Complex ceramic structures. I. Weberites
The weberite structure (A2B2X7) is an anion-deficient fluorite-related superstructure. Compared with fluorites, the reduction in the number of anions leads to a decrease in the coordination number of the B cations (VI coordination) with respect to the A cations (VIII coordination), thus allowing the accommodation of diverse cations. As a result, weberite compounds have a broad range of chemical and physical properties and great technological potential. This article summarizes the structural features of weberite and describes the structure in several different ways. This is the first time that the stacking vector and stacking angle are used to represent the weberite structure. This paper also discusses the crystallographic relationship between weberite, fluorite and pyrochlore (another fluorite-related structure). The cation sublattices of weberite and pyrochlore are correlated by an axial transformation. It has been shown that the different coordination environment of anions is due to the alternating layering of the AB3 and A3B close-packed cation layers. A stability field of weberite oxides is proposed in terms of the ratio of ionic radius of cations and relative bond ionicity. In addition, a selection of weberite compounds with interesting properties is discussed.
The weberite crystal structure (space group: Imma, No. 74), with typical stoichiometry A2B2X7 (A and B are cations, X is an anion, O or F), is a type of anion-deficient fluorite superstructure (AX2). While several other compounds possess the same stoichiometry (pyrochlores, layered perovskites etc.), weberites are isomorphic with the mineral Na2MgAlF7. This mineral was originally found in Ivigtut in southwestern Greenland and was named after Theobald Weber (Bogvad, 1938). In 1944, Byström (1944) determined the crystal structure, basing his studies on the pyrochlore structure, which is another fluorite-related superstructure.
While the structure has a cationic sublattice arrangement similar to that found in the fluorite structure (face-centered cube), owing to distortions in the anion sublattice, the crystal structure has a high potential to accommodate diverse metals. The cations in (011) planes have nearly the same symmetry as in the hexagonal tungsten bronze (HTB) structure. In addition, the triangular network in Na2B2+B3+F7 weberites, which is formed by B2+ and B3+ cations in the HTB-like planes, potentially supports various magnetically ordered systems. To date, fluorine-based weberites such as Na2B2+B3+F7 and Ag2B2+B3+F7 have attracted most of the attention owing to their interesting magnetic properties (Cosier et al., 1970; Dance et al., 1974; Frenzen et al., 1992; Laligant et al., 1989; Laligant, Ferey et al., 1987; Pankhurst et al., 1991; Ruchaud et al., 1992; Thompson et al., 1992; Tressaud et al., 1974; Heger, 1973). Investigations on A2B2O7 weberites have mainly focused on crystallography because of the close relationship between the weberite and the pyrochlore structures (Cordfunke & Ijdo, 1988; Groen & Ijdo, 1988; Klein et al., 2006; Reading et al., 2002; Astafev et al., 1985; Bonazzi & Bindi, 2007; Desgardin et al., 1976; Grey et al., 2001, 2003; Grey & Roth, 2000; Ivanov & Zavodnik, 1990). Both of the structures form three-dimensional BX6 networks and HTB-like layers. Some compounds, for example Ca2Sb2O7, can form a metastable pyrochlore phase, which can be converted into the weberite structure by heating above 973 K (Brisse et al., 1972). Recently, weberite oxides and weberite-related oxides have been reported to possess interesting physical properties (ferroelectric, dielectric and magnetic) as well as photocatalytic activity (Wakeshima et al., 2004; Abe et al., 2004, 2006; Cai & Nino, 2007; Cai et al., 2007; Cava et al., 1998; Ebbinghaus et al., 2005; Ivanov et al., 1998; Grey et al., 2001; Lin et al., 2006; Khalifah et al., 1999; Nishimine et al., 2004, 2005; Plaisier et al., 2002; Wakeshima & Hinatsu, 2006; Hinatsu et al., 2004; Harada & Hinatsu, 2002, 2001; Lam et al., 2003; Wiss et al., 2000; Wltschek et al., 1996; Gemmill et al., 2005).
There are a considerable number of publications on weberite ceramics. However, information on weberites is scattered. While presenting their work on the structure determination of Na2Fe2F7, Yakubovich et al. (1993) devoted more than half of the paper to a comparison of different types of weberite structures in Na2B2+B3+F7 compounds and their relationship to the fluorite and the pyrochlore structures, but their discussion was limited to the crystallographic aspects. Lopatin et al. (1985) and Sych et al. (Sych, Kabanova, Garbuz et al., 1988) focused on the stability-field region of these compounds. However, there is no article that correlates the structure and properties of weberites. Therefore, this paper is intended to provide a discussion of weberite ceramics, covering crystallographic aspects including the relationship between weberite, fluorite and pyrochlore, their stability field with respect to pyrochlore, and their interesting properties.
In §2 the structural features of weberite and the characteristics of weberite-like structures are discussed. Several different descriptions of the structure are given and a stacking vector and stacking angle are used for the first time to represent the weberite structure. The crystallographic relationship between the fluorite and the pyrochlore structures is also discussed. It is also shown that the cation sublattices of pyrochlores can be transformed to the weberite-like lattice. The different stacking of neighboring AB3 and A3B layers lead to the different coordination environments of anions in weberite and pyrochlore. A stability field is developed to predict the formation of pyrochlore and weberite oxides. In §3 ferroelectric and dielectric properties of some weberite compounds are discussed.
The space group of the orthorhombic weberite structure is Imma (No.74) with four formula units per unit cell (Z = 4). However, the correct space group of weberites was a subject of controversy for a long time, as it was described as both Imma and Imm2 (Sych, Kabanova & Andreeva, 1988; Haegele et al., 1978; Giuseppetti & Tadini, 1978; Knop et al., 1982; Byström, 1944). The detailed history of the determination of the space group has been reported by Yakubovich et al. (1993). The two space groups are closely related as Imm2 is a subgroup of Imma. The only evidence ruling out Imma was the observation of very weak (hk0) with h = 2 n + 1 reflections. It was later proven that the existence of (hk0) with h = 2n + 1 reflections from Na2NiFeF7 single crystals and Na2NiAlF7 originated from the Renninger effect (`double reflection' process; Schmidt et al., 1992; Laligant et al., 1989). Thus, there is no doubt that the true space group of the orthorhombic weberite is Imma. The atomic positions and site symmetry are given in Table 1.
