered in this review (as, e.g., in the NH4+ ion) is the result of sp3 hybridization of their valence electron orbitals. 2.2.2. Chemical Nature of Cations A. In order to understand which cations are able to form anion-centered tetrahedra, Krivovichev and Filatov72 suggested to use the bond-valence theory. According to this theory,174−176 the Ai−Xj bond valence, sij, is a function of the Ai−Xj bond length, dij:

Figure 12. The structure of β-K4La6I14Os viewed approximately along [001] featuring the columns of K4I3+ cations and La6Os clusters in the anion chains. Reprinted with permission from ref 153. Copyright 1997 American Chemical Society.

Figure 13. The [SLa]+ layer in the structure of [LaS]Cl. Cl atoms are shown as large circles; La atoms are shown as small circles (atoms below and above the plane of the S atoms are shown as black and white, respectively). Reprinted with permission from ref 155. Copyright 1998 Wiley-VCH Verlag GmbH & Co KGaA.

Fluorine-centered tetrahedra can also be found in lanthanide fluoride,162,163 calcium fluoride,164 and lead fluoride165−167 compounds, but, due to the low charge of the F− anions, they cannot be considered as strong structural entities and will not be dealt with in the present review.

sij = exp[(ro − dij)/b] 6465


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(i) the X and X′, X″, X‴, X(n) anions are chemically different: the cation A forms strong bonds to X, whereas its bonds to other anions are much weaker; (ii) the X and X′, X″, X‴, X(n) anions are chemically identical: in this case, coordination of the cation A must be distorted in such a way that the A-X bonds are stronger than the A−X′, X″, X‴, X(n) bonds. The first case is realized in the structure of Ca4OCl6,184 where the Ca−O bonds are much stronger than the Ca−Cl bonds, which makes description of the structure in terms of (OCa4) tetrahedra physically reasonable. The second case is exemplified by the oxysalts containing “additional” Oa atoms (Table 2). For instance, in the structure of lanarkite, Pb2O(SO4),128 stereoactivity of the 6s2 lone electron pairs on the Pb2+ cations allows for its strongly distorted coordination with short Pb−Oa and long Pb−OS bonds.

where ro and b are empirical parameters defined for each cation−anion pair.177,178 The important concept in the bond-valence theory relevant to the current discussion is the concept of Lewis acid strength179,180 of a cation (LAS), which is defined as following: LAS = [formal valence]/[mean coordination number]

In turn, Lewis base strength of an anion (LBS) may be defined in a similar way as its characteristic bond valence. The definition of Lewis base and acid strengths allows one to define a criterion for the existence of particular structure types, which is known as a valence-matching principle:181 the most stable structures will form when the Lewis acid strength of the cation closely matches the Lewis base strength of the anion. However, the problem to determine the LAS and LBS values is not as simple as it may seem to be, as many cations tend to form distorted coordinations, e.g., due to the Jahn−Teller distortion or the lone electron pair stereoactivity. If applied to the anion-centered XA4 tetrahedra, the necessary conditions are relatively regular coordination of X and the ability of the cation A to form (stable) A−X bonds with the bond valence equal to [formal valence of X]/4. The last principle is crucial in determining which cations do form anion-centered tetrahedra. The Lewis base strengths of the O2− and N3− anions in tetrahedral coordination are equal to 0.50 and 0.75 valence units (v.u.), respectively. Therefore, for the cation A to be able to form (OA4) and (NA4) tetrahedra, it should be able to form the A−O and N−O bonds with the bond-valences close to 0.50 and 0.75 v.u., respectively. Krivovichev and Filatov72 reviewed in detail most common metal cations and their ability to form the A−O bonds with the bond-valence of 0.50 v.u. In compounds with the “additional” Oa atoms, the typical A−O bond valences have been calculated as following (v.u.):182 Cu2+ (0.501), Pb2+ (0.510), Hg2+ (0.608), Bi3+ (0.596), Sb3+ (0.698), Y3+ (0.499), La3+ (0.504), Nd3+ (0.504). These numbers mean that the Cu2+, Pb2+, Y3+, La3+, and Nd3+ cations will form more or less regular OA4 tetrahedra, whereas oxocentered tetrahedra with Hg2+ and Bi3+ cations will be strongly distorted. The Sb3+ cations will be able to form very distorted tetrahedra only, but, in most cases, coordination numbers of “additional” O atoms in the structures of respective Sb3+ compounds are less than 4. As an example, consider the structure of Sb6O7(SO4)2,183 where the Oa atoms form the (2 + 2)-distorted (OSb4) tetrahedra (O−Sb = 2.052x and 2.732x Å), the (3 + 1)distorted tetrahedra (O−Sb = 2.00, 2.20, 2.22, 3.08 Å), and two types of the (OSb3) triangles (O−Sb = 2.11, 2.13, 2.16 Å and 2.032x, 2.35 Å). There are no sufficient crystal chemical data available on some cations such as trivalent actinides, but their chemical similarity with lanthanides suggests that they may be able to form oxocentered tetrahedra as well. Other cations form anioncentered tetrahedra occasionaly, which will be reviewed in section 3.

2.4. Systematics of Tetrahedral Complexes

2.4.1. Basic Parameters. Tetrahedral structures are common in silicates, phosphates, aluminosilicates, aluminophosphates, etc., i.e., in compounds, where units of cationcentered tetrahedra constitute basis of crystalline compounds. As a rule, the cation-centered tetrahedra are corner-linked, and one corner belongs to no more than two tetrahedra. This is the consequence of the high valence of the central cations forming tetrahedral complexes. In the case of anion-centered tetrahedra, the situation is different, as the central ions (e.g., O2− and N3−) are relatively low-charged, and the repulsion between adjacent tetrahedral centers is not so strong as is in the case of cationcentered tetrahedra. The result is that anion-centered tetrahedra may link to each other by sharing common edges (i.e., via two bridging A atoms), and one corner may be shared among more than two tetrahedra. As a consequence, topology of tetrahedral units becomes more complex and more diverse, and additional tools are needed in order to classify different types of units based upon linked (XA4) tetrahedra. A system of classification parameters for tetrahedral structures with edgeand corner-sharing tetrahedra was developed in refs 185 and 186 on the basis of classification of silicate anions proposed by Liebau,187 and briefly described below. (1) The dimensionality of the unit, D, is the number of dimensions in which the complex is of infinite extent. The following values are possible: 0 (finite clusters), 1 (chains), 2 (layers), and 3 (frameworks). (2) The linkedness of the tetrahedron L and the linkedness of the tetrahedra in the complex ML. L is equal to the number of the A atoms shared between two adjacent (XA4) tetrahedra. The possible values of L are 0 (no linkage), 1 (corner linkage), 2 (edge linkage), 3 (face linkage). The parameter ML indicates the way in which it is possible to construct the specified complex by adding individual single tetrahedra. It is determined as the following hierarchical series of values: [3] > [2, 3] > [1, 2, 3] > [1, 3] > [2] > [1, 2] > [1] > [0]. Here it is necessary to make use of the Wells’s rule:188−190 if an edge (or face) is shared by two tetrahedra, then its corners (and edges) are not considered to be shared by these two tetrahedra. (3) The connectivity (the term “connectedness” was used in earlier publications71,185) s of a tetrahedron is equal to the number of polyhedra with which it shares corners, regardless of their linkedness. The tetrahedra are considered as single if s = 0, primary if s = 1, secondary if s = 2, etc. (4) The important concept in systematics of tetrahedral complexes is that of a single chain, which is defined as 1D unit

2.3. Applicability of the Approach

As it was mentioned above, consideration in terms of anioncentered tetrahedra has a strong physical basis only when it adequately describes structural anisotropy of the respective compounds. The latter is in order when the A−X bonds are stronger than all other A−X′, X″, X‴, X(n) bonds formed by the cation A in the structure. This is possible in two cases: 6466


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connectivity diagram on the basis of the Schlegel diagram for a tetrahedron. The Schlegel diagram represents a projection of the edge network of a convex polyhedron onto a 2D plane. For the tetrahedron, the Schlegel diagram is simply the view from above onto a regular tetrahedron placed on one of its triangular bases. The Schlegel diagrams have been used in inorganic crystal chemistry since 1960s.191,192 Henceforth we shall use the following ways of representing the connectivity elements on the connectivity diagram. (1) The corner designated by a circle links the given tetrahedron to another. If the corner links the given tetrahedron to more than one other tetrahedron, then the number of such tetrahedra is indicated next to the corner.

consisting of secondary tetrahedra. Many structures can be considered as resulting from successive polymerization of a few types of topologically simple single chains, which sometimes identified as fundamental chains. (5) The periodicity P of a single chain is the number of structural subunits constituting the period of the chain. For finite ring structures, the number of polyhedra constituting the ring is specified as the periodicity. Liebau187 called this parameter the ring periodicity, Pr. In order to identify chains with different P values, Liebau187 used German adjectives such as einer (for P = 1), zweier (P = 2), dreier (P = 3), etc. (6) The multiplicity M of the complex is the term given to the number of single polyhedra, chains, or layers, which, by linking to one another, form a complex with the same dimensionality as the initial complexes. Figure 15 shows three different einer chains with M = 1 (a), 2 (b), and 3 (c).

(2) The edge identified by a semibold line is common to two polyhedra. The connectivity diagrams will be referred to as equivalent if the relative disposition of the linkage corners and/or edges in them is the same (or is mirror-symmetrical). Wells188−190 suggested that, in polyhedral complexes, polyhedra with the same relative disposition of the shared elements be referred to as topologically equivalent. Within the framework of the approach employed, this means that tetrahedra with equivalent connectivity diagrams are referred to as topologically equivalent tetrahedra in the complex. It is important that the description of the disposition of the shared elements in the tetrahedron (with the aid of the connectivity diagram) is still insufficient to define the position of the tetrahedron in the complex. In the same structure, topologically equivalent tetrahedra may have different environments comprising tetrahedra with which they have common elements. Figure 17a shows the [O9Pb14]10+ tetrahedral layer in

Figure 15. Multiple einer chains of tetrahedra and connectivity diagrams of their tetrahedra. The chains with M = 1 (a), 2 (b), and 3 (c) are shown.

(7) The X:A ratio of the [XnAm] complex. 2.4.2. Topological and Geometrical Classification of Tetrahedra. In complex structural units consisting of (XA4) tetrahedra, different tetrahedra may play different topological functions. In order to distinguish between topologically distinct tetrahedra, it was suggested to use a connectivity formula for the particular tetrahedron as follows: (s : L1 − s1; L 2 − s2 ; ...; Ln − sn)

where L1, L2, ..., Ln are specific values of linkedness, while s1, s2, ..., sn are specific values of connectivity for the given tetrahedron in accordance with the values of linkedness indicated ahead of them. The connectivity formula shows how many tetrahedra are linked to the given tetrahedron and in which way. However, connectivity formula does not fully characterize the linkage topology. Figure 16 shows two tetrahedral units with the Figure 17. The [O9Pb14]10+ layer from the structure of kombatite, Pb14O9(VO4)2Cl4 (a), connectivity diagrams of its tetrahedra (b), and first coronas of the A (c), B (d), C (e), and D (f) tetrahedra.

the crystal structure of kombatite, Pb14O9(VO4)2Cl4.132 There are six crystallographically distinct tetrahedra in the layer denoted as A, B, C, D, E, and F. However, there are only four different topological types of tetrahedra, since the A and B, and C and D tetrahedra have the same connectivity diagrams (Figure 17b). To distinguish between global topological functions played by topologically equivalent tetrahedra in the complex, one has to analyze their configuration. In order to do this, we suggested to use the concept of corona introduced for

Figure 16. The A and B tetrahedra have the same connectivity formulas, but their environments are topologically different.

central tetrahedra (A and B) having the same connectivity formulas, though the topology of their linkage to the adjacent tetrahedra is different. In order to account for the local topological linkage features, it is convenient to employ the 6467


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Table 3. Crystallographic Data for Cu(II) Inorganic Compounds Containing Finite Complexes of (OCu4) Tetrahedra O:Cu 1:4

2:7 2:6

chemical formula

space group

a (Å); α (deg)

b (Å); β (deg)

Compounds with Isolated (OCu4) Tetrahedra TlCu[Cu4O](VO4)3 P1̅ 6.10; 97.70 8.29; 92.25 starovaite KCu[Cu4O](VO4)3 P1̅ 6.08; 97.8 8.26; 92.4 fingerite Cu3[Cu4O]2(VO4)6 P1̅ 8.16; 107.14 8.27; 91.39 ponomarevite K4[Cu4O]Cl10 C2/c 14.74 14.90; 104.79 [Cu4O](PO4)2 Pnma 8.09 6.27 [Cu4O](PO4)2 P1̅ 7.54; 113.65 8.10; 98.42 [Cu4O](AsO4)2 Pnma 8.25 6.41 [Cu4O](AsO4)2 P1̅ 6.41; 98.52 7.65; 112.39 KMg[Cu4O](VO4)3 P21/m 10.71 6.03; 98.08 K5H[Cu4O](B20O32(OH)8)(H2O)3 P1̅ 16.27; 96.37 17.97; 110.93 [Cu4O]Br6(NH3)4 P4̅21c 9.00 9.00 [PbCu3O](TeO6) Pnma 10.49 6.35 Compounds with Multiple Finite Complexes of (OCu4) Tetrahedra burnsite KCd[Cu7O2](SeO3)2Cl9 P63/mmc 8.78 8.78 fedotovite K2[Cu3O](SO4)3 C2/c 19.04 9.48; 111.04 euchlorine NaK[Cu3O](SO4)3 C2/c 18.41 9.43; 113.7 Cu[Cu3O](SeO3)3-II P1̅ 7.99; 77.34 8.14; 65.56 Cu[Cu3O](SeO3)3-I P21/a 15.99 13.52; 90.49 prewittite KPb0.5Cu[PbCu5O2]Zn(SeO3)2Cl10 Pnnm 9.13 19.42

the topological description of space tilings.193 The first corona, C1(T), of the tetrahedron T is the tetrahedron itself plus all tetrahedra with which it has shared elements. The second corona constitutes the first corona plus all tetrahedra with which tetrahedra of the first corona share common elements. By analogy, n-corona, Cn(T) is defined as Cn−1(T) plus all tetrahedra with which tetrahedra of Cn−1(T) share common elements. Two tetrahedra are conf igurationally equivalent if their n-coronas are equivalent for any n. For the topologically equivalent A and B tetrahedra of the complex shown in Figure 17a, the 1-coronas are identical, but their 2-coronas are different (Figure 17c,d), which indicates that these tetrahedra are configurationally nonequivalent. The same applies to the C and D tetrahedra (Figure 17e,f). Thus, the [O9Pb14]10+ layer shown in Figure 17a consists of six different configurational types (which, in this case, coincide with crystallographically different tetrahedra). In general, there is a hierarchical relation between crystallographic, configurational, and topological equivalence. Configurationally equivalent tetrahedra are always topologically equivalent, but topologically equivalent tetrahedra may be configurationally nonequivalent. Crystallographically equivalent tetrahedra are always topologically and configurationally equivalent. It should be noted that configurationally equivalent tetrahedra may be occupied by different chemical elements: if this is the case, they have to be crystallographically nonequivalent. The topological structure of the tetrahedral complexes with edge-sharing tetrahedra may be extremely complex, as it will be shown in the section 3.2 for some layers of edge-sharing (OPb4) tetrahedra.

c (Å); γ (deg)

V (Å3)

ref

10.75; 90.28 10.71; 90.4 8.04; 106.44 8.95 13.38 6.28; 74.19 13.79 8.22; 98.38 8.34 13.65; 111.36 9.731 8.81

538.7 532.4 493.8 1900.1 678.7 337.6 729.7 360.1 533.1 3341.7 788.9 587.2

194 64 41 61, 62 196 123, 196 197, 198 126 199 200 201 202

15.521 14.23 14.21 8.39; 81.36 17.745 13.21

1036.3 2396.8 2258.9 483.9 3835.5 2342.6

29 39 37 124 124 63

(μ4-O)Cu4 core in metal−organic compounds and has been extensively studied due to the interesting magnetic properties.203 In purely inorganic compounds, isolated (OCu4) tetrahedra are present, e.g., in ponomarevite, K4Cu4OCl10,60−62 where central tetrahedral core is surrounded by 10 Cl− anions, with six anions linked to the Cu···Cu edges and four linked to the Cu corners (Figure 18).

Figure 18. The [(OCu 4 )Cl 10 ] 4− anion in the structure of ponomarevite, K4Cu4OCl10.

Linking two (OCu4) tetrahedra via common Cu atom results in the formation of the [O2Cu7]10+ dimer (Figure 19a) observed in the structure of burnsite, KCd[Cu7O2](SeO3)2Cl9.28,29 The

3. ANION-CENTERED TETRAHEDRA IN INORGANIC COMPOUNDS: SYSTEMATIC DESCRIPTION 3.1. OCu4 Tetrahedra in Inorganic Compounds

3.1.1. 0D Units. The list of inorganic compounds based upon finite units of (OCu4) tetrahedra is given in Table 3. The simplest unit is an isolated tetrahedron, which is known as an

Figure 19. The [O2Cu7]10+ dimer (a), the {[O2Cu7](SeO3)2}6+ complex (b), and complex copper oxoselenate framework (c) in the structure of burnsite, KCd[Cu7O2](SeO3)2Cl9. 6468


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(SeO3) groups are attached to the triangular faces of tetrahedra to form the {[O2Cu7](SeO3)2}6+ clusters (Figure 19b) which are linked through the Cu−OSe bonds into a 3D microporous framework (Figure 19c). The framework cavities are occupied by the (Cd2+Cl6)4− octahedra, K+ cations, and Cl− anions. Linkage of two (OCu4) tetrahedra by sharing a common Cu···Cu edge results in the formation of the [O2Cu6]8+ cluster found in the structure of fedotovite, K2[Cu3O](SO4)338,39 (Figure 20). The clusters are coordinated by six (SO4)2− anions to produce the anionic {[O2Cu6](SO4)6]}4− complex. Similar

Figure 22. Crystal structure of Cu[Cu3O](SeO3)3-II containing [O2Cu6] tetrahedral dimers. “Additional” oxygen atoms are shown as red circles with heavy outline.

two modifications of Cu[Cu3O](SeO3)3 (Figure 22). Note that, in this case, there are Cu2+ cations that are not bonded to the “additional” Oa atoms. 3.1.2. 1D Units. There are six different types of chains of (OCu4) tetrahedra observed in the structures inorganic compounds (Table 4). The simplest single chain is formed when tetrahedra share corners so that all tetrahedra are secondary and the resulting chain is einer (Figure 23). Chains of this type are present in the structures of inorganic compounds with the general formula [Cu2MO](B2O5) (M = Mg, Co, Zn).204,205 The zweier chain of this topological type has the [O2Cu6]8+ stoichiometry with the O:Cu ratio equal to 1:3 (the number of atoms is doubled in order to account for P = 2). These chains have been described as basic structure entities in a number of compounds. Recently, Jin et al.116 reported on the structure and properties of NaCu+[(Cu2+3O)(PO4)2Cl] and compared configurations of the [O2Cu6]8+ chains in different compounds (Figure 24). In allochalcoselite, Cu+[PbCu2+5O2](SeO3)2Cl5,21,22 one of the nonshared Cu atoms in every second tetrahedron is replaced by the Pb2+ cation so that the chain has the [O2Cu5Pb]8+ composition (Figure 25). Linking two chains by sharing common Cu...Cu edges of the (OCu4) tetrahedra generates the [O2Cu5]6+ double zweier chain present in the structure of stoiberite, [Cu5O2](VO4)2.65 It is noteworthy that, in the original report,66 description of this structure was given in terms of cation-centered polyhedra, which was reconsidered in our earlier works.71,72 Another kind of a single fundamental chain is formed when OCu4 tetrahedra share trans-edges to produce the [O2Cu4]4+ chains. These chains have been first reported by Effenberger and Zemann59 in the structure of “caratiite”, K4[Cu4O2](SO4)4(Cu0.5Cl) (discredited name,214 the proper name is “piypite”). As in the structure of fedotovite, in piypite oxocentered tetrahedral polycations are surrounded by the (SO4)2− tetrahedra to form anionic 1D rods with the composition {[O2Cu4](SO4)4]4+ (Figure 26). In the structure, these rods are parallel to each other and linked by K+ cations. It is of interest that, in most of the structures, the chains of trans-edge-sharing (OCu4) tetrahedra are 2-periodic; their identity period equals 4.94−4.98 Å (Figure 27a). However, in coparsite, [Cu4O2][(As,V)O4]Cl,32,33 the chains are 4-periodic, owing to their interaction with the Cl− anions through the formation of two Cu−Cl bonds to each anion (Figure 27b). In the resulting structure (Figure 28), the {[O 2 Cu 4 ]Cl} 3+ complexes are interlinked into 3D framework via (As,V)O4

Figure 20. The crystal structure of fedotovite, containing [O2Cu6] dimers of edge-sharing (OCu4) tetrahedra. “Additional” oxygen atoms are shown as red circles.

complexes have recently been reported by Burrows et al.117 in a series of novel Cu metal−organic polymers (Figure 21). The [O2Cu6]8+ dimers have also been described in the structure of

Figure 21. The [O2Cu6] dimer in the structure of (NMe2H2)4[Cu6O2(SO4)6(DMF)4] (a) and its local coordination by (SO4) tetrahedra (b). Reprinted with permission from ref 117. Copyright 2012 American Chemical Society. 6469


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Table 4. Crystallographic Data for Cu(II) Inorganic Compounds Containing Chains of (OCu4) Tetrahedra O:Cu

chemical formula

space group

a (Å); α (deg)

b (Å); β (deg)

c (Å); γ (deg)

V (Å3)

ref

1:3

[Cu2MgO](B2O5) [Cu2ZnO](B2O5) [Cu2CoO](B2O5) cupromolybdite [Cu3O](MoO4)2 [(Cu0.91Zn0.09)3O](MoO4)2 vergasovaite [Cu3O](MoO4)(SO4) allochalcoselite Cu+[PbCu2+5O2](SeO3)2Cl5 NaCu[Cu3O](PO4)2Cl Na2Cu+[Cu2+3O](PO4)2Cl Cu+Cu2+[Cu2+3O](SeO3)Cl5 Cu3[Cu6O2](SeO3)4Cl6 chloromenite Cu3[Cu6O2](SeO3)4Cl6 kamchatkite K[Cu3O](SO4)2Cl [Cu3O](V2O7)(H2O) stoiberite [Cu5O2](VO4)2 parageorgbokiite β-[Cu5O2](SeO3)2Cl2 georgbokiite α-[Cu5O2](SeO3)2Cl2 [Cu5O2](PO4)2 coparsite [Cu4O2][(As,V)O4]Cl piypite K4[Cu4O2](SO4)4(Cu0.5Cl) Na4[Cu4O2](SO4)4(MeCl) (Me = Na, Cu) klyuchevskite K3[Cu3FeO2](SO4)4 alumoklyuchevskite K3[Cu3FeO2](SO4)4 [BiCu2O2][(V0.6P0.4)O4] [BiCu2O2][(V0.88P0.12)O4] [BiCu2O2][VO4] [BiCu2O2][AsO4] [BiCu2O2][PO4]

P21/c P21/c P21/c Pnma Pnma Pnma C2/m P21/c Cmcm P21/m P21/n I2/m Pna21 P21/m P21/c P21/c P21/c P1̅ Pbcm I4 P4/n I121 I121 Pnma Bbmm I2/m Pnma Pnma

3.24 3.20 3.23 7.66 7.69 7.42 18.47 8.39 13.61 9.20 12.92 14.17 9.74 7.44 8.39 5.40 6.03 7.60; 111.66 5.44 13.60 18.45 18.67 18.77 11.97 12.38 13.59 12.25 11.78

14.79; 94.88 14.78; 93.28 14.85; 93.67 6.87 6.90 6.75 6.15; 119.28 6.40; 109.47 10.39 6.23; 91.97 6.26; 112.88 6.26; 113.05 12.86 6.66; 93.57 6.05; 108.09 8.05; 99.26 13.74; 95.75 5.30; 90.19 11.15 13.60 18.45 4.94; 101.5 4.97; 101.66 5.29 5.23 7.88; 112.96 5.28 5.17

9.15 9.10 9.12 14.56 14.59 13.62 15.31 16.67 6.37 9.56 14.04 13.00 7.00 7.76 16.16 11.13 5.56 5.20; 82.56 10.33 4.98 4.95 18.405 18.47 7.81 7.83 15.96 7.58 7.79

436.8 429.4 435.7 766.0 774.6 682.9 1516.4 843.6 900.9 547.8 1046.9 1061.4 876.9 383.8 780.1 477.5 458.6 193.0 627.0 921.1 1685.9 1663.2 1686.4 494.4 507.2 1574.1 490.2 474.6

204 204 205 34 206 68 22 116 122 207 208 31 47 209 66 56 43 125 33 59 210 49 24 101 101 211 212 213

1:3

2:5 2:5

1:2

2:3

(Figure 30a), the chains are linked into layers that are parallel to (100), such that the structure has channels parallel to the c axis (c = 5.579 Å) and occupied by the Cl− anions. In contrast, in parageorgbokiite, the chains are linked into a 3D framework (Figure 30b). Thus, the two polymorphs represent an interesting case of different modular arrangements. 3.1.3. 2D Units. At present time, there are no reports on the layers of (OCu4) tetrahedra that can be formed by successive linkage of tetrahedra by edge sharing (ML = 2). All the known layers (Table 5) can be constructed either by successive corner-linkage (ML = 2) or by both edge- and corner-linkage (ML = 1, 2). There are two types of layers with ML = 1, i.e., which contain corner-sharing tetrahedra only (Figure 31a,b). Both layers have the stoichiometry [O2Cu5]6+ (or [O2Cu3Pb2]6+). The topology of the layers shown in Figure 31 is the same, but they are different in terms of orientations of nonshared corners of tetrahedra relative to the plane of the layer. Therefore, these layers should be considered as geometrical isomers.220−222 They can be distinguished by specifying types of orientation of tetrahedra within the hexagonal rings, which may be considered as their basic entity. The layer shown in Figure 31a is based upon the UDUDUD rings, whereas the layer in Figure 31b consists of the UUDUUD rings. Here U and D indicate the orientation of nonshared tetrahedral corners either up (U) or down (D) relative to the plane of the layer. The UDUDUD layer occurs in the structure of averievite, [Cu5O2](VO4)2(Cu+Cl)27 (Figure 32). This structure is remarkable in that the [O2Cu5]6+ layers, together with the (VO4)3− tetrahedra, form a porous electroneutral 3D framework {[O2Cu5](VO4)2}, which contains separated channels occupied by the Cu+ and Cl− ions. The

Figure 23. The crystal structure of [Cu2MgO](B2O5) (a) as based upon the [OCu2Mg]4+ einer chain (b).

tetrahedra. Combination of two zweier chains of trans-edgesharing tetrahedra results in formation of the [O2A3] double chains (Table 4). Since these chains are known in Cu−Bi oxysalts only, they will be considered in detail in section 3.4 below. A single chain with alternating edge- and corner-linkage of (OCu4) tetrahedra has already been mentioned in the discussion on the structure and thermal expansion of georgbokiite, α-[Cu5O2](SeO3)2Cl243,140 (Figure 8). Parageorgbokiite, β-[Cu5O2](SeO3)2Cl2,55,56 is a dimorph of georgbokiite. Both minerals have the same monoclinic spacegroup, P21/c, but differ in their unit-cell parameters (Table 4). Structural studies of the two minerals have demonstrated that both are based upon the same complex ([O2Cu5][SeO3]2)2+ chains (= 1D modules), represented in Figure 29. However, the arrangements of the chains in the structures are different, as shown in Figure 30. In georgbokiite, α-Cu5O2(SeO3)2Cl2 6470


Chemical Reviews

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Figure 26. The [OCu2](SO4)4 chain in the structure of piypite.

Figure 27. The 2-periodic chain of trans-edge-sharing (OCu4)6+ tetrahedra (a) and its distorted version present in the structure of coparsite, [Cu4O2][(As,V)O4]Cl (b).

Figure 24. Comparison of the linear [O2Cu6] chain of (OCu4) tetrahedra in the structures of (a) NaCu[(Cu3O)(PO4)2Cl], (b) NaCuI[(CuII3O)(PO4)Cl], and (c) CuII3O(MoO4). Reprinted with permission from ref 116. Copyright 2012 Elsevier B. V.

Figure 28. The crystal structure of coparsite, [Cu4O2][(As,V)O4]Cl, projected along the a axis.

