Yttrium pyrogermanate, Y₂Ge₂O₇

The structure of diyttrium digermanate, Y₂Ge₂O₇, has been determined in the tetra­gonal space group P4₃2₁2. It contains one Y, one Ge (both site symmetry 1 on general position 8b) and four O atoms [one on special position 4a (site symmetry ..2) and the remaining three on general positions 8b]. The basic units of the structure are isolated Ge₂O₇ groups, sharing one common O atom and displaying a Ge-O-Ge angle of 134.9 (3)°, and infinite helical chains of penta­gonal YO₇ dipyramids, parallel to the 4₃ screw axis. The crystal investigated here represents the left-handed form of the tetra­gonal R₂Ge₂O₇ compounds (R = Eu³⁺, Tb³⁺, Er³⁺, Tm³⁺ and Lu³⁺).

S1. Comment

The pyrogermanates of the rare-earth elements have attracted some interest owing to their properties, in particular their optical activity (Stadnicka et al., 1990; Das et al., 1999). The first high-quality single crystals of the R₂Ge₂O₇ series with R = Tb³⁺–Lu³⁺ were grown by Wanklyn (1973) using flux growth techniques. Smolin (1970) reported that powder samples of R₂Ge₂O₇ with R = Yb³⁺, Er³⁺, Ho³⁺, Y³⁺, Dy³⁺ and Tb³⁺ are tetragonal. Bondar (1979) published refractive indices for the La³⁺, Nd³⁺, Gd³⁺, Y³⁺ (assumed to be triclinic) and Er³⁺ (tetragonal) pyro-germanates. Subsequently, complete structure determinations have been published for Eu₂Ge₂O₇ (Chiragov et al., 1983), Tb₂Ge₂O₆ (Geller & Gaines, 1987), Er₂Ge₂O₇ (Smolin, 1970), Tm₂Ge₂O₇ (Stadnicka et al., 1990) and Lu₂Ge₂O₇ (Palinka et al., 1995). All of these compounds are tetragonal, space group P4₁2₁2, confirming the observation of Smolin (1970) that the lanthanide pyrogermanate series Eu and Tb–Lu appears to be isostructural. La₂Ge₂O₇, Nd₂Ge₂O₇ and Gd₂Ge₂O₇ are triclinic (Vetter & Queyroux 1988; Vetter et al., 1982; Smolin et al., 1971, respectively).

In the present contribution, the structure of the pyrogermanate Y₂Ge₂O₇ is found to be tetragonal, space group P4₃2₁2. This is in disagreement with the previous assumption of a triclinic structure for the title compound given by Bondar (1979) and confirms the findings of tetragonal symmetry by Smolin (1970). The absolute configuration of Y₂Ge₂O₇, however, is different from that of the other lanthanide pyrogermanates R₂Ge₂O₇, which are reported to crystallize in space group P4₁2₁2. Refinement of the structure of Tm₂Ge₂O₇ in P4₃2₁2 (¯x¯y¯z) by Stadnicka et al. (1990) yielded final agreement factors above 0.3; thus Stadnicka et al. (1990) concluded that their crystal is the P4₁2₁2 (xyz) enantiomorph. The opposite is true for Y₂Ge₂O₇ (see experimental refinement).

The lattice parameters of the pyrogermanate series R₂Ge₂O₇ (R = Eu, Tb–Lu) define an almost linear increase with the ionic radius of the R cation, as given by Shannon & Prewitt (1969), for both the a and the c parameter. The smallest values are found for Lu₂Ge₂O₇ [a = 6.702 (5) Å and c = 12.175 (11) Å (Palinka et al., 1995)], the largest lattice parameters are found in Eu₂Ge₂O₇ [a = 6.909 Å and c = 12.558 Å (Chiragov et al., 1983)]. The data for the title compound perfectly fit into those of the R₂Ge₂O₇ series.

