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.

1. Introduction

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.

2. Crystal structure

2.1. Classic orthorhombic weberite

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.

Table 1
Weberite structure data (origin at A cations) in space group Imma

			Atomic position
Atoms	Wyckoff position	Site symmetry	x	y	z
A1	4d	2/m	0.25	0.25	0.75
A2	4a	2/m	0	0	0
B1	4c	2/m	0.25	0.25	0.25
B2	4b	2/m	0	0	0.5
X1	8h	m	0	y1	z1
X2	16j	1	x2	y2	z2
X3	4e	mm2	0	0.25	z3
X1 is at the center of A3B, X2 is in the A2B2 tetrahedron and X3 is inside A4B2.

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 [100] 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. A₂^VIIIB₂^VIIX₇. 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 [100] direction). The B-2 octahedra are isolated from each other and link the B-1 octahedral chains to form a three-dimensional octahedral network.

Figure 1 B-octahedral network and A cations (a) in the [1, 0.04, 0.07] direction and (b) in the [0.1, 0, 1] direction; the black lines are the unit cell.

Figure 2 (a) A B-1 octahedron in the center and its connection to another six octahedra; (b) trans configuration of B-2 octahedra; (c) cis configuration of B-2 octahedra.

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).

Figure 3 Anion coordination: (a) X-1 in A3B; (b) X-2 in A2B2; (c) X-3 in A4B2.

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.

Figure 4 (a) Kagomé net presentation of A cations on A3B layers; (b) AX8 polyhedral representation of A3B layers, which are parallel to the (011) plane.

Figure 5 (a) Kagomé net presentation of B cations on AB3 layers; (b) BX6 polyhedral representation of AB3 layers, which are parallel to the (011) plane.

Figure 6 Left: Stacking vectors (black arrows) between three sequences of HTB layers; right: Kagomé nets of three successive HTB layers (purple arrows are stacking vectors). This figure is in color in the online version of this paper.

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 [100] 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 [100] direction as in Fig. 7 (Rossell, 1979; Renaudin et al., 1988).

Figure 7 (a) The layer consisting of A1 and B1 lines; (b) A-2 and B-2 layers, viewed in the [010] direction.

2.2. Relationship to fluorite and pyrochlore

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 2^1/2a, 2a and 2^1/2a. 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, 2^1/2a and 2^1/2a. 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).

Table 2
Pyrochlore (A₂B₂X₆X′) structure data in space group Imcm

			Atomic position
Atoms	Wyckoff position	Site symmetry	x	y	z
A	4b	2/m	0	0.5	0
	4c	2/m	0.25	0.25	0.25
B	4a	2/m	0	0	0
	4d	2/m	0.25	0.75	0.25
X	4e	mm2	0.5	x + 0.25	0.25
	4e	mm2	0	x	0.25
	16j	1	x − 0.125	0.125	x + 0.125
X′	4e	mm2	0.25	0.375	0
The x is the oxygen parameter inside the A2B2 tetrahedral site. The value is between 0.3125 and 0.375.

Figure 8 (a) Cationic network on (111) of fluorite; (b) AB3 layer; (c) A3B layer on (011) of weberite; dashed lines are the unit cell; (d) axial transformation of pyrochlore to weberite [black dashed lines: a fluorite cell; blue lines: double pyrochlore cells; red dotted lines: weberite lattice; green shadow (011)w and (111)p]. This figure is in color in the online version of this paper.

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.

Table 3
XRD reflections for fluorite, pyrochlore and weberite

XRD reflections
hkl (fluorite)	hkl (pyrochlore)		hkl (weberite)	Corresponding pyrochlore plane
	111		011	111
			101	200
			020	020
	220		002	202
			121	220
			200
	311		112	311
			211
			031	131
111	222		022	222
			220
200	400		202	400
			040	040
	331		013	313
			132	331
			231
			103	402
			222	420
			301
			141	240
			123	422
			042	242
			321
			240
	333		033	333
	511		213	511
			312
			051	151
220	440		004	404
			242	440
			400
	531		114	513
			233	531
			152	351
			332
			251
			411
	442		024	424
			143	442
			341
			420
			303	600
			060	060
	620		204	602
			323	620
			402
			161	260
	533		134	533
			053	353
			431
311	622		224	622
			062	262
			422
			260
222	444		044	444
			440

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 2^1/2a/2 along [100]_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.

Figure 9 A3B and AB3 slabs of (a) weberite and (b) pyrochlore. Cations connected by dotted lines are on the AB3 layer and by grey lines are on the A3B layer. The red lines (or dotted line) show cation tetrahedra. This figure is in color in the online version of this paper.

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.

In order to check the stability of the X3, the empirical equation by Brese & O'Keeffe (1991) is used to calculate the valence of the X3

where R_ij is the bond-valence parameter, r_ij 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 r_ij 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 (r_ij) 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.