The topologies of the layers with ML = 1, 2 are depicted in Figure 31c,d. The layer in Figure 31c can be constructed by linking fedotovite-type dimers via common Cu corners; this layer has first been detected by Bergerhoff and Paeslack1 in the structure of dolerophanite, Cu2O(SO4) (Figure 1). Layers of the same topological type are present in the structure of francisite, [Cu3BiO2](SeO3)2Cl,143 and francisite-related compounds215−218 (Figures 9 and 10). The layer shown in Figure 31d can be found in the structure of nabokoite, Cu[Cu6TeO4](SO4)5Cl.54 There are three topochemical types of metal atoms in this layer: one (Te) is shared between four OCu3Te tetrahedra, whereas two others (Cu) are shared between two tetrahedra each. 3.1.4. 3D Units. In the structures of two most common Cu oxides, cuprite (Cu+2O)223,224 and tenorite (Cu2+O),225,226 the O atoms are tetrahedrally coordinated. However, the mode of linkage of the OCu4 tetrahedra in the two structures is different. In the structure of cuprite, (OCu4) tetrahedra share corners to

Figure 25. The [O2Cu5Pb]8+ chain (a) in the structure of allochalcoselite, Cu+[PbCu2+5O2](SeO3)2Cl5 (b).

ion-exchange properties of averievite are unknown, but it may be suggested that its oxocopper vanadate framework may have some potential from this point of view. The UUDUUD layer has been observed in the structure of ilinskite, Na[Cu5O2](SeO3)2Cl3.45 The structure of the [O2Cu5]6+ layer and its local coordination by (SeO3)2− groups, Cl− anions and Na+ cations are shown in Figure 33. 6471


Chemical Reviews

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interactions that held the frameworks together were a subject of extensive discussions in the literature.227−229 Replacement of Cu+ by Cu2+ results in the positive charge of the framework, which can be compensated by the introduction of anions into the framework cavities. This is what happens in the structures of melanothallite, Cu2OCl2,52,53 and two polymorphs of [Cu2O](SeO3)124 (Table 5). It is worthy to note that the orthorhombic structure of melanothallite displays negative thermal expansion along one of the crystallographic axes, which is, however, better explained in terms of chains of [CuO4Cl2] octahedra than in terms of the (OCu4) tetrahedral network.53 3.2. OPb4 Tetrahedra in Inorganic Compounds

3.2.1. 0D Units. Selected topological types of 0D units of (OPb4) tetrahedra are shown in Figure 35; a list of respective compounds is provided in Table 6. Isolated (OPb4) tetrahedra (Figure 35) have been found in the structures of [Pb4O]Pb2(BO3)3Cl230 and Pb4O(PO4)2.234 Behm230 described the structure of [Pb4O]Pb2(BO3)3Cl as consisting of oxocentered (OPb 4 ) tetrahedra, (BO 3 ) 3− triangular anions, Cl− anions, and the Pb2+ cations not involved in the formation of tetrahedral polycations (Figure 36). He pointed out structural relationships of the structure of [Pb4O]Pb2(BO3)3Cl to Pb2O(SO4) and Pb3O2(SO4) and noted that one of the Pb···Pb contacts in the oxocentered unit is rather short (3.548 Å) and can be compared to the Pb− Pb distance in Pb metal (3.4924 Å).241 Pb4O(PO4)2 is one of the environmentally important phases that impact Pb2+ activity in soils.242−245 Its structure234 is based upon the (OPb4) tetrahedra linking adjacent (PO4)3− phosphate anions into a 3D framework. More complex oxohydroxo lead(II) unit has been observed in the structure of “plumbonacrite” Pb5O(CO3)3(OH)2,233 a metastable phase that forms in lead corrosion technological products as an intermediate product of lead and lead oxide carbonatization.246 In the structure of “plumbonacrite”, (OPb4) tetrahedron shares three of its Pb−Pb edges with three [(OH)Pb3] distorted triangles to form [O(OH)3Pb7] clusters (Figure 37). Isochemical clusters were observed in the crystal structure of Pb9O(OH)4-A, zeolite 4A exchanged with Pb2+ at pH 6.0 and evacuated at 26 °C.247 In general, the (OPb4) tetrahedral cores surrounded by the (OH)− groups are known as important lead(II) oxo-hydroxo clusters existing in aqueous solutions. In particular, the [Pb6O(OH)n] clusters (Figure 38) are known to exist at the pH values closely associated with drinking water248 and have been a subject of extensive experimental and theoretical investigations.17,249−254 The [O2Pb7]10+ complex shown in Figure 35b consists of two tetrahedra sharing a common Pb atom. In Pb2[Pb7O2](Al8O19),235 the [O2Pb7]10+ complexes are situated in cavities of the anionic tetrahedral framework formed by the AlO4 tetrahedra. The [O2Pb6]8+ complex of two edge-sharing [OPb4]6+ tetrahedra (Figure 35c) is present in the structure of [Pb3O](UO5).236 In this compound, UO6 octahedra share corners to form slightly bended [UO5] chains (Figure 39). An interesting example of a tetrahedral trimer consisting of three edge-sharing (OPb4) tetrahedra (Figure 40) can be found in the recently reported compound Pb4B2O7.237 The authors of the original paper237 assign to this compound the chemical formula Pb4O(BO3)2, which does not reflect its real crystal chemistry. In fact, the structure contains both isolated BO3

Figure 29. The [O2Cu5]6+ (a) and {[O2Cu5](SeO3)2}2+ (b) chains in the structure of parageorgbokiite, β-Cu5O2(SeO3)2Cl2.

Figure 30. The structures of georgbokiite (a) and parageorgbokiite (b) projected along the extension of the [O2Cu5]6+ chains (highlighted). The location of channels occupied by the Cl− anions and lone pairs of electrons of the Se4+ cations is indicated by the symbol Ψ.

form two interpenetrating cristobalite-like [OCu2] frameworks (Figure 34a). The [OCu] framework in tenorite (Figure 34b) can be considered as built by lateral condensation of the piypite-type [O2Cu4]4+ chains of trans-edge-sharing (OCu4) tetrahedra. Each Cu atom in tenorite is shared between four (OCu4) tetrahedra, which corresponds to the 4-fold square coordination of the Cu2+ cations by the O atoms. In the structure of cuprite, the two cristobalite-type [OCu2] frameworks are electrically neutral, and the possible Cu+···Cu+ 6472


Chemical Reviews

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Table 5. Crystallographic Data for Cu(II) Inorganic Compounds Containing Layers and Frameworks of (OCu4) Tetrahedra O:Cu 1:2

2:5 2:5 4:7 1:2

chemical formula

space group

a (Å); α (deg)

b (Å); β, (deg)

Compounds with 2D Units (Layers) of (OCu4) Tetrahedra [Cu3NdO2](SeO3)2Cl Pmmn 6.38 9.63 [Cu3YO2](SeO3)2Cl Pmmn 6.31 9.46 [Cu3BiO2](TeO3)2Cl Pcmn 6.37 9.85 [Cu3BiO2](SeO3)2Br Pmmn 6.39 9.69 [Cu3BiO2](SeO3)2I Pmmn 6.44 9.75 [Cu3ErO2](SeO3)2I Pmmn 6.30 9.43 francisite [Cu3BiO2](SeO3)2Cl Pmmn 6.35 9.63 dolerophanite [Cu2O](SO4) C2/m 9.37 6.32 122.34 averievite [Cu5O2](VO4)2(CuCl) P3 6.38 6.38 [Pb2Cu3O2](NO3)2(SeO3)2 Cmc21 5.88 12.19 ilinskite Na[Cu5O2](SeO3)2Cl3 Pnma 17.77 6.45 nabokoite Cu[Cu6TeO4](SO4)5Cl P4/ncc 9.83 9.83 Compounds with 3D Units (Frameworks) of (OCu4) Tetrahedra [Cu2O](SeO3)-II P21/n 6.99 5.95 92.17 [Cu2O](SeO3)-I P213 8.93 8.93 [Cu2O]Cl2 Fddd 7.47 9.60

c (Å); γ (deg)

V (Å3)

ref

7.09 6.98 14.36 7.29 7.38 6.97 7.22 7.64 8.40 19.37 10.52 20.59

435.5 416.7 901.4 451.4 463.0 413.9 441.8 382.1 295.6 1389.0 1205.6 1990.9

215 215 216 217 217 218 143 18 27 219 45 54

8.43 8.93 9.70

350.3 710.9 695.3

124 124 53

Figure 31. The [O2Cu5]6+ layers in the structures of averievite (a) and ilinskite (b); the [OCu2]2+ layer in the structure of dolerophanite (c); the [O4Cu6Te]8+ layer in the structure of nabokoite (d).

Figure 33. The [O2Cu5]6+ layer (a) in the structure of ilinskite, Na[Cu5O2](SeO3)2Cl3 (b). Reprinted with permission from ref 45. Copyright 2013 Springer Verlag.

triangles and B2O5 dimers. The proper crystal chemical formula of the compound should be written as [Pb8O3](BO3)2(B2O5). The stella quadrangula (“tetrahedral star”) (Figures 35d and 41) complex has been found in [Pb8O4]Br10 and Tl[Pb8O4]Br9.12,13 This [O4Pb8]8+ group is formed by four edge-sharing

Figure 32. The crystal structure of averievite, [Cu5O2](VO4)2(Cu+Cl). 6473


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Figure 34. The [OCu2] framework in the structure of cuprite (a) and the [OCu] framework in the structure of tenorite (b).

Figure 36. The crystal structure of [Pb4O]Pb2(BO3)3Cl (top) and geometry of the OPb4 tetrahedron (bottom).

Figure 35. (a−e) Selected types of finite complexes of OPb4 tetrahedra.

(OPb4) tetrahedra. It is of interest that similar complexes consisting of both Pb2+ and Pb4+ cations were found by Yeom et al.238,239 in the structure of dehydrated zeolite X exchanged with Pb(II) at pH 6.0. The most complex cluster built from eight (OPb4) tetrahedra (Figure 35e) that share a common Pb atom was described in [Pb13O8](OH)6(NO3)4240 (Figure 42). The (OPb4) tetrahedra are additionally linked the OH− groups, thus forming the {[O8Pb13](OH)6}4+ cluster. It is likely that similar clusters may occur in nature during hydrothermal activity in oxidized zones of Pb mineral deposits, and such clusters may also play an important role in the transport of Pb from Pb mineral localities

Figure 37. Structure of the main structural subunits in “plumbonacrite”. (a) Oxocentered [OPb4]6+ tetrahedron; (b) [O(OH)3Pb7] cluster.

to the biosphere. It is interesting that this compound, known previously as “Pb6O3(OH)4(NO3)2”, was described by Kolitsch and Tillmanns255 as formed as a result of anthropogenic processes on a medieval mine dump, probably involving black gunpowder used in the blasting of ore.

Table 6. Crystallographic Data for Pb(II) Inorganic Compounds Containing Finite Units of (OPb4) Tetrahedra O:Pb 1:4

2:7 1:3 3:8 4:8

8:13

chemical formula

space group

a (Å); α, (deg)

b (Å); β, (deg)

Compounds with Isolated (OPb4) Tetrahedra Pbcm 7.02 17.22 Pnma 13.31 10.28 Pn3̅ 9.32 9.32 P63cm 9.09 9.09 P21/c 9.49 7.14; 104.55 Compounds with Finite Complexes of (OPb4) Tetrahedra Pb2[Pb7O2](Al8O19) Pa3̅ 13.26 13.26 [Pb3O](UO5) Pnam 13.72 12.35 [Pb8O3](BO3)2(B2O5) Aba2 15.46 10.81 Pb[Pb8O4]Br10 P4/n 12.28 12.28 Tl[Pb8O4]Br9 P4/n 12.34 12.34 [Pb8O4]2[Si25Al23O96] in Pb442+Pb54+Tl18+O17Sil00Al92O384 Fd3̅ 25.24 25.24 [(Pb2+,Pb4+)4Pb4O4] in Pb442+Pb54+Tl18+O17Sil00Al92O384 Fd3̅ 25.11 25.11 [Pb13O8](OH)6(NO3)4 R3̅ 10.28 10.28 [Pb4O]Pb2(BO3)3Cl [Pb4O]2Bi2(PO4)6 [Pb4O]Pb2[Re6O18] Pb[Pb4O](OH)2(CO3) plumbonacrite Pb4O(PO4)2

6474

c (Å); γ (deg)

V (Å3)

ref

10.95 9.22 9.32 24.92 14.41

1324.0 1262.2 809.02 1784.3 944.91

230 231 232 233 234

13.26 8.21 9.95 8.32 8.21 25.24 25.11 25.47

2331.5 1391.7 1661.3 1255.5 1250.2 16075.5 15849.2 2332.5

235 236 237 13 12 238 239 240


Chemical Reviews

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Figure 38. [Pb6O(OH)6]4+ cluster consisting of [OPb4]6+ core. Reprinted with permission from ref 17. Copyright 1993 American Chemical Society.

Figure 42. Ball-and-stick representation of the structure of [Pb13O8](OH)6(NO3)4 projected along the c axis.

chains through nonshared cis-edges of tetrahedra is shown in Figure 43a. Chains of this type have been observed in the structure of the M′-polymorph of Pb2SiO4,258,282 whose chemical composition and structure are better expressed with the formula Pb8O4(Si4O12) that emphasizes, on one hand, the presence of “additional” O atoms and, on the other hand, the existence of [Si4O12]8− four-membered rings of silicate tetrahedra. The [OPb2]2+ chains of trans-edge-sharing (OPb4) tetrahedra (Figure 43b) are common in minerals and inorganic compounds. They were first described by Sahl128 in the structure of lanarkite, Pb2O(SO4), which is a representative of the family of isotypic compounds with the general formula Pb2O(TO4) (T = S, Cr, Mo, W). These compounds are of interest because of their luminescence properties283 and mineralogical importance. In general, the identity periods of the [OPb2]2+ chains are in the range of 5.68−5.80 Å, since their periodicity is usually equal to 2. The known examples of such chains with a periodicity of 4 have been observed in the structures of [Pb2O]Cu(SO4)(OH)4·H2O (elyite)265 and Pb4O(VO4)2 (Krivovichev, Burns, 2003b),260 where the identity periods of the chains are 11.532 and 11.540 Å, respectively. In the structure of philolithite, [Pb2O]6Mn(Mg,Mn)2(Mn, Mg)4(SO4)(CO3)4Cl4(OH)12,74 the [OPb2]2+ chains have the periodicity of 6 and the identity period of 17.857 Å (Figure 45). In all cases, the identity periods are multiples of 2.73 to 2.98 Å, which is a distance between the imaginary middle points of the two opposite edges of the (OPb4) tetrahedron. Similar chains have also been found in the structure of Pb2+xOCl2+2x,89 or so-called “Pb5O2Cl6” phase,284 which can be considered as composed from two structurally different 2D blocks, L′ and L″, as shown in Figure 46. The L′ block contains fully ordered [O2Pb4]4+ chains and Cl− anions, whereas the L″ block contains low-occupied Pb and Cl sites that form channels extended along the a axis. The presence of rows of cationic and anionic vacancies explains high mobility of the ions occupying these channels284 and outlines possible pathways for ion transfer through the structure. The double [O2Pb3]2+ chain of trans-edge-sharing [OPb4]6+ tetrahedra is shown in Figure 43c. Edge sharing between two tetrahedra leads to repulsion of oxygen atoms and, as a result, the Pb−Pb distances become shorter than those corresponding to the nonshared edges. This type of chains is also quite common in inorganic compounds.269 The identity periods of the [O2Pb3]2+ chains are in the range from 5.71 to 5.95 Å. In mendipite-type Pb3O2X2 (X = Cl, Br, I) compounds,92 the chains are extending along the c axis (Figure 47). They have

Figure 39. The crystal structure of the [Pb3O](UO5) projected along the c axis (a) and the [UO5] chains projected along the a axis (b).

Figure 40. The [O3Pb8]10+ trimer of three edge-sharing OPb4 tetrahedra formed by the “additional” O(2) and O(6) atoms in the structure of [Pb8O3](BO3)2(B2O5).

Figure 41. The octanuclear [O4Pb8]8+ cluster known as stella quadrangula. Reprinted with permission from ref 17. Copyright 1993 American Chemical Society.

3.2.2. 1D Units. Selected topological types of the 1D chains of (OPb4) tetrahedra are shown in Figure 43; crystallographic data on respective compounds are listed in Table 7. The simplest single chain consists of corner-sharing oxocentered tetrahedra and has been observed in the structures of Pb6O2(BO3)3(TO4) (T = S,256 Mo, Cr257) (Figure 44). The double [OPb2]2+ chain formed by the fusion of two [O2Pb6]8+ 6475


Chemical Reviews

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(XA4) tetrahedra to the large halide ions in the crystal structures of some Ln nitro- and oxyhalides suggested by Krivovichev and Filatov.285 Sigman and Korgel84 described synthesis and properties of highly birefringent Pb3O2Cl2 nanostructures and demonstrated that the Pb3O2Cl2 nanobelts exhibit greatly enhanced birefringence compared to the bulk material. In the damaraite-type compounds with the general formula Pb3O2(OH)X (X = Cl, Br), the [O2Pb3] chains are linked through the OH groups to form cationic [Pb3O2](OH)+ sheets. As is common for the structures containing Pb−O/OH clusters, the OH groups form two short (OH)−Pb bonds that results in formation of the (OH)Pb2 dimers. In the structures of Pb7O4(OH)4Cl2275 and Pb7O4(OH)4Br2,87 the [O2Pb3] chains extend along the a axis and are linked by the (OH)Pb2 dimers into a 3D framework, which has channels that host Cl− or Br− anions. The feature of the crystal structure of chloroxiphite, Pb 3 CuO2 (OH)2 Cl 2 ,75 is the presence of Cu 2+ cations octahedrally coordinated by the OH− and Cl− anions. The [Cu2+(OH)4Cl2] octahedra link by sharing edges to form [Cu(OH)2Cl2] octahedral chains (Figure 48). Therefore, the structure of Pb3CuO2(OH)2Cl2 can be considered as consisting of strongly bonded and parallelly oriented cation- and anioncentered units. Mauck et al.264 reported on the crystal structures of Pb3O2(CH3COO)2·0.5H2O and Pb2O(HCOO)2 that, along with plumbonacrite, have been identified as corrosion products of lead and lead−tin alloys used in historic organs in various parts of Europe.286−288 It has been found that structures of both compounds are based upon chains of edge-sharing (OPb4) tetrahedra, either single or double (Figure 49). The chains are linked by organic ligands (acetate or formate) to form a 3D framework structure. Over long period of time, both Pb3O2(CH3COO)2·0.5H2O and Pb2O(HCOO)2 convert to the more stable hydrocerussite (Pb3(CO3)2(OH)2) and cerussite (PbCO3). Linkage of three trans-edge-sharing single chains of (OPb4) tetrahedra results in formation of a triple [O3Pb4]2+ chain shown in Figure 50a. This chain had been observed in the structure of tribasic lead maleate hemihydrate ([Pb4O3]C2H2(CO2)2(H2O)0.5288 (Figure 50b). In the [O3Pb7]8+ (Figure 43d) and [O3Pb8]10+ (Figure 43e) chains, the (OPb4) tetrahedra share corners and edges. In the structure of freedite,135 the [O3Pb8]10+ chains are linked by the AsO3 groups, thus forming layers. The chlorine atoms and [Cu(I)Cl4]3− squares fill the interlayer space. Complex [O3Pb5]4+ chains shown in Figure 43f were first described in the structure of Pb5O4(MoO4)278 (Figure 51) and later found in the structures of Pb 5 O 4 (SO 4 ) 277 and Pb5O4(CrO4).276 In the structures of these compounds, only three out of four additional O atoms form (OPb4) tetrahedra, whereas the remaining O atom forms the (OPb3) triangular groups. The (OPb3) triangles link the adjacent [O3Pb5]4+ chains, which results in formation of a 3D framework of strong Pb−O bonds. The TO4 (T = Cr, S, Mo) groups are located in between the chains. The [O7Pb10]6+ chain shown in Figure 43g has a unique complex topology. It was found in the structure of [Pb10O7](OH)2F2(SO4).281 There are five distinct types of connectivity diagrams, which means that the (OPb4) tetrahedra belong to the five classes of topological equivalence. Although the B and C, D and G (Figure 43) tetrahedra are topologically equivalent, their configurations in the chain are different.

Figure 43. (a−g) Selected chains of oxocentered OPb4 tetrahedra in minerals and inorganic compounds.

two mutually perpendicular lateral orientations and are linked through weak Pb−X bonds only. The φ angle between the faces of two adjacent (OPb 4) tetrahedra (Figure 47b) was determined to analyze the influence of halogen atoms on the structure of the [O2Pb3]2+ chain. From this analysis it was found that different occupancy of one of the two X sites by Cl or Br atoms leads to the greatest φ angle changes. The second site, X2, almost does not influence the [O2Pb3] chain geometry. These observations may be interpreted as a conformation of the [O2Pb3] double chains. This mechanism resembles the scheme of adaptation of [XA2] (X = O, N; A = metal) single chains of 6476


Chemical Reviews

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Table 7. Crystallographic Data for Pb(II) Inorganic Compounds Containing Chains of (OPb4) Tetrahedra O:Pb 1:3

1:2 1:2 1:2 1:2 1:2 1:2 1:2 1:2 1:2 1:2 1:2 1:2 1:2 1:2 1:2 2:3

3:5

3:8 3:7 7:10

space group

chemical formula Pb6O2(BO3)3(SO4) Pb6O2(BO3)3(MoO4) Pb6O2(BO3)3(CrO4) [Pb2O]SiO3 [Pb2O]FCl Pb2[Pb2O](VO4)2 [Pb2O](WO4) [Pb2O](CrO4) phoenicochroite [Pb2O](SO4) lanarkite [Pb2O](MoO4) Pb2+xOCl2+2x (x = 0.16) [Pb2O]6Mn(Mg0.54Mn0.46)2 (Mn0.68Mg0.32)4(SO4) (CO3)4Cl4(OH)12 philolithite Cu5[Pb6O3]Cl11 Pb2O(HCOO)2 [Pb2O]Cu(SO4)(OH)4·H2O elyite [Pb2O]2(OH)2(SO3S) sidpietersite [Pb2O]2(OH)2(SO4) [Pb2O]2BiO2[3n](PO4) Cu[Pb3O2](OH)2Cl2 chloroxiphite [Pb3O2](SO4) [Pb3O2](SeO3) plumboselite [Pb3O2](CO3) [Pb3O2]2(OH)(NO3)(CO3) [Pb3O2](OH)(NO3) [Pb3O2]Cl2 mendipite [Pb3O2]Br2 [Pb3O2]I2 [Pb3O2](OH)Cl damaraite [Pb3O2](OH)Br Pb[Pb3O2]2(OH)4Cl2 Pb3O2(CH3COO)2·0.5H2O Pb[Pb3O2]2(OH)4Br2 [Pb5O3]O(CrO4) [Pb5O3]O(SO4)2 [Pb5O3]O(MoO4)2 [Pb8O3]Cu(AsO3)2Cl5 freedite [Pb2O]2[Pb7O3]O(GeO4) (Ge2O7) [Pb2O]2[Pb7O3]O(SiO4) (Si2O7) [Pb10O7](OH)2F2(SO4)

a (Å); α (deg)

b (Å); β (deg)

c (Å); γ (deg)

V (Å3)

ref

Pnma Cmcm Pnma A2 Acmm Pnma C2/m C2/m C2/m C2/m Fd2d P42/nnm

6.49 18.45 6.42 19.43 5.73 22.73 14.22 14.01 13.77 14.21 5.83 12.63

11.65 6.36 11.64 7.64; 99.33 5.73 11.53 5.81; 113.91 5.64; 115.33 5.70; 115.93 5.76; 114.29 16.06 12.63

17.90 11.66 18.16 12.24 12.56 7.43 7.35 7.10 7.08 7.28 35.53 12.60

507.6 499.5 543.2 3325 2008

256 257 257 258 259 260 261 127 128 262 89 74

C2/c P1̅ P2/c P1̅ P1̅ P1̅ P2/m Cmcm Cmc21 Pnma Pnma Pca21 Pnma Pnma Pnma Pmc21 Pmc21 C1121 Cccm C1121 P21/c P2/c P2/n C2/m P1̅ P1̅ P1̅

21.10 7.24 112.32 14.23 7.46 114.33 6.38 75.26 6.22 100.19 10.46 9.68 10,53 22.19 30.56 14.15 11.81 12.24 17.86 5.81 5.84 5.79 9.40 5.85 10.80 7.30 15.33 13.58 22.26 97.59 22.50 92.52 9.66 110.98

10.23; 124.08 11.53; 101.11 11.53; 100.45 6.50; 89.65 7.45; 79.37 7.44; 103.73 5.76; 97.79 11.96 10.73 9.11 5.81 8.77 5.78 5.87 5.95 6.90 7.07 12.00 10.83 13.45 10.43; 98.08 11.70; 90.93 11.83; 90.10 20.10; 105.73 19.91; 95.15 12.98; 99.17 10.19; 91.80

12.22 13.52; 90.74 14.61 11.21; 88.69 10.31; 88.16 10.5; 90.05 6.70 6.09 5,75 5.74 7.18 5.71 9.48 9.80 7.49 15.14 15.31 19.33; 90.09 5.81 19.67; 90.04 14.61 11.50 11.63 7.46 7.36; 92.35 7.31; 100.29 11.14; 107.02

2185.8 1020.6 2358.4 494.33 465.74 463.65 399.4 705.2 649.5 1160.4 1275.0 708.6 646.8 704.6 796.3 606.7 632.7 1455.0 591.4 1547.7 1629.3 981.3 2109.2 1961.0 3216.0 2069.3 983.5

14 264 265 266 267 268 75 130 77, 269 134 270 271 92 92 272 273 274 275 264 87 276 277 278 135 279 280 281

Siidra et al.86 reported on the synthesis and crystal structures of Pb6LaO7X (X = Cl, Br) (Figure 52) based upon the [O7Pb6La]+ chains of mixed-metal OPbnLa4−n tetrahedra. The topology of the chains can be described as based upon an arrangement of eight tetrahedra that all share the same central La atom. This complex has the [O8Pb10La3] composition and represents a fragment of the fluorite (CaF2) structure, where each Ca atom is shared between eight (FCa4) tetrahedra. It is important to note that the La-free (OPb4) tetrahedra do not participate directly in the [O8Pb10La3] clusters but are attached to them, providing their linkage into a 1D chain. This makes the structures of Pb6LaO7X (X = Cl, Br) even more complex. Despite the number of symmetrically independent atoms, the metal oxide chains in these compounds are topologically and geometrically identical. The halogen ions connect the chains through the weak Pb−X bonds. It is of interest that incorporation of Cl atoms instead of Br atoms into the structure causes a lowering of the symmetry from Cmcm to C2/m. As fas as we know, this is the only example of a Pb

1353.4 1366.6 1356.0 1792.9 1949.1

oxyhalide with such an influence of halogen atoms upon the symmetry of the structure. Mixed lead−lanthanum oxybromides are known as a good luminescent material (U.S. Patent 4029851) which is stimulable or excitable through the intermediary of X-rays for the emission of photographically effective light. 3.2.3. 2D Units. There are two Pb(II) oxides, tetragonal and orthorhombic, known in nature as minerals litharge and massicot, respectively. In the structures of both, the O atoms are tetrahedrally coordinated by four Pb2+ cations, and the resulting (OPb4) tetrahedra link by sharing edges to form continuous [OPb] layers. The topology of linkage of tetrahedra is the same in both cases, and the structures are different in the degree of distortion of the layers. In the structure of tetragonal PbO (litharge),290−292 the [OPb] layers are flat with the (OPb4) tetrahedra distorted as the result of sharing edges with adjacent tetrahedra (the four Pb−O−Pb angles corresponding to the shared Pb···Pb edges are equal to 105.1°, and the two other Pb−O−Pb angles are equal to 118.7°) (Figure 53). The 6477


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Figure 46. The crystal structure of Pb2+xOCl2+2x projected along the a axis. Large gray spheres are Pb2+ cations, small black and white spheres are Cl− and O2− anions, respectively. Only the Pb−O bonds are shown (top). Representation of the crystal structure of Pb2+xOCl2+2x as consisting of two structurally different 2D blocks L′ and L″. The L′ block consists of completely ordered [O2Pb4]4+ chains and Cl− anions, whereas the L″ unit contains a system of Pb and Cl positions with low occupancy (bottom).

