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In the crystal structure of the cation-deficient garnet Pb2.63Cd2V3O12 (lead cadmium vanadium oxide), the Cd and V atoms fully occupy octa­hedral and tetra­hedral sites, respectively, whereas the Pb atoms partially occupy a dodeca­hedral site. The total Pb and Cd content indicates that vanadium is slightly reduced from the +5 oxidation state.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S0108270107021233/bc3044sup1.cif
Contains datablocks I, global

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S0108270107021233/bc3044Isup2.hkl
Contains datablock I

Comment top

Compounds with the garnet-type structure usually crystallize with cubic symmetry (space group Ia3d, a = 12.5–13.5 Å). The structural formula A3B2X3O12 corresponds to three different cation positions; the A (24c) position is surrounded by eight O atoms forming a dodecahedron, the B (16a) position is octahedrally coordinated, and the X (24d) position is tetrahedrally coordinated. O atoms occupy a single (96h) general position. In garnet-type vanadates, the V5+ cations occupy the X position. The interest in these compounds originates from the investigation of garnet-type ferrites since the substitution of V5+ for Fe3+ strongly influences the magnetic properties of these materials (Geller et al., 1964).

A great number of garnet-type vanadates have been reported, viz. NaCa2M2V3O12 (Durif, 1960) and Ca3MLiV3O12 (Bayer, 1965) where M = Mg, Co, Ni, Cu and Zn, Na3Cr2V3O12 (Schwarz & Schmidt, 1967) and Mn3LiMV3O12 (M = Co and Cu; Hrichova, 1970). Ronniger and Mill prepared numerous AB2M2V3O12 compounds (A = Li, Na, K, Cu, Ag, Y, Bi and Pr–Lu; B = Na, Ca, Sr, Cd and Pb; M = Li, Mg, Sc, Mn, Co, Ni, Cu, Zn and Cd) (Ronniger & Mill, 1971, 1973a; Mill & Ronniger, 1973). They also demonstrated that, in the case of vanadates, large cations can be accommodated in the garnet structure (Tl+ and Pb2+ in the A position, Cd2+ in the B position).

Although powder data for most of these compounds are available, the structural information is rather limited. The only reported vanadate with a fully ordered garnet structure is Na3Sc2V3O12 (Belokoneva et al., 1974; Lobanov et al., 1990). Usually, the A and/or B positions are randomly occupied by different cations, for example NaCa2Cu2V3O12 (Lipin & Nozik, 1971), NaCa2Mg2V3O12 (Nakatsuka et al., 2003), NaCa2Zn2V3O12 (Nakatsuka et al., 2004), AgCa2Mn2V3O12 (Rettich & Mullet-Buschbaum, 1998), Na0.9Ca2.38Mn1.72V3O12 (Lobanov et al., 1990), Ca2.3Na0.7Mn2As0.24V2.46Si0.3O12 (Basso, 1987) and Ca2.3Na0.7Mg1.85Mn0.15V2.88P0.12O12 (Krause et al., 1999).

Depending on the valence states of the metal atoms, a cation deficiency may appear in the A or B positions. For example, the structures of Na0.9Ca2.05Co2V3O12 (Dukhovskaya & Mill, 1974) and Ca5Mg3ZnV6O24 (Muller-Buschbaum & von Postel, 1992) revealed a slight deficiency in the A position, while in Ca10Mg5Cu3V12O48 (Vogt & Muller-Buschbaum, 1991) the deficiency was found in the B position. X-ray powder data for some cation-deficient garnets (Ca2.5M2V3O12, M = Mg and Ni; Pb2.5Cd2V3O12) were also reported (Ronniger & Mill, 1973b). However, no structure refinement was performed, and only a simple comparison of experimental and theoretical X-ray diffraction powder patterns was carried out to analyze the cation distributions.

In this work, we present the first structural investigation of Pb2.63Cd2V3O12, a cation-deficient garnet containing lead and cadmium, which is uncommon for this structure type. The Pb atoms partially occupy the dodecahedral (A) sites, while the Cd and V atoms fully occupy the octahedral (B) and tetrahedral (X) sites, respectively. The CdO6 octahedra share all six corners with VO4 tetrahedra, thus forming a three-dimensional framework. The Pb atoms are situated in the interstices of this framework. The PbO8 dodecahedron has two sets of Pb—O distances: 4 × 2.611 (5) and 4 × 2.722 (4) Å. The calculated bond valence sum (BVS) (Brown & Altermatt, 1985) for Pb is 1.82. The two significantly different Pb—O bond lengths may be caused by the presence of a lone electron pair. The BVS is slightly less than the expected value of 2.0 owing to the partial occupation of the Pb site.