The asymmetric unit of Y₂Ge₂O₇ contains one Y–, one Ge- and four O-atom positions (Fig. 1). The Ge⁴⁺ ion is coordinated by a tetrahedron of four non-equivalent O atoms. Two GeO₄ tetrahedra are connected to each other via the corner of atom O1, forming isolated [Ge₂O₇]⁶⁻ units (Fig. 2). The Ge1—O1—Ge1 bridging angle is 136.86 (2)°. This is one major difference from the yttrium pyrosilicate Y₂Si₂O₇, which has a straightened (Si₂O₇)⁶⁻ configuration (Redhammer & Roth 2003). The same pyro-group configuration is also found in Er₂Si₂O₇, Ho₂Si₂O₇, Tm₂Si₂O₇ and Yb₂Si₂O₇, which all show Si—O—Si angles of 180° and are isostructural to thortveitite, Sc₂Si₂O₇ (Smolin 1970). Within the lanthanide pyrogermanate series, the Ge—O—Ge angle ranges between 130.0 (1) and 136.0 (4)° (Table 2); however, no systematic variation is found from literature data. Individual Ge—O bond lengths in Y₂Ge₂O₇ range between 1.733 (3) and 1.780 (3) Å. The two shorter bonds, Ge1—O2 and Ge1—O4, are to O atoms bonded to two additional Y atoms, while the longest one (Ge1—O3) is to an O atom bonded to three Y atoms along with the Ge atom. This fourfold-coordinated O atom obviously contributes less bond strength to the Ge atom; the corresponding Ge—O bond is therefore longer. Smolin (1970) made a similar observation for Er₂Ge₂O₇ where the O atom coordinated by three rare-earth ions also formed the longest bond to its nearest Ge neighbor. Owing to the large variation of the individual Ge—O bond lengths, the GeO₄ tetrahedron in Y₂Ge₂O₇ shows large polyhedral distortion parameters (Table 2). Average Ge—O bond lengths in the pyrogermanate series R₂Ge₂O₇ are similar, with a tendency towards an increase of 〈Ge—O〉 with increasing radius of the R cation. The tetrahedral angle variance (TAV) and the tetrahedral quadratic elongation (TQE) in the title compound are generally high and are among the largest found for germanium compounds. Regular GeO₄ tetrahedra, as realised in the compound Cu(Cu_0.44Cr_4.56)Ge₂O₁₂, have TAV and TQE values of 5.32° and 1.0013 (Redhammer et al., 2007a), while intermediate distortions with TAV values of ~80° are found, for example, in norbergite-type Ca₃GeO₄Cl₂ (Redhammer et al., 2007b) and in Ca₂Ge₇O₁₆ (Redhammer et al., 2007c). TAV and TQE values decrease distinctly with increasing radius of R in the R₂Ge₂O₇ series, remaining constant above a radius of ~1.0 Å (Er³⁺). The values for the title compound, again, perfectly fit the data for the lanthanide series. The GeO₄ tetrahedron shares one edge with a neighbouring Y polyhedron; this O2—O3 edge is the shortest of all tetrahedral edges [2.600 (2) Å], and the angle opposite to this edge is the smallest O—Ge—O bonding angle [95.3 (1)°]. All other edges are unshared and are thus distinctly longer. The bond valence sum (Brese & O'Keeffe 1991) of Ge⁴⁺ is close to the ideal value [S = 3.94 valence units (v.u.)], atom O1, bonded to the two Ge atoms of the Ge₂O₇ unit, is slightly under-bonded (S = 1.89 v.u.), atoms O2 and O3, bonded to two and three Y atoms, respectively, reveal ideal bond valence sums (S = 2.00 v.u.), while atom O4 is over-bonded (S = 2.07 v.u.).

Y³⁺ is sevenfold coordinated by O atoms; the coordination polyhedron can be described as a distorted pentagonal bipyramid with the pyramidal axis almost parallel to the c direction. Within the tetragonal R₂Ge₂O₇ series the average R—O bond lengths are positively and linearly correlated with the ionic radius of the R cation. The average Y—O bond length of the title compound goes along with this trend (Tables 1 and 2). The YO₇ polyhedron shares the O3(y, 1 + x, 1 − z)—O4 and the O3(−1/2 + y, 1/2 − x, 1/4 + z)—O4(−1/2 + y, 3/2 − x, 1/4 + z) edge, both 2.818 (4) Å in length, with two neighbouring YO₇ polyhedra to form helical, left-handed chains along the 4₃ axis (Fig. 3). Three additional edges of the YO₇ polyhedron are shared with neighbouring YO₇ polyhedra, belonging to two different helical chains; one O—O edge is common to the YO₇ polyhedron and the GeO₄ tetrahedron, and the remaining nine edges are unshared. The difference between the average of the shared edges [3.329 (4) Å] and that of the unshared edges [2.797 (4) Å] is large. This indicates distinct distortion of the YO₇ polyhedron, which is also expressed by the large bond-length distortion parameter (Table 1). The bond valence sum for Y³⁺ is almost ideal (S = 3.11 v.u.).

Related literature

For related literature, see: Bondar (1979); Brese & O'Keeffe (1991); Chiragov et al. (1983); Das et al. (1999); Flack (1983); Geller & Gaines (1987); Palinka et al. (1995); Redhammer & Roth (2003); Redhammer et al. (2007a, 2007b); Shannon & Prewitt (1969); Sheldrick (1997); Smolin (1970); Smolin et al. (1971); Stadnicka et al. (1990); Vetter & Queyroux (1988); Vetter et al. (1982); Wanklyn (1973).