In weberites the A ions sit in the 4a and 4d atomic positions with site symmetry 2/m and establish a coordination number of 8 with the anions. The A ions have two different coordination environments. The A1 cations (in atomic position 4d) lie in a highly distorted cube (or square prism) where there are two different A1—X bond lengths. The cubes are edge-shared to form a series of chains in the  direction. The A2 cations (in atomic position 4a) are located within bi-hexagonal pyramids in which anions are spaced at three different distances from the central cations. Each pyramid is corner-shared with two other pyramids and edge-shared with four A1X8 cubes. As presented in Table 1 there are three Wyckoff positions for anions (X1 at 8h, X2 at 16j and X3 at 4e). A1 ions only connect to X1 and X2, while A2 link to all three types of anions (two X1, four X2 and two X3).
The B ions are located in the 4b and 4c Wyckoff positions (site symmetry 2/m) and have a coordination number of 6, i.e. A2VIIIB2VIIX7. The weberite structure can be described as a network of corner-shared BX6 octahedra with the penetration of A cations (see Fig. 1). There are two types of BX6 octahedra: B-1 (B2+ in the case of A2B2+B3+F7, A = Na+ or Ag+) in 4c Wyckoff positions, and B-2 (B3+ in the case of A2B2+B3+F7) in 4b Wyckoff positions. Each of the six vertices of B-1 octahedra connects to another B octahedron, while only four vertices of a B-2 octahedron link to other B octahedra. The two unpaired vertices are in a trans configuration. As will be discussed later, trigonal or monoclinic weberite variants cause a cis configuration (see Fig. 2). The B-1 octahedra are corner-linked to each other and form B-1 octahedral chains parallel to the A1 chains (in the  direction). The B-2 octahedra are isolated from each other and link the B-1 octahedral chains to form a three-dimensional octahedral network.
The arrangements of A and B ions lead to three different cation tetrahedra. Six anions occupy the two A3B (A3BX, X1) and four A2B2 tetrahedral interstices (A2B2X, X2) and none are located inside the two AB3 sites (AB3, where  represents a vacant site) in a formula unit. The remaining anion (X3) maintains four coordination and lies outside the two edge-shared AB3 tetrahedra, very close to the shared B–B edge (see Fig. 3). X3 can also be considered to sit inside the octahedron (A4B2), which shares faces with two adjacent AB3 tetrahedra, and distort towards the B–B edge (Grey et al., 2003).
The weberite structure can also be considered as a stacking of repeated layers or slabs. The most common way to examine the structure is to view it as stacked, alternating close-packed metal layers A3B and AB3 on (011) parallel planes. In A3B layers, four A-1 and two A-2 ions form a hexagonal ring with B-2 occupying the center. In other words the A cations form Kagomé-type networks. [Kagomé in Japanese means a bamboo-basket woven pattern. It is formed by interlaced triangles and each lattice point has four equivalent bonds. `Kagomé' was introduced by Husimi after he and his co-worker Syôzi found a new antiferromagnetic lattice by star-to-triangle transformation from a honeycomb lattice (Mekata, 2003). Syôzi published the first Kagomé paper in 1951 (Syozi, 1951); see Fig. 4.] In AB3 layers the BX6 octahedron arrangement is nearly identical with the basal plane of the hexagonal tungsten bronze (HTB) structures and A-2 cations are in the center of the hexagonal rings. The HTB-like layers can also be simplified by a Kagomé net representation (Fig. 5). The HTB-like layers are displaced with respect to each other by an interlayer stacking vector (SV) which is defined as the projected distance, viewed down the (pseudo-) sixfold axis, between crystallographically similar ions in adjacent layers. White (1984) and Cohelho et al. (1997) used SV as an alternative description for zirconolite, zirkelite, pyrochlore and polymignyte. Here, SV is used to describe weberite. The stacking vectors in the weberite structure are nearly in the ,  and  directions. They are typically of the order 4 Å. The angle between successive stacking vectors (SA) is approximately 120°. The distance between two neighboring HTB-like layers along the (pseudo-) sixfold axis is approximately 5.8 Å. Fig. 6 shows the stacking vectors between three sequences of HTB layers.
There is yet another way to consider the weberite repeated layers. The first layer is formed by the alternating B-1 octahedral chains and A-1 distorted cube (or square prism) chains, which are in the  direction for classic orthorhombic weberites. In this layer the B-1 octahedra are edge-shared with A-1 cubes. The second layer is alternating B-2 octahedra and A-2 bi-hexagonal pyramids in the  direction as in Fig. 7 (Rossell, 1979; Renaudin et al., 1988).
Weberite and pyrochlore (A2B2X7) are both fluorite-related (AX2 or A4X8) superstructures. The coordination number of A and B is the same in both structures. These two structures have a similar cationic sublattice, which is comprised of stacked cubic close-packed cation layers, the same as (111) planes in fluorite. These layers alternate between the compositions A3B and AB3 and are parallel to (111) planes in pyrochlore and (011) planes in weberite. AB3 layers in pyrochlore can also be described as HTB-like layers. The length of SV and the value of SA of the pyrochlore structure are almost the same as weberite. However, the difference between the weberite and the pyrochlore structures is the different stacking of two successive AB3 and A3B layers, which will be discussed later in this section. The crystallographic relationship between the weberite and the pyrochlore structures is further confirmed by the fact that the space group of weberite (Imma) is a subgroup of , the space group of pyrochlore. If the lattice parameter of pyrochlores is 2a with respect to fluorite a (a ≃ 5 Å), then the lattice parameters of the classic orthorhombic weberites are approximately 21/2a, 2a and 21/2a. The rotation of 45° about the b axis of the pyrochlore cation sublattice leads to the weberite-like cation sublattice (Fig. 8). The (111) planes of pyrochlore are transformed to the (011) of the new lattice. The transformation relationship can be written as
The transformation leads to the space group Imcm, which is a different setting of Imma. The Imma lattice can be achieved by the 90° rotation of the coordinate system of Imcm. The transformation matrix is
The resulting lattice parameters in Imma are 2a, 21/2a and 21/2a. In order to match the weberite lattice parameters, the space group Imcm is preferred when presenting the atomic positions of pyrochlore in the weberite-like orthorhombic lattice (Table 2).