Figure 44. The crystal structure of Pb6O2(BO3)3(CrO4) (a) and the structure of the [O2Pb6]4+ chain of OPb4 tetrahedra (b). Reprinted with permission from ref 257. Copyright 2009 Elsevier B.V.

sheet shown in Figure 55i is the [O4Pb9] tetrameric cluster consisting of four (OPb4) tetrahedra sharing edges. The adjacent [O4Pb9] clusters are linked by sharing common Pb atoms. This type of anion-centered unit is observed in the structures of [Pb8O5](TO4)2 (T = P, As).234,275 It is worthy to note that these structures contain additional O atoms with different coordination geometries. For instance, the structure of Pb8O5(PO4)2 contains three additional O atoms: O(1), O(3), and O(4). The O(1) and O(4) atoms form (OPb4) tetrahedra with the average ⟨Pb−O⟩ bond lengths of 2.29 and 2.31 Å, respectively. The O(3) atom forms two short (2.147 and 2.261 Å), two intermediate (2 × 2.576 Å), and two long (>3.00 Å) O−Pb bonds. The resulting O(3)Pb6 configuration is a strongly distorted octahedron. Thus, taking into account nontetrahedral additional O atom, the proper formulation for this compound should be written as Pb[Pb7O4]O(PO4)2. The basis of the structure is the [O4Pb7]6+ layer (Figure 56a). The O(3) and Pb(3) cations are bonded to the sheet; the O(3) atom forms a short O−Pb bond to the Pb(1) cation, two intermediate O−Pb bonds to the Pb(6) cations and two long bonds to the Pb(2) and Pb(4) cations (Figure 56b,c). The structure of [Pb8O5](OH)2Cl483 is based upon the [O5Pb8]6+ layers shown in Figure 55c. This compound is a synthetic analogue of blixite, a rare lead oxychloride mineral first described by Gabrielson et al.302 from Langban, Sweden, and later reported from Mendip Hills, England,303 and Elura, New South Wales, Australia.304 The synthetic analogue of blixite has been obtained by hydrothermal methods by Tavernier and de Jaeger,305 Kiyama et al.,306 and Edwards et al.307 In the structure of blixite, all O atoms form four short

Figure 45. The [O2Pb4]4+ chain of trans-edge-sharing [OPb4]6+ tetrahedra from the structure of philolithite.

[OPb] layers in the structure of orthorhombic PbO (Figure 54) are much more distorted with the geometry of the (OPb4) tetrahedra being far from that of an ideal tetrahedron. The Pb− O−Pb angles are split into three groups: two of 96.6°, two of 100.0°, and two of 119.2°.293,294 The possible deviation is probably associated with the additional O···Pb contact of 3.359 Å, which tends to complement the 4-fold coordination of O to 5fold with square pyramidal geometry. Thus the structure of massicot may be viewed as intermediate in transition from the type of layers observed in alkali metal and thallium hydroxides AOH (A = K, Rb, Cs, Tl295) with square pyramidal coordination of OH groups to the structure of litharge. Most of the known layers of (OPb4) tetrahedra (Table 8) can be derived from the [OPb] layer from the structure of tetragonal PbO (Figure 55). To transform the [OPb] layer into one of its derivatives, one has to excise certain blocks of (OPb4) tetrahedra from the former. The [O3Pb5]4+ layer (Figure 55b) was observed in the structure of [Pb5O3](GeO4).133 In comparison to the [OPb] litharge-type layer, this layer possess vacancies in the form of 3 × 2 tetrahedral blocks. The basic element of the [O4Pb7]6+ 6478


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Figure 48. The crystal structure of chloroxiphite Pb3CuO2(OH)2Cl2 (a) consisting of oxocentered [O2Pb3]2+ and cationcentered [Cu(OH)2Cl2]2− (b) chains.

vacancies of seven tetrahedra. An interesting case of a double layer can be found in the structure of Eu4Pb6O9(PO4)2 (Figure 55f). The layer has the composition [O9Pb6Eu4]6+ and is composed from two kombatite-type [O9A14]10+ layers (A = Pb, Eu) linked through Eu atoms. The [O7Pb10]6+ layer in symesite, [Pb10O7](SO4)Cl4(H2O) (Figure 55d), has vacant blocks with dimensions of 2 × 2 tetrahedra. Comparing deficient PbO-type layers in the structures of the kombatite-sahlinite series and symesite, one may suggest that dimensions of vacancies correlate with the dimensions of incorporated anion (larger (AsO4)3− and (VO4)3− anions in the case of kombatite-sahlinite or smaller (SO4)2− anion in the case of symesite). This hypothesis is supported by the recent discovery of hereroite, Pb32O19(AsO4)2((Si,Mo,V)O4)2Cl10, a new mineral from Kombat mine, Namibia.80 It is based upon the [O19Pb32]26+ layers that have both symesite-type 4-fold and kombatite-type 7-fold vacancies (Figure 57). Larger (AsO4)3− anions occupy the larger 7-fold vacancies, whereas slightly smaller ((Si,Mo,V)O4)x− groups occupy the smaller square-type vacancies. In another highly complex Kombat mineral vladkrivovichevite, {[Pb4Mn2O](BO3)8}[Pb32O18]Cl14,82 the PbO-type layer has the composition [O18Pb32]28+ and contains 12-fold cross-like vacancies (Figure 58) occupied by the {[Pb4Mn2O](BO3)8}14− anionic clusters consisting of the [OMn2Pb4]10+ octahedral oxocentered core surrounded by eight (BO3)3− triangles. The [Pb44O24(OH)12]28+ layer (Figure 55h) in the structure of mereheadite, Pb47O24(OH)13Cl25(BO3)2(CO3),76 can be described as a highly deficient version of an ideal [OPb] layer (Figure 55a). The layer contains square-shaped vacancies occupied by the TO3 groups (T = B, C). The [Pb44O24(OH)12]28+ layer can be obtained from the ideal [OPb] layer via the following procedures: (1) removal of some PbO4 groups that results in formation of square-shaped vacancies; (2) insertion into these vacancies of the TO3 groups; (3) replacement of two O2− anions by one OH− anion with 2-fold coordination that results in formation of the 1 × 2 elongated rectangular vacancy. The structure of [Pb30O22]PbBr10Cl885 (Figure 59a) can be described as a result of incorporation of the [PbX6]4− halide units (Figure 59b) into a defect PbO oxide matrix. The latter represents a 2D [O22Pb30]16+ cationic layer of the (OPb4)

Figure 47. Projection of the crystal structure of the mendipite series Pb3O2Cl2 - Pb3O2Br2. Only the Pb−O bonds are shown. Pb − large dark balls, X (X= Cl, Br) − light balls, O − small gray balls (a). [O2Pb3]2+ double chain of OPb4 tetrahedra. φ is the angle between the Pb2Pb1Pb1 and Pb3Pb1Pb1 faces of the two adjacent tetrahedra (b). The φ angle versus the X1 site (X= Cl, Br) occupancy. The φ angle increases by the reduction of X1 site occupancy by the Br atoms, thus “opening” the square unit formed by the four adjacent tetrahedra in a [O2Pb3]2+ chain. Starting from the M7 -composition the value of φ angle again decreases, thus “pulling together” the unit.

O−Pb bonds, each being at centers of (OPb4) tetrahedra. The tetrahedra are linked by sharing Pb···Pb edges to form [O5Pb8]6+ sheets parallel to (100). The OH groups are attached to the sheets and form two short OH−Pb bonds, which results in (OH)Pb2 dimers, which is usual for the Pb−O/ OH clusters. Taking into account the (OH)Pb2 dimers, the formula of the sheet should be written as {[O5Pb8](OH)2}. The crystal structures of kombatite, [Pb14O9](VO4)2Cl4,132 and sahlinite, [Pb14O9](AsO4)2Cl4,300 are based upon the [O9Pb14]10+ layers shown in Figure 55e. It can be seen that, relative to the parent [OPb] layer, this layer consists groups of 6479


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Figure 50. The [O3Pb4]2+ triple chain of [OPb4]6+ tetrahedra in the structure of tribasic lead maleate hemihydrate ([Pb 4 O 3 ]C2H2(CO2)2(H2O)0.5 (a) and linkage of chains in the structure (b). Reprinted with permission from ref 289. Copyright 2005 American Chemical Society.

Figure 49. Crystal structures of Pb3O2(CH3COO)2·0.5H2O (a) and Pb2O(HCOO)2 (b) shown parallel to the extension of chains of transedge-sharing [OPb4]6+ tetrahedra. The structure of Pb3O2(CH3COO)2·0.5H2O is based upon double chains with acetate ligands linking the chains in the x-direction, whereas the structure of Pb2O(HCOO)2 is based upon single chains with formate ligands linking the chains in the x- and y-directions. Lead atoms are shown in gray, oxygen atoms in red, carbon atoms in black, and hydrogen atoms in blue. Reprinted with permission from ref 264. Copyright 2010 American Chemical Society.

Figure 51. The crystal structure of Pb5O4(MoO4) projected along the c axis.

where the latter symbolize vacancies. Figure 60a shows the 2D array of squares that represents the arrangement of (OPb4) tetrahedra within the [O22Pb30]16+ block in the structure of [Pb30O22]PbBr10Cl8. Each black square is labeled by a number that corresponds to the number of the O site at the center of the (OPb4) tetrahedron. The topological function of a tetrahedron within the layer can be visualized by investigating coronas of a given square (see section 2.4.2). Figure 60b shows the first coronas for the 22 tetrahedra present in the [O22Pb30]16+ block. There are some coronas that are common for several tetrahedra. For instance, the O1Pb4, O7Pb4, O8Pb4, and O10Pb4 tetrahedra have the same coronas consisting of six tetrahedra arranged around the central one in the same way. To further investigate whether topological functions of the

tetrahedra (Figure 59c) that is remarkable for its exceptional topological complexity, which has no analogues among the known PbO derivatives. It consists of 22 symmetrically independent (OPb4) tetrahedra that, in addition, play different roles in the layer architecture. To discuss the topology of the tetrahedral layer in more detail, one may use the square lattice approach developed in ref 85 and 308. A single (OPb4) tetrahedron is symbolized by a black square. Thus, the [OPb] layer in tetragonal PbO corresponds to a 2D layer of black squares that fill the plane without gaps and overlaps. In turn, tetrahedral layers in the PbO derivative structures correspond to 2D arrangements of black and white squares, 6480


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Figure 53. The crystal structure of tetragonal PbO (litharge) projected parallel to the extension of the [OPb] layers (a) and the projection of the [OPb] layer onto the (001) plane.

Figure 52. Projections of crystal structures of Pb6LaO7Br (a) and Pb6LaO7Cl (b). The [O7Pb6La]+ chain in the structure of Pb6LaO7Br and connectivity diagrams of its oxocentered tetrahedral (c).

tetrahedra are different, one has to examine their second coronas. Figure 61a demonstrates that, despite the fact that the first coronas of some tetrahedra are identical, their second coronas are different, and therefore the topological functions of the tetrahedra are different. The situation is more complicated for the O1Pb4 and O8Pb4 tetrahedra because they have identical first and second coronas (Figure 61b). However, their third coronas are different, and therefore their topological functions within the sheet are different. In addition to the layers that can be obtained by excision of certain fragments from the continuous [OPb] layer, there are examples of layers that can be considered as built from 1D modules excised from the former. The structure of Ag2[Pb8O7]Cl414 (Figure 62a) contains modulated [O7Pb8]2+ layers shown in Figure 63. The layers is based upon the 1D modules shown in Figure 62c. Obviously, these modules can be considered as 1D derivatives of the [OPb] layer. In the structure of Ag2[Pb8O7]Cl4, these modules are extended parallel to [101̅] and combined into a 2D layer such that the planes of the adjacent modules are approximately perpendicular to each other (Figure 62b). Another example of a 2D layer obtained by recombination of modules excised from the [OPb] layer is observed in the structure of CdPb2O2Cl2309 (Figure 64).

Figure 54. The crystal structure of orthorhombic PbO (litharge) projected approximately parallel to the c axis (a) and the projection of the [OPb] layer showing degree of distortion of the [OPb4]6+ tetrahedra (b).

The basis of the structure is the [O2Pb2Cd]2+ layer formed by the chains depicted in Figure 43a. The chains are linked through equatorial Cd atoms. 3.2.4. 3D Units. Frameworks consisting of (OPb4) tetrahedra are very rare (Table 9). The [OPb2]2+ framework (Figure 65a) in the structure of Pb 2 OF 2 is of the anticristobalite-type topology. Frameworks of this type are also present in the structures of lead oxide pyrochlores with the general formula [Pb2O][A2O6] (A = Sb, Ti, Zr, Hf, Nb).311 In this framework, the (OPb4) tetrahedra share corners which is not typical for the Pb compounds. In some compounds, additional O sites are vacant with either ordered312,313 or 6481


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Table 8. Crystallographic Data for Pb(II) Inorganic Compounds Containing Layers of (OPb4) Tetrahedra O:Pb

chemical formula

space group

a (Å); α (deg)

b (Å); β (deg)

c (Å); γ (deg)

V (Å3)

ref

1:1 1:1 1:1 1:1 1:1 1:1 3:5 4:7 4:7 5:8 7:8 9:14 9:14 7:10 36:44 22:30 19:32 9:16

[PbO] litharge [PbO] massicot [(Pb,Mo,□)O]8Cl2 parkinsonite [Pb3Sb0.6As0.4)O3](OH)Cl2 thorikosite [Pb12(SiO4)O8]Cl4 asisite Ag[PbO]Br [Pb5O3](GeO4) Pb[Pb7O4]O(AsO4)2 Pb[Pb7O4]O(PO4)2 [Pb8O5](OH)2Cl4 blixite Ag2[Pb8O7]Cl4 [Pb14O9](VO4)2Cl4 kombatite [Pb14O9](AsO4)2Cl4 sahlinite [Pb10O7](SO4)Cl4(H2O) symesite [Pb44O24(OH)12]Pb3Cl25 (BO3)2(CO3)(OH) mereheadite [Pb30O22]PbBr10Cl8 hereroite [Pb32O19](AsO4)2 ((Si,Mo,V)O4)2Cl10 vladkrivovichevite {[Pb4Mn2O](BO3)8}[Pb32O18]Cl14

4/nnm Pbcm I4/mmm I4/mmm I4/mmm P4/nmm Pbca C2/m C2/m C2/c P2/c C2/c C2/c B1̅ Cm P1̅ C2/c Pmmn

3.96 5.89 3.99 3.92 3.89 3.98 17.26 10.78 10.64 26.07 12.41 12.68 12.70 19.73; 82.21 17.37 12.12; 93.10 23.14 12.76

3.96 5.49 3.99 3.92 3.89 3.98 9.28 10.43 98.08 10.21 98.33 5.84 102.61 17.99; 147.01 22.57; 118.11 22.58; 118.37 8.80; 78.08 27.94; 93.15 16.25; 95.81 22.68; 102.09 27.17

5.00 4.75 22.51 12.85 22.80 11.07 11.51 14.61 14.35 22.74 14.79 11.28 11.29 13.63; 100.04 10.67 18.30; 111.25 12.39 11.52

78.5 153.8 358.8 197.4 345.6 175.4 1842.6 1629.3 1542.9 3375.3 1797.4 2847.1 2848.4 2242.4 5169.6 3325.4 6358.8 3992.0

292 294 296 297 298 299 133 276 234 83 14 132 300 301 76 85 81 82

Figure 55. (a−j) Layers of [OPb4]6+ tetrahedra that can be considered as derivatives of the [OPb] layer from the structure of tetragonal PbO.

disordered314,315 distribution of vacancies. In the case of ordered vacancies (e.g., in Pb2Ru2O6.5 = Pb4O[Ru2O6]2), the tetrahedral framework is disrupted into single (OPb4) tetrahedra. Riebe and Keller87 reported on the exceptional framework [O10Pb13]6+ shown in Figure 65b. It is formed by cross-linking of 1D ribbons of edge-sharing (OPb4) tetrahedra and has been observed in the structures of Pb13O10X6 (X = Br, Cl). The 1D modules can obviously be derived from the [OPb] layer observed in the structure of tetragonal PbO. The mixed-metal [O2Pb2Ln]3+ framework of [OPb3La]7+ tetrahedra has been found in the structure of the sodalitetype compounds [Pb2LnO2][Al2O6] (Ln = Ho, Lu, Eu, Gd).316,317 This framework consists of corner-sharing stella quadrangula shown in Figure 41. It is noteworthy that Ln3+ cations occupy nonshared corners of the stella quadrangula, and

these are the corners which are responsible for the linkage of the adjacent clusters. In general, formation of frameworks of (OPb4) tetrahedra is hindered by their tendency to link by sharing common edges. The formation of 3D topology is always achieved by corner linkage, whether this is the linkage of single tetrahedra, tetrahedral clusters, or 1D modules derived from the [OPb] continuous layer. Table 10 provides crystallographic information on inorganic compounds containing units of mixed-metal OPb n A 4−n tetrahedra described in this section. 3.3. Anion-Centered Tetrahedra in Inorganic Lanthanide Compounds

3.3.1. 0D Units. The list of inorganic compounds containing 0D units of (XLn4) tetrahedra (X = O, N) is provided in Table 11. The most simple unit is an isolated (XLn4) tetrahedron found in a number of Ln oxyhalogenides 6482


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Figure 59. Crystal structure of [Pb30O22]PbBr10Cl8 (a), the [PbX6]4− octahedral unit within the array of [OPb4]6+ tetrahedra (b), and the [O22Pb30]16+ 2D layer composed from edge-sharing OPb4 tetrahedra (c). Reprinted with permission from ref 85. Copyright 2006 American Chemical Society. Figure 56. The structure of [Pb8O5](PO4)2 as consisting of [O4Pb7]6+ layers and (PO4)3− tetrahedra (a), [O5Pb10] cluster (b), and distorted octahedral coordination of the additional O(3) atom (c).

Figure 57. The structure of [O19Pb32]26+ layer in hereroite Pb32O19(AsO4)2((Si,Mo,V)O4)2Cl10(H2O)2 as composed from modules of [OPb] defect layer with square-like 4-fold and 7-fold vacancies. Note that the vacancies are occupied by tetrahedral oxoanions.

Figure 60. Topological structure of the [O22Pb30]16+ 2D layer in the structure of [Pb30O22]PbBr10Cl8 (a) and first coronas (local coordinations) of central [OPb4]6+ tetrahedra (shown as black squares) (b). Reprinted with permission from ref 85. Copyright 2006 American Chemical Society.

Figure 58. General projection of the [O18Pb32]28+ layer in the crystal structure of vladkrivovichevite {[Pb4Mn2O](BO3)8}[Pb32O18]Cl14.

and oxychalcogenides known as promising storage phosphors.369 Figure 66 shows the surrounding of the (OSm4) tetrahedron by 18 Br− anions in the structure of Sm4OBr6.350 The Br− ions are classified with relation to their structural role respective to the oxocentered tetrahedron into μ1-, μ2-, and μ3types so that the unit shown in Figure 66 should be described as {[OSm4](μ3-Br)3(μ2-Br)6(μ1-Br)9}12−. The unit has a 3-fold axial symmetry with the symmetry axis running through the apical Sm atom and O atom at the center of the tetrahedron. In

Figure 61. Local coordinations of [OPb4]6+ tetrahedra within the [O22Pb30]16+ 2D layer in the structure of [Pb30O22]PbBr10Cl8. Central tetrahedra are shown in gray, first coronas in blue, second coronas in red. Reprinted with permission from ref 85. Copyright 2006 American Chemical Society. 6483


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the structure of Nd4NS3Cl3,354 the (NNd4) tetrahedron is surrounded by anions in the same fashion with the same symmetry, but with different bridging role of anions (Figure 67). Here the formula of the unit should be written as {[NNd4](μ3-S)3(μ2-S)3(μ2-Cl)3(μ1-S)3(μ1-Cl)6}18−. Figure 68 shows the arrangement of the (NNd4) tetrahedra in the structure of Nd4NS3Cl3. Chambrier et al.343 reported on the structure of La4O[W2O11], which contains isolated (OLa4) tetrahedra and octahedral [W2 O 11 ]10− dimers as basic building units (Figures 69 and 70). The structure of Ce5Pb3O (= Ce[Ce4O]Pb3)370 contains isolated (OCe4) tetrahedra (with ionic bonding) interlinked by the Ce−Pb metal−metal bonds into a 3D framework structure (Figure 71). Another common 0D unit formed by (XLn4) tetrahedra (X = O, N) is a dimer of two edge-sharing tetrahedra. Figure 72 shows [N2La6]12+ unit from the structure of CsNaLa6N2Br14.365 Despite the fact that this compound should be considered as ionic (it has no extra electrons for metal−metal), Lulei365 pointed out the structural similarities of this compound and related La3NBr6 to the representatives of the metal-rich cluster chemistry. The N3− ion at the center of the (NLa4) tetrahedron may be considered as an interstitial atom that stabilizes the respective La4 tetrahedron. Arrangement of the [N2La6]12+ dimers in the structure of CsNaLa6N2Br14 is shown in Figure 73. Analogous dimers based upon O-centered tetrahedra have been found in the structures of the [Ln3O](GeO4)(PO4) (Ln = Nd−Sm) series. It is noteworthy that, in the original work,355 structure description was given in terms of coordination of cations. The oxocentered aspect of the structures was first emphasized in ref 72 and later by Wickleder371 (Figure 74). Figure 75 shows highly unusual hexameric unit consisting of six (NPr3Nb) tetrahedra that all share the Nb atom at the center. This unit was reported by Lulei and Corbett368 in the structure of Cs[Pr9NbN6]Br15. The structure of [Er 13 O 7 ](OH)(GeO 4 ) 6 362 contains {[Er13O7](OH)}24+ oxo/hydroxo cluster that consists of seven (OEr4) tetrahedra sharing the central Er atom (Figure 76). The cluster stabilized by the tridentate hydroxyl group. This cluster can be considered as a fragment of fluorite structure and closely resembles the {[Pb13O8](OH)6}4+ in the structure of Pb13O8(OH)6(NO3)4240 (Figure 42). 3.3.2. 1D Units. 1D units (chains) of (XLn4) tetrahedra can be described as derived from two single chains by their multiplication (sequential growth). The simplest basic chains are a single einer chain of corner-sharing tetrahedra and a single zweier chain of trans-edge-sharing tetrahedra. Multiplication of these chains produces two families of the 1D units in the structures of Ln compounds listed in Tables 12 and 13. The example of the structure with the einer single chain is that of Cs2[Gd6N2]Te7.378 The [NGd3]6+ chains of this kind are formed by linkage of (NGd4) tetrahedra through bridging Gd atoms (Figure 77). In the structure, the chains are linked via Te2− anions to form corrugated layers parallel to (100) (Figure 78). Similar chains but based upon O-centered tetrahedra have been observed in the structure of Y4O(OH)9(NO3)373 (Figure 79). In this structure, [OY3]7+ chains of corner-sharing (OY4) tetrahedra run parallel to [001] and are linked together by additional Y3+ cations and (OH)− groups to produce a porous 3D cationic framework occupied by the (NO3)− groups.

Figure 62. The crystal structure of Ag2[Pb8O7]Cl4 (a), the [O7Pb8]2+ layer viewed along the direction of the 1D modules (b) and the structure of the 1D module (c). In (c) large arrows indicate direction of the extension of the modules, whereas small arrows indicate edges of linkage of the adjacent 1D modules.

Figure 63. Projection of the [O7Pb8]2+ layer in the structure of Ag2[Pb8O7]Cl4. Legend: small gray circles and large dark circles indicate O and Pb atoms, respectively.

Figure 64. Projection of the [O2Pb2Cd]2+ layer in the crystal structure of CdPb2O2Cl2. Chlorine atoms are arranged above and below the cavities of the layer. 6484


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Table 9. Crystallographic Data for Pb(II) Inorganic Compounds Containing Frameworks of (OPb4) Tetrahedra O:Pb

chemical formula

space group

a (Å); α (deg)

b (Å); β (deg)

c (Å); γ (deg)

V (Å3)

ref

1:2 10:13 10:13

[Pb2O]F2 [Pb13O10]Br6 [Pb13O10]Cl6

42/nmc C2/c C2/c

8.15 16.44 16.17

8.15 7.16; 98.39 7.01; 97.75

5.72 23.94 23.58

380.5 2788.8 2647.6

7 310 87

Condensation of two single [XLn3]n+ chains may proceed in two different directions. If tetrahedra in the chain share two edges each with the tetrahedra from the adjacent chain, the result is the [XLn2]m+ double chain shown in Figure 80a. If linkage of tetrahedra occurs via a single edge per tetrahedron, the resulting [XLn2]m+ chain possesses the structure shown in Figure 80b. Lissner et al.387 reported the simultaneous occurrence of the two types of chains in the structure of [La6N3]S4Cl. This compound is one of the very few examples of structures with two different units based upon anioncentered tetrahedra. Further condensation of two chains of the type shown in Figure 80a may again result in formation of two different types of topologies. If the double chains are linked via side edges, the resulting 4-fold [X2Ln3]m+ chain has the structure shown in Figure 81. Chain of this type was observed as a basic unit of the structure of [Nd3N2]SeBr.391 Alternative way of linkage of two double chains is by sharing edge perpendicular to the chain extension (Figure 82). This type of structure topology is observed in [Pr5N3]S2Cl2 and La5O2NS4.111 The proper formulation of the last compound is [La3O2][La2N]S4, since it contains two types of chains: [O2La3]5+ chain of the type shown in Figure 81 and [NLa2]3+ chain of the type shown in Figure 80b. In the structure, the chains are oriented parallel to each other (Figure 83). Sequential condensation of three chains of the type shown in Figure 77 results in formation of triple [X 3 Ln 5 ] m + chains known from the structure of [La5O3]2In6S17389 (Figure 84). In general, the chains that are formed as a result of condensation of chains of the type shown in Figure 77 have the formula [XnLnn+2]m+, where n is a multiplicity of the resulting chain.429 Another basic chain parent to several derivative chains is based upon the trans-edge-sharing (XLn4) tetrahedra (Figure 85). This chain occurs in a large number of Ln compounds listed in Table 13. It is especially common for a number of Ln nitro- and oxo- halogenides and chalcogenides such as [Pr8N3O]Br13408 (Figure 86). Krivovichev and Filatov285 analyzed conformation of the chains as a function of ratio between the size of the tetrahedra and the ionic radius of the charge-compensating

Figure 65. Frameworks of oxocentered [OPb4]6+ tetrahedra in minerals and inorganic compounds: anticristobalite-type framework in Pb oxide pyrochlores (a) and framework based upon 1D modules in the structures of Pb13O10X6 (X = Br, Cl) (b).

McIntyre et al.374 pointed out that compounds with such an architecture is a rare type of framework anion exchangers.