Table 4
Examples of bond-valence sum for anions and cations by Brese and O'Keeffe

X1 in A3B tetrahedra				X2 in A2B2 tetrahedra				X3 outside the AB3 tetrahedra
Bonds	rij (Å)	vij	vij	Bonds	rij (Å)	vij	vij	Bonds	rij (Å)	vij	vij
Na2MgAlF7
Al—F	1.825	0.469	0.972	Mg—F	1.960	0.360	1.022	Mg—F	1.951	0.368	0.866
Na2—F	2.211	0.236		Al—F	1.793	0.512		Mg—F	1.951	0.368
Na1—F	2.423	0.133		Na2—F	2.549	0.095		Na2—F	2.689	0.065
Na1—F	2.423	0.133		Na1—F	2.749	0.055		Na2—F	2.689	0.065
Na1^1+: vij = 0.779; Na2^1+: vij = 0.981; Mg^2+: vij = 2.17; Al^3+: vij = 2.89

Sr2Sb2O7
Sb2—O	1.922	1.056	2.280	Sb1—O	1.971	0.926	2.151	Sb1—F	2.005	0.843	1.963
Sr2—O	2.363	0.515		Sb2—O	2.202	0.512		Sb1—F	2.005	0.843
Sr1—O	2.502	0.354		Sr1—O	2.833	0.145		Sr2—F	2.850	0.138
Sr1—O	2.502	0.354		Sr2—O	2.599	0.273		Sr2—F	2.850	0.138
Sr1^2+: vij = 1.996; Sr2^2+: vij = 2.40; Sb1^5+:vij = 5.39; Sb2^5+: vij = 5.34

Ag2Te2O7
Te2—O	1.825	1.281	1.864	Ag1—O	2.806	0.067	2.041	Ag2—O	2.806	0.067	1.983
Ag2—O	2.388	0.207		Ag2—O	2.549	0.134		Ag2—O	2.806	0.067
Ag1—O	2.465	0.168		Te1—O	1.997	0.806		Te1—O	1.946	0.925
Ag1—O	2.465	0.168		Te2—O	1.905	1.034		Te1—O	1.946	0.925
Ag1^1+: vij = 0.939; Ag2^1+: vij = 1.084; Te1^6+: vij = 5.785; Te2^6+: vij = 5.983
rij is the bond distance, vij is the bond valence.

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 Bi_1.5Zn_0.92Nb_1.5O_6.92 and Tl₂B₂O₆ (B = Nb, Ta and U), Tl₂Os₂O_7-x and Pb₂Os₂O_7-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 Ca_1.56Sb₂O_6.37F_0.44 pyrochlores are stable (Aleshin & Roy, 1962; Aia et al., 1963).

2.3. Weberite-like structures

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 (Ca_0.5Ln_1.5)(Ca_0.5Sb_1.5)O₇ (or CaLn_1.5Sb_1.5O₇, 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.