It is easy to recognize weberite and distinguish the three structures from powder diffraction. As is well known, in Cu Kα radiation to 2θ ≃ 70°, the five fluorite characteristic peaks are (111), (200), (220), (311) and (222). The (111) reflection is at 2θ ≃ 30° with the highest intensity. In pyrochlore, owing to the doubling of the lattice parameter with respect to fluorite, the five fluorite peaks become (222), (400), (440), (622) and (444). The appearance of several weak reflections, especially the (111) peak at 2θ ≃ 15°, is a major difference between the X-ray diffraction (XRD) patterns of fluorite and pyrochlore. In orthorhombic weberite, the five fluorite peaks are split, for example, the most intense (111)f or (222)p are split into (022)w and (220)w. There are several more reflections in weberite, which are systematic absences in pyrochlore, for example, (101)w and (020)w [corresponding to (200)p]. Details on the XRD reflection for fluorite, pyrochlore and weberite are listed in Table 3. For space reasons, only reflections up to (222)f are presented.
It is important to recall that in fluorites, each anion is at the center of the cationic tetrahedra (A4X). The arrangement of A and B leads to different cation tetrahedra: AB3, A3B and A2B2 in weberites, and A4, B4 and A2B2 in pyrochlores. The reason for the formation of different cation tetrahedra is that weberites and pyrochlores are different in stacking two neighboring AB3 and A3B layers, although generally they follow the pattern of cubic close-packed cation layers. The three nearest-neighbor metal ions in these layers form pseudo-equilateral triangles. The distribution of A and B cations in AB3 layers will lead to two types of triangles: AB2 and B3. The cations in the following A3B layer lie above the centers of these triangles. If an AB3 layer is a reference, there are 21/2a/2 along w or P displacement in the above A3B layer between weberite and pyrochlore. As a result, in the A3B layer, A cations are above the center of AB2 triangles and B cations are above B3 triangles in pyrochlore, while in weberite, 2/3 A (A-1) and all B cations are above the AB2 triangles and the remaining A cations (A-2) are above B3 triangles (see Fig. 9). Therefore, these arrangements lead to two AB3, two A3B and four A2B2 in a formula unit of weberite, and in the case of pyrochlore, one A4, six A2B2 and one B4. In addition, different stacking of two neighboring AB3 and A3B layers can explain why the transformation of the pyrochlore cation sublattice into a weberite-like lattice results in a different setting of the space group.
As stated in §2.1, in a formula unit the X3 anion of weberite is located outside the cation tetrahedra and leaves two AB3 tetrahedra with a vacant center. In contrast, all anions in the pyrochlore structure are inside the cation tetrahedra. Therefore, it can be argued that pyrochlore is more closely related to fluorite than weberite since the former preserves all the anions in cation tetrahedral interstices (Yakubovich et al., 1993; Grey et al., 2003). In weberite it is understandable that the X-deficient site is more favorable in B-rich tetrahedra (AB3 than A2B2 and A3B), because B ions have a smaller coordination number (CN). However, it raises the question: why there are two AB3 tetrahedra with a vacant center and the X3 is not inside the cation tetrahedra? Grey et al. (2003) argued that in Ca2Ta2O7 weberite, the sum of valence () in CaTa3 tetrahedra is so highly over-saturated that CaTa3 cannot accommodate X3. Actually, the highly over-saturated AB3 tetrahedra occur in all weberite compounds: A21+B2+B3+F7, A22+B25+O7 and A21+B26+O7. The nominal sum of valence in the center of AB3 is 1.46 for A21+B2+B3+F7, 2.75 for A22+B25+O7, 3.13 for A21+B26+O7. Thus, anions should distort largely towards A cations to meet the required valence, which would then result in a shorter A—X distance than a B—X distance. However, A ions are larger and have a larger CN than B ions and so the A—X bond length should be larger than the B—X bond length. The end result is that anions cannot move towards A cations and the required valence cannot be achieved. By contrast, the sum of valence in the center of AB3 is under-saturated, being 0.875 for A21+B2+B3+F7, 1.58 for A22+B25+O7 and 1.375 for A21+B26+O7. Anions are required to move towards B cations, which is favored by the bond length argument above. As for A2B2 tetrahedra, the sum of valence is 1.08 for A21+B2+B3+F7, 2.17 for A22+B25+O7 and 2.25 for A21+B26+O7. In this case the sum of valence is close to the anion oxidation state.
where Rij is the bond-valence parameter, rij is the bond distance and b is a constant. Three representative compounds were chosen for detailed analysis: Na1+2Mg2+Al3+F7, Sr2+2Sb5+2O7 and Ag1+2Te6+2O7. There are few, if any, reported bond-length data for Ag2B2F7. Na2MgAlF7 was chosen since it is the aristotype of the weberite compounds. The rij of Na1+2Mg2+Al3+F7 is from Knop et al. (1982) based on single-crystal XRD. Sr2+2Sb5+2O7 was chosen because it is a stable weberite even under high pressure and neutron diffraction data are available (Knop et al., 1980; Groen & Ijdo, 1988). As for A21+B26+O7 compounds, only the crystal structure Ag2Te2O7 has been reported (Klein et al., 2006). Table 4 lists the detailed valence information including all three anion types as well as cations by the empirical equation above using the bond-valence parameters (Brese & O'Keeffe, 1991; Brown, 2002) and the bond lengths (rij) from the literature. The valence of X3 is close to its oxidation state in these compounds. It is worth noting that the discrepancy is small in Ag21+Te26+O7 for all three oxygen anions. Therefore, A21+B26+O7 weberites are possible.