S2. Experimental

As part of the investigation of the crystal chemistry of (Na,Li)MGe₂O₆ 1:3 germanate clinopyroxene compounds (Redhammer et al., in preparation [any update?]) the title compound was obtained by chance during attempts to synthesize LiYGe₂O₆ using flux growth methods. A finely ground and homogenized mixture of Li₂CO₃, Y₂O₃ and GeO₂ in the stoichiometry of LiYGe₂O₆ was added to a high-temperature solvent (80 wt% Li₂MoO₄ and 20 wt% LiVO₃) in a ratio of educt to flux of 1 g: 10 g. This staring material was put into a platinum crucible, covered with a lid, heated in a chamber furnace to 1473 K, held for 24 h at this temperature and then cooled to 1073 K at a rate of 1.8 K h⁻¹. After dissolution of the flux in hot distilled water, large thin tabular plates, probably of LiYGe₂O₆ (Redhammer et al., in preparation), YVO₄ and Y₂Ge₂O₇, were obtained. The title compound forms large colourless grains of up to 2 mm, overgrown with the tabular LiYGe₂O₆ crystals.

S3. Refinement

Systematic extinction and intensity statistics yield two possible space groups, P4₁2₁2 and P4₃2₁2. As the title compound appears to be isostructural to Eu₂Ge₂O₇, Tm₂Ge₂O₇ and Tb₂Ge₂O₇ at the first glance, structure solution using direct methods (Sheldrick, 1997) was performed in space group P4₁2₁2, yielding a structure model with one Y, one Ge and four independent O atoms, being in close similarity to that of, for example, Tb₂Ge₂O₇ (Geller & Gaines, 1987). The model refined down to 2.1% in R₁; however, the Flack (1983) parameter was 1.046 (16), indicative of the wrong absolute structure configuration. Refining the P4₁2₁2 model without Flack parameter yielded R₁ ≈ 12%. Thus the structure was inverted and the space group changed to P4₃2₁2, giving now a Flack parameter of 0.0121 (16) for the correct absolute structure model presented here. Duing comparison with literature data it became evident that the O2(y) coordinate of Eu₂Ge₂O₇ (Chiragov et al., 1983) should read −0.0302 instead of +0.0303.

Computing details

Data collection: SMART-Plus (Bruker, 2001); cell refinement: SAINT-Plus (Bruker, 2001); data reduction: SAINT-Plus (Bruker, 2001); program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: Diamond (Pennington, 1999); software used to prepare material for publication: WinGX (Farrugia, 1999).

Figures

	Fig. 1. A view of the asymmetric unit and some symmetry-related atoms of the title compound, showing 95% probability displacement ellipsoids and the atomic numbering scheme·[Symmetry codes: (i) y, 1 + x, 1 − z; (ii) −1/2 + y, 1/2 − x, 1/4 + z; (iii) 1/2 + x, 1 1/2 − y, 1 1/4 − z; (iv) −1/2 + y, 1 1/2 − x, 1/4 + z; (v) −1 + y, 1 + x, 1 − z].
	Fig. 2. A polyhedral representation of the structure of Y2Ge2O7 with only the di-tetrahedral Ge2O7 units shown.
	Fig. 3. A polyhedral representation of the structure of Y2Ge2O7 with only one helical chain of YO7 polyhedra shown for clarity.

diyttrium digermanate

Crystal data

Ge2O7Y2	Dx = 5.046 Mg m^−3
Mr = 435.04	Mo Kα radiation, λ = 0.71073 Å
Tetragonal, P43212	Cell parameters from 6821 reflections
a = 6.8022 (4) Å	θ = 3.4–27.5°
c = 12.3759 (7) Å	µ = 30.45 mm^−1
V = 572.63 (6) Å^3	T = 295 K
Z = 4	Cuboid, colourless
F(000) = 792	0.12 × 0.07 × 0.06 mm

Data collection

Bruker SMART APEX diffractometer	649 reflections with I > 2σ(I)
rotation, ω–scans at 4 different ϕ positions	Rint = 0.062
Absorption correction: numerical [via equivalents using X-SHAPE (Stoe & Cie, 1996)]	θmax = 27.5°, θmin = 3.4°
Tmin = 0.091, Tmax = 0.18	h = −8→8
6886 measured reflections	k = −8→8
661 independent reflections	l = −16→16