Table 10. Crystallographic Data for Pb(II) Compounds Containing Mixed-Metal OPbnA4−n Tetrahedra O:Pb:A 7:6:1 7:6:1 2:1:1 2:1:1 2:1:1 2:2:1 2:2:1 4:4:1 9:6:4 2:2:1

chemical composition

space group

a (Å); α (deg)

b (Å); β (deg)

Compounds with Chains of OPbnA4−n Tetrahedra [Pb6LaO7]Cl C2/m 18.50 8.09 119.06 [Pb6LaO7]Br Cmcm 9.59 16.15 Compounds with 2D Units (Layers) of OPbnA4−n Tetrahedra [PbSbO2]Cl nadorite Cmcm 5.60 12.25 [PbBiO2]Cl perite Bmmb 5.63 5.58 [PbBiO2]I I4/mmm 4.05 4.05 [CdPb2O2]Cl2 C2/m 12.39 3.80; 122.64 [HgPb2O2]Cl2 C2/m 11.79 3.91; 122.6 [AgPb4O4]Cl P4/n 8.20 8.20 Eu4Pb6O9(PO4)2 C2/c 12.48 14.81; 117.04 Compounds with 3D Units (Frameworks) of OPbnA4−n Tetrahedra [Pb2O2A]Al2O6 A = Ho, Lu, Eu,Gd Pn3̅m 9.46 9.46 6485

c (Å); γ (deg)

V (Å3)

9.49 8.15

1241.8 1261.2

86 86

5.45 12.43 13.52 7.66 7.74 6.26 11.13

373.8 389.8 222.1 304.0 300.8 420.4 1833

318 319 320 309 321 322 323

9.46

846.0

316, 317

ref


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Table 11. Crystallographic Data for Ln Inorganic Compounds Containing Finite Units of (XLn4) Tetrahedra X:Ln 1:4

chemical formula [Ln4O]S4Cl2, Ln = Ce, La, Nd [Ln4O]4(Mo21O52), Ln = Ce, Nd [Er4O]Er2(Si11N20) [Ln4O]Ln6S14, Ln = La, Ce, Pr, Nd, Sm, Gd, Pr [Ln4O]Pr6Se14 [Ln4O](AuO4)2, Ln = La, Nd, Sm, Eu [Ln4O](A6O18), Ln = La, Nd, Ce, Pr; A = Re, Os La2[La4O](Mo12O29) [La4(O,N)]LaPb3 [Ce4O](Si4O4N6) [La4O](W2O11) [Ln4O]AX6, Ln = Ce, Nd, La, Sm; X = Se, S; A = Mn, Fe [Ln4O]X6, Ln = Yb, Sm, Eu; X = Cl, Br, I La6[La4O]Se14

1:4

[La4N]S3C13 Pr4NS3Cl3 Nd4NS3Cl3

1:3 1:3 1:3 3:9 7:13 5:13 6:16

[Pr3O](GeO4)(PO4) [Ce3O]NbO3S3 [Ln3O]NbO3S3 Ln = Sm, Gd Na3[La9O3](BO3)8 [Er13O7](OH)(GeO4)6 [Gd13O4F]O3(GeO4)6 [Gd16ON5]Se14Cl3

1:3 1:3 1:3 1:3 1:3 1:3 6:9:1

[La3N]Br6 [Ho3N]Se3 [Pr6N2]Pr4Se12 Nd3NCl6 Gd3NCl6 CsNa[La6N2]Br14 Cs[Pr9NbN6]Br15

space group

a (Å); α (deg)

b (Å); β (deg)

c (Å); γ (deg)

V (Å3)

ref

Compounds with Isolated (OLn4) Tetrahedra P63mc 9.14−9.33 9.14−9.33 P21/c 13.39−13.45 13.37−13.40; 99.92−100.38 P31c 9.79 =a I41/acd 14.75−15.37 =a

6.83−7.01 13.25−13.36

514.89 2332.38−2370.99

324, 325 326, 327

10.59 19.57−20.18

878.48 4256.4−4811.08

328 329, 330

I41/acd Pbcn I23

15.68 11.82−12.12 8.94−9.05

=a 5.99−6.32 =a

20.73 11.80−12.11 =a

5096.72 836.15−927.46 714.41−741.22

331 332, 333 334−339

P63/mmc I4/mcm P213 P212121 P63mc

8.37 8.69 10.35 7.52 9.45−9.76

=a =a =a 10.35 =a

19.15 14.54 =a 12.79 6.82−7.07

1162.75 1097.9 1110.2 995.47 530.77−583.37

340 341 342 343 344

499.42−759.73 5304.5

345−350 351

536.79 512.01 503.72

352 353 354

770.68 784.04 714.98−728.68 598.14 1985.01 2102.16

355 356 357, 358 359−361 362 363 364

2277.8 1332.82 4925.13 1883.48 478.84 1493.86 1741.23

365 366 114 354 367 365 368

P63mc 9.15−10.44 =a 6.89−8.05 I41/acd 15.89 =a 21.01 Compounds with Isolated (NLn4) Tetrahedra P63mc 9.41 =a 7.00 P63mc 9.27 =a 6.88 P63mc 9.23 =a 6.83 Compounds with Finite Complexes of (OLn4) Tetrahedra P21/n 7.02 12.49 107.58 9.22 Pbam 7.06 14.57 7.63 Pn21a 6.65−6.69 7.59−7.66 14.18−14.22 P6̅2m 8.90 =a 8.71 R3 15.62 =a 9.40 R3 15.92 =a 9.57 P1̅ 8.04; 67.77 10.24; 88.27 12.08; 82.82 Compounds with Finite Complexes of (NLn4) Tetrahedra Pbca 11.21 11.83 17.18 C2/c 11.52 10.06; 112.85 12.48 C2/c 50.96 12.52; 90.71 7.72 Pbca 10.50 11.07 16.21 P1̅ 7.11 75.37 8.16 109.10 9.71 114.64 P21/n 10.45 13.19 95.07 10.87 P63/m 12.07 =a 13.80

Figure 66. Isolated [OSm4]6+ tetrahedron surrounded by 18 Br− anions in the crystal structure of Sm4OBr6. Reprinted with permission from ref 350. Copyright 2006 Wiley-VCH Verlag GmbH & Co KGaA.

Figure 67. Isolated [NNd4]9+ tetrahedron surrounded by 9 Cl− and 9 S2− anions in the crystal structure of Nd4NS3Cl3. Reprinted with permission from ref 354. Copyright 2000 Wiley-VCH Verlag GmbH & Co KGaA.

halide ions. It was found that vierer chains (i.e., chains with four tetrahedra within the identity period of the chain) appear at the ratio rX′:h > 0.6, where rX′ is an ionic radius of a halide ion (X′)

and h is the shortest distance between the shared trans-edges of a tetrahedron. At the ratio rX′:h < 0.6, no conformation occurs and the chains are zweier. The [XLn2]m+ chains also occur in a number of rare earth oxysalts, e.g., in the structure of 6486


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Figure 68. Projection of the crystal structure of Nd4NS3Cl3 onto the (001) plane showing arrangement of isolated [NNd4]9+ tetrahedra. Reprinted with permission from ref 354. Copyright 2000 Wiley-VCH Verlag GmbH & Co KGaA.

Figure 71. The Pb atom links the vertexes of four [OCe4] tetrahedra in the structure of Ce5Pb3O. Pb is shown as a white circle and Ce atoms are shown as black circles. Each tetrahedron shaded in light gray houses an interstitial O atom. Reprinted with permission from ref 370. Copyright 2004 American Chemical Society.

Figure 72. The [N2La6]12+ dimer of edge-sharing [NLa4]9+ tetrahedra surrounded by Br− ions in the structure of CsNaLa6N2Br14. Reprinted with permission from ref 365. Copyright 1998 American Chemical Society.

Figure 69. The crystal structure of La4O[W2O11] projected along [100]. The red circles indicate positions of the additional (not bonded to W) O atoms. Reprinted with permission from ref 343. Copyright 2008 Elsevier Inc.

Figure 70. Basic structural units in La4O[W2O11]: isolated [OLa4]10+ tetrahedra and octahedral dimers [W2O11]10−. Reprinted with permission from ref 343. Copyright 2008 Elsevier Inc.

Figure 73. The arrangement of [N2La6]12+ dimers, and Na+ and Cs+ cations in the structure of CsNaLa6N2Br14. Br− ions are omitted for clarity. Reprinted with permission from ref 365. Copyright 1998 American Chemical Society.

[Tb2O](SeO3)2,393 where the [OTb2]4+ chains are linked through (SeO3)2− triangular pyramids to form a 3D framework

with channels occupied by the s2 lone pairs on the Se4+ cations (Figure 87). 6487


Chemical Reviews

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Figure 74. The structure of [Pr3O](GeO4)(PO4) viewed as based upon [O2Pr6]14+ dimers of [OPr4]10+ tetrahedra, and (PO4)3− and (GeO4)4− tetrahedral oxyanions. Reprinted with permission from ref 371. Copyright 2002 American Chemical Society. Figure 76. Crystal structure of [Er13O7](OH)(GeO4)6 (a) as consisting of {[Er13O7](OH)}24+ clusters (b) and (GeO4)4− groups.

n = 3 are more rare due to the increasing topological complexity of the tetrahedral unit. Whereas the chains with n = 1 and 2 contain only one topological type of tetrahedra, the chains with n > 2 must contain tetrahedra of at least two different topological types. The structure of [Ho4O3](Mo4O8)428 contains the [O3Ho4]6+ chains of edge-sharing (OHo4) tetrahedra shown in Figure 90. It is noteworthy that, in the original description, the authors did not consider the oxocentered aspect of this interesting structure. 3.3.3. 2D Units. Construction of all the known layers based upon (XLn4) tetrahedra invariably involves edge-linkage between tetrahedra. A list of compounds containing the [XpLnq]m+ layers is provided in Table 14. The simplest layer has the formula [XLn]m+ and is a rare earth analogue of the [OPb] layer of edge-sharing tetrahedra in tetragonal PbO (see above). It has been found in a number of Ln oxosalts, including the structure of Pr4O4Se3,432 where the [OPr]+ layers are separated by the Se22− and Se2− anions (Figure 91). An interesting case is realized in the structure of [Er2OF][ErS3],441 which is based upon alternating cationic layers [OFEr2]3+ of [(O/F)Er4]m+ tetrahedra (O2− and F− ions are disordered over the same sites) and anionic layers [ErS3]3− of [ErS6]9− octahedra (Figure 92). It is noteworthy that the Er3+ ions in the structure participate in both anion-centered tetrahedral and cation-centered octahedral units. The layers of the type shown in Figure 91 constitute an important element in the structures of superconducting iron oxyarsenides with general formula [LnO][FeAs], where the [OLn]+ layers of edge-sharing (OLn4) tetrahedra alternate with structurally similar [FeAs]− layers consisting of (FeAs4) tetrahedra. In this case the [OLn]+ layers act as charge reservoires, which can be doped to induce superconductivity in the [FeAs]− layers.446 In general, the same structure type is adopted by a large number of layered oxychalcogenide and oxypnictide compounds with important

Figure 75. The structure of the [N6Pr9Nb]14+ cluster of six [NPr 3Nb] 11+ tetrahedra in Cs[Pr 9NbN6]Br 15 . Reprinted with permission from ref 368. Copyright 1995 Wiley-VCH Verlag GmbH & Co KGaA.

Condensation of the [XLn2]m+ single chains through equatorial edges of (XLn4) tetrahedra produces the family of chains with the general formula [XnLnn+1]m+, where n is the chain multiplicity.429 The chain with n = 2 is shown in Figure 88. It has been found in many rare earth oxysalts and, in particular, in the structure of [Tb3O2]Cl(SeO3)2.413 As in the structure of [Tb2O](SeO3), the chains of oxocentered tetrahedra are linked via (SeO3)2− groups into a 3D framework with channels filled by Cl− anions and lone pairs of the Se4+ cations (Figure 89). Similar double chains have been identified by Chambrier et al.427 in the structure of [La3O2][WO5.5]2. The authors pointed out structural similarity between this compound and compounds with the general formula [BiM2O2](AO4) (M = Cu, Mg, Zn, Mn, Ca, Pb; A = P, As, V) described in this review in the section 3.4. It is the description in terms of coordination of “additional” O atoms that allowed Chambrier et al.427 to compare these two chemically different groups of compounds and to find similarities in their structural architecture. The chains with 6488


Chemical Reviews

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Table 12. Crystallographic Data for Ln Inorganic Compounds Containing 1D Units Derived from the Einer [XLn3]7+ Chains of (XLn4) Tetrahedra X:Ln

chemical formula

space group

a (Å); α (deg)

b (Å); β (deg)

c (Å); γ (deg)

V (Å3)

1:3

[Gd3O](OH)5Br2 (Ln3O)Yb(OH)9NO3, Ln = Yb, Y [Y3O](OH)5Cl2 [Ln3N]S3 Ln = La−Nd, Sm, Gd−Dy Cs2[Gd6N2]Te7 [Dy2O]S2-I [Nd2O](TiO4) [La2O]LaGaS5 [Eu2O]TiO4 [Lu2O]SiO4 [Ln4O2]A2O7 Ln = Eu, Pr; A = Al, Ga [Nd4O2]Si2O5N2 [NNd2][N2Nd4]N3S4Cl [La5O3]2In6S17 [La5O3]In3S9 [Nd3N2]SeBr [Pr3N2][Pr2N]S2Cl2 [La3O2][La2N]S4

Pmmn P21 Pnmm Pnma C2/m Pnma Pnam Pnma Pnam C2/c P21/c P21/c Pnma Immm Pbcm Pnma C2/m C2/m

13.95 9.28−9.38 8.24 11.87−12.15 24.03 15.43 10.72 10.78 10.54 14.28 7.61−7.83 7.86 11.38 26.45 4.10 12.88 15.40 15.71

3.76 16.24−16.38; 101.13−101.17 13.23 3.82−4.15 4.24; 103.71 3.80 11.36 4.03 11.30 6.64; 122.22 10.62−11.03; 108.50−109.18 10.78; 110.76 4.00 15.81 26.83 4.05 4.01; 101.24 4.10; 101.20

8.35 3.56−3.62 3.73 12.82−13.22 11.43 6.75 3.84 19.95 3.78 10.25 11.10−11.50 11.02 27.11 4.060 16.02 12.06 16.56 16.81

438.31 526.43−545.74 406.63 578.6−666.6 1131.4 395.48 467.67 866.7 449.69 821.74 850.26−937.35 872.5 1234.05 1697.79 1763.55 629.10 1003.1 1061.4

1:2

1:2 3:5 2:3 2:3

physical properties.514 For instance, the [LnO][CuS] (Ln = La−Nd) materials are known as wide-gap p-type semiconductors with photoluminescent properties.515 Linkage of two [XLn]m+ layers of the [OPb] type by sharing all edges on the one side of the layer results in formation of a double layer with the stoichiometry [X4Ln3]m+. Note that this is one of the rare cases when the X:A ratio in a tetrahedral anioncentered [XpAq]m+ unit is larger than 1 (i.e., p > q). The [OF3Er3]4+ layers of this type are observed in the structure of [Er3OF3]S2,441 where they are separated by the interlayer S2− anions (Figure 93). Note that the O2− and F− anions at the centers of tetrahedra are disordered. Most of the other layers of anion-centered rare earth metal tetrahedra can be considered as derivatives of the [XLn]m+ layer of the [OPb] type, from which they can be obtained by excision of certain blocks (usually 1D units) and their subsequent recombination. We note that two basic single chains shown in Figures 77 and 85 can be obtained from the layer shown in Figure 91 by its slicing either in diagonal or vertical directions. Thus, for the sake of convenience, the layers based upon anioncentered rare earth metal tetrahedra can be subdivided into three groups: (i) layers based upon the [XLn3]m+ chains of corner-sharing tetrahedra (Figure 77); (ii) layers based upon the [XLn2]m+ chains of trans-edge-sharing tetrahedra (Figure 85); (iii) layers based upon finite clusters of tetrahedra. Layers Based upon the [XLn3]m+ Chains of Corner-Sharing Tetrahedra. Technically, the layer shown in Figure 94 can be considered as built by successive condensation of the [XLn3]m+ chains taken in two different orientations. This layer is known for a number of rare earth oxychalcogenides and, in particular, in the structure of [Pr2O2]Se.432 Machida et al.516−519 proposed [La2−2xCe2xO2](SO4), containing layers of the [OPb] type, as a novel oxygen storage material, since its reduction in H2 yields the [La2−2xCe2−2xO2]S phase with the structure based upon the layers shown in Figure 94. The reconstruction involves the reduction of sulfate to S2− and recombination of the anioncentered tetrahedral layer. Splitting of the layers shown in Figure 94 into quadruple chains shown in Figure 81 and their recombination (Figure 95)

ref 372 373, 375 376, 378 379 380 381 382 383 384, 386 387, 389 390 391 392 111

374 377

385 388

result in a rather complex layer with the stoichiometry [X4Ln5]m+, which is realized in the structure of [M3ON]Se2 (M = Ce−Nd) (Figure 96). This structure is remarkable in that it consists of two different anion-centered units: the [(O,N)4M5]m+ layers shown in Figure 95 and the [(O,N)M2]m+ double chains of the type shown in Figure 80a. Thus, the proper formulation of this group of compounds should be written as 3M3ONSe2 = [M5O2N2][M2O0.5N0.5]2Se6, implying the complete O2−/N3− disorder in the anionic part of the tetrahedral structure. Another type of a 2D layer based upon [XLn3]m+ chains have been first found in the structures of [Ln4O4][PdO3] (Ln = La, Nd, Sm, Eu, Gd).473,474 In this structure type, quadruple einer chains of the type shown in Figure 77 are linked by sharing edges of tetrahedra into [Ln4O4]4+ layers parallel to (001). The layers are separated by chains of corner-sharing [PdO4]6+ squares as shown in Figure 97. Layers of the same type have been described by Hammerich et al.476 in the structure of Eu2O2Br. These authors proposed an alternative description of the layer as based upon condensation of alternating chains of the types shown in Figure 80a,b (Figure 98). In the structure of Eu2O2Br, the [Eu2O2]+ layers are separated by Br− anions (Figure 99). Note the presence in this compound of both Eu2+ and Eu3+ cations. Recently, McCabe et al.520 reported on the new family of semiconducting transition metal oxychalcogenides β-La2O2MSe2 (M = Mn, Fe). The structure have been described in terms of (OLa4) and (OLa3M) tetrahedra first linked by edge-sharing into quadruple chains of the type shown in Figure 81 and then linked together into the [O4La4M]6+ layers by sharing equatorial M2+ corners (Figure 100). The layers are separated by the (MnSe4) tetrahedra and Se2− anions. It is remarkable that the planes of the adjacent quadruple chains in the [O4La4M]6+ layer are not parallel to each other so that the layer has an undulating character clearly visible in Figure 100. McCabe et al.520 noted that the structure of Gd4O4TiSe4407 is related to that of β-La2O2MSe2 (M = Mn, Fe), except that its [O4Gd4Ti]8+ layers are not undulated (Figure 101). 6489


Chemical Reviews

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Table 13. Crystallographic Data for Ln Inorganic Compounds Containing 1-D Units Derived from the Zweier [XLn2]4+ Chains of (XLn4) Tetrahedra X:Ln

chemical formula

1:2

[Tb2O](SeO3)2 [Eu2O]I2 [La2O](ReO4) Ln2[Ln2O]A2O10 Ln = La, Nd, Pr; A = Re, Mo [Er2O][WO5] [Sm2O][ReO4] [Yb2O](SiO4) [Er2O](SiO4) [Dy2O](GeO4) La[La2O]Cl(AsO3)2 Ce[Ce2O]Cl(AsO3)2 ß- [La2O]LaRuO6 Lu2[Lu4O2](GeO4)2[Ge2O7] A[Pr4O2]Cl9 A = Na, K [Gd4O2]TiSe4O2 Na2[Ln4NO]X9 Ln = Gd, Pr; X = Cl, Br [Ln8N3O]Br13 Ln = La, Pr Na2[Ln4(ON)]Cl9 Ln = Ce, Nd [Tb3O2]Cl(SeO3)2 [Nd3O2](GaO4) Ln = Nd, Eu, Gd, Sm [La3O2](ReO6) [Y3O2](ReO6) [Pr3O2](ReO6) [Er3O2]F5 [Sm3O2](ReO6) Gd[Gd3O2](WO5)2 Gd[Gd3O2](MoO5)2 [Gd3O2](GaO4) [Sm3O2](GaO4) [Ln3O2](GaO4) Sm[Sm3O2](MoO5)2 Tb[Tb3O2](MoO5)2 Nd[Nd3O2](WO5)2 [Pr3O2](NbO5) [La3O2]2[W2O11] [La4O3][AsS3]2 [Ho4O3][Mo4O8]

2:3

3:4 3:4

space group

a (Å); α (deg)

P42/ncm Imcb I4/m P42/n

10.65 6.49 8.94 12.68−12.99

10.65 7.43 =a =a

5.21 13.07 6.01 5.60−5.65

590.93 630.09 479.88 899.97−953.62

Pbca P4/n B112/b C2/c I2/a P42/mnm P42nm P21/c P2/c P21/m C2/m P21/m

15.77 8.65 14.28 14.37 10.48 13.00 12.86 8.84 10.89 8.12−8.21 15.79 7.96−8.54

10.52 =a 10.28; 122.2 6.70; 122.22 6.83; 101.72 =a =a 5.70; 104.73 6.85; 111.71 11.33− 11.34; 103.94 −106.51 3.76; 117.57 11.12− 11.71; 106.45−106.49

5.52 5.75 6.65 10.36 12.88 5.58 5.56 12.58 10.50 9.38−9.49 9.66 9.16−9.70

915.62 429.61 826.44 843.6 903.19 943.58 919.8 612.68 727.15 828.03−856.67 508.67 778.00−929.94

393 394 137 139, 396, 397 397 398 399 400 401 402 403 404 405 406 407 408, 409

C2/c P21/m Pnma Cmc21

21.97−22.35 8.04−8.13 5.35 8.99−9.18

8.36−8.48; 119.23−119.40 11.34−11.46; 107.11−107.50 15.31 11.28−11.54

16.89−17.04 9.28 −9.42 10.82 5.48−5.58

2700.51−2815.95 808.65−837.04 886.0 555.71−590.69

408, 410 411, 412 413 414

C21 P21/a P21/a Pnma P21/a P212121 C2/c Cmc21 Cmc21 Cmc21 I2/c C2/c I2/c Cmcm C2221 Ibam Pbam

17.54 14.39 14.96 5.62 14.77 5.28 16.49 8.99 9.07 8.99−9.40 15.79 16.46 15.92 10.96 12.63 19.03 10.68

11.89 7.20 7.49 17.10 7.38; 110.95 9.12 11.17; 108.29 11.28 11.41 11.27−11.83 11.28; 91.2 11.11; 108.43 11.39; 92.0 7.52 9.19 12.05 15.85

12.82; 90 6.05; 112.08 6.10; 110.46 5.37 6.08 10.01 5.42 5.48 5.52 5.51−5.71 5.47 5.39 5.51 7.67 5.97 5.85 5.66

2671.8 580.09 642.1 516.97 618.56 481.72 947.6 556.05 571.18 557.7−634.9 974.05 935.85 998.15 632.24 692.3 1342.18 958.13

138, 415 416 396 417 418 419 419 420 421 422 423 424 425 426 427 11 428

b (Å); β (deg)

c (Å); γ (deg)

V (Å3)

ref

trans-edge-sharing tetrahedra may proceed via two different routes: either via corner or edge sharing of tetrahedra from the adjacent chains. Figulla-Kroschel et al.498 described the structure of Ln3AuO6 (= [Ln3O2][AuO4]) (Ln = Sm, Eu, Gd) as based upon the [O2Gd3]5+ layers shown in Figure 103. Within this layer, the adjacent [OGd2]4+ chains are linked together by sharing tetrahedral corners. The interlayer is filled by the [AuO4]5− square anions (Figure 104). Condensation of two single chains by edge sharing leads to the formation of the [X2Ln3]m+ chain shown in Figure 88. Further linkage of these chains via equatorial corners results in the [X4Ln5]m+ layers described in the structure of Ln5Re2O12 (= [Ln5O4][Re2O8]) (Ln = Y, Gd, Dy−Lu). Jeitschko et al.396 noted structural relationships of this structure type to that of Pr3ReO8 (= [Pr3O2][ReO6]), which contains isolated [O2Pr3]5+ double chains (Figure 105). These authors suggest interpretation of twinning of the [Ho5O4][Re2O8] crystals in terms of chemical twinning of the [O4Ho5]7+ layers (Figure 106).

Figure 77. The [NGd3]6+ chain of N-centered Gd4 tetrahedra in the structure of Cs2[Gd6N2]Te7. Reprinted with permission from ref 378. Copyright 2006 Elsevier Inc.

Figure 102 shows two types of complex layers that both can be considered as formed by subsequent condensation of the [OLn3]7+ chains: the [O2Ln3]5+ layer shown in Figure 102a involves condensation of triple, double and single chains by sharing equatorial Ln atoms, whereas the [O4Ln5]7+ layer in Figure 102b is built from hexatuple and double chains. Both layers occur in the structures of Ln oxoborates (Table 14). Layers Based upon the [XLn2]m+ Chains of Trans-EdgeSharing Tetrahedra. Condensation of the [XLn2]m+ chains of 6490


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Figure 78. The structure of Cs2[Gd6N2]Te7 viewed parallel to the extension of the [NGd3]6+ chains. Reprinted with permission from ref 378. Copyright 2006 Elsevier Inc.

Figure 81. Condensation of double [NNd2]3+ chains into 4-fold [N2Nd3]3+ chain observed in the structure of [Nd3N2]SeBr. Reprinted with permission from ref 391. Copyright 2007 Wiley-VCH Verlag GmbH & Co KGaA.

Figure 79. The structure of Y4O(OH)9(NO3) with the [OY4]10+ tetrahedra shown as polyhedra. Reprinted with permission from ref 371. Copyright 2002 American Chemical Society.

Figure 82. Condensation of double [NPr2]3+ chains into 4-fold [N2Pr3]3+ chain observed in the structure of [Pr3N2]S2Cl2. Reprinted with permission from ref 391. Copyright 2007 Wiley-VCH Verlag GmbH & Co KGaA.

like topology, where [ONd2]4+ chains are condensed in a stepwise fashion with height and width of steps being equal to each other (Figure 107). Another version of a “stepwise” condensation is observed in Li[Gd5O5](PO4)2521 (Figure 108). In this case, the height and width of the steps are different and constitute 2 and 3 tetrahedra, respectively. Similarity of the two layer topologies and the same imaginary mechanism of their construction points out to the possibility of the existence of other yet to be discovered types of rare earth oxysalt structures with ladder-like topologies with other step dimensions.

Figure 80. (a, b) Two types of double [NLa2]3+ chains that occur in the structure of [La6N3]S4Cl. Reprinted with permission from ref 387. Copyright 1996 Wiley-VCH Verlag GmbH & Co KGaA.

Condensation of the [XLn2]m+ chains via edge-sharing only (i.e., when each step of condensation involves sharing of at least one edge between adjacent tetrahedra) may also result in formation of rather complex topologies. The structure of [Nd4O4](GeO4)477 contains [Nd4O4]4+ layers with a ladder6491


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Figure 85. [ON3Pr8]13+ chain in the structure of [Pr8N3O]Br13 (top) and its surrounding by Br− anions (bottom). Reprinted with permission from ref 408. Copyright 1995 American Chemical Society. Figure 83. The structure of [La3O2][La2N]S4 as composed from chains of two types: [O2La3]5+ chain (dark gray) of the type shown in Figure 81 and [NLa2]3+ chain (light gray) of the type shown in Figure 80b. Chains are extended parallel to the b axis. Reprinted with permission from ref 391. Copyright 2007 Wiley-VCH Verlag GmbH & Co KGaA.

Figure 86. Layers of the [ON3Pr8]13+ chains parallel to (001) in the structure of [Pr8N3O]Br13 at the levels of z = 0 (a) and z = 0.5 (b). Reprinted with permission from ref 408. Copyright 1995 American Chemical Society.

tetrahedra with the simplest one being a dimer of edge-sharing (XLn4) tetrahedra shown in Figure 72. Linkage of the [X2Ln6]m+ dimers via nonshared Ln corners results in formation of the [XLn2]m+ layers common for the structures of Ln nitride chalcogenides such as [Pr4N2]Se3522 (Figure 109). The same type of layers have also been observed for the O-centered tetrahedral units such as the [OLn2]4+ layers in the structure of Na2[Ln2O](BO3)2 (Ln = Dy, Ho)524 (Figures 110 and 111). In this type of layer, the dimers are linked together to form sixmembered rings (6-MRs) of tetrahedra. Another variation is observed in the structure of [Pr4N2]S3,522 where the layer is composed from 4- and 8-MRs taken in a 1:1 ratio (Figure 112). Linkage of dimers by sharing nonshared corners of one dimer with shared corners of the other results in the formation of the

Figure 84. The structure of [La5O3]2In6S17 (a) and the triple [O3La5]6+ chain (b) as resulting from sequential condensation of three chains of the type shown in Figure 77.

Layers Based upon Finite Clusters of Tetrahedra. There are several types of layers that are based upon finite clusters of 6492


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Figure 87. The structure of Tb2O(SeO3)2 is based upon [OTb2]4+ chains of (OTb4)10+ tetrahedra (highlighted) linked through (SeO3)2− triangular pyramids into a 3D framework with channels occupied by the s2 lone pairs on the Se4+ cations. Reprinted with permission from ref 393. Copyright 2002 Wiley-VCH Verlag GmbH & Co KGaA.

Figure 90. The structure of [Ho4O3](Mo4O8) projected along the [001] axis (a) and the [O3Ho4]6+ chain of edge-sharing (OHo4)10+ tetrahedra extended along [001] (b).

Zitzer and Schleid511 described construction of the layer as follows. The (ONd4) tetrahedra centered by the O1, O2, O3, and O4 atoms share edges to produce the [O4Nd9]19+ tetramers that are further linked into 1D chains by sharing common corners (Figure 115). Two chains are linked together to form [O4Nd7]13+ double chains (Figure 115), which are joned together by the [O2Nd6]14+ dimers to produce 2D [O5Nd7]11+ layers (Figure 116). In the interlayer space, the (SeO3)2− and Cl− anions provide linkage of the tetrahedral layers parallel to the b axis (Figure 117). The structures of Ln[Ln13O8](GeO4)2(BO3)6513 (Ln = Nd, Sm) are based upon the complex [O8Ln13]13+ layers that can be described as built up by condensation of the tetrahedral octamers shown in Figure 118. 3.3.4. 3D Units. The crystallographic data on Ln compounds based upon 3D frameworks of oxocentered tetrahedra are listed in Table 15. The frameworks can tentatively be classified into (i) frameworks based upon finite clusters; (ii) complex frameworks based upon 1D chains; (iii) fluoriterelated frameworks. Frameworks Based upon Finite Clusters. This family of frameworks is represented by the [O2La3]5+ framework formed as a result of polymerization of stella quadrangulae (Figure 41). The structures of [La3O2][A3O9] (A = Ir, Nb)539 contain three interpenetrating frameworks (Figure 119b):559 two frameworks of corner-linked [O4La8]16+ stella quadrangulae (Figure 119a) and the octahedral framework shown in Figure 119c. Note that these compounds are isotypic to Bi3O2[GaSb2O9] first described by Sleight and Bouchard9 (see Introduction). Complex Frameworks Based upon 1D Chains. There are three different frameworks that can be described as based upon multiple einer chains of the type shown in Figure 77. Cyclic condensation of double chains of this kind results in formation of the hexagonal [XLn] framework described in the structures of [Ln3OF2]F3S524,525 (Figure 120). Note that the anioncentered tetrahedra are occupied by O2− and F− anions in a disordered mode. The structures of two novel families of

Figure 88. The [O2Tb3]5+ chain of edge-sharing (OTb4)10+ tetrahedra in the structure of [Tb3O2]Cl(SeO3)2. Reprinted with permission from ref 413. Copyright 2005 Wiley-VCH Verlag GmbH & Co KGaA.