Table 5
List of A₂B₂F₇ weberites

		Space		Lattice parameters							Properties
Type		group	Z	a (Å)	b (Å)	c (Å)	β (°)	RA (Å)	RB (Å)	RA/RB	investigated
2O	Na2MgCrF7 (Chassain, 1969)	Imma	4	7.39	7.15	10.20		1.18	0.667	1.768
2O	Na2MgGaF7 (Chassain, 1969)	Imma	4	7.42	7.16	10.16		1.18	0.67	1.761
2O	Na2MgScF7 (Chassain, 1969)	Imma	4	7.55	7.34	10.43		1.18	0.733	1.611
2O	Na2MgVF7 (Chassain, 1969)	Imma	4	7.45	7.24	10.30		1.18	0.68	1.735
2O	Na2NiFeF7 (Cosier et al., 1970; Laligant et al., 1989; Thompson et al., 1992)	Imma	4	7.2338 (3)	10.3050 (3)	7.4529 (3)		1.18	0.62	1.903	Magnetic
2O	Na2NiAlF7 (Tressaud et al., 1974; Heger, 1973)	Imma	4	7.31 (2)	7.07 (2)	10.04 (2)		1.18	0.603	1.959	Magnetic
2O	Na2NiCoF7 (Tressaud et al., 1974; Cosier et al., 1970)	Imma	4	7.40 (2)	7.20 (2)	10.24 (2)		1.18	0.618	1.911	Magnetic
2O	Na2NiCrF7 (Hansler & Rudorff, 1970; Laligant, Ferey et al., 1987)	Imma	4	7.183 (1)	10.224 (1)	7.414 (1)		1.18	0.653	1.808	Magnetic
2O	Na2CoGaF7 (Koch & Hebecker, 1988)	Imma	4	7.3011 (6)	10.5436 (9)	7.3845 (7)		1.18	0.645	1.829
2O	Na2CoInF7 (Koch & Hebecker, 1988)	Imma	4	7.4032 (6)	10.3892 (8)	7.5302 (9)		1.18	0.745	1.5849
2O	Na2CoScF7 (Koch & Hebecker, 1988)	Imma	4	7.431 (1)	10.546 (1)	7.544 (1)		1.18	0.718	1.645
2O	Na2MnTIF7 (Koch & Hebecker, 1988)	Imma	4	7.371 (1)	10.369 (3)	7.603 (1)		1.18	0.67	1.761
2O	Na2NiGaF7 (Koch & Hebecker, 1988; Dahlke et al., 1998)	Imma	4	7.1805 (7)	10.2433 (9)	7.4256 (7)		1.18	0.655	1.802
2O	Na2NiInF7 (Koch & Hebecker, 1988)	Imma	4	7.3632 (5)	10.3490 (7)	7.5274 (6)		1.18	0.745	1.584
2O	Na2NiScF7 (Koch & Hebecker, 1988)	Imma	4	7.3116 (7)	10.3278 (9)	7.4779 (7)		1.18	0.718	1.645
2O	Na2MgTIF7 (Koch & Hebecker, 1988)	Imma	4	7.3756 (8)	10.418 (1)	7.5496 (8)		1.18	0.695	1.698
2O	Na2ZnFeF7 (Koch & Hebecker, 1988)	Imma	4	7.281 (1)	10.446 (2)	7.459 (1)		1.18	0.645	1.829
	Na2ZnGaF7 (Koch & Hebecker, 1988)	Imma	4	7.2494 (7)	10.3283 (8)	7.3582 (6)		1.18	0.68	1.735
2O	Na2ZnInF7 (Koch & Hebecker, 1988)	Imma	4	7.4077 (6)	10.4759 (9)	7.5732 (6)		1.18	0.77	1.532
2O	Na2ZnTIF7 (Koch & Hebecker, 1988)	Imma	4	7.338 (1)	10.300 (2)	7.539 (1)		1.18	0.705	1.674
2O	Na2MgFeF7 (Pankhurst et al., 1991; Chassain, 1969)	Imma	4	7.49	7.25	10.26		1.18	0.635	1.858	Magnetic
2O	Na2MgAlF7 (Byström, 1944; Knop et al., 1982)	Imma	4	7.501 (1)	9.968 (2)	7.285 (1)		1.18	0.618	1.911
2O	Na2ZnAlF7 (Dahlke & Babel, 1994)	Imma	4	7.092 (1)	10.092 (1)	7.337 (1)		1.18	0.6375	1.851
2O	Ag2CuMnF7 (Koch & Hebecker, 1988)	Imma	4	7.5006 (9)	10.5025 (9)	7.6452 (8)		1.28	0.655	1.954
2O	Ag2CoAlF7 (Koch et al., 1982)	Imma	4	7.252	10.16	7.601		1.28	0.603	2.124
2O	Ag2CoGaF7 (Koch et al., 1982)	Imma	4	7.313	10.35	7.678		1.28	0.655	1.954
2O	Ag2CoInF7 (Koch et al., 1982)	Imma	4	7.544	10.72	7.851		1.28	0.745	1.718
2O	Ag2CoScF7 (Koch et al., 1982)	Imma	4	7.497	10.64	7.789		1.28	0.718	1.784
2O	Ag2MnAlF7 (Koch et al., 1982)	Imma	4	7.360	10.32	7.601		1.28	0.593	2.160
2O	Ag2MnGaF7 (Koch et al., 1982)	Imma	4	7.465	10.62	7.787		1.28	0.645	1.986
2O	Ag2MnScF7 (Koch et al., 1982)	Imma	4	7.634	10.78	7.802		1.28	0.708	1.809
2O	Ag2NiGaF7 (Koch et al., 1982)	Imma	4	7.255	10.28	7.650		1.28	0.655	1.954
2O	Ag2NiScF7 (Koch et al., 1982)	Imma	4	7.463	10.54	7.771		1.28	0.718	1.785
2O	Ag2MgAlF7 (Koch et al., 1982)	Imma	4	7.197	10.01	7.571		1.28	0.618	2.073
2O	Ag2MgGaF7 (Koch et al., 1982)	Imma	4	7.257	10.21	7.664		1.28	0.67	1.910
2O	Ag2MgInF7 (Koch et al., 1982)	Imma	4	7.495	10.62	7.832		1.28	0.76	1.684
2O	Ag2MgScF7 (Koch et al., 1982)	Imma	4	7.427	10.52	7.782		1.28	0.733	1.747
2O	Ag2CuAlF7 (Koch et al., 1982)	Imma	4	7.109	10.22	7.684		1.28	0.623	2.056
2O	Ag2CuGaF7 (Koch et al., 1982)	Imma	4	7.200	10.34	7.755		1.28	0.675	1.896
2O	Ag2ZnAlF7 (Koch et al., 1982)	Imma	4	7.237	10.14	7.590		1.28	0.6375	2.008
2O	Ag2ZnGaF7 (Koch et al., 1982)	Imma	4	7.303	10.32	7.688		1.28	0.68	1.882
2O	Ag2ZnInF7 (Koch et al., 1982)	Imma	4	7.531	10.71	7.841		1.28	0.77	1.662
2O	Ag2CoCrF7 (Koch & Hebecker, 1988)	Imma	4	7.349 (1)	10.376 (1)	7.683 (1)		1.28	0.653	1.962
2O	Ag2CoFeF7 (Koch & Hebecker, 1988)	Imma	4	7.3711 (8)	10.437 (1)	7.7145 (8)		1.28	0.62	2.065
2O	Ag2MnFeF7 (Koch & Hebecker, 1988)	Imma	4	7.490 (1)	10.612 (2)	7.731(1)		1.28	0.61	2.098