The Cd and V atoms form almost regular polyhedra (octahedron and tetrahedron, respectively) typical for the garnet structure. The Cd—O distance is 2.288 (4) Å and the associated BVS is 2.11. The V—O distance is 1.737 (5) Å and the corresponding BVS is 4.80, which indirectly confirms the partial reduction of the V atoms (see Experimental). Tetrahedral coordination is rather unusual for reduced V atoms; only two examples of tetrahedrally coordinated tetravalent vanadium are known, namely, Ba2VO4 (Liu & Greedan, 1993) and β-Sr2VO4 (Gong et al., 1991). In both structures, the V+4O4 tetrahedra are strongly distorted, and at least one V—O distance is longer than 1.8 Å. In Pb2.63Cd2V3O12, the oxidation state of vanadium (+4.93) is very close to +5 and the VO4 tetrahedra are almost regular with V—O distances of 1.72–1.74 Å which are typical of pentavalent vanadium (Shannon & Calvo, 1973).

Oversluizen & Metselaar (1982) reported the formation of reduced vanadium in NaCa2Mg2V3O12, as characterized by optical spectroscopy and electron spin resonance spectroscopy. However, no structural investigation has been performed in this case. Our study of Pb2.63Cd2V3O12 demonstrates that the reduction of V atoms results in minor structural changes in comparison with other garnet-type vanadates. In particular, a dodecahedral–dodecahedral shared edge [3.162 (9) Å] is longer than the shortest dodecahedral unshared edge [3.033 (9) Å] contrary to one of Pauling's rules (Pauling, 1929). A dodecahedral–octahedral shared edge [3.291 (8) Å] is also longer than the octahedral unshared edge [3.181 (7) Å]. On the other hand, Pauling's rule holds for the VO4 tetrahedra; the shared and unshared edges are 2.734 (9) and 2.887 (8) Å, respectively. Long shared edges of metal polyhedra are typical for garnet-type vanadates (Dukhovskaya & Mill, 1974; Nakatsuka et al., 2003, 2004), since the tetrahedral V cation has a high oxidation state (+5), whereas most of the other cations have a lower valence. Thus, the repulsion between the dodecahedral and octahedral cations (Pb and Cd in Pb2.63Cd2V3O12) is weak, and shared edges may become longer than unshared ones.

The present investigation clearly demonstrates that a slight change in the oxidation state of V atoms does not result in a noticeable structural transformation as was observed, for instance, in Na4VO(PO4)2 (Shpanchenko et al., 2006). This is rather surprising since tetrahedral coordination is not typical for reduced vanadium cations and usually such reduction immediately leads to structural changes.

Related literature top

For related literature, see: Basso (1987); Bayer (1965); Belokoneva et al. (1974); Brown & Altermatt (1985); Dukhovskaya & Mill (1974); Durif (1960); Geller et al. (1964); Gong et al. (1991); Hrichova (1970); Krause et al. (1999); Lipin & Nozik (1971); Liu & Greedan (1993); Lobanov et al. (1990); Mill & Ronniger (1973); Muller-Buschbaum & von Postel (1992); Nakatsuka et al. (2003, 2004); Oversluizen & Metselaar (1982); Pauling (1929); Rettich & Mullet-Buschbaum (1998); Ronniger & Mill (1971, 1973a, 1973b); Schwarz & Schmidt (1967); Shannon & Calvo (1973); Shpanchenko et al. (2006); Vogt & Muller-Buschbaum (1991); Zavalij & Whittingham (1999).

Experimental top

Single crystals of Pb2.63Cd2V3O12 were obtained by melting a mixture of Pb2V2O7, CdO, V2O3 and V2O5 (in 3:2:4:1 ratio) at 1143 K in an evacuated (10-5 atm) silica tube, followed by slow cooling (5 K min-1) to room temperature. The products contained roughly equal amounts of Pb2.63Cd2V3O12, CdV2O4 and (Cd,Pb)VO3 (low-pressure modification) phases.

Refinement top

The set of the reflection conditions hkl, h + k + l = 2n; 0kl, k, l = 2n; hhl, 2h + l = 4n; h00, h = 4n led to an unambiguous assignment of the space group, namely Ia3d. The atomic positions for the Pb, Cd, V and O atoms determined by direct methods revealed the garnet-type structure. The full occupancy of the 24c (A-type) special position by Pb atoms gave R = 0.041 and the isotropic displacement parameter for Pb twice as large as for Cd and V (0.031 versus 0.013 and 0.014, respectively). The Pb3Cd2V3O12 composition corresponds to an average oxidation state of +4.67 for vanadium. According to the above discussion (see Comment), the tetrahedral coordination is not typical for reduced V atoms (see for example, Zavalij & Whittingham, 1999); therefore, the partial occupation of the 24c position by Pb atoms was proposed. The subsequent refinement of the thermal displacement parameters and occupancy factor for the Pb atom (gPb) resulted in R = 0.022 and gPb = 0.219 (1). The calculated composition is Pb2.63Cd2V3O12 and the average oxidation state of V atoms is +4.91.