Figure 89. The structure of [Tb3O2]Cl(SeO3)2 as based upon [O2Tb3]5+ chain of (OTb4)10+ tetrahedra (highlighted) linked through (SeO3)2− groups into a 3D framework with channels occupied by Cl− ions and the s2 lone pairs on the Se4+ cations. Reprinted with permission from ref 413. Copyright 2005 Wiley-VCH Verlag GmbH & Co KGaA.

[XLn2]m+ layer shown in Figure 113. It has been observed, for instance, in the structures of [Pr2O]Se2331 and the A-type [Ln2O](SiO4) structure (it is worthy to note that the B-type modification consists of single [OLn2]4+ chains of trans-edgesharing [OLn4]10+ tetrahedra) (Figure 114). Another type of the layer based upon finite clusters of tetrahedra was observed in the structure of [Nd7O5]Cl3(SeO3)4.511 6493


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1:2 1:2 4:3 4:3 2:3

1:2

1:1 1:1 1:2

1:1

1:1

3.99 8.47 8.35 6.08 3.89−3.92 3.92−4.12 14.34 13.67 3.86 3.86 8.40−8.57 14.40 3.74 3.89−3.98 3.93−4.24 13.00 13.22 3.96 3.95 3.80−3.91 3.98 3.85−4.04 3.86 13.47 15.80−15.97; 95.72−96.30 12.64 9.55 7.48 18.65 8.12−8.41 8.97−9.60 16.05 6.75 10.58 10.70−10.75 11.42 17.89 13.00 5.38 5.74−5.80 3.67−3.73; 90.51−90.93

Pnmb Cmca R3̅m P3̅m1 P3̅m1 P3̅m1 P3̅m1 P63/mmc C2/m P1̅ C2/m I2/m Pmc21 C2/m P21/c P21/c Pnma Pnma P21/c P21/c P21/c C2/c C2/c Ccca Pnnm P1̅

[Gd2O]S2 [Ho2O](GeO4)2Na(OH) Na2[Er2O](BO3)2 Na[Ln2O](BO3)2 Ln = Gd, Eu, Sm K[La2O](BO3)2 [Pr4N2]S3 [Nd4N2]Se3 [Er3OF3]S2 [Ln3OF3]S2 Ln = La, Ce [Ln3O2](AuO4) Ln = Gd, Sm, Eu

a (Å); α (deg)

P4/nmm Amm2 P42/m P21/m P4/nmm I4/mmm C2/c C2/c P4/nmm P4/nmm Amm2 C2/c I4/mmm R3m ̅ P4/nmm

1:1

space group

[NdO][CuSe] [Pr4O4]Se3 [Pr4O4](AsO4)Br [GdO](OH) [LnO][CuSe] Ln = Gd, Dy [LnO]2Te Ln = La, Ce, Nd, Gd, Dy, Pr, Sm, Eu, Tb [LaO]2SO4 [EuO]2SO4 [HoO](NO3) [LuO]I [Ln4O4]Se3 Ln = La, Ce, Pr, Nd, Sm [La2O2](CrO4) [Er2OF]ErS3 [LnO][ZnP] Ln = Nd, Gd, Sm, Dy [LnO] AX Ln = La, Nd, Y, Gd, Er, Sm, Ce, Eu, Pr; A = Zn, Fe, Mn, Cu, Co, Ni; X = As, Sb, S, Se, Te, P [Gd2O2](SO4) [La2O2]S2 [NdO]F [Nd2O2]S2 [LnO]2(CN2) Ln = Pr, Nd, Sm, Eu [NdO][ZnP] [Ln2O2]X Ln = Pr, Gd, Sm, Ce, La; X = Se, S [LnO]2(CO3) Ln = La, Nd, Dy [La4O4][PdO3] [Ln4O4][PdO3] Ln = Nd, Sm, Eu, Gd Sm2O2I Eu2O2Br [Nd4O4](GeO4) Li[Gd5O5](PO4)2 [Ln2O]X2 Ln = Dy, Tb, Y, Sm, Er, Tm, Yb, Pr; X = S, Se [Ln2O]AO4 Ln = La, Er, Tm, Ho, Y, Tb, Dy, Yb, Lu; A = Ge, Si, Ru

chemical formula

X:Ln

3.94 21.67 6.21 6.32−6.37; 117.80−117.85 6.68; 117.23 9.86; 134.55 10.09; 90.04 18.92 5.73−5.78 5.60−5.63; 102.89−102.98

8.12 5.94 3.96 3.95 3.80−3.91 3.98 3.85−4.04 3.86 4.03; 133.42 7.11−7.19; 131.24−131.64 4.10; 117.97 4.03; 105.78 5.73 5.63; 117.55 6.76−7.33; 99.55−100.22 5.83−7.47; 105.44−115.78

3.99 4.01 8.35 3.73; 108.79 3.89−3.92 3.92−4.12 4.28; 107.00 4.19; 107.46 3.86 3.86 3.94−4.09 4.41 107.36 3.74 3.89−3.98 3.93−4.24

b (Å); β (deg)

Table 14. Crystallographic Data for Ln Inorganic Compounds Containing 2D Units of (XLn4) Tetrahedra

7.03 6.91 10.20 10.33−10.38 10.81 12.66 6.43 5.38 19.39−19.48 7.06−7.07; 90.82−91.07

4.18 5.93 19.70 6.79 8.25−8.33 30.95 6.66−7.03 15.95 9.45 6.79−6.92; 121.44−122.77 9.76 11.19 17.93 12.01 6.74−7.33 6.59−7.96

8.83 12.89 13.22 4.35 8.71−8.74 12.45−13.10 8.39 8.14 9.69 9.19 12.64−13.16 8.47 20.68 30.31−30.96 8.24−9.56

c (Å); γ (deg)

444.33 1010.74 592.81 617.5−628.6 733.6 1591.44 843.42 548.22 637.55−654.02 141.51−144.52

441.36 466.35 267.25 91.8 103.45−110.54 423.79 85.59−112.08 152.75−228.81 372.14 333.50−353.83 446.8 414.43 767.44 1117.3 364.45−466.19 384.41−486.42

140.34 437.80 921.3 93.38 131.55−134.39 193.22−222.63 492.54 445.07 144.11 136.8 418.35−462.45 513.43 290.65 407.09−423.79 131.85−171.73

V (Å3) ref

430, 431 432 433 434 430, 431 432 435 436 437 438 439 440 441 442, 443 442, 444 −464 465 466 467 468 469 442 432, 470, 471 472 473, 474 474 475 476 477 521 478, 479 401, 480 −491 492, 493 494 361 495, 524 496 522 523 441 497 498

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920.23−957.15 2226.28 2156.1

3.99−4.00 13.98−14.19 11.95; 85.74 9.60; 96.27 9.78 5.65 5.62−5.77 9.02−10.09 15.65 15.67; 84.85 9.44−9.53 25.99 25.83

1130.1−1155.3 805−820 1053.53 565.07 656.25 502.31 476.2−519.7 567.31−721.31 535.76

520 499−501 502 503 413 396, 504 396, 505 506 507−509 510 511 512 513 513

Review

Pna21 Cm P1̅ P1̅ C2/m P21/m C2/m C2/m P21/m P1̅ C2/m P31 P31

17.32−17.54 18.17−18.41 8.54; 68.13 6.80; 97.24 12.29 12.42 12.15−12.36 12.42−12.71 10.10 6.94; 87.82 24.40−24.81 9.95 9.82

16.36−16.48 3.65−3.74; 119.75−119.85 11.45; 78.11 8.82; 95.54 5.46; 90.49 7.51; 107.8 7.46−7.61; 107.52−108.03 5.50−5.69; 90.78−116.45 3.52; 105.45 9.44; 81.85 4.01−4.07; 95.51−95.76 9.95 9.82

Figure 91. The structure of Pr4O4Se3 is based upon the [OPr]+ layers of edge-sharing [OPr4]10+ tetrahedra separated by Se22− and Se2− anions. Reprinted with permission from ref 432. Copyright 2001 Wiley-VCH Verlag GmbH & Co KGaA.

[La2O2M]Se2 M = Mn, Fe [Ln17.33O12]O4(BO3)4(B2O5)2 Ln = Y, Gd, Ho [Yb4O3]Cl2(SeO3)2 [Gd9O8]Cl3(SeO3)4 [Tb5O4]Cl3(SeO3)2 [Dy5O4](Re2O8) [Ln5O4](A2O8) Ln = Y, Tb, Ho, Er, Yb, Lu, Tm; A = Re, Mo [Ln5O4]X(AsO3)2 Ln = Nd, Gd, Pr; A = As, Se, Te; X = Cl, Br 4:5 [Yb5O4]Li(BO3)3 5:7 [Nd7O5]Cl3[SeO3]4 2:3 [Ln3ON]Se2 Ln = Ce, Pr, Nd 8:13 Nd[Nd13O8](GeO4)2(BO3)6 Sm[Sm13O8](GeO4)2(BO3)6

Figure 92. The structure of [Er2OF][ErS3] contains alternating cationic [OFEr2]3+ and anionic [ErS3]3− layers. Reprinted with permission from ref 441. Copyright 2009 Wiley-VCH Verlag GmbH & Co KGaA.

narrow band-gap semiconducting oxo-antimonides [Ln3O3]Sb and [Ln8O8]Sb3526 are based upon different multiple einer chains in a way closely resembling tunnel oxide and hydroxide materials.559 The structure of [Ln3O3]Sb (Figure 121a) is based upon the double and quadruple chains, whereas the structure of [Ln8O8]Sb3 (Figure 121b) is based upon the double and hexatuple chains. More complex arrangements of more complex chains can be found in the structures of Li[Ln6O5](BO3)3553 (Figure 122) and [Ln26O26](OH)2(BO3)8528 (Figure 123). The former structure can be described as based upon complex chains shown in Figure 122a, which are linked together by sharing common corners with oxocentered tetrahedra from the adjacent chains (Figure 122b). In the latter structure, the chains of edge-sharing tetrahedra shown in Figure 123c are first arranged into layers (Figure 123a), which are further linked by croner sharing to form a 3-D framework (Figure 123b). Fluorite-related frameworks. The structure of fluorite, CaF2, is frequently described in terms of a 3-D framework

2:3 2:3 3:4 8:9 4:5

X:Ln

Table 14. continued

chemical formula

space group

a (Å); α (deg)

b (Å); β (deg)

c (Å); γ (deg)

V (Å3)

ref

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Figure 96. Projection of the structure of M3ONSe2 (M = Ce−Nd) along the b axis. Note the presence of two different units of anioncentered tetrahedra: layers comprised by M1, M2, and M3 metal atoms, and chains comprised by M4 and M5 metal atoms. Both layers and chains extend perpendicular to the plane of the Figure. Reprinted with permission from ref 512. Copyright 2008 Wiley-VCH Verlag GmbH & Co KGaA.

Figure 93. The structure of [Er3OF3]S2 contains double [OF3Er3]4+ layers of edge-sharing [(O,F)Er4]m+ tetrahedra. Reprinted with permission from ref 441. Copyright 2009 Wiley-VCH Verlag GmbH & Co KGaA.

Figure 97. The structure of [Ln4O4][PdO3] (Ln = La, Nd, Sm, Eu, Gd) is based upon the [Ln4O4]4+ layers parallel to (001) and separated by the [PdO3]4+ chains of trans-corner-sharing [PdO4]6+ squares. Figure 94. The structure of [Pr2O2]Se contains [O2Pr2]2+ layers separated by Se2− anions. Reprinted with permission from ref 432. Copyright 2001 Wiley-VCH Verlag GmbH & Co KGaA.

Figure 98. The projection of the [O2Eu2]+ layer in the structure of Eu2O2Br. The chains shown in gray and black are of the types shown in Figure 80, panels a and b, respectively. Reprinted with permission from ref 476. Copyright 2006 Wiley-VCH Verlag GmbH & Co KGaA.

formed by edge-linkage (ML = 2) of (FCa4)7+ tetrahedra.560,561 There are many oxides that are isotypic to fluorite, e.g., CeO2562 and UO2.563 There is also a homologous series of mixed-valent lanthanide oxides with the general formula LnnO2n−2m, where n = 7-88 and m = 1-8.564 Crystal structures of these oxides are based upon fluorite-type frameworks with vacant anion sites. In order to describe the existing structures and to predict the unknown ones, Kang and Eyring565,566 developed an elegant method that describes structures of the mixed-valent Ln oxides as consisting of fluorite modules with anion-occupied and

Figure 95. Derivation of the [(O,N)4M5]m+ layers observed in the structure of M3ONSe2 (M = Ce−Nd) by splitting the [XLn]m+ layer of the type shown in Figure 30 into chains and their subsequent recombination by corner linkage. Reprinted with permission from ref 512. Copyright 2008 Wiley-VCH Verlag GmbH & Co KGaA. 6496


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Figure 99. Structure of Eu2O2Br viewed parallel to [010]. Reprinted with permission from ref 476. Copyright 2006 Wiley-VCH Verlag GmbH & Co KGaA.

Figure 102. Complex layers formed by subsequent condensation of the [OLn3]7+ chains: the [O2Ln3]5+ layer (a) involves condensation of triple, double and single chains by sharing equatorial corners of tetrahedra, whereas the [O4Ln5]7+ layer (b) is built from hexatuple and double chains. Panels show views perpendicular (left top) and parallel (left bottom) to the layer extension; on the right given are connectivity diagrams of the topologically different tetrahedra.

Figure 100. Structure of β-La2O2MSe2 (M = Mn, Fe) with (OLa4)10+ and (OLa3M)9+ tetrahedra shown in dark-gray color. Reprinted with permission from ref 520. Copyright 2010 American Chemical Society.

Figure 103. The [X2Ln3]m+ layer of corner-linked [XLn2]m+ chains of trans-edge-sharing tetrahedra and connectivity diagram of its tetrahedra.

viewpoint of energetical considerations, the module with more than two O vacancies is unstable, at least in the homologous series of lanthanide oxides. The module with one vacant oxocentered tetrahedron with the apex pointing up is designated as Ui (there are four possible orientations of this module: U1, U2, U3, and U4) (Figure 124b). The module with one vacant oxocentered tetrahedron with the apex pointing down is designated as Di (there are also four possible orientations of this module: D1, D2, D3, and D4) (Figure 124c). The module with two vacancies can exist if the vacancies are paired along the body diagonal of the cube; this module is designated as Wij, where i = j ± 2 (there are also four possible types of this module: W31, W42, W13, and W24 (Figure 124d). Kang and Eyring565 formulated the modular juxtaposition rules, according to which the modules are arranged in the structures of

Figure 101. Structure of Gd 4 O 4 TiSe 4 with [OGd 4 ] 10+ and [OGd3Ti]11+ tetrahedra shown in dark-gray color. Reprinted with permission from ref 520. Copyright 2010 American Chemical Society.

anion-vacant metal tetrahedra. The fluorite module with no vacancies is simply the fluorite unit cell containing eight (OLn4) tetrahedra. This module is denoted as F (Figure 124a). It was postulated566 that the removal of any one of the eight O atoms in the F module is equally probable. However, from the 6497


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Figure 104. The structure [Ln3O2][AuO4] (Ln = Sm, Eu, Gd) as based upon [O2Gd3]5+ layers of the type shown in Figure 103 and the [AuO4]5− square anions. Reprinted with permission from ref 498. Copyright 2001 Wiley-VCH Verlag GmbH & Co KGaA.

Figure 107. The structure of [Nd4O4](GeO4) as consisting of [Nd4O4]4+ layers and (GeO4)4− tetrahedra.

Figure 108. The structure of Li[Gd5O5](PO4)2 as consisting of [O5Gd5]5+ layers, Li+ cations and (PO4)3− tetrahedra.

Figure 105. The structures of [Ho5O4][Re2O8] (left) and [Pr3O2][ReO6] (right) as based upon layers and chains of [OLn4]10+ tetrahedra (shaded), respectively, and [ReO6] octahedral units. Reprinted with permission from ref 396. Copyright 2001 WileyVCH Verlag GmbH & Co KGaA.

Figure 106. Interpretation of a twin boundary in [Ho5O4][Re2O8]. The [OHo4]10+ tetrahedra and [ReO6] octahedra common to both twin domains are highlighted by shading. Reprinted with permission from ref 396. Copyright 2000 Wiley-VCH Verlag GmbH & Co KGaA.

Figure 109. The [N2Pr4]6+ layer from the structure of [Pr4N2]Se3. Reprinted with permission from ref 522. Copyright 2005 Wiley-VCH Verlag GmbH & Co KGaA. 6498


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Figure 110. The [O2Ln4]6+ layer from the structure of Na2[Ln2O](BO3)2 (Ln = Dy, Ho). Figure 113. The [OPr2]4+ layer in the structure of [Pr2O]S2. Reprinted with permission from ref 331. Copyright 2001 WileyVCH Verlag GmbH & Co KGaA.

Figure 111. The structure of Na2[Ln2O](BO3)2 (Ln = Dy, Ho) viewed along [010]. The Na(1)O6 and Na(2)O7 polyhedra are shown as blue and purple, respectively; the (OLn4)10+ tetrahedra are shown as red.

Figure 112. The [N2Pr4]6+ layer from the structure of [Pr4N2]S3. Reprinted with permission from ref 522. Copyright 2005 Wiley-VCH Verlag GmbH & Co KGaA.

Figure 114. Crystal structures of A- (top) and B- (bottom) modifications of [Ln2O](SiO4) structure. The A structure contains [OLn2]4+ layers, whereas the B structure contains [OLn2]4+ chains of trans-edge-sharing [OLn4]10+ tetrahedra. Reprinted with permission from ref 371. Copyright 2002 American Chemical Society.

homologous series of lanthanide oxides. In particular, the fluorite-type modules can share whole faces only. Figure 125 shows modular model of the structure of the iota-phase of the LnnO2n−2m oxide with n = 7 and m = 1, i.e., Ln7O12.shows

modular model of the structure of the iota-phase of the LnnO2n−2m oxide with n = 7 and m = 1, i.e., Ln7O12. 6499


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Figure 117. The structure of [Nd7O5]Cl3(SeO3)4 projected parallel to the a axis. Reprinted with permission from ref 511. Copyright 2010 Wiley-VCH Verlag GmbH & Co KGaA.

Figure 115. Scheme describing formation of the [O4Nd7]13+ double chains in the structure of [Nd7O5]Cl3(SeO3)4. Reprinted with permission from ref 511. Copyright 2010 Wiley-VCH Verlag GmbH & Co KGaA. Figure 118. The complex [O8Ln13]13+ layers in the structures of Ln[Ln13O8](GeO4)2(BO3)6 (Ln = Nd, Sm) (b) can be described as based upon the tetrahedral octamers (a).

these modules the Kang-Eyring system appears to be insufficient. As its extension, the following system was suggested:568 (i) the empty fluorite module O was introduced, which contains no (XA4) tetrahedra (this module can be used in the structure description only in combination with other modules); (ii) the Ui and Dj symbols are conserved to designate the modules with one tetrahedral vacancy at the top or at the bottom of the module, respectively; (iii) for the description of other modules the W-symbol is extended to n ij... mW ij..., where n, m are number of vacancies at the top and at the bottom part of a module, respectively; i, j, k, l are the indices of vacancies at the top (superscript) and at the bottom (subscript) of the module. If all tetrahedra at the top or at the bottom of the module are removed, the symbols are transformed into 4mWij... or n4Wij..., respectively, but not 4 1234 n ij... mW ij... or 4W 1234. As an example, consider the module shown in Figure 126g. It has two vacancies at the top and three vacancies at the bottom. Therefore, it has the symbol 23W24234. Evidently, modules of the same type may have different symbols. For instance, Figure 127 shows six different orientations of the module shown in Figure 126m. In general, a total number of 280 different modules exist, which correspond to the 22 module types. Two modules belong to the same type if there is a symmetry operation, which transforms one module into another. To construct the classification scheme of binary rare earth oxides, Kang and Eyring566,567 used their linkage by sharing

Figure 116. The [O5Nd7]11+ layers in the structure of [Nd7O5]Cl3(SeO3)4 as formed as a result of condensation of the [O4Nd7]13+ double chains shown in Figure 115 (light-gray) and the [O2Nd6]14+ dimers (dark-gray). Reprinted with permission from ref 511. Copyright 2010 Wiley-VCH Verlag GmbH & Co KGaA.

The structures of fluorite-related lanthanide oxo-compounds with additional anionic and cationic complexes can be based upon fluorite-type modules with more than two vacant tetrahedra in a module. In order to construct full theory of fluorite-related structures that can be described using the modular approach, Krivovichev568,569 derived all possible types of fluorite modules shown in Figure 126. To denote each of 6500


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Table 15. Crystallographic Data for Ln Inorganic Compounds Containing 3D Frameworks of (OLn4) Tetrahedra O:Ln

chemical formula

space group

a (Å); α (deg)

b (Å); β (deg)

c (Å); γ (deg)

=a 3.76−4.11; 118.21−118.60 3.76−3.86; 106.9− 107.1 10.48 10.52 12.62−12.90; 99.70−100.17 12.66; 99.78 12.92 =a =a 10.40 10.67−10.79 9.47−9.50 7.52−7.63 7.42−7.45 10.38−10.53 7.39−7.46

3.67−3.78 11.68−12.34

280.0−295.7 511.9−616.7

525, 526 527

14.87−15.23

702.7−758.3

527

10.54 10.58 14.50−14.79

1748.05 1767.21 1214.12−1299.86

528 528 529

14.27; 90.51 14.57 9.31−9.33 9.53−9.98 10.40 10.67−10.79 9.47−9.50 7.62−7.75 7.45−7.48 10.38−10.53 7.41−7.61

1204.51 1285.51 768.1−768.4 846.5−947.3 1124.86 1214.77−1259.61 848.2−857.1 624.96−660.5 579.57−586.34 1119.55−1168.77 584.21−636.31

7.72 =a 15.36−15.97; 131.97−133.26 =a 7.79; 70.40 10.21; 71.10 =a

11.10 =a 11.86−12.34

650.66 1327.37 1100−1274

529 530 531, 532 533, 534 535 536, 537 538, 539 540−549 540−542 540−542 547, 550, 551 552 553 554

25.70 9.86; 70.40 10.25; 70.00 =a

2423.10 549.5 655.16 9699.03

555 556 557 558

1:1 1:1

[Ln3OF2]F3S [Ln3O3]Sb Ln = La, Gd, Sm, Ho

P63/m C2/m

9.39−9.61 13.01−13.86

1:1

[Ln8O8]Sb3 Ln = La, Gd, Sm, Ho

C2/m

13.14−13.46

1:1

[Er10O10][W2O11] [Y10O10][W2O11] [Ln26O26](OH)2(BO3)8 Ln = La, Nd

Pbcn Pbcn P21/c

15.82 15.88 6.74−6.91

[Nd26O26]O2(BO3)8 [La26O27](BO3)8 [Ln6O6](WO6) F12 Ln = Y, Tb [Ln6O6](UO6) Ln = La, Eu [Nd2F][Ta2O6] [Ln2O][A2O6] Ln = La, Pr; A = Te, Zr [La3O2][A3O9] A = Ir, Nb [Ln3O2][NbO5] Ln = Nd, La [Ln3O2][AO5] Ln = Gd, Y; A = Ta, Sb [Ln3O2][AO5] Ln = Nd, Gd, Y; A = Nb, Sb [Ln3O2][AO5] Ln = Nd, Pr, Sm, Eu, La; A = Ru, Ir [La3O2][MoO5] [Nd5O4](MoO4)3 Li[Ln6O5](BO3)3 Ln = Pr, Nd, Sm, Eu, Gd, Tb, Dy, Y, Ho, Er, Tm [Gd7O6](BO3)(PO4)2 [Pr11O10](GeO4)(PO4)3 [La11O10](V4+O4)(V5+O4)3 [Tb55O59](GeO4)12

P1̅ P21/c R3̅ R3̅ Fd3m ̅ Fd3̅m Pn3̅ Cmcm C2221 Fd3̅m Cmcm

6.76; 90.55 6.92 9.75−9.76 10.13−10.47 10.40 10.67−10.79 9.47−9.50 10.91−11.17 10.48−10.52 10.38−10.53 10.67−10.98

P212121 Pn3̅n P21/c

7.59 10.99 8.30−8.68

P31 P1 P1̅ I43̅d

9.71 6.98; 88.63 7.09; 89.59 21.33

1:1

1:1 1:2 2:3 2:3

4:5 5:6 6:7 10:11 59:55

V (Å3)

ref

Figure 119. The crystal structure of [O2La3][Ir3O9] (b) as based upon interpenetrating frameworks of corner-linked oxocentered stella quadrangulla (a) and framework of (IrO6) octahedra (c).

faces. This mode of linkage is also common in lanthanide oxysalt compounds. Figure 128a shows the fluorite-related framework in the structure of [Nd5O4](MoO4)3.553 Its modular description is shown in Figure 128b. The framework can be built by alternating O and F modules in all three dimensions. The structure therefore can be described as the 2 × 2 × 2 fluorite superstructure. The family of structures with the general formula [Ln3O2][MO5]540−552 can also be considered as a fluorite superstructure (Figure 129). The fluorite-type modules contain two edge-sharing (OLn4) tetrahedra each. The modules are linked in such a way that a 3D framework is formed that possesses large channels occupied by the chains of corner-sharing (MO6) octahedra (M = Ru, Os, Nb, Ta, Sb, etc.). The structures of [Ln10O10][W2O11] (Ln = Er, Y)528 are the 2 × 3 × 2 fluorite superstructures; the types of modules and their arrangement in the structures are shown in Figure 130. The 4 × 4 × 4 fluorite superstructure is exemplified by the structure of [Tb55O59](GeO4)12558 (Figure 131).

Figure 120. The crystal structure of [Dy3OF2]F3S as based upon framework formed by the condensation of double chains of oxocentered tetrahedra running parallel to the c axis (highlighted). Reprinted with permission from ref 525. Copyright 2002 Wiley-VCH Verlag GmbH & Co KGaA.

In some cases, it is more convenient to consider linkage of fluorite-type modules by sharing quarters of faces. For instance, the structure of the [Ln6O6]6+ lanthanide-oxide framework in [Ln6O6](MO6) (Ln = Y, Tb, La; M = W, U)531−534 can be described as the arrangement of modules with two vacancies paired along the body diagonal (Figure 124t). The modules are linked by sharing quarters of faces, which creates framework cavities occupied by the (MO6)6− octahedra (Figure 132). The [O10Pr11]13+ framework in [Pr11O10](GeO4)(PO4)3556 can be described as built up by fluorite-type modules linked by sharing 6501


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Figure 121. The crystal structures of [Ln3O3]Sb (a) and [Ln8O8]Sb3 (b) as based upon 3D frameworks of corner-linked multiple einer chains of (OLn4)10+ tetrahedra. The framework in (a) is based upon double and quadruple chains, whereas the framework in (b) is based upon double and hexatuple chains.

Figure 124. Four varieties of fluorite-type modules: F (a), Ui (b), Di (c), and Wij (d). Reprinted with permission from ref 567. Copyright 1998 Elsevier B. V. Figure 122. The [O5Ln6]8+ framework in the structure of Li[Ln6O5](BO3)3 (a) can be considered as built up by linkage of complex chains of (OLn4)10+ tetrahedra (b). The section of the chain is outlined in (b).

Figure 123. The [O26Ln26]26+ framework in the structure of [Ln26O26](OH)2(BO3)8 (b) can be described as based upon complex layers (a), which, in turn, can be viewed as formed by condensation of complex chains of edge-sharing oxocentered tetrahedra (c).

Figure 125. The arrangement of face-sharing fluorite-type modules in the (112) plane in the structure of the iota-phase of Ln7O12. When these planes are stacked vertically, with the appropriate shift, the 3D structure is formed. The unit cell projection is outlined. Reprinted with permission from ref 566. Copyright 1998 Elsevier B. V.