Refinement

Refinement on F^2	w = 1/[σ^2(Fo^2) + (0.0184P)^2 + 2.215P] where P = (Fo^2 + 2Fc^2)/3
Least-squares matrix: full	(Δ/σ)max = 0.001
R[F^2 > 2σ(F^2)] = 0.020	Δρmax = 0.88 e Å^−3
wR(F^2) = 0.051	Δρmin = −0.71 e Å^−3
S = 1.19	Extinction correction: SHELXL97, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
661 reflections	Extinction coefficient: 0.0539 (16)
53 parameters	Absolute structure: refinement of absolute structure parameter (Flack, 1983)
0 restraints	Absolute structure parameter: 0.0121 (16)

Special details

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.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Y1	0.35253 (7)	0.87655 (6)	0.63502 (3)	0.00521 (17)
Ge1	0.09884 (6)	0.84685 (8)	0.38026 (4)	0.00476 (18)
O1	0.1966 (5)	0.8034 (5)	0.25	0.0112 (11)
O2	−0.0774 (5)	1.0315 (5)	0.3763 (3)	0.0084 (7)
O3	−0.0635 (5)	0.6617 (5)	0.4290 (3)	0.0065 (6)
O4	0.3138 (5)	0.8577 (6)	0.4552 (3)	0.0085 (7)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Y1	0.0056 (2)	0.0059 (2)	0.0042 (2)	0.00003 (16)	−0.00023 (18)	−0.00015 (17)
Ge1	0.0045 (3)	0.0052 (3)	0.0045 (3)	0.00007 (17)	0.00001 (18)	0.0006 (2)
O1	0.0144 (17)	0.0144 (17)	0.005 (2)	0.005 (2)	0.0013 (14)	0.0013 (14)
O2	0.0059 (14)	0.0074 (17)	0.0119 (17)	0.0022 (12)	−0.0007 (15)	−0.0024 (14)
O3	0.0092 (15)	0.0041 (16)	0.0062 (14)	−0.0036 (14)	0.0005 (12)	0.0002 (13)
O4	0.0057 (16)	0.0162 (17)	0.0034 (15)	−0.0012 (14)	−0.0011 (12)	0.0004 (14)

Geometric parameters (Å, º)

Y1—O2^i	2.211 (4)	Y1—Y1^vi	3.5993 (8)
Y1—O4	2.245 (3)	Y1—Y1^ii	3.6049 (4)
Y1—O4^ii	2.279 (3)	Y1—Y1^vii	3.6049 (4)
Y1—O3^iii	2.284 (3)	Y1—Y1^viii	3.8201 (4)
Y1—O2^iv	2.373 (3)	Ge1—O4	1.733 (3)
Y1—O3^v	2.386 (3)	Ge1—O2	1.737 (3)
Y1—O3^iv	2.552 (3)	Ge1—O1	1.769 (2)
Y1—Ge1^iv	3.2345 (6)	Ge1—O3	1.780 (3)
O2^i—Y1—O4	80.17 (13)	O2^iv—Y1—O3^v	80.07 (12)
O2^i—Y1—O4^ii	84.75 (13)	O2^i—Y1—O3^iv	68.24 (12)
O4—Y1—O4^ii	115.62 (12)	O4—Y1—O3^iv	95.97 (12)
O2^i—Y1—O3^iii	149.58 (13)	O4^ii—Y1—O3^iv	134.25 (12)
O4—Y1—O3^iii	76.96 (12)	O3^iii—Y1—O3^iv	133.72 (9)
O4^ii—Y1—O3^iii	87.31 (12)	O2^iv—Y1—O3^iv	63.59 (11)
O2^i—Y1—O2^iv	128.69 (10)	O3^v—Y1—O3^iv	79.92 (13)
O4—Y1—O2^iv	88.06 (13)	O4—Ge1—O1	100.24 (16)
O4^ii—Y1—O2^iv	143.32 (13)	O2—Ge1—O1	110.76 (19)
O3^iii—Y1—O2^iv	70.43 (12)	O4—Ge1—O3	111.85 (16)
O2^i—Y1—O3^v	108.25 (13)	O2—Ge1—O3	95.32 (16)
O4—Y1—O3^v	168.06 (12)	O1—Ge1—O3	115.08 (12)
O4^ii—Y1—O3^v	74.31 (11)	Ge1—O1—Ge1^ix	134.9 (3)
O3^iii—Y1—O3^v	97.69 (9)

Symmetry codes: (i) y−1, x+1, −z+1; (ii) y−1/2, −x+3/2, z+1/4; (iii) y, x+1, −z+1; (iv) y−1/2, −x+1/2, z+1/4; (v) x+1/2, −y+3/2, −z+5/4; (vi) −y+1, −x+1, −z+3/2; (vii) −y+3/2, x+1/2, z−1/4; (viii) x−1/2, −y+3/2, −z+5/4; (ix) −y+1, −x+1, −z+1/2.