2O	Ag2MnInF7 (Koch & Hebecker, 1988)	Imma	4	7.6747 (8)	10.856 (1)	7.8641 (7)		1.28	0.735	1.742
2O	Ag2MgCrF7 (Koch & Hebecker, 1988)	Imma	4	7.2746 (6)	10.3128 (9)	7.7060 (7)		1.28	0.668	1.918
2O	Ag2MgFeF7 (Koch & Hebecker, 1988)	Imma	4	7.3100 (7)	10.335 (1)	7.6972 (9)		1.28	0.635	2.016
2O	Ag2MgTIF7 (Koch & Hebecker, 1988)	Imma	4	7.2506 (9)	10.362 (2)	7.497 (1)		1.28	0.695	1.842
2O	Ag2CuCrF7 (Koch & Hebecker, 1988)	Imma	4	7.2103 (6)	10.454 (1)	7.7871 (8)		1.28	0.673	1.903
2O	Ag2CuFeF7 (Koch & Hebecker, 1988)	Imma	4	7.2435 (9)	10.474 (2)	7.769 (1)		1.28	0.64	2
2O	Ag2CuInF7 (Koch & Hebecker, 1988)	Imma	4	7.3461 (6)	10.7501 (9)	7.9098 (6)		1.28	0.765	1.673
2O	Ag2ZnCrF7 (Koch & Hebecker, 1988)	Imma	4	7.3165 (7)	10.362 (1)	7.6877 (8)		1.28	0.678	1.889
2O	Ag2ZnFeF7 (Koch & Hebecker, 1988)	Imma	4	7.359 (1)	10.409 (2)	7.706 (1)		1.28	0.645	1.985
2O	Ag2ZnMnF7 (Koch & Hebecker, 1988)	Imma	4	7.408 (1)	10.503 (1)	7.6972 (9)		1.28	0.66	1.939
2O	Ag2NiAlF7 (Dance et al., 1974)	Imma	4	7.564 (6)	7.210 (6)	10.139 (15)		1.28	0.603	2.124	Magnetic
2O	Ag2NiCrF7 (Dance et al., 1974)	Imma	4	7.673 (6)	7.305 (6)	10.285 (9)		1.28	0.653	1.962	Magnetic
2O	Ag2NiFeF7 (Dance et al., 1974)	Imma	4	7.692 (6)	7.345 (6)	10.345 (9)		1.28	0.62	2.065	Magnetic
2O	Ag2NiInF7 (Dance et al., 1974)	Imma	4	7.822 (6)	7.499 (6)	10.622 (9)		1.28	0.745	1.718	Magnetic
2O-II	Na2CuInF7 (Ruchaud et al., 1992)	Pmnb	4	7.318	10.602	7.712		1.18	0.765	1.542	Magnetic
2O-II	Na2CuCrF7 (Kummer et al., 1988; Koch & Hebecker, 1985)	Pmnb	4	7.100 (1)	10.338 (1)	7.518 (1)		1.18	0.673	1.755
2O-II	Na2CuScF7 (Dahlke & Babel, 1994)	Pmnb	4	7.260 (1)	10.534 (1)	7.658 (1)		1.18	0.7375	1.6
2O-III	Na2NiInF7 (Frenzen et al., 1992)	Pmnb	4	7.356	10.334	7.523		1.18	0.745	1.584	Magnetic
2O-III	Na2MgInF7 (Caramanian et al., 2001)	Pnma	4	10.435 (1)	7.345 (1)	7.533 (1)		1.18	0.76	1.553	Magnetic
2M	Na2CuGaF7 (Ruchaud et al., 1992)	C2/c	8	12.325 (5)	7.318 (1)	12.780 (5)	109.29 (2)	1.18	0.675	1.748	Magnetic
2M and 4M	Na2CuFeF7 (Welsch & Babel, 1992; Yakubovich et al., 1990; Kummer et al., 1988)	C2/c	8	12.46 (1)	7.363 (8)	12.93 (1)	109.36 (7)	1.18	0.64	1.844
		C2/c	16	12.444 (2)	7.343 (1)	24.672 (5)	99.27 (3)
3T	Na2MnAlF7 (Koch & Hebecker, 1988)		6	7.2854 (4)		17.844 (1)		1.18	0.593	1.992
3T	Na2MnInF7 (Koch & Hebecker, 1988)		6	7.6006 (3)		18.617 (1)		1.18	0.735	1.605
3T	Na2MnScF7 (Koch & Hebecker, 1988)		6	7.5442 (4)		18.479 (1)		1.18	0.708	1.668
3T	Na2MnGaF7 (Courbion et al., 1988)	P3121	6	7.421 (3)		18.166 (6)		1.18	0.645	1.829
3T	Na2MnCrF7 (Courbion et al., 1988)	P3121	6	7.401 (1)		18.091 (2)		1.18	0.6425	1.837
3T	Na2MnVF7 (Peschel & Babel, 1997)	P3121	6	7.467		18.216		1.18	0.655	1.802
3T	Na2MnFeF7 (Verscharen & Babel, 1978; Cosier et al., 1970; Boireau et al., 1993)	P3121	6	7.488 (2)		18.257 (6)		1.18	0.61	1.934	Magnetic
3T	Ag2MnInF7 (Koch & Hebecker, 1988)		6	7.751 (1)		18.838 (4)		1.28	0.735	1.741
4M	Na2CoAlF7 (Boireau et al., 1993; Gravereau et al., 1992)	C2/c	16	12.378 (4)	7.210 (3)	24.019 (9)	99.67 (2)	1.18	0.613	1.927	Magnetic
4M	Na2ZnGaF7 (Dahlke et al., 1998)	C2/c	16	12.519	7.303	24.353	99.74	1.18	0.68	1.735
4M	Na2ZnFeF7 (Dahlke et al., 1998)	C2/c	16	12.610	7.359	24.538	99.70	1.18	0.645	1.829
4M	Na2FeVF7 (Peschel et al., 1995)	C2/c	16	12.710 (3)	7.429 (1)	24.716 (5)	100.03 (3)	1.18	0.625	1.888
4M	Na2CoVF7 (Peschel et al., 1995)	C2/c	16	12.703 (5)	7.391 (3)	24.651 (5)	100.02 (3)	1.18	0.645	1.829
4M	Na2FeCrF7 (Peschel et al., 1995)	C2/c	16	12.625 (3)	7.391 (1)	24.695 (5)	99.93 (3)	1.18	0.6125	1.927
4M	Na2Fe2F7(Yakubovich et al., 1993; Cosier et al., 1970; Tressaud et al., 1974)	C2/c	16	12.676 (3)	7.422 (1)	24.710 (5)	99.97 (3)	1.18	0.58	2.034	Magnetic
4M	Na2CoFeF7 (Welsch & Babel, 1992; Cosier et al., 1970; Tressaud et al., 1974; Boireau et al., 1993)	C2/c	16	12.622 (10)	7.360 (4)	24.516 (20)	99.71 (5)	1.18	0.62	1.903	Magnetic
4M	Na2CoCrF7 (Boireau et al., 1993; Peschel et al., 1995)	C2/c	16	12.578 (3)	7.335 (1)	24.415 (5)	99.64 (3)	1.18	0.653	1.808	Magnetic
4M	Na2FeAlF7 (Dahlke et al., 1998; Tressaud et al., 1974)	C2/c	16	12.426	7.278	24.206	99.99	1.18	0.563	2.098	Magnetic