The possibility of fixing the oxidation state of vanadium as +5 was also checked. There are at least two ways to do so. The first is an increase of the deficiency in lead position to gPb = 0.20833, which corresponds to the Pb2.5Cd2V3O12 composition. The second is to constrain the occupancies in the A- and B-type positions as gPb + gCd = 0.375, which corresponds to 4.5 divalent cations per formula unit: Pb2.5 + xCd2 - xV3O12. The first approach resulted in R = 0.024, while the second led to R = 0.022 and x = 0.06 (1). Thus, single-crystal structure refinement suggests three almost equivalent possibilities for the composition of lead–cadmium–vanadium garnet-type oxide, viz. Pb2.63Cd2V3O12, Pb2.5Cd2V3O12 and Pb2.56Cd1.94V3O12.

We have prepared three powder samples of the corresponding compositions using solid-state reaction (in air and in evacuated silica tube in the case of reduced vanadium) at 1033 K for 30 h followed by additional annealing at 1073 K for 30 h and the cell parameters of the garnet-type phases were compared. An increase of the number and/or size of the divalent cations in the unit-cell results in a corresponding increase of the cell parameter [Pb2.5Cd2V3O12, a = 13.1741 (3) Å; Pb2.56Cd1.94V3O12, a = 13.1792 (2) Å; and Pb2.63Cd2V3O12, a = 13.2233 (2) Å]. The cell parameter determined at 173 K for the single-crystal [a = 13.1857 (5) Å] is also in good agreement with a decrease of average oxidation state for V atoms. Thus, the garnet-type phases containing pentavalent vanadium only have a smaller lattice parameter than the single-crystal (even when measured at 173 K). Note that the powder pattern of Pb2.63Cd2V3O12 taken at room temperature revealed a larger lattice parameter owing to thermal expansion. One may consider the cell parameter versus composition trend as an indirect proof of the correctness of the Pb2.63Cd2V3O12 composition determined from single-crystal refinement. The formation of reduced V atoms in the crystal can be easily explained by the synthetic procedure using an evacuated silica tube. A dark-grey color of the crystals additionally supports the conclusion about the presence of the reduced V atoms in the structure since all compounds synthesized in air were yellow in colour.

Computing details top

Data collection: SMART (Bruker, 1997); cell refinement: SMART; data reduction: SAINT (Bruker, 1997); program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: program (reference)?; software used to prepare material for publication: SHELXL97.

Figures top
[Figure 1] Fig. 1.  
lead cadmium vanadium oxide top
Crystal data top
Pb2.63Cd2V3O12Dx = 6.452 Mg m3
Mr = 1114.55Mo Kα radiation, λ = 0.71073 Å
Cubic, Ia3dCell parameters from 8263 reflections
Hall symbol: -I 4bd 2c 3θ = 3.8–28.2°
a = 13.1857 (5) ŵ = 44.44 mm1
V = 2292.50 (15) Å3T = 173 K
Z = 8Transparent, irregular shape, grey
F(000) = 38100.08 × 0.05 × 0.03 mm
Data collection top
Bruker SMART APEX CCD
diffractometer
240 independent reflections
Radiation source: sealed tube193 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.038
ϕ and ω scansθmax = 28.2°, θmin = 3.8°
Absorption correction: multi-scan
(Bruker, 1997)
h = 1617
Tmin = 0.125, Tmax = 0.349k = 1716
8263 measured reflectionsl = 1717
Refinement top
Refinement on F20 restraints
Least-squares matrix: fullPrimary atom site location: structure-invariant direct methods
R[F2 > 2σ(F2)] = 0.023Secondary atom site location: difference Fourier map
wR(F2) = 0.058 w = 1/[σ2(Fo2) + (0.0267P)2 + 28.7753P]
where P = (Fo2 + 2Fc2)/3
S = 1.12(Δ/σ)max < 0.001
240 reflectionsΔρmax = 1.18 e Å3
18 parametersΔρmin = 0.55 e Å3
Crystal data top
Pb2.63Cd2V3O12Z = 8
Mr = 1114.55Mo Kα radiation
Cubic, Ia3dµ = 44.44 mm1
a = 13.1857 (5) ÅT = 173 K
V = 2292.50 (15) Å30.08 × 0.05 × 0.03 mm
Data collection top
Bruker SMART APEX CCD
diffractometer
240 independent reflections
Absorption correction: multi-scan
(Bruker, 1997)
193 reflections with I > 2σ(I)
Tmin = 0.125, Tmax = 0.349Rint = 0.038
8263 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0230 restraints
wR(F2) = 0.058 w = 1/[σ2(Fo2) + (0.0267P)2 + 28.7753P]
where P = (Fo2 + 2Fc2)/3
S = 1.12Δρmax = 1.18 e Å3
240 reflectionsΔρmin = 0.55 e Å3
18 parameters
Special details top