Another significant difference is the formation of BX6 networks. All of the anions in weberites participate in the formation of BX6 octahedra, but only 6/7 of the anions in pyrochlores do. The BX6 octahedral network in both structures is fairly rigid. Therefore, in order to maintain the octahedral network it is difficult for the weberite to form vacancies at anion sites. By contrast, the pyrochlore structure tolerates X deficiency or paired A and X deficiencies relatively easily. Examples of such pyrochlore oxides are Bi1.5Zn0.92Nb1.5O6.92 and Tl2B2O6 (B = Nb, Ta and U), Tl2Os2O7-x and Pb2Os2O7-x (Nino, 2002; Subramanian et al., 1983; Reading et al., 2002). In addition, the substitution of small amounts of oxygen by F− may prevent the formation of weberites. For example, Ca2Sb2O7 pyrochlore transforms into weberite irreversibly above 973 K, but CaNaSb2O6F and Ca1.56Sb2O6.37F0.44 pyrochlores are stable (Aleshin & Roy, 1962; Aia et al., 1963).
The weberite structures show a wide variety of different modifications including monoclinic and trigonal variants. Grey et al. (2003) proposed the use of the nomenclature of the International Mineralogical Association Commission New Minerals and Mineral Names (IMA-CNMMN), which was initially approved for zirconolite CaZrTi2O7 (Bayliss et al., 1989). As discussed above, the basic building unit is a slab formed by one A3B and one AB3 layer. The differences between weberites are the crystal system and the number of slabs (N) in a unit cell. A notation which combines N and the first letter of the crystal system is used to indicate different weberites. For example, the notation of the classic orthorhombic weberite is 2O because it has two slabs in a unit cell. The reported weberites include 2O, 2M, 3T, 4M, 5M, 6M, 6T, 7M and 8O. Tables 5 and 6 list different types of A2B2F7 and A2B2O7 weberites, respectively. (NaCu)Cu2F7 (or NaCu3F7, space group C2/c) and (Ca0.5Ln1.5)(Ca0.5Sb1.5)O7 (or CaLn1.5Sb1.5O7, space group I2/m11, Ln = La, Pr, Nd and Y) are special 2M weberites and more like pseudo-2O weberites for they maintain the structural feature of 2O rather than 2M, as will be discussed later. Ca2Ta2O7-based compounds are important in the weberite family since for N > 4, only Ca2Ta2O7-based compounds have been reported. Grey and co-workers (Grey et al., 1999, 2001, 2003; Grey & Roth, 2000) have shown that Ca2Ta2O7 compounds can crystallize into 3T, 4M, 5M, 6T, 6M and 7M by different doping or synthesis methods and later Ebbinghaus et al. (2005) also synthesized an 8O Ca2Ta2O7 single crystal using the optical floating zone method.
A significant difference between 2O and non-2O weberites is that the AB3 and A3B layers are parallel to the (011) planes for 2O and parallel to the (001) planes for other weberites, except for NaCu3F7 and CaLn1.5Sb1.5O7 (Ln = La, Pr, Nd and Y). The formula unit (Z) of NaCu3F7 and CaLn1.5Sb1.5O7 is also consistent with 2O weberites, four rather than eight, the latter the formula unit for other 2M weberites. As in §2.2 the lattice parameters of 2O weberites are approximately 21/2a, 2a and 21/2a (a ≃ 5 Å, the lattice parameters for fluorite). The lattice parameters of 2M weberites are nearly 61/2a, 21/2a and 61/2a. The ,  and  vectors of 2O become ,  and  of 2M. The lattice parameter difference between 2M, 4M, 5M, 6M and 7M is mainly on the c axis. The lattice parameters for nM (n = 2, 4, 5 and 7) are approximately 61/2a, 21/2a and [n(6)1/2/2]a and they are nearly 21/2a, 61/2a and 3(6)1/2/a for 6M (Grey et al., 1999, 2001, 2003; Grey & Roth, 2000). The 8O weberite is closely related to a monoclinic variant rather than 2O in both the orientation of the AB3 and A3B layers and the lattice parameters. The lattice parameters are nearly 21/2a, 61/2a and 4(6)1/2/a. As for 3T, the , [−0.5,−0.5, 0.5] and  vectors in 2O are transformed into the basal vectors. The resulting lattice parameters are approximately 21/2a, 21/2a and 2(3)1/2a. The relationship of 2O, 2M and 3T weberites is shown in Fig. 10. Meanwhile, the lattice parameters of 6T are approximately 21/2a, 21/2a and 4(3)1/2a, just double the length of the basal vector in the c axis.
For 2O weberites there are two special types in which the body-center symmetry is lost. The first case is when Cu2+ is introduced into Na2B2+B3+F7 at B-1 sites such as Na2CuCrF7 and Na2CuInF7 (Kummer et al., 1988; Ruchaud et al., 1992). The common Jahn–Teller distortion (the CuF6 octahedra are elongated perpendicular to the B-1 chains) in CuF6 octahedra leads to the lowering of symmetry, while maintaining the orthorhombic lattice. The space group is reduced to Pmnb, a subgroup of Imma (Yakubovich et al., 1993). Another case of losing I-centering symmetry happens when the ionic radius of B-2 is larger than that of B-1. In a classic 2O weberite structure the ionic radius of B-2 is equal to or smaller than that of B-1. When a larger B-2 ion appears in a weberite compound, the anions, which are shared by two B-1 octahedral neighbors, distort toward B-2 ions. As a result, the A-2 ions cannot hold eight-coordination and change to seven-coordination. The B-2 ion keeps octahedral coordination with a seventh anion relatively close to it. As in the case of Na2NiInF7, the distance between the distorted anion and B-2 (In3+) is only 1.3 times larger than the shortest In—F bond length in B-2 octahedra (Frenzen et al., 1992). In a 2O weberite structure, the ratio of the two distances is higher, such as 1.97 in Na2MgAlF7 or 1.83 in Ca2Os2O7 (Wyckoff, 1963; Reading et al., 2002). The distortion of the anion excludes the I-centering of the structure and results in the space group Pnmb (Yakubovich et al., 1993). The notation of 2O-II and 2O-III is used for the first and the second condition, respectively.