Table 6
List of weberite oxides with R_A/R_B and the relative ionicity of the A—O bond

		Lattice parameters								Properties
Type		a (Å)	b (Å)	c (Å)	β (°)	RA (Å)	RB (Å)	RA/RB	IA/(IB + IA)	investigated
2O	Ca2Sb2O7 (Bystrom, 1945; Ivanov et al., 1998; Sato et al., 2002; Lin et al., 2006)	7.28	7.44	10.18		1.12	0.6	1.86667	0.60636	Ferroelectric and photocatalytic
		7.3060	7.4627	10.2263
		7.2900	10.2000	7.4500
2O	Cd2Sb2O7 (Brisse et al., 1972; Bystrom, 1945)	7.21	7.33	10.14		0.9	0.6	1.5	0.56093
2O	Sr2Sb2O7 (Knop et al., 1980; Groen & Ijdo, 1988; Lin et al., 2006; Sato et al., 2002)	7.452	7.687	10.381		1.26	0.6	2.1	0.61038	Ferroelectric and photocatalytic
		7.4557 (2)	10.3708 (3)	7.6860 (1)
		7.4557	10.3708	7.6860
2O	Pb2Sb2O7 (Ivanov & Zavodnik, 1990; Ivanov et al., 1998)	7.484 (1)	7.857 (1)	10.426 (2)		1.29	0.6	2.15	0.54792	Ferroelectric
		7.4774	7.8549	10.4250
2O	Ca2Os2O7 (Reading et al., 2002; Weller et al., 2003)	7.2104 (2)	10.1211 (3)	7.3813 (2)		1.12	0.575	1.94783	0.55518	Electronic
2O	Sr2Bi2O7 (Knop et al., 1980)	7.70	7.91	10.58		1.26	0.76	1.65789	0.58305
2O	Ba2U2O7 (Cordfunke & Ijdo, 1988)	8.1665 (15)	11.3081 (21)	8.1943 (16)		1.42	0.76	1.86842	0.5232
2O	Na2Te2O7 (Knop & Demazeau, 1981)	7.233 (5)	10.104 (7)	7.454 (5)		1.18	0.56	2.10714	0.64905
2O	Ag2Te2O7 (Klein et al., 2006)	7.266 (2)	10.1430 (9)	7.6021 (17)		1.28	0.56	2.28571	0.60811
2O	CaPbSb2O7 (Ivanov et al., 1998)	7.3577	7.5362	10.3521		1.205	0.6	2.00833	0.59219	Ferroelectric
2O	DyNaSb2O7 (Desgardin et al., 1977)	7.26 (6)	7.41 (5)	10.20 (6)		1.1035	0.6	1.83917	0.6051
2O	GdNaSb2O7 (Desgardin et al., 1977)	7.29 (1)	7.47 (0)	10.20 (7)		1.1165	0.6	1.86083	0.60468
2O	EuNaSb2O7 (Desgardin et al., 1977)	7.30 (0)	7.47 (2)	10.21 (4)		1.123	0.6	1.87167	0.6088
2O	SmNaSb2O7 (Desgardin et al., 1977)	7.30 (8)	7.45 (7)	10.22 (7)		1.1295	0.6	1.8825	0.60636
2O	NdNaSb2O7 (Desgardin et al., 1977)	7.32 (7)	7.49 (2)	10.24 (2)		1.1445	0.6	1.9075	0.60636
2O	PrNaSb2O7 (Desgardin et al., 1977)	7.33 (7)	7.50 (6)	10.25 (5)		1.153	0.6	1.92167	0.58322
2O	LaNaSb2O7 (Desgardin et al., 1977)	7.37 (8)	7.50 (1)	10.28 (8)		1.17	0.6	1.95	0.60594
2O	KLuSb2O7 (Klein et al., 2006; Sych, Kabanova & Andreeva, 1988; Sych, Kabanova, Garbuz & Kovalenko, 1988)	7.23	10.23	7.39		1.2435	0.6	2.0725	0.60759
2O	KYbSb2O7 (Klein et al., 2006; Sych, Kabanova & Andreeva, 1988; Sych, Kabanova, Garbuz & Kovalenko, 1988)	7.24	10.25	7.40		1.2475	0.6	2.07917	0.61077
2O	KErSb2O7 (Klein et al., 2006; Sych, Kabanova & Andreeva, 1988; Sych, Kabanova, Garbuz & Kovalenko, 1988)	7.26	10.25	7.41		1.257	0.6	2.095	0.6088
2O	KHoSb2O7 (Klein et al., 2006; Sych, Kabanova & Andreeva, 1988; Sych, Kabanova, Garbuz & Kovalenko, 1988)	7.26	10.25	7.42		1.2625	0.6	2.10417	0.6092
2O	KYSb2O7 (Klein et al., 2006; Sych, Kabanova & Andreeva, 1988; Sych, Kabanova, Garbuz & Kovalenko, 1988)	7.26	10.25	7.43		1.2645	0.6	2.1075	0.6088