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.

Refinement. Refinement of F2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F2, conventional R-factors R are based on F, with F set to zero for negative F2. The threshold expression of F2 > σ(F2) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F2 are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Pb0.00000.25000.62500.0305 (2)0.875 (5)
Cd0.00000.00000.00000.0191 (4)
V0.00000.25000.37500.0201 (5)
O0.0513 (3)0.3401 (3)0.4563 (4)0.0274 (10)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Pb0.0368 (3)0.0368 (3)0.0180 (3)0.0065 (2)0.0000.000
Cd0.0191 (4)0.0191 (4)0.0191 (4)0.0001 (2)0.0001 (2)0.0001 (2)
V0.0166 (6)0.0166 (6)0.0270 (10)0.0000.0000.000
O0.021 (2)0.019 (2)0.042 (3)0.0031 (17)0.0014 (19)0.0027 (19)
Geometric parameters (Å, º) top
Pb—Oi2.611 (5)V—O1.737 (5)
Pb—Oii2.611 (5)V—Oxv1.737 (5)
Pb—O2.611 (5)V—Oxvi1.737 (5)
Pb—Oiii2.611 (5)V—Oi1.737 (5)
Pb—Oiv2.722 (4)V—Pbxiv3.2964 (1)
Pb—Ov2.722 (4)O—Cdxvii2.288 (4)
Pb—Ovi2.722 (4)O—Pbxviii2.722 (4)
Pb—Ovii2.722 (4)O—Oi2.734 (9)
Pb—Vviii3.2964 (1)O—Oxv2.887 (8)
Pb—V3.2964 (1)O—Oxvi2.887 (8)
Cd—Oix2.288 (4)O—Oxix3.033 (9)
Cd—Ox2.288 (4)O—Ovii3.162 (9)
Cd—Oxi2.288 (4)O—Oxx3.181 (7)
Cd—Oxii2.288 (4)O—Oxxi3.181 (7)
Cd—Oxiii2.288 (4)O—Oxxii3.291 (8)
Cd—Oxiv2.288 (4)
Oi—Pb—Oii164.09 (18)Ov—Pb—V99.74 (9)
Oi—Pb—O63.1 (2)Ovi—Pb—V99.74 (9)
Oii—Pb—O119.3 (2)Ovii—Pb—V80.26 (9)
Oi—Pb—Oiii119.3 (2)Vviii—Pb—V180.0
Oii—Pb—Oiii63.1 (2)Oix—Cd—Ox91.95 (16)
O—Pb—Oiii164.09 (18)Oix—Cd—Oxi91.95 (16)
Oi—Pb—Oiv72.70 (15)Ox—Cd—Oxi91.95 (16)
Oii—Pb—Oiv121.81 (9)Oix—Cd—Oxii180.0
O—Pb—Oiv90.51 (11)Ox—Cd—Oxii88.05 (16)
Oiii—Pb—Oiv76.18 (18)Oxi—Cd—Oxii88.05 (16)
Oi—Pb—Ov121.81 (9)Oix—Cd—Oxiii88.05 (16)
Oii—Pb—Ov72.70 (15)Ox—Cd—Oxiii88.05 (16)
O—Pb—Ov76.18 (18)Oxi—Cd—Oxiii180.0
Oiii—Pb—Ov90.51 (11)Oxii—Cd—Oxiii91.95 (16)
Oiv—Pb—Ov67.7 (2)Oix—Cd—Oxiv88.05 (16)
Oi—Pb—Ovi76.18 (18)Ox—Cd—Oxiv180.00 (8)
Oii—Pb—Ovi90.51 (11)Oxi—Cd—Oxiv88.05 (16)
O—Pb—Ovi121.81 (9)Oxii—Cd—Oxiv91.95 (16)
Oiii—Pb—Ovi72.70 (15)Oxiii—Cd—Oxiv91.95 (16)
Oiv—Pb—Ovi115.9 (2)O—V—Oxv112.38 (16)
Ov—Pb—Ovi160.51 (17)O—V—Oxvi112.38 (16)
Oi—Pb—Ovii90.51 (11)Oxv—V—Oxvi103.8 (3)
Oii—Pb—Ovii76.18 (18)O—V—Oi103.8 (3)
O—Pb—Ovii72.70 (15)Oxv—V—Oi112.38 (16)
Oiii—Pb—Ovii121.81 (9)Oxvi—V—Oi112.38 (16)
Oiv—Pb—Ovii160.51 (17)O—V—Pbxiv128.11 (15)
Ov—Pb—Ovii115.9 (2)Oxv—V—Pbxiv51.89 (15)
Ovi—Pb—Ovii67.7 (2)Oxvi—V—Pbxiv51.89 (15)
Oi—Pb—Vviii148.43 (10)Oi—V—Pbxiv128.11 (15)
Oii—Pb—Vviii31.57 (10)O—V—Pb51.89 (15)
O—Pb—Vviii148.43 (10)Oxv—V—Pb128.11 (15)
Oiii—Pb—Vviii31.57 (10)Oxvi—V—Pb128.11 (15)
Oiv—Pb—Vviii99.74 (9)Oi—V—Pb51.89 (15)
Ov—Pb—Vviii80.26 (9)Pbxiv—V—Pb180.0
Ovi—Pb—Vviii80.26 (9)V—O—Cdxvii132.1 (2)
Ovii—Pb—Vviii99.74 (9)V—O—Pb96.54 (19)
Oi—Pb—V31.57 (10)Cdxvii—O—Pb97.35 (16)
Oii—Pb—V148.43 (10)V—O—Pbxviii128.4 (2)
O—Pb—V31.57 (10)Cdxvii—O—Pbxviii94.32 (15)
Oiii—Pb—V148.43 (10)Pb—O—Pbxviii98.40 (15)
Oiv—Pb—V80.26 (9)
Symmetry codes: (i) x, y+1/2, z; (ii) y1/4, x+1/4, z+5/4; (iii) y+1/4, x+1/4, z+5/4; (iv) x1/4, z+3/4, y+1/4; (v) z1/2, x+1/2, y+1; (vi) z+1/2, x, y+1; (vii) x+1/4, z1/4, y+1/4; (viii) x, y+1/2, z+1/2; (ix) y1/2, z+1/2, x; (x) x, y1/2, z+1/2; (xi) z+1/2, x, y1/2; (xii) y+1/2, z1/2, x; (xiii) z1/2, x, y+1/2; (xiv) x, y+1/2, z1/2; (xv) y+1/4, x+1/4, z+3/4; (xvi) y1/4, x+1/4, z+3/4; (xvii) x, y+1/2, z+1/2; (xviii) y, z+1, x+1/2; (xix) z1/4, y+3/4, x+1/4; (xx) y1/2, z, x+1/2; (xxi) z+1/2, x+1/2, y; (xxii) y+1/2, z+1, x+1/2.