One extreme case for 2O-III is Ln2(B,Ln)O7 (or Ln3BO7, where Ln3+ is a rare-earth element, and B is Os5+, Re5+, Ru5+, Re5+, Mo5+, Ir5+, Sb5+, Nb5+ or Ta5+). B-2 ions are the same as A ions. As a result, the B-2 sites and A-2 sites are indistinguishable. The structure has an arrangement of BO6–LnO8 layers (much like weberites), but a different cation configuration with VII coordination between the layers (Fig. 11). Due to the fact that this type of structure does not maintain the three-dimensional BO6 octahedral network, it is considered a weberite-type structure rather than the weberite structure, or sometimes it is reported as a La3NbO7-type structure (Rossell, 1979; Allpress & Rossell, 1979; Rooksby & White, 1964; Abe et al., 2004, 2006; Cai & Nino, 2007; Cai et al., 2007; Wakeshima et al., 2004; Groen et al., 1987; Wakeshima & Hinatsu, 2006; Nishimine et al., 2007; Gemmill et al., 2007; Khalifah et al., 1999, 2000; Wiss et al., 2000; Bontchev et al., 2000; Harada & Hinatsu, 2001; Harada et al., 2001; Nishimine et al., 2005; Gemmill et al., 2004, 2005; Vanberkel & Ijdo, 1986; Kahnharari et al., 1995; Wltschek et al., 1996; Greedan et al., 1997; Lam et al., 2002; Plaisier et al., 2002; Lam et al., 2003; Barrier & Gougeon, 2003; Hinatsu et al., 2004; Vente & Ijdo, 1991). Table 7 lists examples of Ln3BO7 and their properties that have been investigated. Details on the dielectric properties of Ln3NbO7 have been reported and will be covered in §3.2.2.
There is a special type of weberite (B+2B+3F5·2H2O) named inverse weberite (please see Table 7 for examples). In this structure A cations are missing. In order to maintain charge neutrality, two H2O molecules take the place of two F− ions. This structure has the same characteristic B octahedral network, just like the 2O weberite structure. The space group and Wyckoff positions of B cations and anions are the same as in the 2O weberite. However, B2+ ions take B-2 sites while B3+ cations lie at B-1 sites in this structure, which is opposite to the classic weberite structure (Laligant, Calage et al., 1986; Laligant, Leblanc et al., 1986; Laligant, Pannetier et al., 1986; Laligant, Pannetier et al., 1987; Weil & Werner, 2001; Leroux et al., 1995; Subramanian et al., 2006).
The investigation of Na2B2+B3+F7 weberites indicates that the resulting structure type is determined by the size of the B2+ cations. With increasing ionic radius of B2+, the structure changes from 2O to 2M, 4M and to 3T, gradually (Yakubovich et al., 1993). As for oxide weberites, it is clear that the A cation still plays an important role, for example, 2O Ca2Sb2O7, 3T Ca1.5Mn0.5Sb2O7 and 3T Mn2Sb2O7 (Ivanov et al., 1998; Bonazzi & Bindi, 2007; Scott, 1990; Butler et al., 1950; Bystrom, 1945). The occurrence of the monoclinic and trigonal variants may be closely related to the ionic radius ratio of the A and B cations. However, due to the limited number of compounds reported in each weberite-like structure, it is difficult to define the factors that determine when the variants occur.
As discussed before, the unpaired vertex (terminal anions) of B-2 octahedra are in trans configurations in 2O weberites. The trigonal and monoclinic variants produce another type of B-2 octahedra with the cis configuration (see Figs. 2b and c). Grey and co-workers (Grey & Roth, 2000; Grey et al., 2003) figured out that the relative position of the terminal anions is a characteristic of weberite polytypes. In 2M and 3T polytypes cis-B2 are only in A3B layers, while trans-B2 are only in AB3 layers (Grey et al., 2003; Yakubovich et al., 1993). The 4M and 6T weberites have alternative cis and trans configurations in successive A3B layers (Grey & Roth, 2000; Grey et al., 2003).
Several research groups (Yakubovich et al., 1993, 1990; Dahlke et al., 1998; Verscharen & Babel, 1978; Welsch & Babel, 1992) proposed that the formation of B-1 chains is a characteristic of Na2B2+B3+F7 weberite polytypes. The detailed description about the different stacking sequence and the orientation of B-1 chains in 2O, 2M, 3T and 4M variants has been reported by Yakubovich et al. (1993). Here, the discussion is expanded to include all 2O, 2M, 3T, 4M, 5M, 6M, 6T, 7M and 8O variants. There are three different orientations for B-1 chains: type α, type β and type γ. These three orientations are correlated with each other by a threefold rotation. For 2O weberites (including 2O-II and 2O-III), the stacking sequence of B-1 chains is ααα… (the orientation is parallel to the  direction). The same applies for pseudo-2O NaCu3F7 and CaLn1.5Sb1.5O7 (Ln = La, Pr, Nd and Y), special cases of 2M (Renaudin et al., 1988; Au et al., 2007). The directions of the B-1 chains for 2M (except NaCu3F7 and CaLn1.5Sb1.5O7) and 4M weberites are either nearly parallel to  (type β) or  (type γ). The stacking array for 2M is βγβγ, while it is ββγγββγγ for the 4M polytype. As for 3T and 6T, the directions of the B-1 chains are nearly parallel to ,  or . The sequence of B-1 chains is αβγ in 3T and ααββγγααβγγ in 6T weberites.