2O	KYTa2O7 (Gade & Chincholkar, 1979)	7.78	10.82	7.50		1.2645	0.64	1.97578	0.5324
2O	KDyTa2O7 (Gade & Chincholkar, 1979)	7.80	10.88	7.70		1.2685	0.64	1.98203	0.53282
2O	KGdTa2O7 (Gade & Chincholkar, 1979)	7.84	10.86	7.72		1.2815	0.64	2.00234	0.5324
2O	KSmTa2O7 (Gade & Chincholkar, 1979)	7.86	10.82	7.76		1.2945	0.64	2.02266	0.53405
2O	NaDyV2O7 (Gade & Chincholkar, 1979)	7.53	10.94	7.44		1.1035	0.54	2.04352	0.53496
2O	NaGdV2O7 (Gade & Chincholkar, 1979)	7.56	10.88	7.46		1.1165	0.54	2.06759	0.54352
2O	NaSmV2O7 (Gade & Chincholkar, 1979)	7.58	10.86	7.48		1.1295	0.54	2.09167	0.54526
2O	NaNdV2O7 (Gade & Chincholkar, 1979)	7.62	10.82	7.50		1.1445	0.54	2.11944	0.54526
2O	NaSrSbTeO7 (Burchard & Rudorff, 1979)	Not reported				1.22	0.58	2.10345	0.62891
2O	NaCdSbTeO7 (Burchard & Rudorff, 1979)	Not reported				1.04	0.58	1.7931	0.60778
2O	NdCaSbTeO7 (Burchard & Rudorff, 1979)	Not reported				1.15	0.58	1.9828	0.62694
2O	Na0.5Cd1.5(Fe0.5Te1.5)O7 (Burchard & Rudorff, 1979)	7.131	7.317	10.183		1.12	0.5575	2.00897	0.59584
2O	Na0.5Ca1.5(Fe0.5Te1.5)O7 (Burchard & Rudorff, 1979)	Not reported				1.135	0.5575	2.0358744	0.626874
2O	Ba0.5Ca1.5(Fe0.5Te1.5)O7 (Burchard & Rudorff, 1979)	7.176	7.464	10.140		1.195	0.5725	2.08734	0.627674
2M	CaLa1.5Sb1.5O7 (Au et al., 2007)	7.5753 (3)	10.6870 (5)	7.5482 (3)	90.346 (3)	1.15	0.7	1.6428571	0.57329
2M	CaPr1.5Sb1.5O7 (Au et al., 2007)	7.5188 (3)	10.6111 (4)	7.4952 (2)	90.315 (2)	1.1245	0.7	1.6064286	0.569502
2M	CaNd1.5Sb1.5O7 (Au et al., 2007)	7.5019 (2)	10.5890 (3)	7.4770 (2)	90.298 (2)	1.11175	0.7	1.5882143	0.569502
2M	CaY1.5Sb1.5O7 (Au et al., 2007)	7.3905 (1)	10.4563 (2)	7.3894 (1)	90.049 (1)	1.04425	0.7	1.4917857	0.55821
3T	Ca1.5Mn0.5Sb2O7 (Bonazzi & Bindi, 2007)	7.282 (2)		17.604 (4)		1.04	0.6	1.73333	0.59369
3T	Mn2Sb2O7 (Scott, 1990)	7.191		17.402		0.96	0.6	1.6	0.540094
3T	Ca1.92Ta1.92Nd0.08Zr0.08O7 (Grey et al., 2003)	7.356 (1)		18.116 (1)		1.11956	0.61728	1.8136988	0.529853
3T	Ca2Ta2O7 (Cava et al., 1998; Grey et al., 1999)	7.355 (1)		18.09 (1)		1.12	0.64	1.75	0.52985	Dielectric
4M	Ca1.92Ta1.92Nd0.08Zr0.08O7 (Grey et al., 2003)	12.761 (1)	7.358 (1)	24.565 (1)	100.17	1.12	0.64	1.75	0.52922
5M	Ca1.8Ta1.8Sm0.24Ti0.17O7 (Grey & Roth, 2000)	12.763 (1)	7.130 (1)	30.190 (1)	94.09 (1)	1.13635	0.62743	1.81113	0.52523
5M	Ca2Ta1.8Nb0.2O7 (Grey et al., 2001)	12.749 (1)	7.347 (1)	30.23 (1)	94.23 (1)	1.12	0.64	1.75	0.52866	Dielectric
6M	Ca2Ta2O7 (Grey et al., 1999)	7.348 (3)	12.727 (3)	36.44 (5)	95.9 (1)	1.12	0.64	1.75	0.52985
6T	Ca1.89Ta1.86Sm0.16Ti0.1O7 (Grey & Roth, 2000)	7.353 (1)		36.264 (1)		1.1792	0.63505	1.85686	0.52649
7M	Ca2Ta1.9Nb0.1O7 (Grey et al., 2001)	12.714 (1)	7.370 (1)	42.45 (1)	95.75 (1)	1.12	0.64	1.75	0.52925	Dielectric
8O	Ca2Ta2O7 (Ebbinghaus et al., 2005)	7.3690 (2)	12.7296 (3)	48.263 (1)		1.12	0.64	1.75	0.52985	Dielectric and optical
R is the ionic radius from Shannon (1976), χ is the electronegativity from Allred & Rochow (1958), I is the bond ionicity.