Table 16. Crystallographic Data for the Bi Oxide Polymorphs Containing Units of Polymerized (OBi4) Tetrahedra

3.4. OBi4 Tetrahedra in Inorganic Compounds

chemical formula

space group

a (Å); α (deg)

b (Å); β (deg)

c (Å); γ (deg)

V (Å )

ref

α-(Bi2O)O2 β-(Bi2O)O2 δ-(Bi2O3□1) ε-(Bi2O)O2 Bi2O4

C21/c P4̅21 I23 Pbnb C2/c

5.84 7.74 10.27 4.96 12.37

8.16; 112.9 =a =a 5.59 5.12; 107.8

7.50 5.63 =a 12.73 5.57

329 338 1083 352 335.4

573 574 575 572 570

3

3.4.1. General Remarks. The Bi3+ cation is isoelectronic with Pb2+ and usually has a highly irregular coordination due to the pronounced stereochemical activity of its p-hybridized 6s2 lone electron pair. This effect is even more pronounced for Bi3+ (r = 1.03 Å in VI coordination) than for Pb2+ (r = 1.19 Å) due to the shortest Bi−O distances. One of the most striking examples to illustrate this effect is the crystal structure of Bi3+Bi5+O4,570 which adopts the β-Sb2O4 type with the Bi5+ cation at the center of the regular O6 octahedron (Bi5+−O = 2.10 Å), while the Bi3+ cation occupies one corner of the BiO4

both faces and quarters of faces (Figure 133). First, the modules share faces to form extended columns, which are then linked by sharing quarters of faces into a 3D framework. 6502


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Figure 129. The [O2Ln3]5+ framework of (OLn4)10+ tetrahedra in the structure of [Ln3O2][MO5] (a) and its description in terms of fluoritetype modules (b).

Figure 126. (a−v) Twenty-two types of fluorite modules.

Figure 130. Modular description of the construction of the [O10Ln10]10+ framework in the structure of [Ln10O10][W2O11]. Figure 127. Six possible orientations of the fluorite-type module shown in Figure 126m.

Figure 128. The [O4Nd5]6+ framework of (ONd4)10+ tetrahedra in the structure of [Nd5O4](MoO4)3 (a) and its description as a combination of the O and F fluorite-type modules (b). Figure 131. Modular description of the construction of the [O59Tb55]48+ framework in the structure of [Tb55O59](GeO4)12.

square pyramid (Bi3+−O = 2.2 Ǻ ) (Figure 134a). The vacant space in the coordination environment is commonly described as occupied by the electron lone pair. As in the case with Pb2+ cations, the irregular coordination of such lone-pair active cations justifies the extensive use of the oxocentered

coordination polyhedra in structural description of Bi-based oxides and (oxy)salts. However, the typical Bi3+−O bond 6503


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valence is 0.596 v.u.182 which is slightly higher than the 0.5 v.u. needed to form an ideal (OBi4) tetrahedron (see section 2.2.2) with four equal bonding contributions on the central oxygen. As a result of this overbonded character of central oxygen atoms, the (OBi4) tetrahedra are usually strongly distorted, which often leads to the deterioration of the tetrahedral geometry and formation of the OBi3 triangles or bent OBi2 groups. However, the latter two configurations are usually complemented by one or two long (>3 Å) O−Bi bonds to balance the oxygen charge. The structure of smirnite, [Bi2O2](TeO3),572 is a representative example. It is based upon the [O2Bi2]2+ layers parallel to (100) and consisting of three oxocentered groups with different degrees of distortion (Figure 134b). The coordination of the oxygen atoms can be considered as distorted tetrahedral: O(2) is located with four neighboring Bi at the distances less than 2.7 Å; the coordination of the atoms O(4) and O(5) can be described as (2 + 2) and (3 + 1), respectively. However, for the sake of clarity and convenience, in the following, we shall consider long Bi3+−O bonds as parts of the (OBi4) tetrahedra, when the Bi−O−Bi angles approach the ideal value of 109.5°. On this basis, before the detailed examination of the various topologies built up from the O(Bi,M)4 tetrahedra, it sounds rather pertinent to validate the existence of those antistructural (anion-centered) units in various Bi2O3 polymorphs. In fact, it was recently shown that the most convenient way to rationalize the structural relationships between the Bi2O3 polymorphs is to compare them in terms of the chains of edge-sharing (OBi4) tetrahedra linked by borderline oxygen atoms in triangular OBi 3 coordination.572 Figure 135a−d shows that the structures of the α-, β-, ε-, and δ-polymorphs of Bi2O3573−575 differ from each other in terms of rotation of the chains. The published DFT calculations show that the electron localization function (ELF) iso-surface at 0.64 electron for the ε-form clearly indicates the hybridized 6s2 excrescence (Figure 135a, inbox). 572 Figure 135c shows idealized model of the controversial structure of the δ-polymorph (oxygen-deficient fluorite), since the neutron diffraction experiments by Battle et al.576 and Yashima and Ishimura577 indicate the regular fcc sublattice for the Bi3+ cations, space group Fm3̅m, with two sets of partially occupied oxygen sites. Taking into account different O−Bi3+ bonds in the OBin polyhedra, the validity of the anioncentered model is pertinent in terms of relationships between various topologies but does not fully reflect “true” covalent subunits linked by weaker bonds. The fine analysis of intra- and interchain distances in the four Bi2O3 polymorphs comfort that the distances within the (OBi4) tetrahedra can be shorter or longer than those within the OBi3 triangles, reminiscent of a high degree of flexibility and distortion for the OBin polyhedra. Crystallographic data for the Bi oxide polymorphs under discussion are given in Table 16. Accordingly to the abundance of examples of Bi−O structures that include both tetrahedral and triangular coordinations of “additional” O atoms, in the following, triangles will be also considered within the general approach when necessary. Also, in the following sections, we will consider several topologies formed by mixed O(Bi,M)4

Figure 132. Modular description of the [Ln6O6]6+ lanthanide-oxide framework in [Ln6O6](MO6) (Ln = Y, Tb, La; M = W, U) (a) and the scheme of module arrangement (b).

Figure 133. Modular description of the [O10Pr11]13+ framework in [Pr11O10](GeO4)(PO4)3 (a), the scheme of the columnar arrangement of the modules (b), and view from above onto the stacking of columns (c).

Figure 134. Coordination of Bi5+ and Bi3+ cations in the structure of Bi3+Bi5+O4 (a) and combination of (OBi4), (OBi3+1), and (OBi2+2) in the structure of (Bi2O2)(TeO3) (b).

Table 17. Crystallographic Data for Bi(III) Inorganic Compounds Containing Finite Units of (OBi4−nMn)m+ Tetrahedra O:Bi:M

chemical formula

space group

a (Å); α (deg)

b (Å); β (deg)

c (Å); γ (deg)

V (Å3)

ref

1:3:1 2:3:2

K[KBi3O] (PO4)3 [Sr2Bi3O2](VO4)3

Pnma P1̅

13.14 7.08; 97.46

10.41 7.17; 98.70

9.24 14.11; 110.99

1264.0 648

578 579

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Figure 135. Reorganization of the [OBi2]O2 chains in the structures of the metastable ε-Bi2O3 (a; the DFT vizualization of lone-pair electronic density is shown in the inbox), α-Bi2O3 (b), the ideal fluorine deficient δ-Bi2O3 (c), and β-Bi2O3 (d). Legend: large yellow circles = Bi, small red circles = O, green ellipsoids designate orientation of lone electron pairs of electrons.

Figure 136. The [O(Bi3K)] tetrahedron in the structure of K[KBi3O](PO4)3 (a), the linear [Sr4Bi6O4] tetramer in the structure of [Sr2Bi3O2](VO4)3 (b), the [O4Bi8] stella quadrangulla in (Bi3O2)(Ru3O9) (c), and protonated [(O,OH)8Bi6] polycationic clusters observed in Bi oxo-hydroxo nitrates (d).

tetrahedra in inorganic Bi-based compounds, M bringing the stability of the antitetrahedra for the reasons given above. 3.4.2. 0D Units. Compared to other metal cations considered above, there are not so many reports in the literature on the Bi3+ based compounds based upon 0D units of oxocentered O(Bi,M)4 tetrahedra (Table 17). Considering the bond valence effects discussed above, the (OBi4) regular tetrahedra would not be stabilized in the 0D units, whereas mixed (Bi, A) corners would decrease the geometrical symmetry of the finite clusters. One of the rare examples is the structure of K(OKBi3)(PO4)3,578 where the O−Bi bonds (2.2−2.3 Å) are considerably shorter than the O−K bond (2.62 Å) (Figure 136a). Linkage of four O(Bi,Sr)4 tetrahedra by edge-sharing results in the formation of linear tetramers in (Sr2Bi3O2)(VO4)3,579 where Sr, (Sr,Bi) and Bi positions alternate with O−Sr = 2.8 Å > O−Bi/Sr = 2.3 Å > O−Bi = 2.1−2.2 Å (Figure 136b). In the structures of (Bi3O2)(GaSb2O9)9 and (Bi3O2)(Ru3O9),580,581 the [O4Bi8] stella quadrangulae exist in the cages of the KSbO3-type framework, as already discussed for [O2La3][Ir3O9] (Figure 119). The strongly connected [O4Bi8] units share their peripheral corners to form the [O2Bi3] 3D network which propagate inside the M3O9 network (Figure 136c). In addition to the two representative examples of the 0D units formed by O(Bi,M)4 tetrahedra, it is worth mentioning the [Bi6(O,OH)8] polycationic-clusters reported in several bismuth basic nitrates.582−584 They are formed from eight OBi3 triangular pyramids, each sharing three edges with three adjacent (OBi3) units (Figure 136d). The majority of the OBi3 groups shows the configurations, which are intermediate between flat triangles and triangular pyramids. This indicates the disordered and eventually dynamical protonation of oxygen centers. Since these salts have been crystallized from aqueous solutions, the clusters probably represent ones of the most stable agglomerates of Bi3+ species in liquid media. 3.4.3. 1D Units. Crystallographic data for Bi inorganic compounds containing 1D units of (OBi4) tetrahedra are given in Table 18. The simplest 1D chain corresponds to the chain of

corner-sharing OM4 tetrahedra, which can merge by sharing common M atoms into multiple chains (cf. section 2.4). In fact, this configuration is very rarely observed in the structures of Bi-based compounds. The single exception concerns the [O2Bi4] double chains found in (Bi4O2)Ta2O9,616 where the chains are isolated by chains of corner-sharing TaO6 octahedra. In the perpendicular plane, the connectivity between the double chains is achieved by oxygen atoms strongly involved in short Ta−O bonds (Figure 137a). Another example is the complex [O5Bi6]8+ chain in the 3 × 3 octahedra channels of the todorokite derivative (O5Bi6)(Rh12O14).617 The Rh12O14 framework is related to the rutile-tunnel framework series that can accommodate 1 × 1 tunnels (rutile), 1 × 1/2 × 2 (hollandite), 1 × 1/2 × 3 (psilomelane), 1 × 1/3 × 3 (todorokite)... tunnels. Here the large section of the tunnels are compatible with chains formed from edge-sharing adjacent (OBi4) dimers connected through the common corners along the channel extension (Figure 137b). The most common 1D chains are the ones of trans-edgesharing tetrahedra, [O(Bi,M)2]n+, and their multiple varieties. The [OBi2]4+ single chain was described in the structure of [Bi2O](AuO4),591 where chains are located in between the stacks of the AuO 4 square-planes (Figure 137c). In (OBi2)0.5(Bi2)0.5AuO4 [= Bi4O(AuO4)2] half of the chains are reported to be anion-free.591 Finally, in the isotypic compound Bi2(CuO4) (kusachiite),618,619 all the chains are anion-free. Ordered mixed Bi/M sites exist in the chains observed in the structures of the compounds with general formula [BiMO](XO4) (M = Ni, Co, Mn, Pb, etc.; X = P, V, As), while similar (O2Bi4) chains bordered by the (OBi3) triangles can be found in the structure of schlegelite (Bi 4 O 2 )(BiO) 2 Bi(MoO4)2(AsO4)3585 (Figure 137d). It is noteworthy that in 6505


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Table 18. Crystallographic Data for Bi(III) Inorganic Compounds Containing Chains of (OBi4−nMn)m+ Tetrahedra O:A 1:2

1:2, 5:6 2:3

3:4 3:4, 4:5 3:4 , 4:5 1:1 3:4, 2:3 7:8, 5:6 7:8, 1:2 6:7 10:11 1:1 14:15 8:9 5:6 5:6 3:4 6:7 5:6 5:7 5:6 5:6 5:6

chemical formula

space group

a (Å); α (deg)

b (Å); β (deg)

c (Å); γ (deg)

V (Å3)

ref

(Bi4O2)(BiO)2Bi(MoO4)2(AsO4)3 schlegelite [BiNiO]PO4 [BiCoO]PO4 [BiPbO]MO4, M = P, V, As [BiMnO]MO4, M = P, V, As [Bi2O]Cu(SeO3)3·H2O [Bi2O](AuO4) [NaBi3O2](VO4)2 [BiPbO]VO4 [BiCaO]VO4 [BiCdO]VO4 [BiMgO]VO4 [Bi4O2](UO2)O2(AsO4)2·H2O orthowalpurgite [Bi4O2](UO2)O2(AsO4)2·H2O walpurgite [Bi2O](AsO3)Cl [Bi2O][Bi6O5](AsO3)2(AsO4)2 [BiZn2O2]PO4 [BiCd2O2]AsO4 [BiCa2O2]AsO4 [BiMn2O2]MO4 M = P, V, As [BiMg2O2]MO4 M = P, V, As [BiPb2O2]MO4 M = P, V, As [Bi1.2M0.8O1.5]M0.4PO4 (M = Mn, Co, Zn) (Bi5Cu3O6)4(Bi2.4Cu3.6O4)2 Cu1.4(PO4)20 (Bi4Cd4O6)(Bi2Cd3.44M0.56O4)M0.5(PO4)3 M = Co, Cu, Zn [Bi2PbO3]Mn0.6(PO4)2 [O6Bi4.57Cd3.43]2 [O4Bi2Cd3.56Cu0.44]1(PO4)14Cu5.43 [Bi14Cu2O14][Bi11.24Cu0.76O10] Cu2.2(PO4)6 [Bi12Cd4O14][Bi4Cd4O4]Cd2(PO4)10 [Bi10M4O12]M2(PO4)6, M = Cu, Cd [Bi19.79Cu2.21O20](Cu1.1Li1.1)(PO4)20 [Bi6ZnO7](PO4)2 [Bi28.64Zn1.36O28]Li4.104Zn2.61(PO4)14 (O16Bi14Cd4)(PO4)8Bi.1..2Cd1.6 Ca[Bi6O5]2O4(MoO4)4(CrO4) Pb(Bi6O5)2O4(MoO4)5 (O6Bi8) O2(MoO4)4 (Bi7O6)2O4(SO4)5 [Bi6O5]O2(CrO4)2 (O5Bi7)O2I Pb(Bi6O5)2O4(MoO4)5 Bi(Bi6O5)2(MoO4)4(VO4) Bi(Bi5Te1O5)O4(MoO4)2(VO4)3

Pnca P21/n P21/n C2/m P1̅ Abm2 P4/ncc P1 P1̅ Pbca Pc21n P21/n Pbcm P1̅ C2/c I2/a Pnma Cmc21 Cmc21 Pnma Cmcm Pmcn Ibam Pn21a Abmm P42̅ 1c average A2/m P21/m Pbam Ibm2 Bbm2 I2 Im I4/m average P2/c P2/c P21/c C2/m Ccc2 C2/m P2/c P2/c P2/c

5.30 7.17 7.25 13.53 6.87 109.5 11.01 8.67 7.06; 113.3 7.08; 111.9 11.20 5.51 7.54 5.49 7.14; 101.5 13.08 24.37 11.89 8.62 8.88 12.04 7.8 9.1 ∼15.0 11.6 11.53 13.28 11.51 11.6 23.02 11.66 11.57 19.73 11.58 13.76 11.69 11.72 17.24 21.64 12.30 18.38 11.72 11.65 11.64

16.15 11.21; 107.3 11.28; 107.8 5.58; 114.1 6.91; 95.9 16.2 8.67 7.21; 84.5 7.28; 95.0 5.43 11.70 11.62; 107.4 13.32 10.43; 110.8 5.44; 107.1 5.53; 99.1 5.28 11.95 11.97 5.37 11.89 11.5 ∼11.2 5.21 5.48 13.28 5.42 5.32; 91.02 5.44 5.38 5.43 5.44; 131.9 5.48; 90.28 13.76 5.78; 101.9 5.8; 102.1 22.43; 90.49 5.66; 119.1 19.87 4.249 5.80; 102.1 5.79; 101.38 5.77; 101.16

23.98 5.17 5.23 7.07 5.36; 109.3 5.64 6.03 5.53; 112.2 5.59; 108.9 15.56 14.28 5.31 20.69 5.49; 88.2 15.81 29.90 7.82 5.44 5.55 8.13 5.27 5.94 ∼5.4 37.54 23.24 5.55 53.94 24.74 20.44 25.06 41.6 16.97 59.01 5.69 24.72 24.69 5.59 15.09 5.88 13.25; 108.1 24.69 24.42 24.22

2054 396.7 407 487 220 1008 453 239 246 946.2 919 444 1514 374.0 1074.9 3978 490 560 590 526 489 621 ∼920 2272 1468 978 3361 1526 2560 1272.5 2614 1354 3741.2 1077 1636 1640 2160.4 1613.6 1438 984 1641 1616 1596

585 586 587 588 589 590 591 592 593 594 595 596 597 598 118 118 96 599 595 600 601 602 603 604 97 605 606 100 100 100 109 607 99 110 608 609 610 611 612 613 614 614 615

more complex [O5Bi6]8+ chains (Figure 138). Usually, the cohesion between the ribbons is provided by the isolated (XO4) groups (X = P, V, As...). It was observed that the edge sites of the ribbons could be occupied by either Bi or mixed Bi/M or M atoms, which frequently generates a strong disorder of the (XO4) tetrahedra with several configurations depending upon the degree of the Bi/M disorder.620 Figure 139 shows several examples of intergrowths between the multiple ribbons. In the case of phosphates, which yield the highest number of original homologues, the stability of the structure with n > 3 ribbons is provided by perpendicular O−Bi excrescences that decorate ribbons every three tetrahedra along their width (Figure 139e). The O−Bi excrescences are formed by extra oxygen atoms possessing tetrahedral coordination with one additional longer distance (>3 Å) that leads to the

the structures with chains of trans-edge-sharing tetrahedra, one of the unit-cell parameters is approximately equal to 5.5 Å, which corresponds to the extension of the chains. In fact, this parameter is very often found in bismuth salts, which denotes the predominance of tetrahedral edge-sharing for bismuth compounds. It is clear that the multiple possibilities of association of such chains by edge-sharing in the directions perpendicular to the chain extension yield a number of 1D ribbons with various thickness (n-tetrahedra wide), until the 2D extension, i.e., the [Bi2O2]2+ planes commonly found in many structure types as discussed below. The multiple 1D ribbons are commonly found in Bi oxo-phosphates, oxo-vanadates, oxoarsenates, and different ribbons may coexist in the same material.97,604 One of the interesting examples concerns the structure of [Bi2O][Bi6O5](AsO3)2(AsO4)2,118 which contains two different types of chains: the [OBi2]4+ single chain and 6506


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Figure 138. The [OBi2]4+ (a) and [O5Bi6]8+ (b) chains of the (OBi 4 ) 10+ tetrahedra in the structure of [Bi 2 O][Bi 6 O 5 ](AsO3)2(AsO4)2. Reprinted with permission from ref 118. Copyright 2013 Elsevier B. V.

The possibility to tune the filling ratio of these tunnels in addition with the aliovalent occupancy of edges of ribbons extend the domain of existence of every homologue out of a stoichiometric compositions. So far, ribbons with the width from n = 2 to n = 12 tetrahedra have been prepared as single-phases or observed as local defects.109 One important aspect of some of these compounds is that, owing to the particular location of the excrescence O−Bi units for n = 3n′ + 2, the ribbons possess polarity and can be arranged in a “ferro” manner leading to the acentric structures with second harmonic generation.106,109 The example shown in Figure 139f is the n = 11/n = 11 intergrowths with the Im-symmetry (pseudo-Ibm2 symmetry) while compounds with the n = 5/n = 5 and n = 8/n = 8 intergrowths were reported with space groups Pbn21 and Bbm2 respectively. In the series of compounds with the versatile 1D ribbons consisting of edge-sharing O(Bi,M)4 tetrahedra, the high resolution electron microscopy (HREM) for the investigation of local defects, intergrowth, and so forth has shown its efficiency for structure prediction.98,99 Indeed, the scale of the HREM observations is particularly well-suited for the identification of single crystallite, eventually in multiphased samples. The HREM contrasts are very strong between the Bi-rich and surrounding PO4-rich zones and can be directly interpreted using the schemes of the oxocentered tetrahedra ribbons of all sizes, and their arrangements in the projected plane. This task can be performed using an image code deduced from prior HREM images of parent compounds. A welloriented image leads to the direct structural deduction and possible formulation of microdomains from the image codes on the basis of empirical laws derived from the known [BixMyOz]/ PO4 materials. The main stages of such research are briefly summarized in Figure 140. The possibility of the infinite ribbons to expand in the third dimension (i.e., perpendicular to the ribbon width) results in the columnar 1D units. The simplest case was observed in the recently reported compound [O16Bi14Cd4](PO4)8Bi1.2Cd1.6, which has the cross-section of the size of 2 × 2 tetrahedra with mixed Bi/Cd corners and mixed Bi/Cd tunnels with modulated occupancies.110 More specific topologies exists such as 3 × 3 crosses are observed in [Bi6O5]O2(CrO4)2,612 Ca[O5Bi6]2O4(MoO4)4(CrO4),608 and Pb[O5Bi6]2O4(MoO4)5.609 The ribbons with the 4 × 3 cross-like cross sections have been found in the high-temperature γ-Bi2MoO6 phase (= [O6Bi8]O2(MoO4)4),610 whereas the four-tetrahedra-wide ribbons with

Figure 137. The [O2Bi4]8+ chains in the structure of [Bi4O2][Ta2O9] and their relative disposition (a), the [O5Bi6]8+ chains in [Bi5O6][Rh12O14] (b), projection of the structure of [Bi2O][AuO4] featuring the [OBi2] chains (c) and the structure of schlegelite, [O2Bi4](BiO)2Bi(MoO4)2(AsO4)3 (d).

formal [4 + 1] coordination. This family of compounds has been intensively rationalized, which allowed to predict new structural arrangements via the “design-like” prestage.106,109 The necessary stage of formulation of the chemical composition of the ribbons on the basis of core-, edge-, and excrescence-atoms and the surrounding XO4 groups gives: 3 ≤ n → ribbon: [(M/Bi)edge 4 Bicore 2n − 2O2n], number surrounding XO4 : 2n + 2

n > 3 → ribbon: [(M/Bi)edge 4 Bicore 2n − 2Biexcr.2Int[(n − 1)/3], number surrounding XO4 : 2[(n + 1) − (Int[n − 1]/3)]

It may happen that the cationic channels are created between four adjacent XO4 groups parallel to the axis of the ribbons. 6507


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Figure 139. The chains of edge-sharing [O(Bi,M)4] tetrahedra: (a) single [OBiNi]3+ chains in [BiNiO](PO4); (b) double [O2Cu2Bi] ribbons in BiCu2O2(PO4); (c) intergrowths of double and triple chains in (Bi4Cd4O6)(Bi2Cd3.44M0,56O4)M0.5(PO4)3 (M = Co, Cu, Zn; M0.5 denotes the cations within channels); (d) tetragonal arrangement of triple ribbons in [Bi2PbO3]Mn0.6(PO4)2; (e) intergrowths of quadruple and hexatuple ribbons in [Bi14Cu2O14][Bi11.24Cu0.76O10]Cu2.2(PO4)6 with [OBi] excressences occurring for n > 3 (extra O in a 5-coordination); (f) the “ferro” arrangement of polar n = 11 ribbons with the non-centrosymmetric space group Ibm2. The symbol ⊗ denotes the direction of infinite extension of the ribbons perpendicular to the plane of the figure).

two “shifted” 2 × 4 crosses have been observed in [O6Bi7]2O4(SO4)5.611 In these structures, the space at the internal angles of the cross-like ribbons are completed by oxygen atoms in triangular (OBi3) coordinations (these O atoms appear as isolated in the previous formulas). Various topologies of this type are shown in Figure 141. It should be noted that there are structures with disordered columns such as that reported for Bi7−xAs1+xMo3O21 (0 < x < 1).622 If the fundamental chain is the einer chain of corner-sharing tetrahedra, such chains can also form multiple chains or dense 1D columns. In the monoclinic form of Bi5O7I,613 these columns have a cross-section consisting of 10 einer chains. The chains are bordered by triangular (OBi3) groups and are isolated from each other by the I− ions (Figure 141e) that leads to the topological formula [O5Bi5]O2I where the O2 amount denoted O atoms in triangular coordination. 3.4.4. 2D Units. The list of inorganic compounds based upon layers of (OBi4) tetrahedra and their crystallographic

parameters are given in Table 19. Tentatively, all the layers observed can be subdivided into dense and porous layers, which are considered below separately. Dense Layers. A number of 2D layers are reported with more or less exotic topologies depending on the ratio between corner- and edge-sharing connections of oxocentered tetrahedra. In [Bi2O2][UO4],622 the uranyl-based layers are separated by the double [Bi2O2]2+ layers formed by two layers of corner-sharing tetrahedra superimposed by edge-connections (Figure 142a). Each (OBi4) tetrahedron in the layer shares three corners and three edges with adjacent tetrahedra. The most representative topology of dense 2D layers of (OBi4) tetrahedra is the [Bi2O2]2+ layered prototype that corresponds to the 2D infinite extension of the 1D ribbons of edge-sharing tetrahedra discussed in the previous section. Within these layers, each (OBi4) tetrahedron shares edges with four adjacent (OBi4) units (Figure 142b). This layer is known as an elementary building block found in simple oxo-salts such as 6508


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Figure 140. From HREM images to structure deduction: subsequent stages of research using an intergrowths of D (= double) and T (= triple) ribbons as an example.

excrescences have recently been isolated in Bi4MP2O12 [= (Bi2O2)11/6(BiO)1/3M1(PO4)] (M = Mg, Zn). This material provides the opportunity to check the recurrence of the alternation of two XO4 groups and one BiO unit along the direction of the [Bi2O2]2+ layers. The XO4 groups create channels similarly to those observed in between 1D ribbons (Figure 142f). It should be noted however that in the structure of LiBi7.33P3O21633 [= [Bi2O2]5(BiO)4Li2Bi0.67(PO4)6], this sequence is changed into -(two PO4 -one BiO- one PO4- one BiO)-, owing to the partial presence of small Li+ ions in the channels (Figure 142g). The [...two XO4 - one BiO...] sequence emulates the [...two V5+O4 - one (VO)2+...] modified perovskite slab in the reduced Aurivilius compound Bi4V2O10.66 and in the other Aurivilius phases and oxo-fluorides such as Bi6TiP2O16 and Bi6ZnP2O14F2 (Figure 142h).634,635,658 Substitution of Bi3+ by other metal cations such as Pb2+ and Ln3+ provides the possibility for mixed but ordered 2-D [Bi2−xMxO2]n+ layers observed, e.g., in perite, [PbBiO2]Cl.636 The double layers shown in Figures 142i, 145c, and 146 have the chemical composition [(M,Bi)3O4]. They have been observed in the structures of [Bi2O2][BaBi2O4]I2,637 [YBi2O4](NO3),638 and [YBi2O4]YCu2Se2;639 note that cations within the layers are ordered with non-Bi atoms locating in the middle part of the layers (Figure 142i). Typically, these thick nonmagnetic insulating cationic layers can be imagined as crystalline barriers in single-phase materials with magnetic or electric isolated blocks. Connection of finite ribbons in different ways results in formation of zigzag or cresnel-like one-tetrahedron-thick layers. The ribbons may be connected together by (i) edge sharing of tetrahedra and (ii) corner sharing of tetrahedra.

oxo-halides (BiOF, BiOBr) and oxo-carbonates ([Bi2O2]CO3). Recently, Cong et al.628 reported on the syntheses and crystal structures of two new Bi oxoborates, [Bi2O2][B3O5(OH)] and [Bi2O2](BO2(OH)), based upon the [O2Bi2]2+ layers. It is of interest that the layers may be significantly distorted, depending upon the chemical nature of the interlayer species (Figure 143). It is also noteworthy that the majority of simple Bi oxo-salts are formed of the flat “rhombic” [O2Bi2]2+ groups, the role of which in the transport of Bi3+ in water solutions is suggested as very probable. The layered [Bi2O2]2+ motif is also well-known as a building block sandwiching the perovskite blocks of variable thickness (n-octahedra thick) in the Aurivilius651−653 series (Figure 144) and in the Sillén654−656 phases (Figure 145) as recently reviewed by Charkin.657 The structures of these phases contain either single or double layers of (OBi4) tetrahedra, which are then considered as “fluorite blocks”, e.g., slabs excised from the fluorite-type δ-Bi2O3 structure (Figure 146). The fluorite blocks are also compatible with rock-salt layers, which gives rise to a number of predicted and observed compounds based upon changing the thickness of the blocks or their sequence in the crystal structure.658 Figure 142c shows several examples of intergrowths of the [Bi2O2]2+ layers in various structural types. We note the existence of the [Bi2O2]2+ layers linked by (OBi3) triangles in the orthorhombic modification of Bi5IO7 [= (Bi2O2)(Bi4/3O8/3)I2/3]631 (Figure 142d), significantly differ from the monoclinic form that is based upon the 1D columns discussed previously. In the same system, the structure of [Bi4O5]I2632 displays infinite layers with every seven tetrahedra decorated by the adjacent (OBi4) tetrahedra (Figure 142e) and OBi3 triangles. In mixed Bi/M oxophosphates, the infinite extension of the 1D [O2n(Bi/M)2n+1] ribbons decorated by the Bi−O 6509