It is important to note that the close-packed cation layers are stacked the same as f.c.c. (face-centered cubic: cubic stacking in which the stacking sequence is ABCABC…) in 2O, 2M, 3T, 4M and 6T polytypes. The cation layers in 5M, 6M, 7M and 8O polytypes (Ca2Ta2O7-based compounds) are a mixture of cubic stacking and hexagonal stacking. The hexagonal stacking layers act as mirror glide planes for the cations, for example, the stacking sequence of 5M is ABCCBAAB in a unit cell (the underline letters indicate a hexagonal stacking; Grey et al., 1999, 2001). Therefore, 5M, 6M, 7M and 8O polytypes are not pure weberite. The weberite blocks are separated by h-stacking layers. A simpler approach is to describe the stacking of c as cubic and h as hexagonal. The stacking sequence is ccchccchcc for 5M [simplified as (3c)h(3c)h(2c), the integers indicating the number of c stacking layers], (5c)h(5c)h for 6M, (5c)h(7c)h for 7M and (4c)h(7c)h(3c) for 8O (Ebbinghaus et al., 2005; Grey et al., 1999, 2001, 2003; Grey & Roth, 2000). There are several structural features resulting from the introduction of h stacking:
Both pyrochlores and weberites have BX6 octahedral networks. Owing to the fact that B-2 octahedra have two unpaired vertices, the BX6 octahedral network in weberite is typically less compact. Therefore, weberite has more potential to permit larger radii of A ions. Fig. 13 shows a diagram of RA versus RB for 159 pyrochlore oxides and 131 weberite compounds (83 weberite fluorides and 48 weberite oxides, see Tables 5 and 6 for a complete list and references). The 159 pyrochlore oxides are taken from two articles (Subramanian et al., 1983; Isupov, 2000). Fig. 13 indicates that the majority of pyrochlores have RA ranging from 0.97 to 1.13 Å, while most weberites have RA values ranging from 1.10 to 1.30 Å. Weberite Ba2U2O7 has the highest RA value of 1.42 Å (Cordfunke & Ijdo, 1988; Shannon, 1976). This clearly shows that larger RA values prefer the formation of the weberite (Brisse et al., 1972). The ratio of RA/RB for the weberite is between 1.5 and 2. The two end-members are Cd2Sb2O7 and Ag2Te2O7. However, the range of RA/RB for weberite greatly overlaps with the stability field for pyrochlore: 1.46–1.8 for A23+B24+O7 and 1.4–2.2 for A22+B25+O7 (Subramanian et al., 1983). Therefore, the ionic radius ratio is not the only determining factor in the structural stability.
Electronegativity (χ) is another important factor in the field of existence, because the formation of weberites is closely related to the covalent character of the bonds (Sych, Kabanova, Garbuz et al., 1988; Lopatin et al., 1985; Weller et al., 2003; Burchard & Rudorff, 1979). Weller et al. (2003) used only χA and χB to picture the stability field of the weberite, but their study only included a limited number of compounds. Lopatin et al. (1982, 1985) successfully utilized χA and RA/RB to distinguish pyrochlores and weberites, and χB and RA/RB to determine the different regions of the weberite and the layered perovskite. They chose Allred–Rochow (Allred & Rochow, 1958) electronegativities (which were completed by Little & Jones, 1960) because Allred–Rochow electronegativities are more precise when measuring the degree of covalent character of the bonds. Sych et al. (Sych, Kabanova, Garbuz et al., 1988) introduced RA/RB versus the relative ionicity of the A—O bond, which is the ratio of the ionicity of the A—O bond to the sum of the ionicity of the A—O and B—O bonds. The ionicity of the A—O bond is calculated as
They used the electronegativities for the crystalline state calculated by Batanov (1975). The advantage of relative ionicity is that it contains the information for both A—O and B—O bonds. Therefore, the relative ionicity of A—O versus RA/RB is used to determine the stability field in this study, as shown in Fig. 14. Here, the electronegativities of Allred–Rochow (Allred & Rochow, 1958) and Little–Jones (Little & Jones, 1960) were used in calculating the ionicity. In Fig. 14(a) there is no obvious separation between weberites and pyrochlores. The reason for this may be that both A22+B25+O7 and A23+B24+O7 pyrochlore compounds are plotted. There are very few, if any, A23+B24+O7 weberites reported. Most weberites are A22+B25+O7 or (A, A′)22+(B, B′)25+O7 and several A21+B26+O7 (Na2Te2O7 and Ag2Te2O7). The inclusion of A23+B24+O7, particularly high-pressure phases, complicates the stability field, therefore, Fig. 14(b) only contains A22+B25+O7, (A, A′)22+(B, B′)25+O7 compounds Na2Te2O7 and Ag2Te2O7 (all weberites points in Fig. 14b are listed in Table 6). Observing the plotted data in Fig. 14(b), there is a clear separation between weberites and pyrochlores. The dashed line is for visual effect – above the line is the weberite region. Weberites prefer a higher ratio of IA—O/(IA—O + IB—O) and a higher ratio of RA/RB than pyrochlores.
It is worth mentioning four specific compounds: Cd2Sb2O7 (RCd 2+ = 0.9 Å) in the pyrochlore region, and Ca2Sb2O7, Ca2Os2O7 (RCa2+ = 1.12 Å) and Pb2Sb2O7 (RPb2+ = 1.29 Å) in the weberite region (Shannon, 1976). A high-pressure study has been performed on the first three compounds to investigate the transformation of the pyrochlore and weberite phases. Cd2Sb2O7 can form a metastable phase of weberite, which can be fully converted to pyrochlore under high pressure. Ca2Sb2O7 weberite is more stable than Cd2Sb2O7 weberite. The same high-pressure condition only results in mixed phases of Ca2Sb2O7 pyrochlore and weberite (Knop et al., 1980). At one atmosphere, Ca2Sb2O7 crystallizes as a pyrochlore below 973 K, above which it transforms to a weberite (Brisse et al., 1972). Meanwhile, Ca2Os2O7 weberite is stable and the synthesis of pyrochlore Ca2Os2O7 under pressure leads to calcium-deficient Ca1.7Os2O7 (Reading et al., 2002; Weller et al., 2003). The reported crystal structure of Pb2Sb2O7 also strongly depends on the synthesis conditions. Low-temperature firing or wet chemical synthesis resulted in a cubic pyrochlore phase. The cubic phase was metastable and readily transformed into weberite or rhombohedrally distorted pyrochlore (Ivanov et al., 1998; Brisse et al., 1972). These four compounds can crystallize as different polymorphs depending on the processing history, as presented in Fig. 14(b). It is worth noting that although the ionic radii ratio and bond ionicity are two major factors, there may be some additional crystallochemical characteristics or parameters that play a role in determining the prevalence of weberite over pyrochlore or vice versa. It would be interesting to perform some computational calculations (e.g. density functional theory) to shed light on the comparative lattice energy and stability field of pyrochlore and weberite.