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 CaLn_1.5Sb_1.5O₇ (Ln = La, Pr, Nd and Y). The formula unit (Z) of NaCu₃F₇ and CaLn_1.5Sb_1.5O₇ 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 2^1/2a, 2a and 2^1/2a (a ≃ 5 Å, the lattice parameters for fluorite). The lattice parameters of 2M weberites are nearly 6^1/2a, 2^1/2a and 6^1/2a. The [], [100] and [011] vectors of 2O become [100], [010] and [001] 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 6^1/2a, 2^1/2a and [n(6)^1/2/2]a and they are nearly 2^1/2a, 6^1/2a 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 2^1/2a, 6^1/2a and 4(6)^1/2/a. As for 3T, the [100], [−0.5,−0.5, 0.5] and [012] vectors in 2O are transformed into the basal vectors. The resulting lattice parameters are approximately 2^1/2a, 2^1/2a 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 2^1/2a, 2^1/2a and 4(3)^1/2a, just double the length of the basal vector in the c axis.

Figure 10 (a) Relationship between 2O, 2M and 3T weberites (origin at the A2 site); large spheres: A ions; small spheres: B ions; blue solid lines: multiple unit cells of 2O; red dotted lines: the unit cell of 2M; green dashed lines: the unit cell of 3T. (b) (001) plane of 3T (green dashed lines) and 2M [red dotted lines, also indicating (011) of 2O].

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.

Table 7
Examples of weberite-type Ln₃BO₇ and inverse weberites

		Space		Lattice parameters			Properties
Type	Compounds	group	Z	a (Å)	b (Å)	c (Å)	investigated
Weberite type	La3NbO7 (Abe et al., 2004, 2006; Allpress & Rossell, 1979)	Cmcm	4	11.167 (1)	7.629 (1)	7.753 (1)	Dielectric and photocatalytic
Weberite type	La3TaO7 (Allpress & Rossell, 1979; Abe et al., 2004, 2006)	Cmcm	4	11.1863 (4)	7.6152 (3)	7.7556 (3)	Catalytic and magnetic
Weberite type	Pr3NbO7 (Vente et al., 1994)	Cmcm	4	10.959 (1)	7.5240 (7)	7.6676 (7)	Magnetic
Weberite type	Pr3TaO7(Vente et al., 1994)	Cmcm	4	10.973 (1)	7.5230 (7)	7.6721 (7)	Magnetic
Weberite type	Nd3NbO7 (Cai et al., 2007; Allpress & Rossell, 1979)	Cmcm	4	10.905 (2)	7.517 (2)	7.624 (1)	Dielectric
Weberite type	Gd3NbO7 (Cai et al., 2007; Allpress & Rossell, 1979; Astafyev et al., 1985)	C2221	4	10.610 (1)	7.521 (1)	7.550 (1)	Dielectric
Weberite type	Gd3TaO7 (Wakeshima et al., 2004)	C2211	4	10.6259 (4)	7.5234 (3)	7.5446 (3)	Magnetic
Weberite type	Dy3TaO7 (Wakeshima et al., 2004)	C2221	4	10.5332 (3)	7.4447 (2)	7.4816 (2)	Magnetic
Weberite type	Ho3TaO7 (Wakeshima et al., 2004)	C2221	4	10.4873 (4)	7.4292 (3)	7.4499 (3)	Magnetic
Inverse	Fe2F5(H2O)2 (Laligant, Pannetier et al., 1986; Greneche et al., 1988; Hall et al., 1977)	Imma	4	7.447 (1)	10.8623 (2)	6.652 (1)	Magnetic
Inverse	ZnFeF5(H2O)2 (Laligant, Calage et al., 1986)	Imma	4	7.475 (1)	10.766 (1)	6.594 (1)	Magnetic
Inverse	MnFeF5(H2O)2 (Laligant, Calage et al., 1986; Laligant, Pannetier et al., 1987; Greneche et al., 1988)	Imma	4	7.5635 (2)	10.901 (1)	6.7319 (3)	Magnetic
Inverse	MnAlF5(H2O)2 (Subramanian et al., 2006)	Imma	4	7.229 (2)	10.487 (4)	6.816 (2)
Inverse	MgAlF5(H2O)2 (Subramanian et al., 2006; Weil & Werner, 2001)	Imma	4	7.057 (2)	10.125 (4)	6.798 (2)	Electrical resistivity
Inverse	MnVF5(H2O)2 (Subramanian et al., 2006; Leroux et al., 1995)	Imma	4	7.607 (2)	10.912 (4)	6.728 (2)	Magnetic

Figure 11 Weberite-type Ln3BO7, viewed in the [0.05, 0.05, 1] direction. The layers of LnO8 and BO6 lines are parallel to the (001) plane. Between the layers are Ln with a coordination number of 7.

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 Ca_1.5Mn_0.5Sb₂O₇ 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 [100] direction). The same applies for pseudo-2O NaCu₃F7 and CaLn_1.5Sb_1.5O₇ (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 CaLn_1.5Sb_1.5O₇) and 4M weberites are either nearly parallel to [110] (type β) or [10] (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 [010], [100] or [110]. 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:

• (i) h stacking only occurs in the CaTa₃ cation layers;

• (ii) h stacking causes the appearance of B-3 octahedra on the CaTa₃ cation layers and the neighboring Ca₃Ta cation layers, which have only one unpaired vertex (B-1 octahedra have no unpaired vertex and B-2 have two);

• (iii) in h stacking layers B-3 chains are formed, but no B-1 chains.