Chemical Reviews

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In the case of corner linkage between the n-tetrahedra-wide ribbons, the resulting layers have the formula [O2n(Bi,M)2n+1]. Layers of this kind exist in the structures of three representative compounds corresponding to n = 2 in [O4Bi5]O0.5(PO4)2644 and [O4Bi2Cu3](AsO4)2 H2O,646 n = 3 in [O6Cu3Bi4](VO4)2645 and n = 4 in [O8Bi8.67]O(SO4)4611 (Figure 150). Porous 2D Layers. In the structure of namibite, [O2CuBi2]OH(VO4),649 the [O2CuBi2]4+ layers are formed by condensation of the double einer chains of the type shown in Figure 137a (Figure 151a). Several porous layers shown in Figure 151b−d display the systematic presence of mixed O(Bi,M)4 tetrahedra and the combination of edge-sharing and corner-sharing connections, which results in formation of open cavities. In the structure of francisite-type compounds [O2BiCu3](SeO3)2X (see section 3.1) the pores have a hexagonal outline. In [O3Ba3Bi]Cl3,647 the linkage of tetrahedra in the layers is dense, but the existence of empty Cu4 tetrahedra creates window, which is open for some of the chloride anions of the interlayer. In the series of porous layered compounds, the most striking case is the structure of Bi7Ta3O18 (= [Bi7O4][Ta2O9][TaO5]), where (OBi4) tetrahedra connect together to form nanotubules with hexagonal pores occupied by chains of corner-sharing (TaO6) octahedra.648 The tubules share faces to create a honeycomb-like layers as shown in Figure 151c. The condensation of zigzag chains can eventually also lead to porous 2-D networks. In Bi6O4Mx(PO4)4 (M = Bi, Pb, Ca, Cd, Sr, K, Na, Li) zigzag chains are formed by units of four (OBi4) and (OBi3M) tetrahedra overlapping at their terminal tetrahedra by edge sharing.95,659 The condensation between these chains is performed by corner sharing at the level of the junction. In fact, the common corner can be partially vacant (Mx = 2/3 Bi3+) or replaced by fully occupied M2+ cations (Mx = Mg2+, etc.) in Bi6MO4(PO4)4 compounds (Figure 151e). An interesting case of porous layers formed by condensation of (OBi4) tetrahedra has recently been reported for the structure of Bi6O5(SeO3)3Br2.115 In this structure, complex chains of edge-sharing tetrahedra are linked by the [O2Bi6] tetrahedral dimer to form porous [O5Bi6]8+ layers oriented parallel to (011) (Figure 152). 3.4.5. 3D Units. The structures of several Bi oxychlorides such as (M 5 Cl)[Bi 8 O 9 ] 6 O 5 Cl 30 (M + = Cu or Ag), (Bi6O7)2OCl6, and (Bi6O6F)OCl3 consist of porous 3D networks of (OBi4) terahedra (Figure 153a−c; Table 20). In their construction principle, these structures are very similar to the structures of tunnel oxides.560 In the latter, chains of edgesharing cation-centered octahedra share edges to form multiple chains that are further arranged perpendicularly to each other into frameworks with variable channel dimensions. The channels have rectangular sections and are filled by water molecules or cations such as Bi3+ in square-planar coordination in the hollandite-type phase Bi1.7V8O16.665 In the Bi oxochlorides, the [OnBin+2] chains are condensed to form 3-D frameworks with channels that have triangular sections with n = 9, 4 and 16, 4, and 10 in (M5Cl)[Bi8O9]6O5Cl30, (Bi6O7)2OCl6, and (Bi6O6F)OCl3, respectively. The channels are filled by chloride ions, except for (M5Cl)(Bi8O9)6O5Cl30, where the channels host M+ cations as well. In Bi8La10O27 [= (Bi4La10O16)pores(Bi8O11)host], the infinite [(Bi/La)2O2] planes form the walls of the pores, which are closed by the (OLa4) tetrahedra (Figure 153d). The channels host disordered Bi8O11 chains.666 Other anionic species such as nitrate ions can also be hosted in the tunnels, as in Bi5O7[NO3].667 In these compound, even the extension of

Figure 141. The columnar 1D units of [O(Bi,M)4] tetrahedra (the oxygen atoms in triangular coordination are marked by “3”): (a) 3 × 2 cross-section of the chains in [Bi6O5]O2(CrO4)2; (b) idealized view of the modulated (O16Bi14Cd4)(PO4)8Bi1.2Cd1.2 with 2 × 2 tetrahedra columns; (c) columns with the 4 × 3 cross-section in γ-Bi2MoO6; (d) shifted 2 × 4 cross-section columns in (Bi6O7)2O4(SO4)5; (e) packing of the decatuple chains of tetrahedra in Bi5O7I. The symbol ⊗ denotes the direction of infinite extension of the ribbons perpendicular to the plane of the figure.

Landa-Canovas et al.642 recently reported on the representative series of oxides with general formulas Bi2nMon−2O6n−6 with n varying from 5 to 8. In this series, n denotes the number of tetrahedra (= width) across the elementary ribbons that overlap by terminal edge sharing to create zigzag layers (Figures 147a− d). Starting from the parent 2D [Bi2O2]2+ layers, zigzag layers are in fact created by crystallographic shear (CS) operations as shown in the Figure 148. The extra-oxygen atoms in a triangular coordination complete the empty spaces located at the angles of the Cresnel-type junctions of the ribbons. Several other examples are reported in the literature, such as zigzag ribbons with overlapping of n = 8 ribbons in Bi9V2ClO18640 and n = 8 ribbons sharing edges with perpendicular n = 3 ribbons in Bi18.71Cr0.27P6O43.22641 (Figure 147e). This kind of ribbon overlapping can also be applied to other kinds of layers. In [Bi6O7]4O3Cl10,643 the n = 12 finite ribbons overlap with the n = 3 ribbons as shown in Figure 147f. However, the topology of the junction is strongly modified since the direction of the overlapping is rotated by ∼45° in comparison with the usual overlapping mode (Figure 149). 6510


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Table 19. Crystallographic Data for Bi(III) Inorganic Compounds Containing Layers of (OBi4−nMn)m+ Tetrahedra O:A 1:1 1:1

5:4 1:1

4:3

10:9 19:18 11:10 13:12 15:14 17:16 7:6 5:4 6:7 4:5 8:9 1:2 3:4 4:7 4:9 2:3

chemical formula

space group

a (Å); α (deg)

b (Å); β (deg)

c (Å); γ (deg)

V (Å3)

ref

[Bi2O2][UO4] [Bi2O2](TeO3) [Bi2O2](CO3) bismutite Ca[Bi2O2](CO3)2 beyerite [BiO]F zavaritskite [BiO]Cl bismoclite [Bi2O2](SiO3) [Bi2O2](GeO3) [Bi2O2][B3O5(OH)] [Bi2O2](BO2(OH)) [BiO](IO3) [Bi2O2](MoO4) [Pb0.6Bi1.4O2]Cs0.6Cl2 [Bi3O3]IBi2O4 [Bi4O5]I2 [Bi2O2]11/6(BiO)1Zn1(PO4)2 [Bi2O2]11/6(BiO)1Mg1(PO4)2 [Bi2O2]7Li2Bi0.67(PO4)6 [Bi2O2]3ZnF2(PO4)2 [Bi2O2]3TiO2(PO4)2 [PbBiO2]Cl perite [BaBi2O4]Bi2I2 [YBi2O4](NO3) [YBi2O4]Cu2Se2 [Bi9O10]Cl(VO4)2 [Bi17.98O18.62](Bi0.73Cr0.27O0.6)(PO4)6 [Bi10O11]O(MoO4)3 [Bi12O13]O(MoO4)4 [Bi14O15]O(MoO4)5 [Bi16O17]O(MoO4)6 [Bi6O7]4Cl10O3 [O4Bi5]O0.5(PO4)2 [Bi4Cu3O6](VO4)2 Na2[Bi2Cu3O4](AsO4)2(H2O) [Bi8.67O8]O(SO4)4 [BiCu3O2]Cl(SeO3)2 [Ba3BiO3]Cl3 [Bi7O4](Ta2O9)(TaO5) [Bi6.67O4](PO4)4 [Bi2CuO2](OH)(VO4) namibite

C2 Abm2 Imm2 Immm P4/nmm P4/nmm Cmc21 Cc Pbca Cm Pca21 Pca21 I4/mmm Ibca P21 C2/c Pbca C2/c C2/c I2 Bmmb I4/mmm P4mm I4/mmm P21/m P1̅ C2 P2 C2 P2 A2/m C2/c P1̅ C2 C2/c Pmmn Pnma C2/m P1̅ P1̅

6.87 11.60 3.87 3.77 3.76 3.89 15.17 15.69 6.03 5.47 5.66 5.49 3.91 16.27 14.95 33.50 16.67 30.82 16.41 11.23 5.63 4.076 3.87 3.86 11.67 19.31 103.8 23.73 14.53 34.47 19.98 9.99 13.09 5.32; 74.6 9.72 24.67 6.35 7.05 34.01 9.19; 112.2 6.21; 90.1

4.01; 90.16 16.46 3.86 3.77 =a =a 5.47 5.49; 90.01 11.36 14.66; 135.59 11.04 16.23 =a 5.34 5.69; 99.8 10.82; 121.9 5.3 5.27; 122.84 5.43; 110.0 5.41; 95.13 5.58 =a =a =a 5.46; 93.67 5.55; 90.34 5.65; 95.87 5.65; 97.98 5.64; 99.69 5.63; 101.02 3.97; 88.7 5.71; 98.24 7.92; 89.4 5.2; 115.03 5.64; 97.67 9.63 11.99 7.61; 109.2 7.55; 93.9 7.40; 108.73

9.69 5.52 13.68 21.73 6.23 7.35 5.31 5.38 19.35 3.91 5.75 5.13 20.86 23.02 11.27 27.65 23.27 24.53 15.99 11.23 12.42 33.57 10.19 24.42 14.79 9.50 90.48 8.69 8.66 8.64 8.63 29.44 15.29 8.1; 70.4 13.36 15.14 7.22 12.09 6.64 6.93; 106.9 7.47 107.47

267 1054.8 204.1 309.4 88.0 111.1 441.2 463.2 1325.5 219.4 359.0 491 320 2001 945 8510 2056 3347 1339 679.9 389.8 557.9 152.4 365 941 988 1158 704 1657 954 1168 1131 308.2 612 2091.3 441.8 1022 1621 418 308.2

622 571 623 623 624 625 626 627 628 628

the “counted” Bi−O bonds until 3.2 Ǻ leaves two of the seven independent O atoms in a triangular coordination, leading to the general formula [Bi5O5]O2(NO3). However, taking into account the (OBi4) tetrahedra only, the structure contains a 3D porous network formed by edge-linkage of tetrahedra along the a axis and both edge- and corner-linkage along the b axis. Similar cavities can also be found in (Bi3O2)(BiO)(BO3)2,660 where two-thirds of the additional O atoms form (OBi4) tetrahedra, though sometimes containing long Bi−O bonds (>3.2 Å) (Figure 153e). Another example of a porous framework can be found in the structure of complex oxide Bi4Ag18O12,668 where (OAg4) and (OAg3Bi) tetrahedra share corners to create elongated hexagonal channels with ∼4 × 8 Å dimensions. It is noteworthy that all O-(Bi, Ag) bonds are shorter than 2.2 Å, which indicates a rather strong bonding, despite the ionic character of the Ag−O interactions. Much more dense frameworks are present in the same chemical system in the structures of BiAg3O3 and BiAg5O4,669 where frameworks are formed by

629 630 631 632 110 110 633 634 635 636 637 638 639 640 641 642 642 642 642 643 644 645 646 611 143 647 648 95 649

linkage of the (OBi2Ag2) and (OBiAg3) tetrahedra. In these two compounds, the linkage proceeds via both corners and edges sharing of tetrahedra with oxygen−metal bond lengths shorter than 2.3 Å. It is noteworthy that some Bi atoms are shared between five oxocentered tetrahedra. The ultimate condensation of (OBi4) units by edge-sharing corresponds to the fluorite structure, as found in δ-Bi2O3 with 1/4 of empty □Bi4 tetrahedra. Because of the easy substitution of Bi3+ by other cations such as Ln3+, or tetrahedrally coordinated Xn+ cations (e.g., S6+, P5+, V5+, As5+... etc), it is rather difficult to rationalize the number of modified arrangements in terms of the O(Bi,M)4 tetrahedra. For instance, the case of lanthanide-for-bismuth substitutions has largely been developed in the devoted review article.670 In general, depending upon the cationic size and the substitution ratio, several forms can be prepared which possess structural features inherited from the Bi2O3 polytypes. The multitude of structural rearrangement is even greater in the case of XO 4 n− substitutions, considering that the XO4 amount can be adjusted 6511


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Figure 142. Structures with dense layers based upon (OBi4) tetrahedra: (a) the [Bi2O2]2+ double layers in [Bi2O2][UO4]; (b) the [Bi2O2]2+ single layers in koechlinite, γ-Bi2MoO6; (c) the [Bi2O2]2+ single layers in various polytypes with rock-salt-type layers; (d) the [Bi2O2]2+ single layers in [Bi2O2][Bi4/3O8/3]I2/3; (e) complex layers in the structure of Bi4O5I2; (f) layers with the O−Bi excressences in [Bi2O2]11/6[BiO]1/3M1(PO4)2; (g) different sequence of O−Bi excressences in [Bi2O2]5(BiO)4Li2Bi0.67(PO4)6); (h) the structure of [Bi2O2]3[ZnF2](PO4)2; (i) double layers of the (OBi2Y2) tetrahedra in [O4YBi2]YCu2Se2. The symbol ⊗ denotes the direction of infinite extension of the ribbons perpendicular to the plane of the figure.

Figure 143. Different degrees of distorion of the [O2Bi2]2+ layers in the structures of [Bi2O2](CO3) (a), [Bi2O2][B3O5(OH)] (b), and [Bi2O2](BO2(OH)) (c). Reprinted with permission from ref 628. Copyright 2011 American Chemical Society.

generally most of these phases can be considered as distorted lacunar fluorite-type frameworks. Note also that the XO4 localization in the unit cell can be very dispersed over the oxocentered tetrahedra framework as in the case of

by tuning the charge of the main framework using aliovalent substitution on the Bi site, as in Bi17Pb5O23(PO4)5671 or Bi18Pb5(PO4)4.672 The tetrahedral XO4 groups induce strong local constraints able to rule out the main framework, even if 6512


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Figure 144. The scheme showing construction of the Aurivillius phases from single [O2Bi2]2+ layers of (OBi4) tetrahedra and multiple slabs of octahedra. Legend: BO6 octahedra are gray; (OBi4) tetrahedra are red; Bi atoms are shown as yellow circles.

Figure 145. (a−c) The scheme showing structures of the Sillen phases. (OBi4) tetrahedra are red; Bi atoms are shown as yellow circles; halide anions are light-blue.

3.5. O- and N-Centered Tetrahedra in Hg Compounds

3.5.1. General Remarks. As it was mentioned in the Introduction, the first systematic review on anion-centered tetrahedra in Hg(I)−Hg(II) compounds was provided by Magarill and co-workers in a series of papers.73,675,676 The main difference between the Hg compounds and other compounds considered in the present review is the tendency of the Hg atoms to form Hg−Hg bonds, which results in formation of various types of [Hg]n units.677 In compounds with “additional” oxygen atoms this favors linkage of (OHg4) tetrahedra via Hg−Hg bonds that provides stabilization of structure types and, in general, explains structural differences between the Hg compounds and their chemical analogues. For instance, Hg3O2Cl2 crystallizes in two structure types, and neither has even far resemblance to the structure of Pb3O2Cl2 (mendipite). The average O−Hg bond valence is equal to 0.608 v.u. that explains internal geometrical distortions frequently observed for the (OHg4) tetrahedra and the general ability of Hg+ and Hg2+

Figure 146. Double (c) and single (b) fluorite-type blocks of (OBi4) tetrahedra in the structures of Aurivillius and Sillen phases as derivatives of the structure of fluorite (a). Legend as in Figure 144.

Bi 46 O 57 (PO 4 ) 8 , 673 or organized in groups of versatile dimensionality such as in Bi14O15(PO4)4,674 which shows a pronounced 2D-character in terms of the (OBi4) tetrahedra linkage. 6513


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Figure 147. Cresnel-type 2D units of (OBi4) tetrahedra (⊗ denotes the infinite character of the ribbons perpendicular to the plane of the figure): Cresnel-type edge-sharing junctions in Bi2nMon‑2O6n‑6: n = 5 (a), 6 (b) 7 (c), 8 (d). The 8 × 3 Cresnel junctions by edge sharing of tetrahedra in Bi18.71Cr0.27P6O43.22 (e); the structure of [Bi6O7]4O3Cl10 with mixed edge and corner sharing junctions between the n = 12 ribbons.

Figure 148. (a, b) Application of the crystallographic shear (CS) operation to the structure of [Bi2O2](MoO4) (koechlinite) (upper part) results in formation of the [Bi16O18](MoO4)6 structure (bottom part). Gray lines indicate the CS operation. Figure 149. Topology of the junction between tetrahedra ribbons in Bi9V2ClO18 (a; 1 tetrahedron thick junction, edge sharing) and (Bi6O7)4O3Cl10 (b; 3 tetrahedra thick, edge and corner sharing).

cations to form (OHg3) triangular configurations, which will not be covered in this review. 3.5.2. 0D Units. Table 21 provides a list of Hg compounds containing various finite units based upon oxocentered tetrahedra. Single (OHg4) tetrahedra have been observed in several compounds, including Hg4OF6 (Figure 154), Hg4−xO1−y(VO)(PO4)2(H2O) (Figure 155), and Hg2[Hg4O](CrO4)2

(Figure 156). An interesting case that highlights the ability of Hg+/2+ cations to form oxocentered tetrahedra and Hg−Hg bonds at the same time is the structure of [Hg4O][Pb(NO3)3]2680 (Figure 157). Here (OHg4) tetrahedra are linked via Hg−Hg 6514


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Figure 150. 2D Cresnel-type layers formed by linkage of ribbons by corner sharing of O(Bi,M)4 tetrahedra: (a) n = 2 tetrahedral ribbons in [O4Bi5]O0.5(PO4)2; (b) n = 3 tetrahedral ribbons in [O6Cu3Bi4](VO4)2; (c) n = 4 tetrahedral ribbons in [O8Bi8.67]O(SO4)4 (⊗ denotes the infinite character of ribbons running perpendicular to the plane of the figure).

Figure 151. Porous 2D layers of (OBi4) tetrahedra: (a) the structure of namibite, [O2CuBi2]OH(VO4); (b) hexagonal pores in francisite, [O2BiCu3](SeO3)2Cl2; (c) rows of (OBi4) tetrahedra nanotubules in [Bi7O4][TaO5][Ta2O9]; (d) the structure of [O3Ba3Bi]Cl3 case with voids (= V) created by the empty Ba4 tetrahedra superposed by Cl− anions; (e) the structure of Bi6O4Mx(PO4)4 with zigzag chains formed by four (OBi4) and (OBi3M) tetrahedra connected by sharing edges. The porous layers are isolated by PO4 groups; ⊗ denotes the infinite character of ribbons perpendicular to the plane of the figure.

Figure 152. The 2D network formed by (OBi4) tetrahedra in the structure of [Bi6O5](SeO3)3Br2: (a) dimer of edge-sharing (O(5)Bi4) tetrahedra; (b) the junction of the (O(2)Bi4), (O(5)Bi4), and (O(4)Bi4) tetrahedra; (c) the [O5Bi6]8+ layer; (d) the projection of the structure along the a axis. Reprinted with permission from ref 115. Copyright 2012 Elsevier B. V. 6515


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Figure 153. Porous 3D networks of O(Bi,M)4 tetrahedra: (a) triangular pores in (M5Cl)[Bi8O9]6O5Cl30; (b) the structure of [Bi6O6F]OCl3; (c) the structure of [Bi6O7]2OCl; (d) connection of infinite ribbons by the (OLa4) tetrahedra in Bi8La10O27; (e) the structure of (Bi3O2)(BiO)(BO3)2. See text for details.

Table 20. Crystallographic Data for Bi(III) Inorganic Compounds Containing Frameworks of (OBi4−nMn)m+ Tetrahedra O:Bi

chemical formula

space group

a (Å); α (deg)

b (Å); β (deg)

c (Å); γ (deg)

V (Å3)

ref

4:3 7:5 20:14 15:14 7:6 20:14

(Bi3O2)(BiO)(BO3)2 [Bi5O7]I [Bi14O20](SO4) Bi14O15Cl6 Bi6O7FCl3 [Bi48O59]Cl30(ClCu5)

P21/c Ibca I4/m Pnma Pnma P6̅2m

11.11 16.27 8.66 40.53 20.11 20.02

6.63 91.04 5.34 8.66 3.87 3.89 =a

11.04 23.02 17.28 15.49 15.43 7.74

812.8 2001 1297.3 2428.5 1207.5 2686.5

660 631 661 662 663 664

tedhadleyite are remarkable in that they contain two different types of oxocentered tetrahedral polycations each. Vasilyevite has single (OHg4) tetrahedra and [O2Hg6] dimers, whereas tedhadleyite can be considered as based upon alternating A and B layers. The A layer contains the [O2Hg6] dimers and I− anions, and the B layer contains the [O2Hg5] chains of the [O2Hg6] dimers linked by sharing common Hg atoms, and Cl− and Br− anions (Figure 160). 3.5.3. 1D Units. There are four different basic topologies of [OnHgm] chains in Hg compounds (Table 22). The simplest chain is formed as a result of linkage of (OHg4) tetrahedra by sharing common corners. Chains of this type have the O:Hg ratio equal to 1:3. Figure 161a shows the structure of [Hg3O]2(CrO4)2, which can be considered as based upon the [O4Hg12] chains shown in Figure 161b. The chains in

bonds to form a 3-D framework with the cristobalite topology. The framework has nanometer-size cavities occupied by the large [Pb(NO3)3]− anions. Linkage of two oxocentered tetrahedra via common corner leads to the formation of [O2Hg7] polycations that can be recognized in deansmithite, Hg3[Hg7O2](CrO4)2S4. The structure of Hg2[Ag4Hg3O2](AsO4)2 (Figure 158) contains [O2Hg3Ag4] dimers formed by mixed-metal (O(Hg/Ag)4) tetrahedra. The structures of poyarkovite (Hg 3OCl), vasilyevite ([Hg 4 O] 2 [Hg 6 O 2 ] 2 I 3 (Br,Cl) 3 (CO 3 )), and tedhadleyite ([Hg6O2][Hg5O2]I2(Cl,Br)2) contain the [O2Hg6] dimers of tetrahedra linked by sharing a common edge. In poyarkovite, the dimers are linked by the Hg−Hg bonds into a 3D framework (Figure 159). The structures of vasilyevite and 6516


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Table 21. Crystallographic Data for Hg Inorganic Compounds Containing Finite Complexes of (OHg4)n+ Tetrahedra O:Hg 1:4

2:7 2:6

chemical formula

space group

a (Å); α (deg)

b (Å); β (deg)

Compounds with Isolated (OHg4) Tetrahedra [Hg4O]F6 P63mc 7.75 7.75 [Hg4−xO1−y](VO)(PO4)2(H2O) P212121 6.36 12.42 [Hg4O][Pb(NO3)3]2 Fd3̅m 15.43 15.43 Hg2[Hg4O](CrO4)2 P212121 7.36 8.03 [Hg4O]O(SeO4)2 P21/c 9.62 7.13; 109.81 vasilyevite [Hg4O]2[Hg6O2]2I3(Br,Cl)3(CO3) P1̅ 9.34; 93.26 10.65; 90.55 Compounds with Multiple Finite Complexes of [OHg4] Tetrahedra Hg2[Ag4Hg3O2](AsO4)2 P31c 6.03 6.03 deansmithite Hg3[Hg7O2](CrO4)2S4 P1̅ 8.13; 100.36 9.49; 110.16 poyarkovite Hg3OCl C2/c 19.01 9.02; 110.82 vasilyevite [Hg4O]2[Hg6O2]2I3(Br,Cl)3(CO3) P1̅ 9.34; 93.26 10.65; 90.55 tedhadleyite [Hg6O2][Hg5O2]I2(Cl,Br)2 A1̅ 7.01; 115.58 11.85; 82.58 [Cd2Hg4O2]O2(SeO4)2 P1̅ 6.91; 74.59 7.18; 68.23 [Pb4Hg2O2]O2(CrO4)2 P1̅ 6.51; 91.82 7.20; 92.17

c (Å); γ (deg)

V (Å3)

6.01 14.23 15.43 20.28 14.87 18.27; 115.42

312.1 1124.1 3674.4 1198.7 960.3 1638.3

678 679 680 681 682 683

21.58 6.89; 82.98 16.85 18.27; 115.42 12.60; 100.62 7.46; 63.89 7.61; 111.33

678.6 490.1 2699.6 1638.3 927.0 306.0 331.2

684 685 686, 687 683 688 689 690

ref

Figure 154. The crystal structure of Hg4OF6 containing [OHg4]6+ tetrahedra. Reprinted with permission from ref 678. Copyright 2004 Wiley-VCH Verlag GmbH & Co KGaA.

this compound are 4-periodic (or vierer according to the Liebau’s classification) and have a zigzag-like geometrical structure. In contrast, the structure of [Hg3O](OH)(NO3) (Figure 161c) is based upon zweier [O2Hg6] chains shown in Figure 161d. Alternation of edge- and corner-linkage of tetrahedra generates the [O2Hg5] chain observed in the structure of Hg2[Hg5O2](PO4)2 (Figure 162) as well as in the structure of tedhadleyite, [Hg6O2][Hg5O2]I2(Cl,Br)2 (Figure 160). The chain with the same stoichiometry, [O2Hg5], but with different topology is present in the structure of [Hg5O2](CrO4) (Figure 163). This chain can be considered as a double chain formed by condensation of two 2-periodic chains shown in Figure 161d via common Hg−Hg edge. The structure of [Hg2O](CN)2 (Figure 164a) also contains double chains, but with different topology (Figure 164b). 3.5.4. 2D Units. The layers of (OHg4) tetrahedra (Table 22) may be described as a result of condensation of the [O2Hg6] tetrahedral dimers formed by linkage of two tetrahedra by sharing a common edge (Figure 165a). In the structure of [Hg2O]4(OH)(NO3)2, the [O2Hg6] dimers are linked via nonshared vertices to form a layer similar to the one observed in the structure of dolerophanite, Cu2O(SO4)18 (Figure 165b). The layer can be described as built up from six-membered rings

Figure 155. The crystal structure of Hg4‑xO1‑y(VO)(PO4)2(H2O) along the a axis. Legend: black polyhedra = VO6 octahedra, PO4 tetrahedra are hatched; Hg and O atoms are shown black and gray circles; H2O molecules are shown as white circles. Reprinted with permission from ref 679. Copyright 2002 American Chemical Society.