For fluorine-based weberites, the magnetic properties attract most of the attention. The triangular network formed by B2+ and B3+ cations in the HTB-like planes generally support three different magnetically ordered systems:
As for weberite oxide, various properties have been investigated including the photocatalytic properites (Abe et al., 2004, 2006; Sato et al., 2002; Lin et al., 2006), the resistivity of Ca2Os2O7 weberite (Reading et al., 2002), magnetic properties (Khalifah et al., 1999; Wakeshima et al., 2004; Wakeshima & Hinatsu, 2006), ferroelectric properties (Ivanov et al., 1998; Astafev et al., 1985) and dielectric properties (Cai & Nino, 2007; Cava et al., 1998; Grey et al., 2001). The interest in the properties is first due to the fact that the weberite structure is considered more favorable for the realisation of a ferroelectric state than the pyrochlore structure (Astafev et al., 1985). The Sb-based compounds are the most investigated weberites for ferroelectric properties. Ten years ago, Cava et al. (1998) found that the temperature coefficients of the dielectric constant (TC∊r) of the Ca2Ta2O7–Ca2Nb2O7 system can be close to zero. A series of investigations on Ca2Ta2O7-based weberites have followed (Grey et al., 1999, 2001, 2003; Grey & Roth, 2000; Ebbinghaus et al., 2005). Ln3BO7 (where Ln = rare-earth elements and B is Nb or Ta) are also interesting weberite-type compounds. The crystal structure is related to the ionic radius of Ln3+, which provides a stage for the study of structure-dielectric properties relationships. This section will focus on the ferroelectric properties and dielectric properties of weberite oxides.
A2Sb2O7 (A = Ca2+, Pb2+ and Sr2+) are perhaps the most studied weberites owing to their ferroelectric properties. Second-harmonic generation and heat-capacity measurements indicated a possible ferroelectric phase transition in Pb2Sb2O7. Dielectric constants showed a thermal hysteresis around the Curie temperature (Tc) in Pb2Sb2O7 (Astafev et al., 1985; Milyan & Semrad, 2005). Single-crystal X-ray and powder neutron diffraction were performed in detailed crystallographic studies (Ivanov & Zavodnik, 1990; Astafev et al., 1985). Below Tc, there is a slight distortion from a centrosymmetric structure and ionic displacements cause spontaneous polarization in this structure. The results indicated a non-centrosymmetric (space group I2cm) to centrosymmetric (space group Imam, another setting of Imma) phase transition (Astafev et al., 1985; Ivanov et al., 1998; Ivanov & Zavodnik, 1990). Tc depends on the A cation: 510 K for Pb2Sb2O7,110 K for Ca2Sb2O7 and 90 K for Sr2Sb2O7. The substitution of Ca by Pb in Ca2Sb2O7 causes a shift of Tc towards a higher temperature: 200 K for CaPbSb2O7 weberite. Therefore, the A sublattice seems more likely to be the ferroelectrically active one.
It is worth noting that Pb2Sb2O7 can also form rhombohedrally distorted pyrochlore (Brisse et al., 1972). The pyrochlore phase is paraelectric even at room temperature. Actually, Pb2Sb2O7 weberite has a higher Tc than most Pb-based pyrochlores. These facts may serve as evidence that the weberite structure is more suitable for the appearance of the ferroelectric state (Astafev et al., 1985; Isupov, 2000).
According to Grey and co-workers (Grey et al., 1999) the structure of pure Ca2Ta2O7 is 3T weberite up to 1673 K, where it transforms to the 7M polytype. The structure can be easily modified by doping and different synthesis routines (Grey et al., 1999, 2001, 2003; Grey & Roth, 2000; Ebbinghaus et al., 2005). One of the most interesting dielectric properties of Ca2Ta2O7 is that the temperature coefficient of the dielectric constant (TC∊r) is 0 when mixing with 18 mol% of Ca2Nb2O7, meeting the requirement for the application of microwave dielectrics (Cava et al., 1998). TC∊r ≃ 0 can be easily understood because TC∊r is negative for Ca2Ta2O7 (−444 p.p.m. K−1 at 295 K) and positive for Ca2Nb2O7 (231 p.p.m. K−1 at 295 K). Extensive studies on the structure of the (1-x)Ca2Ta2O7 - xCa2Nb2O7 system have been performed by powder and single-crystal X-ray diffraction, and powder neutron diffraction (Grey et al., 2001). The system forms 7M weberite solid solutions up to x = 0.1 and Ca2Nb2O7-type solid solutions from x = 0.2–1. When x = 0.1, the structure transforms into 5M. The solubility limit is reached when the substitution of Ca2Nb2O7 increases to 15 mol% and Ca2Nb2O7 forms as a second phase. The presence of Ca2Nb2O7 thus results in TC∊r compensation, making it approximately zero.
Another interesting aspect is that most of the (1-x)Ca2Ta2O7 - xCa2Nb2O7 compounds have higher dielectric constants (above 30) than pure Ca2Ta2O7 and Ca2Nb2O7 at 1 MHz (Cava et al., 1998). However, another set of published dielectric constants of 5M Ca2Ta1.8Nb0.2O7 and 7M Ca2Ta1.9Nb0.1O7 are approximately 18 and 20 at 1 MHz, respectively, which are lower than the previous publication (Grey et al., 2001). It is not clear what causes the discrepancy in dielectric constant measurement. It may be due to different firing conditions and measurement methods. Dielectric properties at radio frequency have also been investigated. The dielectric constants of 3T Ca1.6Nd0.4Ta1.6Zr0.4O7, 5M Ca2Ta1.8Nb0.2O7 and 7M Ca2Ta1.9Nb0.1O7 are approximately stable (18–19) from 100 kHz up to 5 GHz and reach a maximum (22, 24.5 and 26.1, respectively) at ∼ 8 GHz. The dielectric constant is comparable for some important microwave dielectrics, such as BaMg1/3Ta2/3O3 (∼ 24; Reaney & Iddles, 2006). However, the problem with these systems is that they have low quality factors (Q ≃ 200) for technical applications (Grey et al., 2001).