In these cases type α is nearly parallel to [100] for 8O or [010] for 5M and 7M. Type β is nearly parallel to [110] and type γ is nearly parallel to []. The directions of the B chains are βαγ for 5M, βγγβ for 6M, γγαββ for 7M and αβγαβγ for 8O (B-3 chains are underlined). In summary, the stacking sequence of B chains changes with different weberite variants (see Fig. 12) and the formation of B chains is a characteristic of all weberites.

Figure 12 B chains in different weberite-like structures. The vectors across the octahedra indicate the orientations of the B chains. (a) 2O, (b) 2M, (c) 3T, (d) 4M, (e) 5M, (f) 6T, (g) 6M, (h) 7M and (i) 8O.

2.4. Stability field

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 R_A versus R_B 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 R_A ranging from 0.97 to 1.13 Å, while most weberites have R_A values ranging from 1.10 to 1.30 Å. Weberite Ba₂U₂O₇ has the highest R_A value of 1.42 Å (Cordfunke & Ijdo, 1988; Shannon, 1976). This clearly shows that larger R_A values prefer the formation of the weberite (Brisse et al., 1972). The ratio of R_A/R_B for the weberite is between 1.5 and 2. The two end-members are Cd₂Sb₂O₇ and Ag₂Te₂O₇. However, the range of R_A/R_B 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.

Figure 13 Summary of RA versus RB for weberites (including oxide and fluorine) and pyrochlore oxides.

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 χ_A and χ_B 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 χ_A and R_A/R_B to distinguish pyrochlores and weberites, and χ_B and R_A/R_B 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 R_A/R_B 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 R_A/R_B 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 I_A—O/(I_A—O + I_B—O) and a higher ratio of R_A/R_B than pyrochlores.

Figure 14 Stability field for weberite.

It is worth mentioning four specific compounds: Cd₂Sb₂O₇ (R_{Cd ²⁺} = 0.9 Å) in the pyrochlore region, and Ca₂Sb₂O₇, Ca₂Os₂O7 (R_Ca²⁺ = 1.12 Å) and Pb₂Sb₂O₇ (R_Pb²⁺ = 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 Ca_1.7Os₂O₇ (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.

3. Interesting properties and potential applications

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:

• (i) the diamagnetic B³⁺ ions separate linear chains of paramagnetic B²⁺ ions, for example, antiferromagnetic Na₂NiAlF₇, Na₂FeAlF₇ and Na₂NiInF₇ (Frenzen et al., 1992; Heger, 1973);

• (ii) both B²⁺ and B³⁺ are paramagnetic ions, like ferromagnetic Na₂NiFeF₇ and antiferromagnetic Na₂NiCrF₇ (Laligant et al., 1989; Thompson et al., 1992; Heger, 1973; Frenzen et al., 1992);

• (iii) diamagnetic B²⁺ forming linear chains which isolate the paramagnetic B³⁺ such as antiferromagnetic Na₂MgFeF₇ (Pankhurst et al., 1991).

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.

3.1. Ferroelectric properties

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 (T_c) 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 T_c, 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). T_c 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 T_c 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 T_c 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).

3.2. Dielectric properties

3.2.1. Ca₂Ta₂O₇-based compounds

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)Ca₂Ta₂O_{7 - x}Ca₂Nb₂O₇ 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)Ca₂Ta₂O_{7 - x}Ca₂Nb₂O₇ 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 Ca₂Ta_1.8Nb_0.2O₇ and 7M Ca₂Ta_1.9Nb_0.1O₇ 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 Ca_1.6Nd_0.4Ta_1.6Zr_0.4O₇, 5M Ca₂Ta_1.8Nb_0.2O₇ and 7M Ca₂Ta_1.9Nb_0.1O₇ 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 BaMg_1/3Ta_2/3O₃ (∼ 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.

3.2.2. Weberite-type Ln₃NbO₇

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.

Table 8
Structural comparison of three weberite-type structures (Allpress & Rossell, 1979; Rossell, 1979)

	La3NbO7	Nd3NbO7	Gd3NbO7
ΔdLn—O/(dLn—O)av in LnO8 cube (%)	13.33	7.14	13.06
Deviation of O—Ln—O angle from perfect cube (°)	−9.87–6.46	−2.37–2.47	−5.77–8.88
ΔdNb—O/(dNb—O)av in NbO6 octahedra (%)	1.64	0.41	4.86
Deviation of O—Nb—O angle from perfect octahedra	−1.58–1.58	0.27–0.42	−5.63–5.63
dLn—O and dNb—O represents the bond length between Ln^3+ and O^2− and the bond length between Nb^5+ and O^2−, respectively. ΔdLn—O means the difference of longest and shortest bond length between Ln^3+ and O^2− in LnO8 distorted cubes. ΔdNb—O is the difference of the longest and shortest bond length between Nb^5+ and O^2− in NbO6 distorted octahedra. (dLn—O)av is the average bond length between Ln^3+ and O^2− in LnO8 distorted cubes. (dNb—O)av is the average bond length between Nb^5+ and O^2− in NbO6 distorted octahedra.

Figure 15 Dielectric properties between 1 kHz and 1 MHz of (a) La3NbO7, (b) Nd3NbO7, (c) Gd3NbO7 and (d) Arrhenius analysis of Gd3NbO7.

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 (T_m), 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, E_a is the activation energy and k_B is Boltzmann's constant. T_m 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 E_a 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 (Ba_0.8Sr_0.2)(Ti_1-xZr_x)O₃ (Johnson et al., 1969; Cheng et al., 2004). Thus, the calculated E_a 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.

4. Conclusions

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 R_A and R_B, 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.