Figure 156. The crystal structure of Hg2[Hg4O](CrO4)2 as consisting of Hg+ cations, [OHg4]2+ polycations, and CrO4 tetrahedra.

of tetrahedra. Within a single ring, the sequence of linkage of tetrahedra can be written as −T=T−T−T=T-T-, where T stands for a tetrahedron. Each Hg atom at the corner of the 6517


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[M″2Hg2O2](M′O4)2(H2O), where M″ = Cd, Zn, Co and M′ = Se, S.696 These layers can also be viewed as formed by condensation of six-membered rings, but with the sequence of tetrahedra linkage described as −T=T−T−T− T=T- (Figure 165c). As in the layers shown in Figure 165b, Hg atoms are shared between two adjacent (OHg4) tetrahedra each. In contrast, the layer depicted in Figure 165d, which is observed in the structure of Hg2OI,697 consists of [O2Hg6] dimers that link in such a way that, for a single tetrahedron, three Hg vertices are shared between three tetrahedra and one remains nonshared. In the structure of hanawaltite, [Hg7O3]Cl2,698,699 [O2Hg6] dimers are linked via single (OHg4) tetrahedra to produce the cationic layer with the [O3Hg7]2+ composition (Figure 165e). 3.5.5. 3D Units. The compounds that are based upon frameworks of (XHg4) tetrahedra are listed in Table 23. From the viewpoint of topology, they can be classified into frameworks with corner-linked tetrahedra only and frameworks, in which corner- and edge-linkage of tetrahedra are combined. Frameworks of Corner-Linked Tetrahedra. There are several frameworks of corner-linked (XHg4) tetrahedra, which possess topologies similar to those observed in silicates.187 The simplest are the cristobalite- and tridymite-like [NHg2]+ frameworks, which occur in the structures of natural minerals mosesite and kleinite, respectively (Figure 166). It is of interest that, in contrast to silicates, the frameworks bear a positive charge, whereas the framework cavities are filled with anions and water molecules. The cristobalite-like topology is wellrecognized for the framework of anion-centered tetrahedra that occur in the structure of Hg−Sb pyrochlore, [Hg2O][Sb2O6]701 (Figure 167). Weil703 reported synthesis and structure of [Hg2O](SeO3)(H2O)0.167, an amazing compound, which, under the inspection from the viewpoint of O-centered tetrahedra, appears to be an inverted analogue of cancrinite, a common aluminosilicate framework mineral713,714 (Figure 168). Another interesting compound of the same sort is [Hg2N](NO3),704 which again possess the [NHg2]+ framework, but with rather complicated topology consisting of three- and four-membered rings (Figure 169). It is noteworthy that the frameworks bear a positive charge, whereas their cavities are filled with anions of different kinds. This makes these compounds of great interest from the viewpoint of their potential applications as anionexchangers. Frameworks of Corner- and Edge-Linked Tetrahedra. By analogy with layers, many frameworks of anion-centered tetrahedra in Hg compounds can be considered as resulting from condensation of [O2Hg6] tetrahedral dimers. Figure 170 shows four different types of such frameworks. The first one (Figure 170a) consists of dimers linked via corners into linear tetramers that represent fragments of the [O2Hg5] chains shown in Figure 162b. The tetramers are further linked by sharing Hg atoms involved in the Hg−Hg edge shared in the other dimer. More simple arrangement of dimers is observed in the structure of BaHg2O2Cl2 (Figure 170b), where they link into double chains that form channels hosting Cl− anions. Alternatively, the framework can be considered as a result of condensation of four-membered rings of tetrahedra. The structure of terlinguaite, [Hg2O]Cl2 (Figure 170c), is also based upon tetrahedral dimers. Its oxocentered framework can be obtained by condensation of the [O2Hg5] chains shown in Figure 162b via corners not involved in either corner- or edgelinkage of tetrahedra inside the chains. The structure of [SrHg2O2]Cl2 (Figure 170d) displays a more complex

Figure 157. Crystal structure of [Hg4O][Pb(NO3)3]2: from left to right: (top, left) perspective view of the cationic network [Hg4O]2+ consisting of OHg4 tetrahedra linked via strong Hg−Hg bonds; (top, right) projection of the crystal structure on (100); (bottom, left) one cage with the [Pb(NO3)3]− anion; (bottom, right) space-filling model of one cage encapsulating a ball with the 1 nm diameter (O and Hg atoms are shown as blue and gray spheres, respectively). Reprinted with permission from ref 680. Copyright 2006 Wiley-VCH Verlag GmbH & Co KGaA.

Figure 158. (a, b) The crystal structure of Hg2[Ag4Hg3O2](AsO4)2. Legend: AsO4 tetrahedra are green, OHg4 tetrahedra are light-brown, Hg atoms are gray.

Figure 159. [O2Hg6] dimers of OHg4 tetrahedra linked via Hg−Hg interactions into 3D framework in the structure of poyarkovite, Hg3OCl. Legend: (OHg4) tetrahedra are light-brown; Cl anions are light-blue.

tetrahedra is shared between precisely two (OHg4) groups. Layers consisting of corner-sharing [O2Hg6] dimers but with a different topology have been observed in the structures of 6518


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Figure 160. The structure of tedhadleyite, [Hg6O2][Hg5O2]I2(Cl,Br)2 (a) can be considered as alternation of the A (b) and B (c) layers. The A layer contains [O2Hg5] chains and I− anions, whereas the B layer contains [O2Hg6] dimers and Cl− and Br− anions.

Table 22. Crystallographic Data for Hg Inorganic Compounds Containing Chains and Layers of (OHg4)n+ Tetrahedra O:Hg 1:3 2:5

2:5 1:2 1:2 1:2

1:2 3:7

chemical formula [Hg3O](OH)(NO3) [Hg3O]2(CrO4)2 Hg2[Hg5O2](PO4)2 [Hg5O2][Re2O8] tedhadleyite [Hg6O2][Hg5O2]I2(Cl,Br)2 wattersite [Hg5O2](CrO4) [Hg2O][CN]2 [Hg2O]4(OH)(NO3)2 [Cd2Hg2O2](SeO4)2(H2O) [Cd2Hg2O2](SO4)2(H2O) [Zn2Hg2O2](SeO4)2(H2O) [Zn2Hg2O2](SO4)2(H2O) [Zn2Hg2O2](SO4)2(H2O) [Hg2O]I hanawaltite [Hg7O3]Cl2

space group

a (Å); α (deg)

b (Å); β (deg)

Compounds with Chains of OHg4 Tetrahedra Pbca 6.44 11.36 Pca21 11.47 9.44 P21/c 6.25 9.94; 95.78 P1121/b 6.40 7.98 A1̅ 7.01; 115.58 11.85; 82.58 C2/c 11.27 11.67; 98.19 Pnma 18.90 3.90 Compounds with Layers of OHg4 Tetrahedra C2/c 6.77 11.67; 96.85 P2/n 7.99 6.33; 102.80 P2/n 7.76 6.23; 102.02 Pbcm 6.20 11.45 Pbcm 6.13 11.26 Pbcm 6.13 11.27 C2/c 17.60 6.98; 101.61 Pbma 11.80 13.89

c (Å); γ (deg)

V (Å3)

ref

15.96 10.35 9.67 11.54; 98.87 12.60; 100.62 6.60 7.08

1166.7 1120.8 597.3 582.4 927.0 859.8 521.8

712 681 691 692 688 693 694

24.49 10.57 10.40 13.36 12.96 12.97 6.70 6.47

1921.3 521.5 492.2 948.0 894.8 895.6 806.6 1060.3

695 696 696 696 696 696 697 698

described in the structures of swedenborgite, Na(Be4O)(SbO 6 ), 715−717 and in two modifications of (Be 4 O)(NO3)6.718,719 In the latter, the (OBe4)6+ tetrahedral group is surrounded by six (NO3)− triangles so that each triangle is attached to the Be···Be edge of the tetrahedron (Figure 174). 3.6.2. Ca, Sr, Ba. The Ca2+, Sr2+, and Ba2+ cations usually have quite high coordination numbers with more or less symmetrical coordination. However, in some specific cases, they are able to form bonds with the bond-valences close to 0.5 v.u. Reckeweg and DiSalvo720 reviewed occurrences of the (OA4) tetrahedra in alkaline earth oxyhalides with the general formulas (A4O)X6 and [A2O]X2 (A = Ca, Sr, Ba; X = Cl, Br, I).184,721−724 The structures of (A4O)X6 contain isolated (OA4)6+ tetrahedra (Figure 175), whereas the structures of [A2O]X2 are based upon the [OA2]2+ chains of trans-edgesharing (OA4)6+ tetrahedra (Figure 176). The same type of chains have been reported for the metal-rich compound Na[Ba2O].726 In oxocompounds, the only example known to us is the structure of Ca4O(PO4)2,726 containing isolated (OCa4)6+ tetrahedra. 3.6.3. Scandium. Because of the similarity of scandium and lanthanides, Sc oxocompounds based upon units of (OSc4) tetrahedra are isotypic to the corresponding Ln compounds. The examples include Sc 2O2S,728 ScOF,729 and Sc 2O(GeO4).730

arrangement of oxocentered tetrahedra, where the [O2Sr2Hg4] tetrahedral dimers are linked through (OHg2Sr2) tetrahedra by corner-sharing. According to Magarill et al.,73 the structure of α-Hg3O2Cl2 is based upon the layers of the type shown in Figure 165d linked by sharing corners not participating in the intralayer bonding of tetrahedra (Figure 171). The [O4Hg5] framework in pinchite, [Hg5O4]Cl2 (Figure 172), can be considered as based upon the layers shown in Figure 172a. These layers are formed by linkage of double chains with alternating edge and corner sharing of tetrahedra (Figure 165b). Connection between the layers is provided by sharing apical corners that are nonshared within the layers. The same type of framework can be found in the structure of [Pb2Hg3O4](CrO4) (Figure 173). In order to be considered from the viewpoint of oxocentered tetrahedra, some long Pb− O contacts (2.9−3.2 Å) have to be included into consideration, which means that the anion-centered description in this case has more geometrical than physical meaning. However, it provides a way to describe the structures of pinchite and [Pb2Hg3O4](CrO4) within the same coherent crystal chemical approach. 3.6. Miscellaneous

3.6.1. Beryllium. The most stable coordination of Be2+ in oxocompounds is tetrahedral, which means that the average Be2+−O bond valence is 0.5 v.u., ideal for the formation of (OBe4) tetrahedra. Isolated (OBe4) tetrahedra have been 6519


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Figure 163. The crystal structure of wattersite, [Hg5O2](CrO4) (a) is based upon the [O2Hg5]2+ chains of [OHg4] tetrahedra (b).

Figure 164. The crystal structure of [Hg2O][CN2] (a) contains double chains of (OHg4) tetrahedra (b).

Figure 161. The crystal structures of [Hg3O]2(CrO4)2 (a) and [Hg3O](OH)(NO3) (c) contain 4-periodic (b) and 2-periodic (d) chains of corner-sharing [OHg4] tetrahedra, respectively.

Figure 165. The [O2Hg6] dimer of edge-sharing [OHg4] tetrahedra (a) and layers that can be considered as the result of condensation of the dimers (b−e). See text for details.

Figure 162. The structure of Hg2[Hg5O2](PO4)2 (a) contains chains with alternating edge- and corner-sharing [OHg4] tetrahedra (b).

3.6.4. Actinides. In their low-valent oxidation states, crystal chemistry of actinides is very similar to that of lanthanides, which is manifested in isotypic relationships between structure types of lanthanide and actinide oxocompounds. Eight-fold coordination is typical for the Th4+ and U4+ oxocompounds, which means that these cations are able to form cation-oxygen bonds with bond-valences around 0.5 v.u. The structures of uraninite, UO2, and thorianite, ThO2, belong to the fluorite structure type with O atoms in tetrahedral coordination to metal atoms. Among other Th and U compounds with oxocentered tetrahedra, the following can be mentioned: ThOX′ (X′ = S, Se, Te),731−733 [UO]4S4LuS,734

Figure 166. Frameworks of corner-sharing (NHg4) tetrahedra in the structures of mosesite (a) and kleinite (b).

[UO]UCu2As3,735 U4O4Te3,736 [UO]X′ (X′ = Se, S),737,738 [UO]CuP.739 As lanthanides, actinides show tendency to form nitrocentered (N3‑A4) tetrahedra. Among examples, one may select [UN]X′ (X′ = Cl, Br, I),740,741 [U2N2]X′ (X′ = P, S, As, Se, Sb, Te, Bi),742,743 [Th2N2]X′ (X′ = Sb, Te, Bi),743 6520


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Table 23. Crystallographic Data for Hg Inorganic Compounds Containing Frameworks of (XHg4)n+ Tetrahedra (X = O, N) X:Hg

chemical formula

space group

a (Å); α (deg)

b (Å); β (deg)

c (Å); γ (deg)

V (Å3)

ref

1:2

mosesite [Hg2N](Cl, SO4, CO3, H2O) [Hg2O][Sb2O6] kleinite [Hg2N](SO4)0.25Cl0.5)(H2O)0.5 [Hg2O](SeO3)(H2O)0.167 [Hg2N](NO3) schuetteite [Hg3O2](SO4) [Hg3O2](CrO4) terlinguaite [Hg2O]Cl2 [BaHg2O2]Cl2 [SrHg2O2]Cl2 α-[Hg3O2]Cl2 pinchite [Hg5O4]Cl2 [Pb2Hg3O4](CrO4)

F43̅ m Fd3̅m P63/mmc R3̅ P43212 P31 P3221 C2/c P4/mbm P21/n P21/c Ibam P21/c

9.52 10.35 6.76 15.40 15.40 7.05 7.14 11.95 11.84 9.94 7.15 11.62 6.54

=a =a =a =a =a =a =a 5.90 105.6 =a 7.02 102.4 6.86 126.90 6.11 21.95 109.30

=a =a 11.07 10.05 9.10 10.02 10.02 9.47 4.29 8.29 6.86 11.71 6.97

863.9 1109.5 438.3 2064.2 2158.7 431.0 441.9 643.4 601.3 556.1 269.3 830.6 943.9

700 701 702 703 704 705 706 707 708 709 694 710 711

1:2 1:2 1:2 2:3 1:2 2:3 2:3 2:3 4:5

Figure 167. The crystal structure of [Hg2O][Sb2O6] as interpenetration of octahedral pyrochlore-like framework [Sb2O6] (dark gray) and tetrahedral framework [OHg2] consisting of corner-sharing (OHg4) tetrahedra (light gray). Reprinted with permission from ref 701. Copyright 2008 Elsevier B. V.

Figure 169. The structure of [Hg2N](NO3) (a) is based upon the framework of corner-sharing (NHg4)5+ tetrahedra (b).

module with two vacant tetrahedra paired along the body diagonal. From the viewpoint of the electronic structure, the formula of the compound can be written as (A′)(Th4+)12(N3−)6(X′)29(e−)2, which means that there are two extra electrons per cluster. Extended Hückel calculations demonstrated that these electrons are delocalized within the Th6 octahedron at the core of the cluster, thus forming a sixcenter two-electron bond. Crystal chemistry of the Ac3+, Pa4+, Np3+, Np4+, Pu3+, Pu4+, Am3+, Cf3+, Bk3+ is poorly investigated, due to the obvious reasons. However, the (OA4) can be found in the structures of [AO]F (A = Ac, Cf),746,747 [NpO]X′ (X′ = S, I),731,747 [A2O2]S (A = Pu, Cf),6,748 [AmO]X′ (X′ = Cl, Br).749,750 In the structure of PaOCl2,751 the O2− and Pa4+ ions form a 1D chain with the composition [PaO]2+. In this chain, half of the O

Figure 168. The crystal structure of [Hg2O](SeO3)(H2O)0.167 (a) is based upon the [Hg2O]2+ polycationic framework of corner-sharing [OHg4]6+ tetrahedra (b) with the cancrinite topology (c).

Th2(N,O)2X′ (X′ = P, S, As, Se).742 Braun et al.744,745 reported on the syntheses and crystal structures of inorganic compounds with the formula A′Th12N6X′29 A′ = Li, NA, K, Rb; X′ = Cl, Br). Their structures contain the [N6Th12] finite cluster shown in Figure 177. The cluster itself can be considered as a fluorite 6521


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Figure 172. Layers of OHg4 tetrahedra (a) and their linkage into a 3D framework (b) in the structure of pinchite, Hg5O4Cl2. Circles indicate positions of the Cl atoms. Cl atoms are shown as light-blue spheres.

Figure 170. The crystal structures of frameworks with corner- and edge-sharing tetrahedra: (a) framework in the structure of schuetteite, [Hg3O2](SO4); (b) the structure of [BaHg2O2]Cl2; (c) the structure of terlinguaite, [Hg2O]Cl2; (d) the structure of [SrHg2O2]Cl2.

Figure 173. The crystal structure of [Pb4Hg2O2]O2(CrO4)2 is based upon the pinchite-type framework of oxocentered tetrahedra that arrange into layers (a) that further link via nonshared Pb vertices (b).

Figure 171. Layers of OHg4 tetrahedra (a) and their linkage into a 3D framework (b) in the structure of α-Hg3O2Cl2. Cl atoms are shown as light-blue spheres.

atoms possess tetrahedral coordination, whereas the other half are coordinated by three metal cations each. 3.6.5. Pd, Pt. The structures of PdO and PtO290,752 are isotypic to tenorite, CuO, which means that they both can be described on the basis of oxocentered tetrahedra. Since the 2+ oxidation state is more typical for Pd, there are several examples of structures based upon (OPd4) tetrahedra. Pd2OCl2753 contains anticristobalite framework of oxocentered tetrahedra with cavities filled by the Cl− anions. Interesting examples of oxo-palladium clusters have been reported by Kortz and co-workers.754,755 The structure of Na8[Pd13As8O34(OH)6]· 42H2O (= Na8{[Pd13O8](AsO3(OH))6(AsO4)2}·42H2O)754 contains icosahedral [Pd13O8]10+ core, which is identical to the [Pb13O8]10+ cluster found in the structure of [Pb13O8](OH)6(NO3)4240,255 (Figure 178). Less distorted configuration

Figure 174. The [(Be4O)(NO3)6]0 complex in the structure of cubic (Be4O)(NO3)6.

of the [Pd13O8]10+ core consisting of eight (OPd4)6+ tetrahedra sharing a common Pd2+ cation has been found in Na6[Pd13Se8O32]· 10H2O (= Na6{[Pd13O8](SeO3)8}·10H2O755 (Figure 179). 3.6.6. Cd, Ni. For Cd2+ and Ni2+ cations, formation of the oxocentered (OA4) tetrahedra is a rarity. However, several structures have been reported that contain additional O2− anions in tetrahedral coordination by these cations. The 6522


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Figure 179. The structure of the {[Pd13O8](SeO3)8}6− cluster in the structure of Na6{[Pd13O8](SeO3)8}·10H2O. Reprinted with permission from ref 755. Copyright 2009 American Chemical Society.

Figure 175. The crystal structure of A4OX6 (A = Ca, Sr, Ba; X = Cl, Br, I) along the c axis. The (OA4) tetrahedra are gray, X atoms are displayed as light-blue spheres.

Figure 176. Perspective view of the crystal structure of Ba2OI2 along the c axis. The (OBa4) tetrahedra are drawn as gray, the I atoms are displayed as light-blue spheres.

Figure 180. The [O4Cd8]8+ cluster in the structure of Cd2+-exchanged, fully dehydrated zeolite Y. Reprinted with permission from ref 757. Copyright 2005 Elsevier B. V.

Figure 181. The {[O4Ni8](H2O)4}8+ cluster in the structure of Ni2+exchanged, vacuum-dehydrated zeolite Y. Reprinted with permission from ref 758. Copyright 2009 American Chemical Society.

Figure 177. The [N6Th12] finite cluster consisting of six (NTh4) tetrahedra in the structures of A′Th12N6X′29 (A′ = Li···Rb; X′ = Cl, Br).

Table 24. Average Values of the A−O−A Bond Angles in Oxocentered (OA4) Tetrahedra versus the A−O Bond Lengths ⟨A−O−A⟩a (deg)

Figure 178. The icosahedral Pd13 skeleton (left) and its occupation by eight O2− anions (right) in the [O8Pd13]10+ core of the oxo-hydroxo Pd−As cluster in the structure of Na8{[Pd13O8](AsO3(OH))6(AsO4)2}·42H2O. Reprinted with permission from ref 754. Copyright 2008 Wiley-VCH Verlag GmbH & Co KGaA.

bond

⟨A−O⟩ [Å]

for the angle opposite to the shared A···A edge

Cu−O Sn−O Pb−O La−O

1.94 2.26 2.33 2.36

93.5 (12) [91.4−95.9] 101.8 (3) [98.1−104.4] 103.1 (83) [98.2−109.2] 104.4 (32) [101.6−107.6]

for all angles in a tetrahedron 109.6 109.0 109.5 109.4

(72) (6) (120) (48)

a

Numbers in curled brackets indicate the number of observations taken into account; numbers in square brackets shown variations of individual angles.

structure of Cd3O2Cl2756 is based upon 3D framework of (OCd4)6+ tetrahedra with Cl− ions in framework cavities. Seff and co-workers757,758 reported structures of Cd2+-exchanged fully dehydrated and Ni2+-exchanged vacuum-dehydrated zeolite

Y. In both cases, sodalite cavities of the aluminosilicate framework are occupied by the [O4A8]8+ stella quadrangula clusters formed by four (OA4)6+ tetrahedra each (Figures 180−182). 6523


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Table 25. Average A···A Distances in Anion-Centered (XA4) Tetrahedra

a

A

Na

⟨A···A⟩ [Å]

Cu Pb Bi Y La Ce Pr Nd Sm Eu Gd Tb Yb

168 450 180 60 186 90 72 174 96 36 66 54 36

3.14 3.74 3.84 3.62 3.90 3.84 3.82 3.82 3.88 3.76 3.72 3.70 3.68

N = number of distances taken into account.

The maximal number of tetrahedra sharing a common corner observed so far in inorganic compounds is eight. It is typical for fluorite-type frameworks and fluorite-derivative structural units such as [O8A13]10+ clusters reported in the structures of Pb and Pd compounds discussed above.240,255,754,755 3°. One tetrahedral edge (A...A) may be shared between two and, in very rare cases, between three (XA4) tetrahedra. The latter case can be observed in the structure of Bi4Ag18O12.71,668

Figure 182. The [O4Ni8]8+ stella quadrangula cluster inside the sodalite cavity of the Ni2+-exchanged, vacuum-dehydrated zeolite Y. Reprinted with permission from ref 758. Copyright 2009 American Chemical Society.

4.2. Bond-Length Variations

In general, the higher the number of the (XA4) tetrahedra sharing the same A atom, the longer the X−A bond. Figure 183 shows statistics of the variations of the O−Pb bond lengths in the (OPb4) tetrahedra with different numbers of edge and corner links. It can be seen that the dependence of the O−Pb bond lengths on the number of links is not linear, which can be explained by the relative weakness of the O−Pb bond, which makes possible a higher degree of distortion of the (OPb4) tetrahedra in comparison to tetrahedral units in silicates, sulfates, phosphates, etc. 4.3. Bond-Angle Variations

The major variations of the A−X−A bond angles occur when two (XA4) tetrahedra share the same A···A edge. Because of the repulsion between the Xm− anions, the A−X−A bond angles opposite to the shared A···A edges experience significant contraction. This effect depends upon the size of the An+ cation, as summarized in Table 24. As it can be seen, the average ⟨A− X−A⟩ angle in the (XA4) tetrahedral is usually very close to the value of 109.5° observed for an ideal tetrahedral geometry.

Figure 183. Statistics of the variations of the O−Pb bond lengths in the (OPb4) tetrahedra with different numbers of edge and corner links. The connectivity diagrams of specific tetrahedral corners are shown.

4. TOPOLOGICAL AND GEOMETRICAL VARIATIONS 4.1. Topological Rules

4.4. Variations of the A···A Distances

The review of complexes of anion-centered tetrahedra provided in section 3 allows one to formulate basic topological rules of linkage of (XA4) tetrahedra in crystal structures of inorganic compounds. 1°. The (XA4) tetrahedra may link by sharing common corners (A) and/or common edges (A···A). In the case of fluorine-centered tetrahedra,162 face sharing is rarely observed, when the X···X distance is large, due to the large size of the respective An+ cations. The edge sharing of (XA4) tetrahedral becomes possible due to the relatively low charge of the Xm− anions at the centers of the tetraheda, which diminishes repulsive forces between adjacent tetrahedral centers. 2°. One tetrahedral corner occupied by the A atom may be shared by more than two but less than nine (XA4) tetrahedra.

Table 25 provides average ⟨A···A⟩ distances in the (XA4) tetrahedra formed by different metal atoms. It is of interest that, in some cases, the A···A distances approach the metal−metal distances observed in the structures of respective metals.121

5. CONCLUDING REMARKS The inorganic compounds based upon anion-centered tetrahedra reviewed in this work possess a number of interesting properties, usually depending upon the electronic properties of the respective metal atoms. For instance, lanthanide compounds with oxocentered (OLn4) tetrahedra are known as luminophors, whereas Cu compounds are of interest due to their magnetic properties specified by the arrangement of the Cu2+ ions into arrays of oxo6524


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bridged cationic complexes. Bi and partially Pb compounds containing oxocentered tetrahedra may possess ion-conducting properties, sometimes related to cationic disorder inside the oxocentered framework. A certain interest and potential lies in the possible properties of the compounds based upon anion-centered tetrahedra as anion-exchangers, since their structures are usually based upon polycationic structural units; in this regard, oxyhalide compounds deserve special attention. Many of the compounds considered in this review are interesting from the mineralogical, geochemical, and environmental points of view. In particular, the complexes of (OCu4) tetrahedra very likely play an important role in the transport of Cu and other metals by volcanic gases. The oxo- and hydroxocentered Pb, Hg, and Bi polynuclear clusters, existing in aqueous solutions, determine mobility of these metals in oxidation zones of mineral deposits, as well as in the environment in general. Finally, the viewpoint developed in this review may seem to be contradictory to the traditional approach to the structures of inorganic compounds, which are usually considered in terms of coordination of cations. However, a large number of compounds reviewed above provide essential evidence that, in some cases, it is anions that determine anisotropy of the chemical bond distribution, which should not be neglected in inorganic structural chemistry.

Olivier Mentré was born in Dunkerque, France, in 1966. He obtained his D.Sc. (1994) and H.D.R. (Habilitation a Diriger les Recherches) in 2004 at the Université des Sciences et Technologies de Lille (USTL) in the field of crystal chemistry of mixed valent oxides and various inorganic compounds. In 1995−1996, he was at the University of Texas at Austin in the group of crystallography of Hugo Steinfink as a Welch-foundation fellow. He joined the CNRS as a Chargé de Recherches at the LCPS (Laboratoire de Cristallochimie et Physicochimie du Solide, Lille) as chargé de Recherches in 1996 and was promoted to Directeur de Recherches at the UCCS (Unité de

AUTHOR INFORMATION

catalyse et Chimie du Solide, Lille) in 2010. He is the head of the

Corresponding Author

OXIN group, dedicated to research on new inorganic materials with

*E-mail: [email protected].

specific properties.

Notes

The authors declare no competing financial interest. Biographies

Oleg I. Siidra was born in 1981 in St. Petersburg. During his Ph.D. studies, he spent one year in 2005/2006 in the University of Kiel as a DAAD fellow with Prof. Wulf Depmeier. He obtained his Cand. Sci. degree from St. Petersburg State University in 2007. Since 2009, he is

Sergey V. Krivovichev was born in 1972 in St. Petersburg. He obtained his Cand. Sci. (1997) and Dr. Sci. (2002) degrees from St. Petersburg State University. In 1999−2005, he spent several years working in the U.S. (University of Notre Dame) as a NSF-NATO fellow, in Germany (Kiel) as a Humboldt fellow, and in Austria (Innsburck University) as a Lise-Meitner fellow of the Austrian Science Foundation. Since 2006, he is Full Professor and Chairman of the Department of Crystallography, St. Petersburg State University. In 2008, he had received the President of Russian Federation Young Scientist Award in Science and Technology.

Associate Professor at the Department of Crystallography at the same university. In 2011, he received the Struchkov Prize for the best research work in the field of X-ray crystallography. In 2012 he visited University of Lille as an invited professor. His research interests include X-ray crystallography, materials science, mineralogy, lone-pair elements (Pb, Tl) oxysalts, uranyl compounds. He is a lecturer and coauthor of around 80 publications and more than 40 communications at international meetings. 6525


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Marie Colmont was born in 1979 in Lille, France. She obtained her D.Sc. in 2004. She spent one year in Stockholm in the Arrhenius Laboratory, working with Prof. Osamu Terasaki, as a Wenner-Gren foundation fellow. Since 2005, she is a full Associate Professor at ENSCL (Ecole Nationale Supérieure de Chimie de Lille). Her research interests are solid state synthesis, X-Ray diffraction and electron microscopy.

Stanislav K. Filatov was born in 1940 in the Voronezh region, Russia. He graduated from St. Petersburg State University in 1963 and obtained his Cand. Sci. (1969) and D. Sci. (1988) degrees from the same University. In 1989−2002 he was Full Professor and Chairman of the Department of Crystallography, St. Petersburg State University; since 2002 he is Full Professor at the same department. He is an Honored Scientist of the Russian Federation (1999). In 2008 he was awarded the Georg Agricola Medal of the German Mineralogical Society.

ACKNOWLEDGMENTS This work was supported for S.V.K., O.I.S., and S.K.F. by the internal grant of St. Petersburg State University (3.38.83.2012) and the Russian Foundation for Basic Research (13-05-00684). This work was carried out under the framework of the MultiInMaDe project supported by the ANR (Grant ANR 2011-JS08 003 01). S.V.K. and O.I.S. are grateful to the University of Lille for the Invited Professor fellowships and to the French coauthors for their hospitality. REFERENCES (1) Bergerhoff, G.; Paeslack, J. Z. Kristallogr. 1968, 126, 112. (2) Smith, P.; Garcia-Blanco, S.; Rivoir, L. Z. Kristallogr. 1961, 115, 460. (3) Tulinsky, A.; Wobthinoton, C. R.; Pignataro, E. Acta Crystallogr. 1959, 12, 623. (4) Burnham, C. W. Z. Kristallogr. 1963, 118, 337. 6526


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