It is interesting to see that 8O Ca2Ta2O7, which is synthesized by the optical floating zone melting method from 3T Ca2Ta2O7 powder, has a relatively high dielectric constant (∼ 60) at room temperature (Ebbinghaus et al., 2005). And ∊r increases to 90 at 50 K. The high dielectric constant may result from a net dipole created by the off-center Ta5+ in the TaO6 octahedra of the Ca3Ta layers. The shifting of Ta5+ also produces two short Ta—O bonds and two long Ta—O bonds, leading to the distortion of TaO6 octahedra. The high dielectric constant and the ability to tailor it are interesting for scientific study and possible electronic applications.
In addition, the crystallographic study of Nd2Zr2O7 and Sm2Ti2O7 doping Ca2Ta2O7 has been conducted by Grey et al. (Grey et al., 2003; Grey & Roth, 2000). The resulting phases include 3T, 4M, 5M and 6T weberites. The great structural flexibility of Ca2Ta2O7-based compounds is interesting in a crystallographic study and may have potentials in technical applications.
As stated in §2.3, Ln2(Nb,Ln)O7 (or Ln3NbO7, where Ln is La3+, Pr3+, Nd3+ and Gd3+) is a weberite-type structure. It is an extreme case of 2O-III weberite structure, in which A-2 and B-2 are the same. Our recent study on the dielectric properties of Ln3NbO7 (Ln = La3+, Nd3+ and Gd3+) showed some interesting results (Cai et al., 2007; Cai & Nino, 2007). As shown in Fig. 15, all three compounds exhibited a dielectric relaxation behavior similar to that observed in pyrochlore compounds (Roth et al., 2008; Nino et al., 2001). The permittivity increases sharply with increasing temperature until a maximum is reached. After that, the permittivity decreases slightly with an increase in temperature. The permittivity is between 35 and 60 for La3NbO7 and 34–47 for Gd3NbO7 from 113 to 473 K, and is between 34 and 62 for Nd3NbO7 from 113 to 673 K at 1 MHz. These three compounds have close permittivity at 113 K. The relaxation temperatures are different, 183, 473 and 323 K for La3NbO7, Nd3NbO7 and Gd3NbO7, respectively. The difference in relaxation temperature indicates the possibility of tailoring the temperature at which dielectric relaxation occurs through variations in compositions. As for the origin of different dielectric relaxation temperatures, a possible explanation is provided by comparing the structure. The main difference between the structure is that in Gd3NbO7 the polyhedra are more distorted (Wakeshima et al., 2004; Allpress & Rossell, 1979; Rossell, 1979). In Table 8 polyhedral distortions are quantified in the deviation of bond length and bond angle. The calculation is based on the atomic positions after Rossell (1979). Nd3NbO7 has nearly perfect NbO6 octahedra, while Gd3NbO7 has the most distorted octahedra. The LnO8 cube in Nd3NbO7 is the least distorted while LaO8 and GdO8 cubes have comparable distortion. These distortions are attributed to the `openness' of the structure which causes an easier polarization of the material and results in a lower relaxation temperature (Astafyev et al., 1985). Additional details on the relationship of dielectric relaxation and polyhedral distortions are ongoing and will be a matter for future publications.
Owing to the interesting dielectric loss behavior observed in Gd3NbO7 its characterization includes more frequencies (1, 4, 6, 10, 30, 80, 100, 300, 800 kHz and 1 MHz), as shown in Fig. 15(c). The temperature (Tm), at which the loss peak occurs increases with increasing measuring frequency. To better understand the phenomena, the Arrhenius function is used to model the relaxation behaviour of Gd3NbO7
where v is the measuring frequency, the pre-exponential v0 is the attempt-jump frequency, Ea is the activation energy and kB is Boltzmann's constant. Tm is determined for each measuring frequency by fitting the loss peak to a Gaussian function. The non-symmetric tails of loss peaks are cut off during fitting. The resulting Arrhenius plot is presented in Fig. 15(d). From the linear fit, v0 = 1.51 × 1011 Hz, and the activation energy Ea is 0.45 eV, which is larger than typical values observed in Nb-based pyrochlores, for example 0.32 eV in Ca–Ti–Nb–O pyrochlore and 0.14 eV in Bi–Zn–Nb–O pyrochlore (Roth et al., 2008; Nino, 2002). However, other ionic and dipolar compounds systems have even higher activation energies; for example, 0.53 eV for CaF2-doped NaF and 1.02 eV for (Ba0.8Sr0.2)(Ti1-xZrx)O3 (Johnson et al., 1969; Cheng et al., 2004). Thus, the calculated Ea is acceptable.
The dielectric study of Ln3NbO7 compounds points to the possibility of tailoring the dielectric relaxation and develop further a paradigm for the compositional design of fluorite-related ceramics with optimized dielectric properties.
There are a considerable number of weberite compounds (A2B2X7) that have been studied to date. Here the stability field in terms of the ratio of RA and RB, and the relative bond ionicity has been established. This structure can be interpreted in different ways. As an anion-deficient fluorite structure, it has similar close-packed cationic networks as fluorite and pyrochlore. It is presented here that the cation sublattices of the weberite and the pyrochlore structures are correlated by an axial transformation and that the different stacking inside an AB3 and A3B cation slab leads to a different coordination environment of anions in weberite and pyrochlore. There are various types of weberite-like structures. They can be distinguished by the number of AB3 and A3B slabs and the crystal system. B chains are a characteristic of all weberite structures even for weberite polytypes with N > 4. The stacking sequence and the orientation of B-chains changes with respect to monoclinic and trigonal variants.
So far, investigations have primarily focused on the crystallographic aspects of weberites and some weberite compounds are reported to have interesting properties. It is clear that they are of great scientific interest. However, few studies have concentrated on the properties and possible applications. There is no doubt that weberite compounds possess various useful properties that can be tailored owing to the fact that many metal cations can be introduced into this structure as well as that a large diversity of variants exist in this structure. The realisation of the potential of weberites for electrical applications will grow as more extensive studies are conducted and knowledge of the structures increases.
The authors would like to thank the financial support by the US National Science Foundation for funding CAREER grant (DMR-0449710).
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