Experimental details

Crystal data
Chemical formulaPb2.63Cd2V3O12
Mr1114.55
Crystal system, space groupCubic, Ia3d
Temperature (K)173
a (Å)13.1857 (5)
V3)2292.50 (15)
Z8
Radiation typeMo Kα
µ (mm1)44.44
Crystal size (mm)0.08 × 0.05 × 0.03
Data collection
DiffractometerBruker SMART APEX CCD
diffractometer
Absorption correctionMulti-scan
(Bruker, 1997)
Tmin, Tmax0.125, 0.349
No. of measured, independent and
observed [I > 2σ(I)] reflections
8263, 240, 193
Rint0.038
(sin θ/λ)max1)0.666
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.023, 0.058, 1.12
No. of reflections240
No. of parameters18
w = 1/[σ2(Fo2) + (0.0267P)2 + 28.7753P]
where P = (Fo2 + 2Fc2)/3
Δρmax, Δρmin (e Å3)1.18, 0.55

Computer programs: SMART (Bruker, 1997), SMART, SAINT (Bruker, 1997), SHELXS97 (Sheldrick, 1997), SHELXL97 (Sheldrick, 1997), program (reference)?, SHELXL97.

Selected bond lengths (Å) top
Pb—O2.611 (5)Cd—Oii2.288 (4)
Pb—Oi2.722 (4)V—O1.737 (5)
Symmetry codes: (i) x1/4, z+3/4, y+1/4; (ii) y1/2, z+1/2, x.
 

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